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ಖಾತೆ ಹಂಚಿಕೆ ಸಿ.ಎಂಗೆ ಪರಮಾಧಿಕಾರ: ಸಚಿವ ಹಾಸನ: ಸಚಿವರ ಖಾತೆ ಬದಲಾವಣೆ ಬಗ್ಗೆ ಮಾಹಿತಿ ಇಲ್ಲ, ಯಾವುದೇ ಖಾತೆಗಳನ್ನು ನೀಡುವ ಪರಮಾಧಿಕಾರ ಮುಖ್ಯಮಂತ್ರಿಗೆ ಇದೆ ಎಂದು ಜಲಸಂಪನ್ಮೂಲ ಸಚಿವ ರಮೇಶ್ ಜಾರಕಿಹೊಳಿ ಹೇಳಿದರು. ಅಸಮಾಧಾನಗೊಂಡ ಯಾವ ಶಾಸಕರು ನನ್ನ ಜತೆ ಮಾತನಾಡಿಲ್ಲ. ಯಾರಾದರೂ ಅಸಮಾಧಾನಗೊಂಡಿದ್ದರೆ ಬೆಂಗಳೂರಿಗೆ ತೆರಳಿದ ಬಳಿಕ ಅವರೊಂದಿಗೆ ಮಾತನಾಡುವೆ. ಕೋವಿಡ್ ಸಂಕಷ್ಟದಲ್ಲಿ ತುಂಬ ಯಶಸ್ವಿಯಾಗಿ ಆಡಳಿತ ನಿಭಾಯಿಸಿದ್ದೇವೆ. ಹಾಗಾಗಿ ಮುಖ್ಯಮಂತ್ರಿ ಬೆಂಬಲಕ್ಕೆ ನಿಲ್ಲುವಂತೆ ಮಿತ್ರ ಮಂಡಳಿ ಹಾಗೂ ಇತರೆ ಶಾಸಕರಲ್ಲಿ ಮನವಿ ಮಾಡುತ್ತೇನೆ. ಸಣ್ಣಪುಟ್ಟ ವ್ಯತ್ಯಾಸಗಳಿದ್ದರೆ ಅವುಗಳನ್ನು ಮುಖ್ಯಮಂತ್ರಿ ಸಮರ್ಥವಾಗಿ ನಿಭಾಯಿಸುತ್ತಾರೆ ಎಂದರು. ಇದೇ ವೇಳೆ ಜಲಸಂಪನ್ಮೂಲ ಸಚಿವರು ಸುರಂಗ ಮಾರ್ಗ ವೀಕ್ಷಣೆಗೆ ಭೇಟಿ ನೀಡಿರುವ ಸುದ್ದಿ ತಿಳಿದು ಸ್ಥಳಕ್ಕೆ ಬಂದಿದ್ದ ಯೋಜನೆ ಭೂ ಸಂತ್ರಸ್ತ ಪಡುವಳಲು ಗ್ರಾಮದ ಚಂದ್ರೇಗೌಡ ಮಾತನಾಡಿ, ಇದುವರೆಗೂ ಪರಿಹಾರ ನೀಡಿಲ್ಲ. ಜಮೀನು ಬಿಡುವಂತೆ ಹೆದರಿಸುವುದು ನಿರಂತರವಾಗಿ ನಡೆಯುತ್ತಿದೆ. ಪರಿಹಾರದ ಹಣ ನೀಡುವ ವರೆಗೂ ಯೋಜನೆಗೆ ಜಮೀನು ಬಿಡುವುದಿಲ್ಲ ಎಂದು ಆಕ್ರೋಶ ವ್ಯಕ್ತಪಡಿಸಿದರು. ಬೆಟ್ಟದಾಲುರು ಗ್ರಾಮದ ಚಂದ್ರಶೇಖರ್ ಮಾತನಾಡಿ, ನಮ್ಮ 3 ಎಕರೆ ಜಮೀನು ಸ್ವಾಧೀನಪಡಿಸಿಕೊಳ್ಳಲಾಗಿದೆ. ಕಾಮಗಾರಿ ನಡೆಸಲು 1,600 ಕೋಟಿ ಹಣ ಬಿಡುಗಡೆಯಾಗಿದೆ. ಆದರೆ, ರೈತರಿಗೆ ಪರಿಹಾರ ನೀಡಲು ಸರ್ಕಾರದ ಬಳಿ ಹಣವಿಲ್ಲ. ತಾತ್ಕಾಲಿಕ ಪರಿಹಾರ ಬೇಡ, ಭೂಮಿಗೆ ಬೆಲೆ ನಿಗದಿ ಮಾಡಿ. ಇಲ್ಲದಿದ್ದರೆ ಮುಂದಿನ ಕಾಮಗಾರಿ ನಡೆಸಲು ಬಿಡುವುದಿಲ್ಲ ಎಂದರು. ಸಚಿವರು ಮಾಧ್ಯಮಗೋಷ್ಠಿ ಮುಗಿಸುತ್ತಿದ್ದಂತೆ ಸಂತ್ರಸ್ತರು ಪರಿಹಾರ ನೀಡುವಂತೆ ಆಕ್ರೋಶ ವ್ಯಕ್ತಪಡಿಸಿದರು. ಶಾಸಕ ಕೆ.ಎಸ್. ಲಿಂಗೇಶ್ ಮಾತನಾಡಿ, ಎತ್ತಿನಹೊಳೆ ಯೋಜನೆಗೆ 3,900 ಎಕರೆ ಜಮೀನನ್ನು ರೈತರು ಕಳೆದುಕೊಳ್ಳುತ್ತಿದ್ದಾರೆ. ಕಾಮಗಾರಿ ಬೇಗ ಮುಗಿಸುವ ಉದ್ದೇಶದಿಂದ ತಾತ್ಕಾಲಿಕವಾಗಿ 50 ಸಾವಿರದಂತೆ ಬೆಳೆ ಪರಿಹಾರ ನೀಡಿ, ಕಾಮಗಾರಿ ನಡೆಸಲಾಗಿದೆ. ಸರ್ಕಾರ 1:4 ಅನುಪಾತದಲ್ಲಿ ಪರಿಹಾರ ನೀಡಬೇಕು ಎಂದರು. | kannad |
സൗജന്യ ഡയാലിസിസ് കേന്ദ്രത്തിന് ഏഷ്യാ ബുക്ക് ഒഫ് റെക്കാഡിന്റെ അംഗീകാരം തിരുവനന്തപുരം: ശ്രീ സത്യസായി ഓര്ഫനേജ് ട്രസ്റ്റ് കേരളയുടെ നവജീവനം സൗജന്യ ഡയാലിസിസ് ഏഷ്യാ ബുക്ക് ഒഫ് റെക്കാഡില് ഇടം നേടി. രാജ്ഭവനില് നടന്ന ചടങ്ങില് ഗവര്ണര് ആരിഫ് മുഹമ്മദ് ഖാന് ശ്രീസത്യസായി ഓര്ഫനേജ് ട്രസ്റ്റ് കേരളയുടെ ഫൗണ്ടറും എക്സിക്യുട്ടീവ് ഡയറക്ടറുമായ കെ.എന്. ആനന്ദകുമാറിന് സര്ട്ടിഫിക്കറ്റ് കൈമാറി. ട്രസ്റ്റ് ചെയര്മാന് ജസ്റ്റിസ്.എ. ലക്ഷ്മിക്കുട്ടി, ട്രസ്റ്റ് സീനിയര് വൈസ് ചെയര്മാന് കെ. ഗോപകുമാരന് നായര്, സായിഗ്രാമം സോഷ്യല് ടൂറിസം പ്രോജക്ട് ഡയറക്ടര് പ്രൊഫ.ബി. വിജയകുമാര്, ട്രസ്റ്റ് ഡയറക്ടര് ബോര്ഡ് മെമ്ബര് ശ്രീകാന്ത് പി. കൃഷ്ണന് എന്നിവര് പങ്കെടുത്തു. | malyali |
ಕೂಲಿಗೆ ಹೊರಟವರು ಮಸಣಕ್ಕೆ: ಭೀಕರ ಅಪಘಾತಕ್ಕೆ 6 ಮಂದಿ ಬಲಿ ಬೆಳಗಾವಿ: ಜಿಲ್ಲೆಯ ಸವದತ್ತಿ ಬಳಿ ಸಂಭವಿಸಿದ ಭೀಕರ ಅಪಘಾತದಲ್ಲಿ 6 ಮಂದಿ ಬಲಿಯಾಗಿದ್ದು, 15ಕ್ಕೂ ಹೆಚ್ಚು ಮಂದಿ ಗಾಯಗೊಂಡಿರುವ ಘಟನೆ ನಡೆದಿದೆ. ಧಾರವಾಡ ಜಿಲ್ಲೆಯ ಮೊರಬ ಗ್ರಾಮದ ಜಮೀನಿನಲ್ಲಿ ಕೂಲಿ ಕೆಲಸ ಮುಗಿಸಿ ಊರಿನ ಕಡೆಗೆ ಕೂಲಿ ಕಾರ್ಮಿಕರನ್ನು ತುಂಬಿಕೊಂಡು ಹೊರಟಿದ್ದ ಬೊಲೆರೋಗೆ, ಸವದತ್ತಿ ಕಡೆಗೆ ಬರುತ್ತಿದ್ದ ಟಾಟಾ ಏಸ್ ಆಟೋ ಡಿಕ್ಕಿ ಹೊಡೆದಿದೆ. ಸ್ಥಳದಲ್ಲೇ ಕಾರು ಚಾಲಕ ಹಾಗೂ ಐವರು ಮಹಿಳೆಯರು ಮೃತಪಟ್ಟಿದ್ದಾರೆ. ಮೃತಪಟ್ಟವರೆಲ್ಲ ರಾಮದುರ್ಗ ತಾಲೂಕಿನ ಕೆಂಚನೂರು, ಚುಂಚನೂರ ಗ್ರಾಮದವರು ಎಂದು ಹೇಳಲಾಗಿದೆ. ಅಪಘಾತದ ರಭಸಕ್ಕೆ ಎರಡೂ ವಾಹನಗಳು ನಜ್ಜು ಗುಜ್ಜಾಗಿದ್ದು, ಮೂವರ ಮೃತದೇಹಗಳ ಗುರುತು ಪತ್ತೆಯಾಗಿದೆ. ಚುಂಚನೂರ ಗ್ರಾಮದ ಯಲ್ಲವ್ವ 65, ಪಾರವ್ವ 35, ರುಕ್ಮವ್ವ 35 ಎಂದು ತಿಳಿದು ಬಂದಿದೆ. ಅಪಘಾತದಲ್ಲಿ 15ಕ್ಕೂ ಹೆಚ್ಚು ಮಂದಿ ಗಾಯಗೊಂಡಿದ್ದು, ಸರ್ಕಾರಿ ಆಸ್ಪತ್ರೆಗೆ ದಾಖಲು ಮಾಡಲಾಗಿದೆ. ಸ್ಥಳಕ್ಕೆ ಹೆಚ್ಚುವರಿ ಎಸ್ಪಿ ಅಮರನಾಥ ರೆಡ್ಡಿ ಭೇಟಿ ನೀಡಿ ಪರಿಶೀಲನೆ ನಡೆಸಿದರು. ಸವದತ್ತಿ ಠಾಣೆಯಲ್ಲಿ ಪ್ರಕರಣ ದಾಖಲಾಗಿದೆ. | kannad |
ஆஸ்திரேலியாவில் இன்று அதிகாலை நிலநடுக்கம் ஆஸ்திரேலியாவில் இன்று அதிகாலை நிலநடுக்கம் ஏற்பட்டது. மெல்போர்ன் நகரில் இருந்து 200 கிலோ மீட்டர் தொலைவில் உள்ள மன்ஸ்பீல்டு பகுதியில் 5.8 ரிக்டர் அளவில் நில நடுக்கம் ஏற்பட்டது. இந்த நில நடுக்கம் 10 கிலோ மீட்டர் ஆழத்தில் மையம் கொண்டிருந்தது. கட்டிடங்கள் குலுங்கியதால் பீதியடைந்த பொதுமக்கள் வீடுகளை விட்டு வெளியேறி சாலைகளில் தஞ்சம் அடைந்தனர். அங்குள்ள சேப்பல் தெருவில் உள்ள ஒரு கட்டிடம் சேதம் அடைந்தது. அதிலிருந்த செங்கற்கள் இடிந்து விழுந்தது. தேர்தலில் வெற்றி பெற்ற கனடா பிரதமர் ஜஸ்டின் ட்ரூடோவுக்கு பிரதமர் மோடி வாழ்த்து ஐ.நா. சபையில் ஆப்கானிஸ்தான் சார்பில் பங்கேற்று பேச அனுமதி அளிக்கும்படி தலிபான்கள் வலியுறுத்தல் | tamil |
شاداب بھی بہت جلد دلہا بنیں گے اور ان کی ایک نہیں چار شادیاں ہوں گی سامعہ رزو فوٹو فائل لاہورقومی کرکٹر حسن علی کی نئی نویلی دلہن سامعہ رزو نے سپنر شاداب خان کی شادیوں کی پیش گوئی کردی حسن علی کی بیوی سامعہ رزو کا کہنا ہے کہ شاداب بھی بہت جلد دلہا بنیں گے اور ان کی ایک نہیں چار شادیاں ہوں گیحسن علی کی شادی کےموقع پر دلہے کے دوست کی شادی سے متعلق ایک رسم ادا کی گئی یہ بھی پڑھیںحسن علی کا نکاح کے بعد خوشی میں رقص ویڈیو سوشل میڈیا پر وائرل دلہن سامعہ رزو نے شاداب کو کرسی پر بیٹھا کر ہار توڑا ہار جلد ٹوٹا اور چار حصوں میں بٹ گیا رسم کے مطابق ہار جلد ٹوٹے تو شادی جلدی ہوتی ہے جتنے حصوں میں تقسیم ہو تو دلہے کے دوست کی شادیاں بھی اتنی ہی ہوتی ہیں ادھر شاداب خان کا کہنا ہے کہ جوڑے سمانوں پر بنتے ہیں جب اللہ کی رضا ہو گی والدین کی مرضی سے شادی کروں گا | urdu |
LIC Saral Pension Plan: এলআইসির সুপারহিট প্ল্যান! প্রিমিয়াম মাত্র একবার, জীবনভর ১২ হাজার টাকা করে পেনশন যদি বয়স ৪০ বছর হয়ে থাকে পেনশন পেতে চান সেক্ষেত্রে আপনার জন্য এলআইসির এই প্রকল্পটি অত্যন্ত জরুরি এখনও পর্যন্ত যা শোনা যায় তাতে ৬০ বছর বা তারপর থেকেই পান সাধারণত মানুষ প্রতীকী ছবি তবে এমনই এক সরকারি প্রকল্প আছে যা অত্যন্ত স্পেশ্যাল শুধুই স্পেশ্যালই নয় ৪০ বছর বয়সে পেতে পারেন পেনশনও ভারতীয় জীবন বিমা নিগম বা এলআইসি এমন এক প্রকল্প বাজারে নিয়ে এসেছে যেখানে এককালীন টাকা পাওয়া সম্ভব প্রতীকী ছবি এলআইসির এই যোজনার নাম সরল পেনশন যোজনা Saral Pension এটি সিঙ্গেল প্রিমিয়াম পেনশন প্ল্যান, বয়স ৪০ হলে ঠিক তখন থেকেই পেতে থাকবেন পেনশন প্রতীকী ছবি এরপরে সারা জীবন ধরে পেনশন পাওয়া যাবে পলিসি ধারকের মৃত্যুর পরে নমিনিকে সিঙ্গেল প্রিমিয়াম ফেরত্ দেওয়া যাবে প্রতীকী ছবি আসলে সরল পেনশন যোজনা একটি এমিডিয়েট অ্যানিউটি প্ল্যান অর্থাত্ পলিসি গ্রহণ করার পর থেকেই পেনশন পেতে শুরু করবেন পলিসি ধারকেরা প্রতীকী ছবি এই পলিসির বিশেষত্ব এটাই যে এই পলিসি কোনও একজনের নামে থাকবে যদিন পেনশন ধারক জীবিত থাকবেন ততদিন তিনি পেনশন পাবেন তাঁর মৃত্যুর পরে বেস প্রিমিয়ামের টাকা নমিনিকে ফেরত্ দেওয়া হবে প্রতীকী ছবি এই পলিসিতে পলিসি ধারক ও তাঁর জীবনসঙ্গী কভারেজ পাবেন যতদিন প্রাইমারি পেনশন ধারক জীবিত থাকবেন ততদিন তিনি পেনশন পাবেন আর তাঁর মৃত্যুর পরেও জীবনসঙ্গী সারা জীবন পেনশন পাবেন প্রতীকী ছবি পেনশন নিতে গেলে চারটি বিকল্প আছে যা পলিসি ধারকেই নির্ণয় করতে হবে প্রতি মাসে পেনশন নিতে পারেন, প্রতি তিন মাস ছাড়া পেনশন নিতে পারেন, প্রতি ছয় মাস ছাড়া পেনশন নিতে পারেন ও প্রতি ১২ মাস বা একবছর ছাড়া পেনশনের টাকা নিতে পারেন প্রতীকী ছবি এই সরল পেনশন যোজনার ক্ষেত্রে কতটাকা জমা দিতে হবে এটা নিজেকেই বাছতে হবে যতটাকার পেনশন অ্যামাউন্ট বাছবেন ঠিক সেই অনুসারেই টাকা জমা দিতে হবে প্রতীকী ছবি মাসে কমপক্ষে ১,০০০ টাকা পেনশন হলে তিন মাসে ৩,০০০ টাকা, ৬ মাসে ৬,০০০ টাকা, ১২ মাসে ১২,০০০ টাকা ন্যূনতম নিতে হবে সর্বাধিক টাকার কোনও সীমা পরিসীমা নেই প্রতীকী ছবি যদি কোনও ব্যক্তি ৪০ বছরে ১০ লক্ষ টাকার সিঙ্গেল প্রিমিয়াম জমা করলে বছরে ৫০ হাজার টাকা করে পেনশন পাবেন মোট টাকা হবে ৫০,২৫০ টাকা যা আজীবনই পেয়ে যাবেন প্রতীকী ছবি যদি মাঝখানে জমা টাকা ফেরত্ পেতে চান সেক্ষেত্রে ৫ শতাংশ টাকা কেটে বাকি জমা টাকা ফেরত্ দেওয়া হবে যদি কোনও কঠিন অসুখ হয় সেক্ষেত্রে সরল পেনশন যোজনায় জমা টাকা ফেরত্ পেতে পারেন প্রতীকী ছবি কঠিন অসুখের তালিকা দেওয়া হয়ে থাকে পলিসি সারেন্ডার করার পরে ৯৫ শতাংশ টাকা ফেরত্ দেওয়া হয় সরল পেনশনের অন্তর্গত saral pension plan ঋণের ব্যবস্থাও আছে যোজনা শুরু হওয়ার ৬ মাস পরে ঋণের জন্য আবেদন করতে পারেন প্রতীকী ছবি | bengali |
મોરબીની જૂની આરટીઓ નજીક પેપરમિલમાં આગ, ફાયરની ટીમ દોડી ગઈ મોરબીમાં પેપરમિલમાં આગ લાગવાના બનાવોનું પ્રમાણ વધતું હોય તેવું લાગી રહ્યું છે થોડા દિવસો આગાઉ વાંકાનેરના રાતાવીરડા નજીક પેપરમિલમાં વિકરાળ આગની જ્વાળાઓ હજુ સમી નથી ત્યાંથી વધુ એક પેપરમિલમાં આગ ભભૂકી ઉઠી છે મળતી માહિતી મુજબ મોરબીની જૂની આરટીઓ કચેરી નજીક આવેલ નેક્ષા પેપરમિલમાં ગત રાત્રીના ૨ વાગ્યાની આસપાસ વેસ્ટ પેપરના જથ્થામાં આગ ભભૂકી ઉઠી હતી તો ધટનાની જાણ થતા પેપરમિલના માલિકો સહિતના કર્મચારીઓ દોડી આવ્યા હતા અને મોરબી ફાયર વિભાગને જાણ કરવામાં આવતા ફાયર અધિકારી દેવેન્દ્રસિંહ જાડેજા સહિતનો ફાયરનો સ્ટાફ સ્થળ પર દોડી જઈને કામગીરી હાથ ધરી છે તેમજ ફાયર વિભાગની ૩ ગાડીઓ આગની કામગીરીમાં લાગી હોવાનું પણ ફાયર અધિકારીએ જણાવ્યું હતું તો મહદઅંશે આગ પર કાબુ મેળવ્યો તેમ પણ જણાવ્યું છે.જો કે નેક્ષા પેપરમિલમાં આગ ક્યાં કારણોસર લાગી તે જાણી શકાયું નથી | gujurati |
Illinois High School Hall of Fame coach Ron Guegenti is conducting a Skill’s Development Camp prior to the start of our 2016 - 2017 season.
Members can attend one or all sessions, based on need. There is no additional member cost for the camp.
This years training will include instruction in pre-game stretching and base running and all field positions. Simulated games will be played to focus on enhancing skills. Additionally, there will be clinics in Coaching and Umpiring.
Camp will take place over a 11 day span, with at least one day off in between sessions. It will start on Mon. Oct 17th and end Weds. Oct 26th. Sessions will run from 8:30 until 11:30. The detailed schedule is below.
Fill out the form below and we will send you more information as we get closer to the dates.
Hope to see you there as we get ready for the 2016 / 2017 seasons. | english |
Education Budget 2022: स्किल गैप को कम करने पर जोर, डिजिटल DESH ईपोर्टल की होगी स्थापना नई दिल्ली, एजुकेशन डेस्क। Budget 202223 for Skill Development: वित्तीय वर्ष 202223 के लिए केंद्र सरकार का बजट आज, 1 फरवरी 2022 को लोक सभा में प्रस्तुत करते हुए केंद्रीय वित्तमंत्री निर्मला सीतारमण ने कौशल विकास को लेकर महत्वपूर्ण घोषणाएं की। वित्त मंत्री ने अपने बजट भाषण के दौरान कहा कि इंडस्ट्रीएकेडेमिया स्किल गैप को कम करने के लिए सरकार लगातार प्रयास कर रही है। देश में स्किल्ड मैनपॉवर को बढ़ावा देने के लिए हमारे युवाओं के स्किलिंग, अपस्किलिंग और रिस्किलिंग पर इस साल अधिक फोकस किया जाएगा। इसके लिए एक डिजिटल ईपोर्टल लांच किया जाएगा।वहीं, अपने बजट भाषण में वित्तमंत्री ने शिक्षा क्षेत्र को लेकर भी महत्वपूर्ण घोषणाएं की। राष्ट्रीय शिक्षा नीति एनईपी 2022 में क्षेत्रीय भाषाओं में शिक्षा को बढ़ावा देने का प्रावधान किया गया है। इसी क्रम में वित्त मंत्र ने वर्ष 202223 में क्षेत्रीय भाषा में शिक्षा को बढ़ावा देने के लिए वन क्लास वन चैनल कार्यक्रम का विस्तार 200 चैनलों तक किए जाने की घोषणा की है। वहीं, एनईपी के ऑनलाइनऑफलाइन हाईब्रिड मोड के शिक्षा के उद्देश्यों के लिए डिजिटल यूनिवर्सिटी की स्थापना की भी घोषणा वित्तमंत्री ने की। Education Budget 2022: वन क्लास वन टीवी चैनल कार्य़क्रम का विस्तार 200 टीवी चैनल, डिजीटल यूनिवर्सिटी की स्थानबता दें कि स्किल डेवेलपमेंट सेक्टर में काम कर रहे देश भर के विभिन्न कंपनियों और संस्थानों की मांग थी कि सरकार को स्किलिंग पर वर्तमान में लगे 18 जीएसटी पर फिर से विचार करना चाहिए। इन संस्थानों का मानना है कि अत्यधिक जीएसटी के कारण महामारी के दौर में महंगी स्किलिंग प्रमाणी उन छात्रों के लिए बहुत ही निराशाजनक है जो कौशल से संबंधित शिक्षा हासिल करना चाहते हैं। वहीं कई स्किल डेवलेपमेंट के संस्थानों की मांग थी कि प्रशिक्षण और कौशल विकास केंद्रों के लिए बजट में अलग से आवंटन होना चाहिए ताकि उद्योगों, विशेषतौर पर स्टार्टअप में जरूरत के अनुसार स्किल्ड मैनपॉवर उपलब्ध हो सके। Education budget 2022: वित्त मंत्री ने अपने चौथे बजट में युवाओं को दिया बड़ा तोहफा, 60 लाख नौकरियों का किया ऐलान | hindi |
Greenville is located in the northwestern corner of the state of South Carolina. Greenville and the surrounding areas, situated at the foothills of the Blue Ridge Mountains, are commonly referred to as the Upstate.
Greenville’s public school system is the largest in the state, and includes 11 magnet academies for special study at the elementary, middle, and high school levels. Learn more about education.
Over 10 colleges and universities are located in and within close proximity of Greenville.
Greenville is the cultural and entertainment center for the upstate, including an award winning downtown, a major performing arts center, a 17,000 seat arena, a 340,000-square-foot convention and exhibition center, nationally recognized museum collections, and 39 parks, playgrounds and recreation centers. | english |
தீய சக்திகள் அழிய நிம்ப தீபம் வழிபாடு! தீய சக்திகள் அழிய நிம்ப தீபம் வழிபாடு! கோயில்களில் இறைவழிபாட்டு பூஜைகளின் போது சாமிக்கு தீபாராதனை காட்டப்படும். இது பூஜையின் முக்கிய அங்கம். சாமிக்கு காட்டப்படும் தீபாராதனையின் போது அர்ச்சகர் பல வகையான தீபங்களை காட்டுவார்கள். தீபங்கள் பெரும்பாலும் பித்தளை உலோகங்களினால் செய்யப்படுகின்றன. தீபாராதனைக்கு உரிய தீபங்கள் பெரும்பாலும் பித்தளை போன்ற உலோகங்களினால் செய்யப்படுகின்றன. ஒரு முக தீபம், அடுக்குத் தீபம், பஞ்சமுக தீபம், வில்வ தீபம், இடப தீபம், கும்ப தீபம், கற்பூர தீபம் என்று தீபங்களில் பல வகைகள் உண்டு. இது தவிர, தூபம், மஹா தீபம், நாக தீபம், விருஷப தீபம், அலங்கார தீபம், அஷ்வ தீபம், கற்பக விருட்ச தீபம், புருஷா மிருக தீபம், கஜ தீபம், சிம்ம தீபம், மயூர தீபம், ஐந்தட்டு தீபம், பூரண கும்ப தீபம், துவஜ தீபம், வ்யாக்ர தீபம், மேரு தீபம் என்பவையும் அடங்கும். மாலா தீபம்: இது அடுக்கு தீபம் ஆகும். மாலை போன்று தீப தட்டுகள் இருபுறம் அமைந்தும், கீழிருந்து மேலாக வட்ட அடுக்கடுக்காக பெரிய அளவு தொடங்கி சிறியனவாக இருக்கும். சித்திர தீபம்: மாக்கோலம் போட்டு மணி விளக்குகளை ஏற்றி அதனை வட்டமாக அமைத்துக் கொண்டு தீப அலங்காரம் செய்தல் ஆகும். நவுகா தீபம்: நவுகா என்பதற்கு படகு என்று அர்த்தம். படகு போன்று வடிவமைத்து, அதில் தீபம் ஏற்றி அதனை நீரில் மிதக்கவிடுவதைக் குறிக்கும்.sச் ஆகாச தீபம்: உயரமான இடங்கள் அல்லது வீடுகளின் மொட்டை மாடியில் ஏற்றப்படும் தீபத்திற்கு ஆகாச தீபம் என்று பெயர். ஒவ்வொரு ஆண்டும் ஐப்பசி மாதம் தீபாவளிக்கு முன்னும், கார்த்திகை மாத சதுர்த்தி நாளிலும் இந்த தீபத்தை ஏற்றி வழிபடுகிறார்கள். இந்த தீபம் ஏற்றி வழிபட்டால் எம பயம் நீங்கும். அதோடு கெட்ட கனவுகளிலிருந்தும் விடுதலை கிடைக்கும் என்பது ஐதீகம். ஜல தீபம்: தண்ணீரில் மிதக்கவிடும் சிறிய சிறிய தீப விளக்குகளை குறிப்பது ஜல தீபம். கங்கை நீரில் இது போன்ற தீபங்களை மிதக்கவிட்டு அது செல்லும் அழகை கண்டு மகிழ்வது உண்டு. வட இந்தியாவில் ஜல தீபங்கள் மிதக்கவிடுவதை உற்சாகமாக கொண்டாடி மகிழ்கின்றனர். பம்பா நதிக்கரையில் மகர சங்கராந்திக்கு முன்னதாக விளக்குகள் தண்ணீரில் மிதந்து வரும். இதனை பம்பா ஜலதீபம் என்றும், கும்ப தீர்த்த தீபம் என்றும் சொல்கின்றனர். சர்வ தீபம்: வீடு முழுவதிலும் விளக்குகளை ஏற்றி வைத்து தீப பிரகாசம் ஒளிமயமாக திகழ்வதை சர்வ தீபம் என்கின்றனர். கோபுர தீபம்: கோயில் கோபுரங்களின் மீது ஏற்றப்படும் தீபங்களுக்கு கோபுர தீபம் என்று பெயர். கார்த்திகை நாளன்று திருவண்ணாமலையில் உள்ள 2600 அடி உயரம் கொண்ட மலை மீது தீபம் ஏற்றப்படும். செப்புக் கொப்பறையில் நெய் ஊற்றி, கற்பூரம், கோடியான வெள்ளைத் துணி ஆகியவற்றுடன் தீபம் ஏற்றப்படும். இந்த தீபமானது பல மைல் தூரம் வரையில் பிரகாசமாக தெரியும். அதோடு, கொஞ்ச நாட்கள் வரையில் இந்த தீபமானது அணையாமல் இருக்கும். திருவண்ணாமலையில் அண்ணாமலையார் ரிஷப வாகனத்தில் வீதி உலா வருவதும், மலை மீது மகா தீபம் சுடர்விட்டு எரிவதும் ஒன்றாகவே நிகழும். இது ஆகாச தீப தத்துவத்தை பிரகடனப்படுத்துவதாக இருக்கும். ஏக முக தீபம்: இந்த ஏக முக தீபத்தை பகவதி தீபம் என்றும், துர்கா தீபம் என்றும் கூறி வருகின்றனர். சர்வ சக்திகளும், தன்னுள் இருக்க, தான் ஒருத்தியே ஏகமாக பிரகாசிப்பதை ஏகமுக தீபம் குறிக்கிறது. ஆகையால், தான் துர்கா பூஜையின் போது ஏக முக தீபமும், லலிதா சஹஸ்ரநாம பூஜைக்கு ஐந்து முக தீபமும் பயன்படுத்தப்படுகிறது. நிம்ப தீபம்: இலுப்பை எண்ணெய் ஏற்றி இந்த தீபம் ஏற்றப்படுகிறது. பொதுவாக பேய்கள் அகலுவதற்கு நிம்ப தீபம் ஏற்றுவார்கள். மேலும், மாரியம்மனின் அருள் கிடைக்க நிம்ப தீபத்தை முறைப்படி ஏற்ற வேண்டும். வீடுகளில் இந்த தீபத்தை ஏற்றலாம். விளக்கெண்ணெய், இலுப்ப எண்ணெய், வேப்ப எண்ணெய், தேங்காய் எண்ணெய், பசு நெய் கலந்த எண்ணெய் ஆகியவை பஞ்ச தீப எண்ணெய்கள் ஆகும். இந்த பஞ்ச தீப எண்ணெயா | tamil |
ऑस्ट्रेलिया की टीम को देखकर पाकिस्तान क्रिकेट बोर्ड ने दिया यह बयान कराची : पाकिस्तान क्रिकेट बोर्ड पीसीबी इस बात से बेहद खुश है कि ऑस्ट्रेलिया ने आगामी सीरीज के लिए अपनी मजबूत टीम की घोषणा की है। पहले इस बात की आशंका जताई जा रही थी कि कुछ शीर्ष खिलाड़ी पाकिस्तान का दौरा नहीं करना चाहते। पीसीबी के मुख्य संचालन अधिकारी फैसल हसनैन ने कहा कि इस घोषणा से उन्हें आश्वासन मिलता है कि सीरीज निर्धारित कार्यक्रम के अनुसार होगी। हसनैन ने कहा कि पाकिस्तान क्रिकेट और प्रशंसकों के लिए यह वास्तव में अच्छी खबर है कि उन्होंने मजबूत टीम की घोषणा की है क्योंकि उन्हें डर था कि उनके कुछ खिलाड़ी दौरे से बाहर हो सकते हैं। ऑस्ट्रेलिया की टीम 4 मार्च से 5 अप्रैल के बीच पाकिस्तान में तीन टेस्ट, तीन वनडे और एक टी20 मैच खेलेगी। उन्होंने विश्वास व्यक्त किया कि एक बार जब ऑस्ट्रेलिया अपना दौरा पूरा कर लेगा तो दूसरी बड़ी टीमें भी अंतरराष्ट्रीय मैचों के लिए पाकिस्तान का दौरा करेंगी। इससे देश में आईसीसी अंतरराष्ट्रीय क्रिकेट परिषद और एसीसी एशियाई क्रिकेट परिषद की प्रतियोगिताओं की मेजबानी का रास्ता साफ होगा। पिछले साल न्यूजीलैंड की टीम पाकिस्तान पहुंचने के बाद सुरक्षा कारणों से सीरीज शुरु होने से पहले स्वदेश लौट गई थी जबकि इंग्लैंड ने इस देश का अपना दौरा रद्द कर दिया था। ऑस्ट्रेलिया की टीम 1998 के बाद पहली बार पाकिस्तान का दौरा करेगी। | hindi |
ಕೋವಿಡ್ ಆತಂಕದ ನಡುವೆಯೂ ಕೊಡಗಿನ ಪ್ರವಾಸಿತಾಣಗಳಲ್ಲಿ ಪ್ರವಾಸಿಗರ ದಂಡು ಮಡಿಕೇರಿ : ಕೋವಿಡ್ ನಿರ್ಬಂಧಗಳು ಮತ್ತು ಆತಂಕದ ನಡುವೆಯೂ ದಕ್ಷಿಣ ಕಾಶ್ಮೀರ ಕೊಡಗು ಜಿಲ್ಲೆಗೆ ಪ್ರವಾಸಿಗರ ದಂಡು ಹರಿದು ಬರತೊಡಗಿದೆ. ಕ್ರಿಸ್ಮಸ್ ಸಾಲು ಸಾಲು ರಜೆ ಹಾಗೂ ಹೊಸ ವರ್ಷಾಚರಣೆಯ ಹಿನ್ನೆಲೆಯಲ್ಲಿ ದೇಶದ ವಿವಿಧ ಭಾಗಗಳ ಪ್ರವಾಸಿಗರು ಕೊಡಗಿಗೆ ಲಗ್ಗೆ ಇಟ್ಟಿದ್ದಾರೆ. ಮಡಿಕೇರಿಯ ರಾಜಾಸೀಟು, ಅಬ್ಬಿಫಾಲ್ಸ್, ಮಾಂದಲ್ ಪಟ್ಟಿ, ಕುಶಾಲನಗರದ ದುಬಾರೆ, ಕಾವೇರಿ ನಿಸರ್ಗಧಾಮ, ಸೋಮವಾರಪೇಟೆಯ ಮಲ್ಲಳ್ಳಿ ಜಲಪಾತ ಸೇರಿದಂತೆ ಎಲ್ಲೆಡೆ ಪ್ರವಾಸಿಗರು ಸಾವಿರಾರು ಸಂಖ್ಯೆಯಲ್ಲಿ ಜಮಾಯಿಸಿ ರಜೆಯ ದಿನಗಳನ್ನು ಕಳೆಯುತ್ತಿದ್ದಾರೆ. ಬೆಂಗಳೂರು, ಮೈಸೂರು, ಕೇರಳ, ತಮಿಳುನಾಡು, ತೆಲಂಗಾಣ ಮತ್ತಿತ್ತರ ಕಡೆಗಳಿಂದ ಹೆಚ್ಚಿನ ಸಂಖ್ಯೆಯ ಪ್ರವಾಸಿಗರು ಆಗಮಿಸುತ್ತಿದ್ದಾರೆ. ನಗರ, ಪಟ್ಟಣದ ರಸ್ತೆಗಳಲ್ಲಿ ವಾಹನದಟ್ಟಣೆ ಕಂಡು ಬಂದಿದ್ದು, ಹೋಂಸ್ಟೇ, ಲಾಡ್ಜ್ಗಳು ಪ್ರವಾಸಿಗರಿಂದ ಭರ್ತಿಯಾಗುತ್ತಿವೆ. ಹೊಟೇಲ್, ಬಾರ್ ಗಳಲ್ಲಿ ವ್ಯಾಪಾರ ಜೋರಾಗಿಯೇ ನಡೆಯುತ್ತಿದೆ. ಪ್ರಕೃತಿ ರಮಣೀಯ ಮಡಿಕೇರಿಯ ರಾಜಾಸೀಟು ಉದ್ಯಾನವನದಲ್ಲಿ ಕಾಲಿಡಲು ಕೂಡ ಸಾಧ್ಯವಾಗದ ಪರಿಸ್ಥಿತಿ ಸಂಜೆ ವೇಳೆಯಲ್ಲಿ ಕಂಡು ಬಂದಿದೆ. ಮಹಾಮಳೆ ಹಾನಿ ಮತ್ತು ಲಾಕ್ಡೌನ್ ನಂತರ ಮತ್ತೆ ಪ್ರವಾಸೋದ್ಯಮ ಚೇತರಿಕೆ ಕಾಣುತ್ತಿರುವ ಬಗ್ಗೆ ಪ್ರವಾಸೋದ್ಯಮದಲ್ಲಿ ತೊಡಗಿರುವವರು, ವರ್ತಕರು, ಟ್ಯಾಕ್ಸಿ, ಆಟೋಚಾಲಕರು, ಹೊಟೇಲ್ ಉದ್ಯಮಿಗಳು ತೃಪ್ತಿ ವ್ಯಕ್ತಪಡಿಸಿದ್ದಾರೆ. ಕೋವಿಡ್ ಗೆ ಡೋಂಟ್ ಕೇರ್ ಪ್ರವಾಸಿಗರ ಆಗಮನ ಮತ್ತು ಮಾರ್ಗಸೂಚಿಯ ಉಲ್ಲಂಘನೆಯನ್ನು ಗಮನಿಸಿದರೆ ಪ್ರವಾಸಿಗರಲ್ಲಿ ಕೋವಿಡ್ ಆತಂಕವೇ ಇಲ್ಲ ಎಂಬಂತ್ತಾಗಿದೆ. ರಾಜ್ಯದ ಇತರ ಜಿಲ್ಲೆಗಳಿಗೆ ಹೋಲಿಸಿದರೆ ಕೊಡಗು ಜಿಲ್ಲೆಯಲ್ಲಿ ಕೊರೊನಾ ಪ್ರಕರಣಗಳ ಸಂಖ್ಯೆ ಅತ್ಯಂತ ಕಡಿಮೆ ಇದೆ. ಇದೇ ಕಾರಣಕ್ಕೆ ಪ್ರವಾಸಿಗರು ತಮ್ಮ ಸುರಕ್ಷಿತ ಪ್ರವಾಸಕ್ಕಾಗಿ ಈ ಜಿಲ್ಲೆಯನ್ನು ಆಯ್ಕೆ ಮಾಡಿಕೊಂಡಿದ್ದಾರೆ ಎನ್ನುವ ಅಭಿಪ್ರಾಯವಿದೆ. ಪ್ರವಾಸಿಗರು ಮೋಜು ಮಸ್ತಿಯಲ್ಲಿ ಮೈ ಮರೆತಿದ್ದು, ಬಹುತೇಕರು ಸಾಮಾಜಿಕ ಅಂತರ ಕಾಯ್ದುಕೊಳ್ಳದೆ, ಮಾಸ್ಕ್ ಧರಿಸದೆ ನಿರ್ಲಕ್ಷ್ಯ ವಹಿಸುತ್ತಿರುವುದು ಕಂಡು ಬಂದಿದೆ. ಧರ್ಮಸ್ಥಳ: ಜನರ ಆಕರ್ಷಣೆಯ ಪರಿಸರ ಸ್ನೇಹಿ ಹೈಡ್ರಾಲಿಕ್ ಎತ್ತಿನಗಾಡಿ! ಆನಂದ್ ಮಹೀಂದ್ರ Tweet ಕೋವಿಡ್ ನಿಯಂತ್ರಣದಲ್ಲಿರುವ ಕೊಡಗಿನಲ್ಲಿ ಪ್ರವಾಸಿಗರಿಂದ ಮತ್ತೆ ಸೋಂಕು ಹೆಚ್ಚಾಗುವ ಆತಂಕ ಜಿಲ್ಲೆಯ ಜನರನ್ನು ಕಾಡುತ್ತಿದೆ. ಮಡಿಕೇರಿ ರಾಜಾಸೀಟಿನಲ್ಲಿ ಕೊರೊನಾ ನಿಯಮಗಳನ್ನು ಪಾಲಿಸದ ಪ್ರವಾಸಿಗರಿಗೆ ನಗರ ಪೊಲೀಸರು ದಂಡ ವಿಧಿಸುವ ಮೂಲಕ ಬಿಸಿ ಮುಟ್ಟಿಸಿದ ಪ್ರಸಂಗವೂ ನಡೆಯಿತು. ಹೊಸ ವರ್ಷಾಚರಣೆಗೆ ಸಂಬಂಧಪಟ್ಟಂತೆ ಬೆಂಗಳೂರು, ಮೈಸೂರು ಮಹಾನಗರಗಳಲ್ಲಿ ನಿರ್ಬಂಧ ಹೇರುವ ಸಾಧ್ಯತೆಗಳಿರುವುದರಿಂದ ಹೆಚ್ಚಿನ ಪ್ರವಾಸಿಗರು ಕೊಡಗು ಜಿಲ್ಲೆಯೆಡೆಗೆ ಮುಖ ಮಾಡಿದ್ದಾರೆ. ವಿವಿಧ ರೆಸಾರ್ಟ್ಗಳು, ಹೋಂಸ್ಟೇಗಳನ್ನು ಕೂಡ ಮುಂಗಡವಾಗಿ ಬುಕಿಂಗ್ ಮಾಡಲಾಗಿರುವ ಬಗ್ಗೆಯೂ ಮಾಹಿತಿ ಲಭಿಸಿದೆ. ಜಿಲ್ಲಾಡಳಿತ ಕೋವಿಡ್ ಮಾರ್ಗಸೂಚಿಗಳನ್ನು ಕಡ್ಡಾಯವಾಗಿ ಪಾಲಿಸುವಂತೆ ರೆಸಾರ್ಟ್, ಹೋಂ ಸ್ಟೇ, ಲಾಡ್ಜ್ ಹಾಗೂ ಹೊಟೇಲ್ಗಳಿಗೂ ಸೂಚಿಸಿದೆ. ಹೊಸ ವರ್ಷಾಚರಣೆಯ ನೆಪದಲ್ಲಿ ಹೆಚ್ಚು ಜನ ಸೇರುವುದನ್ನು ಜಿಲ್ಲಾಡಳಿತ ಹಾಗೂ ಪೊಲೀಸ್ ಇಲಾಖೆ ನಿಯಂತ್ರಿಸಬೇಕು ಮತ್ತು ನಿರ್ಬಂಧಗಳನ್ನು ಹೇರಬೇಕು ಎಂದು ಜಿಲ್ಲೆಯ ಜನ ಒತ್ತಾಯಿಸಿದ್ದಾರೆ. | kannad |
Yellow Kite has acquired the “very special” first book by Buddhist monk and meditation teacher Gelong Thubten.
The Hodder & Stoughton imprint will publish A Monk’s Guide to Happiness in hardback and ebook formats on 13th June. Liz Gough, Yellow Kite and lifestyle publisher at Hodder, bought world rights direct from the author.
Thubten became a monk at the age of 21, turning to Buddhism after suffering from severe anxiety and burnout. He teaches non-religious meditation and mindfulness to everyone from Silicon Valley tech giants and celebrities to prisoners and schoolchildren. He and neuroscientist Ash Ranpura previously collaborated with Ruby Wax on bestselling book How to be Human, the Manual, and are touring the country with a live show. | english |
package mono.debugger;
import javax.annotation.Nonnull;
/**
* @author VISTALL
* @since 05.01.2016
*/
public abstract class ValueTypeValueMirror<T> extends ValueImpl<T>
{
private TypeMirror myTypeMirror;
private Value[] myValues;
public ValueTypeValueMirror(VirtualMachine aVm, @Nonnull TypeMirror typeMirror, Value[] values)
{
super(aVm);
myTypeMirror = typeMirror;
myValues = values;
}
public abstract boolean isEnum();
@Nonnull
public Value[] fieldValues()
{
return myValues;
}
@Nonnull
@Override
public TypeMirror type()
{
return myTypeMirror;
}
}
| code |
విహారయాత్రలో తారక్! ఆర్ఆర్ఆర్ షూటింగ్తో బిజీగా గడుపుతున్న జూ.ఎన్టీఆర్ చాలాకాలం తర్వాత విహారానికి వెళ్లారు. ఆర్ఆర్ఆర్తోపాటు ఎవరు మీలో కోటీశ్వరులు టీవీ షోతో బిజీగా గడుపుతున్న తారక్ కొంత విరామం తర్వాత ఫ్యామిలీ కోసం సమయాన్ని కేటాయించారు. తాజాగా ఆయన కుటుంబ సభ్యులతో కలిసి పారిస్ టూర్కి వెళ్లారు. అక్కడ తన పెద్ద తనయుడు అభయ్రామ్ను ఎత్తుకుని ముద్దాడుతున్న ఫొటో ప్రస్తుతం సోషల్ మీడియాలో చక్కర్లు కొడుతోంది. క్యూట్ ఎక్స్ప్రెషన్ ఇచ్చిన అభయ్రామ్ ఫొటో ఆకట్టుకుంటోంది. తారక్ తన బిడ్డపై చూపించే ఎఫెక్షన్ కనిపిస్తోంది. | telegu |
গ্রেট ইন্ডিয়ান লুট, রান্নার গ্যাসের মূল্যবৃদ্ধি নিয়ে সরব মুখ্যমন্ত্রী রান্নার গ্যাস সহ জ্বালানির লাগাতার দামবৃদ্ধির সঙ্গে ব্রিটিশদের ভারত লুট গ্রেট ইন্ডিয়ান লুটের সঙ্গে তুলনা করলেন মুখ্যমন্ত্রী মমতা বন্দ্যোপাধ্যায় একইসঙ্গে লাগাতার মূল্যবৃদ্ধি নিয়ে কড়া ভাষায় কেন্দ্রের সমালোচনাও করলেন তিনি একইসঙ্গে কেন্দ্রকে মমতার বার্তা, দেশবাসীকে যন্ত্রণা দেওয়া বন্ধ করুন The Union government must immediately STOP TORMENTING the people of India! By repeatedly increasing fuel prices, LPG prices prices of essentialcommodities, BJP4India is actually conducting a GreatIndianLoot. PEOPLE ARE BEING FOOLED. Sad to see the Media SILENT BLIND. Mamata Banerjee MamataOfficial শনিবার মোদী সরকারের ঘোষণা অনুযায়ী আবারও সিলিন্ডার পিছু গৃহস্থের রান্নার গ্যাসের দাম বেড়েছে ৫০ টাকা অর্থাত্ আরও একবার সাধারণ মানুষের পকেট কেটে মুনাফা লোটার পথে কেন্দ্রের বিজেপি সরকার রান্নার গ্যাসের দাম কলকাতায় আজ থেকে সিলিন্ডার প্রতি বেড়ে দাঁড়াল ১০২৬ টাকা আগে এই ১৪ কেজির রান্নার গ্যাসের দাম ছিল ৯৭৬ টাকা এদিন টুইট করে কেন্দ্রের বিজেপি সরকারকে আরও একবার কড়া ভাষায় আক্রমণ করেছেন মমতা বন্দ্যোপাধ্যায় এদিন টুইট করে মুখ্যমন্ত্রী বলেছেন, কেন্দ্রীয় সরকারকে অবিলম্বে ভারতের সাধারণ মানুষকে কষ্ট দেওয়া বন্ধ করতে হবে এলপিজি, নিত্যপ্রয়োজনীয় জিনিসের দাম, জ্বালানির দাম বারবার বৃদ্ধি করে লুঠের রাজত্ব চালাচ্ছে মানুষকে বোকা বানানো হচ্ছে এতে মিডিয়া নিরব ও অন্ধের ভূমিকা পালন করতে দেখে দুঃখিত | bengali |
પ્રિમોન્સુનનું માઈક્રો પ્લાનિંગ, કમિશનરે અધિકારીઓને આપી કડક સુચના My samachar.in:જામનગર દરવર્ષ ચોમાસું આવે એ પૂર્વે જામનગર મહાનગરપાલિકા દ્વારા અંદાજે અડધા કરોડના ખર્ચે પ્રિ મોન્સુન કામગીરી કરવામાં આવતી હોય છે, પણ આ કામગીરીને લઈને દરવર્ષે આક્ષેપો થતા રહે છે, એવામાં જામનગર મનપાની કમાન કમિશ્નર વિજયકુમાર ખરાડી સંભાળી રહ્યા હોય તેવોએ મીટીંગમાં જ અધિકારીઓને જણાવી દીધું છે કે પ્રિ મોન્સુનને નામે પૈસાનો વેડફાટ નહિ ચાલે નક્કર કામગીરી જોશે....માટે આ વખતે આ કામગીરી ખરેખર અસરકારક બનશે તેમ લાગે છે.જામનગરમાં પ્રિમોન્સુન કામગીરી અંતર્ગત મહાપાલિકાના કમિશ્નરે અધિકારીઓ સાથે કરેલી બેઠકમાં વરસાદી પાણીના નિકાલની કેનાલની સફાઇ સમયમર્યાદામાં કરવા અધિકારીઓને તાકીદ કરી હતી. આ સાથે ભારે વરસાદ, પૂરની સ્થિતિને પહોંચી વળવા સુચારૂં વ્યવસ્થાની સૂચના આપી હતી.. આગામી ચોમાસાની સીઝનને ધ્યાને લઇ શહેર વિસ્તારમાં ભારે વરસાદના કારણે પાણી ન ભરાઇ તે માટે મંગળવારે મનપાના કમિશ્નરના અધ્યક્ષ સ્થાને મહાપાલિકાની જુદીજુદી શાખાના અધિકારીઓની મીટીંગ યોજાઇ હતી. જેમાં કમિશ્નરે ભૂગર્ભ શાખા હસ્તકની ચાલુ પ્રિમોન્સુન કામગીરીની સમીક્ષા કરી હતી.આ સાથે શહેરની વરસાદી પાણીના નિકાલની ખુલ્લી કેનાલની સફાઇ નિયત સમય મર્યાદામાં કરવા તાકીદ કરી હતી. તદઉપરાંત શહેરમાં ભારે વરસાદ, પૂર, વાવાઝોડા વગેરેની સ્થિતિને પહોંચી વળવા જરૂરી આનુસંગીક વ્યવસ્થા ગોઠવવા અધિકારીઓને સૂચના આપી હતી. બેઠકમાં મનપાની જુદીજુદી શાખાના અધિકારીઓ હાજર રહ્યા હતાં. | gujurati |
ফের বাড়ল আক্রান্তের সংখ্যা, একদিনে ১০হাজার ছাড়াল! প্রথমে কলকাতাই রাজ্যে জারী রয়েছে করোনা বিধিনিষেধ বিধিনিষেধ জারী করার পরেই রাজ্যে কমে দাঁড়িয়েছিল করোনার সংক্রমণের সংখ্যা তবে টানা কয়েকদিন করোনার সংক্রমণ কম থাকার পরে এদিন মঙ্গলবার ফের ১০হাজারের গন্ডি পেরোল করোনা পরীক্ষা বাড়ার সাথে সাথেই ১০হাজার টপকালো করোনা সংক্রমণের সংখ্যা পাশাপাশি কিছুটা বেড়ে দাঁড়িয়েছে মৃত্যুর সংখ্যাটাও মঙ্গলবার স্বাস্থ্য ভবনের দেওয়া রিপোর্টে বলা হয়েছে, গত একদিনের মধ্যে রাজ্যে করোনায় আক্রান্ত হয়েছেন ১০হাজার ৪৩০জন এদিন মৃত্যু হয়েছে ৩৪জনের তবে ভাড়ি হচ্ছে সুস্থতার পাল্লাও, এই সময়ে করোনার হাত থেকে রেহাই পেয়ে সুস্থ হয়ে উঠেছেন ১৩হাজার ৩০৮জন এবং প্রথম স্থানে রয়েছে, শহর কলকাতা কলকাতায় আক্রান্তের সংখ্যা রয়েছে ২হাজার ২০৫জন দ্বিতীয় স্থানে রয়েছে উত্তর ২৪ পরগনা, করোনায় আক্রান্ত হয়েছেন এখানে ১হাজার ৭৬১জন আবার এদিকে, তৃতীয় স্থানে রয়েছে আক্রান্তের সংখ্যার মধ্যে দক্ষিণ ২৪ পরগনা সেখানে আক্রান্তের সংখ্যা রয়েছে ৮৮৫জন | bengali |
आलिया भट्ट को ऑडिशन के समय संजय लीला भंसाली ने किया था रिजेक्ट ,जानिए क्या थी इसकी असली वजह बॉलीवुड के फेमस डायरेक्टर संजय लीला भंसाली की फिल्म गंगूबाई काठियावाड़ी का फैंस को बेसब्री से इन्तजार है यह फिल्म ाक रिलीज होने वाली है अब आलिया भट्ट ने संजय लीला भंसाली को लेकर एक बढ़ा खुलासा किया है ये कहा जा रहा है है की आलिया भट्ट एक बार संजय लीला भंसाली की फिल्म के लिए ऑडिशन देने गई थी लेकिन उन्होंने आलिया भट्ट को रिजेक्ट कर दिया था यह बात तब की है जब संजय लीला भंसाली फिल्म ब्लैक बना रहे थे जिसमें अमिताभ बच्चन के साथ रानी मुखर्जी नजर आई थी लेकिन ऑडिशन के समय संजय ने आलिया भट्ट को रिजेक्ट कर दिया था आलिया ने इंटरव्यू में बताया की वो ऑडिशन के लिए संजय सर के पास गई थी उनको कहा जाता है की वह प्रीति जिंटा की तरह नजर आती है उनकी ममी छाती थी की उनकी बेटी अभिनेत्री बने यही सोचकर वो ऑडिशन के लिए गई थी इसी के साथ कहा की जैसे ही आलिया अंदर गई तो वो देखती ही रह गई उनको समझ नहीं आया की वो क्या करने जा रही है वो अंदर गई और सब कुछ बकवास करके आ गई और इसी कारण इस फिल्म के लिए सिलेक्ट नहीं हुई और वो इस फिल्म का हिस्सा नहीं बन सकी आलिया भट्ट ने अपने करियर में कई शानदार फ़िल्में दी है और अब वह संजय लीला भंसाली की फिल्म गंगूबाई काठियावाड़ी में नजर आने वाली है जिसके गाने और ट्रेलर ने हर तरफ हंगामा मचा रखा है आलिया भट्ट पहली बार संजय लीला भंसाली की फिल्म में काम कर रही है | hindi |
లాల్ దర్వాజ బోనాల ఉత్సవాలకు ఏర్పాట్లు పూర్తి:మంత్రి ఇంద్రకరణ్ రెడ్డి హైదరాబాద్: ఆషాఢ బోనాల జాతర ఉత్సవాల్లో భాగంగా పాతబస్తీలోని లాల్ దర్వాజా సింహవాహిని మహంకాళి బోనాల ఉత్సవాలకు అన్ని ఏర్పాట్లు పూర్తి చేశామని దేవాదాయ శాఖ మంత్రి అల్లోల ఇంద్రకరణ్ రెడ్డి తెలిపారు. బోనాలకు తరలివచ్చే భక్తులకు అసౌకర్యం కలగకుండా ప్రభుత్వం, దేవాదాయ శాఖ ఆద్వర్యంలో అన్ని సదుపాయాలను సిద్ధం చేశామన్నారు. ప్రభుత్వం తరఫున పట్టువస్త్రాలు, అధికార లాంఛనాలు సమర్పిస్తామని పేర్కొన్నారు. బోనాలు సమర్పించేందుకు వచ్చే భక్తులు తప్పనిసరిగా కోవిడ్ నిబంధనలు పాటించాలని, మాస్కులు ధరించాలని కోరారు. వేల సంఖ్యలో వచ్చే భక్తులకు ఎలాంటి ఇబ్బందులు కలగకుండా పోలీసులు పటిష్టమైన బందోబస్తు ఏర్పాటు చేశారని మంత్రి తెలిపారు. శాంతి భద్రతలను కాపాడేందుకు ప్రత్యేక పోలీసు బలగాలను కూడా ప్రభుత్వం ఏర్పాటు చేసిందన్నారు. | telegu |
ఏఆర్ రెహమాన్ ఎవరో నాకు తెలియదు.. భారతరత్న చెప్పుతో సమానం: బాలయ్య నందమూరి బాలకృష్ణ తాజాగా చేసిన కొన్ని వ్యాఖ్యలు ఇప్పుడు వివాదాస్పదంగా మారుతున్నాయి. ఆదిత్య 369 30 ఏళ్లు పూర్తి చేసుకున్న సందర్భంగా ఓ ఇంటర్వ్యూలో మాట్లాడుతూ తెలుగు ఇండస్ట్రీకి మా కుటుంబం ఎంతో చేసిందని అవార్డులతో దానిని పోల్చలేమని చెప్పుకొచ్చారు బాలయ్య. అంతేకాకుండా భారతరత్న అనేది ఎన్టీఆర్ కాలిగోటితో, చెప్పు తో సమానం అని పేర్కొన్నారు. అలాగే మ్యూజిక్ డైరెక్టర్ ఏ ఆర్ రెహమాన్ ఎవరో తనకు తెలియదని పదేళ్లకు ఒకసారి హిట్ ఇచ్చే ఆయనకు ఆస్కార్ అవార్డు ఇచ్చారని ఒక్కో మ్యూజిక్ డైరెక్టర్ కి ఒక్కో శైలి ఉంటుందని.ఇళయరాజా సంగీతం ఆదిత్య369 చిత్రానికి అద్భుతమని అన్నారు. కాగా భారత రత్నను చెప్పు తో పోల్చడం, రెహమాన్ ఎవరో తెలియదు అని చెప్పటంతో ఇప్పుడు బాలయ్యపై ట్రోల్స్ విపరీతంగా జరుగుతున్నాయి. అయితే బాలయ్య నిప్పురవ్వ సినిమాకు గతంలో ఏ ఆర్ రెహమాన్ సంగీతం అందించిన సంగతి తెలిసిందే. | telegu |
Brahamastra Shooting: બ્રહ્માસ્ત્રનું શૂટિંગ 5 વર્ષ બાદ પૂર્ણ, આલિયારણબીર કાશી મંદિરના શરણે આલિયા ભટ્ટ અને રણબીર કપૂરે Alia Bhatt and Ranbir kapoor ફિલ્મ બ્રહ્માસ્ત્રનું શૂટિંગ Brahamastra Shooting પૂરું કરી લીધું છે. આ ફિલ્મ છેલ્લા પાંચ વર્ષથી બની રહી હતી. હવે ફિલ્મનું શૂટિંગ કાશીમાં પૂર્ણ થઈ ગયું છે.ન્યૂઝ ડેસ્ક: આલિયા ભટ્ટ અને રણબીર કપૂર Alia Bhatt and Ranbir kapoor પ્રથમ વાર સ્ક્રીન પર સાથે જોવા મળશે. કપલી આગામી ફિલ્મ બ્રહ્માસ્ત્રનું શૂંટિંગ પૂર્ણ Brahamastra Shooting પણ થઇ ગયું છે. તાજેતરમાં જ આ ફિલ્મના પહેલા પાર્ટનું અંતિમ શેડ્યૂલ કાશીમાં પૂર્ણ કરવામાં આવ્યું છે. આ ફિલ્મના ડાયરેક્ટર અયાન મુખર્જી અને લીડ સ્ટારકાસ્ટ આલિયા ભટ્ટ અને રણબીર કપૂરે શૂંટિગ પૂરુ કરી કાશી મંદિર ખાતે પહોંચ્યાં હતા. આ દરમિયાન તેણે ફોટોસેશન પણ કરાવ્યું હતુ. classaligntexttop noRightClick twitterSection data ફિલ્મનું શૂટિંગ વારાણસીની ગલીઓ કરાયું: આ પેહલા પણ આલિયા અને રણબીર વારાણસીમાંથી તસવીરો અને વીડિયો સોશિયલ મીડિયા Social Media પર વહેતા થયા હતા. આ દરમિયાન આલિયારણબીર ઘણી જગ્યાએ શૂટિંગ કરતા જોવા મળ્યા હતા. ફિલ્મનું શૂટિંગ વારાણસીની ગલીઓમાં અને નદી કિનારે કરવામાં આવ્યું છે. ફિલ્મના નિર્માતા કરણ જોહર છે.Brahamastra Shooting: બ્રહ્માસ્ત્રનું શૂટિંગ 5 વર્ષ બાદ પૂર્ણ, આલિયારણબીર કાશી મંદિરના શરણેઆ પણ વાંચો: RRR Collection: RRRએ વિશ્વભરમાં 500 કરોડની કમાણી કરી સર્જ્યો રેકોર્ડપાંચ વર્ષ લાગ્યો આ ફિલ્મ બનાવતા: લગભગ પાંચ વર્ષ પછી ફિલ્મનું શૂટિંગ પૂરું કર્યા બાદ અયાન, રણબીર અને આલિયાએ જગવિખ્યાત કાશી મંદિરની મુલાકાત લીધી હતી. જેની તસવીરો સોશિયલ મીડિયા પર શેર કરવામાં આવી છે. આ તસવીરોમાં જોવા મળી રહ્યું છે કે, તેના ગળામાં ફુલોની હારમાળા અને કપાળ પર તિલક લગાવેલું છે. આ તસવીરો શેર કરતા નિર્દેશક અયાન મુખર્જીએ તેના ઈન્સ્ટાગ્રામ પર લખ્યું, અને આખરે ફિલ્મનું શૂટિંગ પૂર્ણ થયું, બ્રહ્માસ્ત્રનું પહેલો શોર્ટ લીધાના 5 વર્ષ પછી, અમે આખરે અમારો છેલ્લો સીન શૂટ કર્યો, એકદમ અવિશ્વસનીય, પડકારજનક, જીવનભરની મુસાફરી.Brahamastra Shooting: બ્રહ્માસ્ત્રનું શૂટિંગ 5 વર્ષ બાદ પૂર્ણ, આલિયારણબીર કાશી મંદિરના શરણેશિવનું શૂટિંગ અમે વારાણસીમાં પૂર્ણ કર્યું: અયાન મુખર્જી અયાને આગળ કહ્યું, ભાગ1 શિવનું શૂટિંગ અમે વારાણસીમાં પૂર્ણ કર્યું, જે ભગવાન શિવની ભાવનાથી ઓતપ્રોત છે અને તે પણ સૌથી પવિત્ર કાશી વિશ્વનાથ મંદિરમાં, જે આપણને પવિત્રતાનું વાતાવરણ પ્રદાન કરે છે. ખુશી અને આશીર્વાદ, ફિલ્મ બ્રહ્માસ્ત્ર આ વર્ષે 9 સપ્ટેમ્બરે રિલીઝ Brahamastra release date થવા જઈ રહી છે.આ ફિ્લ્મમાં આલિયા અને રણબીર સિવાય આ કલાકારો: આલિયા ભટ્ટે તેના ઇન્સ્ટાગ્રામ એકાઉન્ટ પર વારાણસીની કેટલીક તસવીરો શેર કરી અને લખ્યું, અમે આ ફિલ્મનું શૂટિંગ વર્ષ 2018માં શરૂ કર્યું હતું અને હવે બ્રહ્માસ્ત્ર ભાગ1નું શૂટિંગ પૂર્ણ થઈ ગયું છે, 09.09.09ના રોજ સિનેમાઘરોમાં મળીશું. 2022. ઉલ્લેખનીય છે કે, આ ફિલ્મમાં અમિતાભ બચ્ચન, નાગાર્જુન અને મૌની રોય પણ મહત્વની ભૂમિકામાં જોવા મળશે.આ પણ વાંચો: Geeta Rabari in US: યૂક્રેન પીડિતોની મદદ માટે કચ્છી કોયલ ગીતા રબારીએ માનવ ધર્મનું કર્યું પાલન, ડાયરામાં 2 કરોડ કર્યાં એકત્રિત | gujurati |
Dookudu10Years: హేయ్.. మళ్లి ఏసేశాడు! మహేశ్ బాబుసమంత దూకుడుకి పదేళ్లు.. పదేళ్ల క్రితం మహేశ్ బాబుసమంత నటించిన దూకుడుబాక్సాఫీస్ ను షేక్ చేసింది. మహేశ్ అభిమానుల ఆనందాన్ని అంబరమంటేలా చేసింది. 2006లో వచ్చిన పోకిరి తర్వాత మళ్లీ బ్లాక్ బస్టర్ హిట్టందే దూకుడు అనే చెప్పాలి. ఎప్పుడొచ్చామన్నది కాదన్నయ్యా బుల్లెట్ దిగిందా లేదన్నట్టు దాదాపు ఐదేళ్ల తర్వాత తమ హీరో మూవీ భారీ హిట్టందుకోవడంతో ఘట్టమనేని అభిమానుల ఆనందానికి అవధుల్లేవు. పోకిరి 2006లో ప్లాటినమ్ జూబ్లీ జరుపుకుంది. ఆ తర్వాత వచ్చిన సైనికుడు, అతిథి ఆశించిన స్థాయిలో ఆకట్టుకోలేక పోయాయి. మళ్ళీ బిగ్ స్క్రీన్ పై కనిపించేందుకు రెండేళ్ళు గ్యాప్ తీసుకున్నాడు. 2010లో వచ్చిన ఖలేజా అభిమానులకు నిరాశ కలిగించింది. అంటే పోకిరి తరువాత మహేశ్ నటించిన మూడు చిత్రాలూ కాస్త నిరాశపర్చాయనే చెప్పాలి. అలాంటి సమయంలో వచ్చిన దూకుడు బాక్సాఫీస్ వద్ద దూసుకు పోయింది. మహేశ్ బాబుసమంత కలసి నటించిన తొలి సినిమా ఇది. 2003లో విడుదలైన జర్మన్ మూవీ గుడ్ బై, లెనిన్ ఆధారంగా దూకుడు తెరకెక్కింది. అందులో భర్త వెస్ట్ జర్మనీకి వెళ్ళగా, ఈస్ట్ జర్మనీలోనే తన పిల్లలతో ఉంటూ క్రిస్టెనా అనే తల్లి సోషలిస్ట్ యూనిటీ పార్టీ ప్రచారంలో పాలు పంచుకుంటూ ఉంటుంది. ఆమె తనయుడు అలెక్స్ మాత్రం ప్రభుత్వానికి వ్యతిరేకంగా పోరాడతాడు. అతణ్ణి అరెస్ట్ చేస్తారు. అరెస్టయిన తనయుణ్ణి చూసి ఆ తల్లి తట్టుకోలేదు. గుండెపోటుకు గురై కోమాలోకి పోతుంది. ఆమె కోమాలో ఉండగా బెర్లిన్ గోడ కూలిపోయి, ఈస్ట్, వెస్ట్ జర్మనీలు కలసి పోతాయి. కొన్నాళ్ళకు కోమానుండి అలెక్స్ తల్లి కోలుకుంటుంది. ఆమెకు షాక్ కలిగించే విషయాలు చెబితే చాలా ప్రమాదం అని చెబుతారు డాక్టర్లు. దాంతో ఆమె సంతోషం కోసం అలెక్స్ ఈస్ట్ జర్మనీ అంతకు ముందుఎలా ఉందో అలా చూపించడానికి పలు పాట్లు పడతాడు. వెస్ట్ కు వెళ్ళి మరో పెళ్లి చేసుకున్న అలెక్స్ తండ్రి కొడుకు కోరిక మేరకు తిరిగొచ్చేలోగా జర్మనీ రాజకీయ పరిణామాలు తెలుసుకున్న క్రిస్టెనా కన్నుమూస్తుంది. ఇది విషాదంతో ముగిస్తే దీనికి మెరుగులు దిద్దిన దర్శకుడు సుఖాంతం చేశాడు. ఆద్యంతం నవ్వులు పూయించిన దూకుడు యాభైకి పైగా కేంద్రాల్లో శతదినోత్సవాలు జరుపుకుంది. విదేశాలలోనూ రికార్డు కలెక్షన్లు రాబట్టింది. అంతకు ముందు మగధీర, సింహా నెలకొల్పిన ఫస్ట్ వీకెండ్ కలెక్షన్లను ఈ సినిమా అధిగమించింది. ఆ రోజుల్లో 57 కోట్ల రూపాయలు వసూలు చేసిన చిత్రంగా దూకుడు నిలచింది. బెంగాలీలో ఛాలెంజ్2గానూ, కన్నడలో పవర్గానూ రీమేక్ అయి సక్సెస్ అయింది. ఆ ఏడాదికి ఏడు నంది అవార్డులు అందుకోవడం విశేషం. ఈ సినిమాలో ప్రకాశ్ రాజ్, బ్రహ్మానందం, ఎమ్మెస్ నారాయణ, సోనూ సూద్, కోట శ్రీనివాసరావు, తనికెళ్ళ భరణి, చంద్రమోహన్, నాజర్, సుమన్, సయాజీ షిండే, ప్రగతి, షఫీ, వెన్నెల కిశోర్, నాగబాబు, ధర్మవరపు సుబ్రహ్మణ్యం తదితరులు నటించారు. పువ్వాయ్ పువ్వాయ్. పాటలో పార్వతీ మెల్టన్, నీ దూకుడు. సాంగ్ లో మీనాక్షి దీక్షిత్ ఐటమ్ గాళ్స్ గా అలరించారు. ఇక నీ దూకుడు., ఇటు రాయె. ఇటు రాయె. సహా పాటలన్నీ అలరించాయి. శ్రీనువైట్ల దర్శకత్వంలో రామ్ ఆచంట, గోపీచంద్ ఆచంట, అనిల్ సుంకర 14 రీల్స్ ఎంటర్ టైన్ మెంట్స్ పతాకంపై నిర్మించారు. వెండితెరపైనే కాదు ఇప్పటికీ బుల్లితెరపై దూకుడు దూసుకుపోతూనే ఉంది. ఈ సినిమా పదేళ్ళు పూర్తి చేసుకున్న సందర్భంగా సెప్టెంబర్ 23వ తేదీ రాత్రి 9 గంటలకు హైదరాబాద్ క్రాస్ రోడ్స్ లోని సుదర్శన్ 35 ఎమ్.ఎమ్.లో స్పెషల్ షో ప్రదర్శించనున్నారు. ఇక మహేష్ బాబు ప్రస్తుత సినిమాల విషయానికి వస్తే.. పరుశురామ్ పెట్లా దర్శకత్వంలో సర్కారు వారి పాట రూపొందుతోంది. Also Read: Horoscope Today:ఈ రాశులవారు అప్రమత్తంగా ఉండాలి, ఈ రోజు ఏ రాశిఫలాలు ఎలా ఉన్నాయో చూద్దాం.. Also Read: చిరంజీవి 43 ఏళ్లు సినీ జర్నీపై రామ్ చరణ్ ఇంట్రెస్టింగ్ ట్వీట్ Als Read: మరింత పెరిగిన పసిడి ధర.. హైదరాబాద్లో ఇంకా.. వెండి కూడా అదే దారిలో.. ఇంట్రస్టింగ్ వీడియోలు, విశ్లేషణల కోసం ABP Desam YouTube Channel సబ్స్క్రైబ్ చేయండి | telegu |
ٹوبہ ٹیک سنگھنامہ نگارپنجاب حکومت عوام کو معےاری اشےائے خوردونوش کی سستے داموں فراہمی کےلئے ٹھوس اقدامات کررہی ہے صارفےن کے حقوق پر ڈاکہ ڈالنے والے گراں فروشوں اور ذخےرہ اندوزوں کے خلاف سخت قانونی کاروائی عمل مےں لائی جارہی ہے ان خےالات کا اظہار صوبائی سےکرٹری پلاننگ اےنڈ ڈوےلپمنٹ سےم اجمل چو ہدری نے جھنگ روڈ پر لگائے گئے مضا با زار کے دورہ کے موقع پر کےا | urdu |
Nepal-India joint border security meeting held last week has decided to monitor the movement of Myanmar’s Rohingya refugees in border areas. Both countries have collected evidences that substantiate the claim that Rohingya refugees are illegally entering Nepal through border points despite efforts made by the authorities to prevent such movement.
These security lapses, according to the Ministry of Home Affairs, may pose security challenges to both countries. The joint border security meeting held last Saturday at Khakrola of Lakhimpur Kheri in the Indian state of Uttrar Pradesh decided to carefully monitor movement of illegal immigrants as well as extremist Muslim groups in border areas and share information on their activities.
Armed Police Force DSP Bishnu Prasad Bhatta led the seven-member Nepali delegation to the meeting. The six-member Indian delegation was led by Narayan Ram Khalaw, deputy commandant of Border Security Force (3rd Battalion) based in Lakhimpur, Khiri. Both the teams have forwarded the meeting’s outcomes to their respective governments.
Rohingyas are Muslims predominantly from Rakhine state of Myanmar. But the Myanmar government has denied citizenship to Rohingyas since 1982, turning them into stateless people. Since the 1970s, they have often become victims of state-led crackdowns, forcing hundreds of thousands to flee the country. Their flight from the home country intensified in 2017 when Rohingya militants launched deadly attacks on security forces of Myanmar.
Some one million Rohingyas have fled from Myanmar and are staying in different countries, including 0.7 million in Bangladesh. Some of them have entered Nepal via open border with India after the 2017 violence.
Nepal does not recognise Rohingyas, who have illegally crossed the border, as refugees. They are considered as illegal immigrants.The Office of the United Nations High Commissioner for Refugees has certified around 360 Rohingyas residing in Kathmandu as refugees. These refugees are residing in two camps, with one housing 183 and the other 177.
UNHCR is providing basic health support to Rohingyas living in Nepal and is sending their children to schools based in Kathmandu. The UNHCR is in the process of certifying around 40 more. But the Home Ministry says over 650 Rohingyas are living in Nepal, as some of them entered Nepal in the 1990s and 2012.
“The flow of illegal Rohingya immigrants into Nepal has lately petered out due to strict surveillance. Yet some of them may have succeeded in crossing the border clandestinely,” Ram Krishna Subedi, spokesperson for the Ministry of Home Affairs, told THT. “We have directed our three security agencies to prevent them from entering Nepal,” he added.
In September, Indian security forces intercepted entry of Rohingyas travelling on fake visas to Nepal via Kolkata. It is said human traffickers ferry Rohingyas from Bangladesh to Nepal via India.
A version of this article appears in print on October 31, 2018 of The Himalayan Times. | english |
Amal Clooney might just get the prize for the best-dressed guest at today's royal wedding. The human rights lawyer – who arrived with husband George – wore a beautiful yellow dress with a matching hat.
The mustard yellow shift dress – which was designed by Stella McCartney – featured a long floor-length sash. She teamed the ensemble with metallic heels and box clutch bag.
It was confirmed by Amal's hairstylist, Miguel Pirez – who is also rumoured to be doing Meghan Markle's hair on the day – that the Clooneys would be attending.
In an interview with Spanish publication Hola! Pirez was asked if he was styling Markle's hair on the day. He refused to confirm or deny the news and instead said: "What I can confirm is that I will be in charge of Amal's hair that day."
The Clooneys are joined by a number of other famous guests including David and Victoria Beckham, Carey Mulligan and Oprah. | english |
10 வயதில் பிக்பாஸ் பிரபலங்களின் புகைப்படம்.. அண்ணாச்சி உங்கள பார்த்தாலே காமெடியா இருக்கு விஜய் டிவியின் பிரபல பொழுதுபோக்கு நிகழ்ச்சியாக மாறிக்கொண்டிருக்கும் பிக்பாஸ் சீசன்5 நிகழ்ச்சியானது 50 நாட்களை எட்ட உள்ளது. இந்நிலையில் போட்டியாளர்களின் சிறுவயது புகைப்படம் வெளியாகி இணையத்தில் வைரலாகி வருகிறது. இதில் கடந்த வாரம் பிக் பாஸ் வீட்டில் இருந்து வெளியேறிய கானா பாடகியான இசைவாணியின், இப்போது இருப்பதை விட சிறுவர்களின் செம க்யூட்டாக இருக்கிறார். அதேபோல் ஒரு திரைப்பட நடிகராகவும் தொகுப்பாளராகவும் நகைச்சுவை நடிகராக விளங்கி மேலும் அரசியல்வாதியாகவும் கலக்கி வருகிறார் இமான் அண்ணாச்சி. இவர் 1968ல் தூத்துக்குடியில் பிறந்தவர். தற்பொழுது இவரின் சிறுவயது புகைப்படமும் கிடைத்துள்ளது. தற்போது கருகருவென இருக்கும் இமான் அண்ணாச்சி 10 வயதில் வெள்ளை வெளேர் என்று இருக்கிறார். அடுத்தபடியாக அடுத்த போட்டியாளர் வருண். ஐசரி வேலனின் பேரன் வருண். ஒருநாள் இரவில் படத்தின் மூலம் திரைப்பட நடிகராக அறிமுகமானார். மேலும் இவர் போகன் படத்திலும் நடித்துள்ளார். இவரின் சிறுவயது புகைப்படமும் வெளியாகியுள்ளது. அதில் இவர் சிறுவயதில் உள்ளது போல அச்சு அசலாக இப்போதும் இருந்து வருகிறார். அதைத்தொடர்ந்து விஜய் டிவியின் பல ரியாலிட்டி ஷோக்களில் பிரபலமான நம்பர் 1 பெண் தொகுப்பாளராக இருந்து வருபவர் பிரியங்கா தேஷ்பாண்டே. கர்நாடகத்தில் பிறந்தவர். இவரின் சிறுவயது புகைப்படமும் வெளியாகி ரசிகர்களை பெரிதும் ஆச்சரியத்தில் ஆழ்த்தியுள்ளது. இவர்களைத் தொடர்ந்து அடுத்த போட்டியாளர் அபிநய். இவரின் சிறுவயது புகைப்படமும் முழுவதுமாக அடையாளமே தெரியாத அளவிற்கு உள்ளது. இவர் விஜய சாமுண்டீஸ்வரி அவர்களின் மகனும், சாவித்திரி ஜெமினி கணேசன் அவர்களின் பேரனும் ஆவார். அடுத்ததாக உலக அழகி பட்டத்தை வென்ற அக்ஷரா ரெட்டி தற்பொழுது பிக்பாஸ் சீசன் 5 இல் போட்டியாளராக கலக்கி வருகிறார். மேலும் இவர் சென்னையை சேர்ந்தவர். மாடலிங் துறையில் பல சாதனைகளைப் படைத்துள்ளார். இவரின் இயற்பெயர் ஷ்ரவ்யா. இவரின் சிறுவயது புகைப்படமும் அச்சு அசலாக அவர் தற்பொழுது இருப்பது போலவே வெளியாகி ஆச்சரியத்தை ஏற்படுத்தியுள்ளது. இதைப்போல் மிகவும் சிறப்பாக பிக் பாஸ் நிகழ்ச்சியில் தற்பொழுது விளையாடி மக்களின் மனங்களை அதிகம் கொள்ளை கொண்டு வருபவர் ராஜூ ஜெயமோகன். இவர் ஒரு எழுத்தாளர், திரைப்பட நடிகர் மேலும் பல சின்னத்திரை சீரியலிலும் நடிகராகவும் பல பரிமாணங்களை கொண்டு திகழ்கிறார். இவரின் சிறுவயது புகைப்படமும் இவர் இப்பொழுது இருப்பது போலவே அப்படியே இருக்கிறது. அடுத்தபடியாக நாடகக் கலைஞராகவும் நாட்டுப்புற பாடகியாகவும் இருப்பவர் பிக் பாஸ் சீசன் 5 போட்டியாளர் தாமரைச்செல்வி. இவர் தற்பொழுது அட்டகாசமாக விளையாடி வரும் நிலையில் இவரின் சிறுவயது போட்டோவும் வெளியாகி இணையத்தை அசத்தி வருகிறது. அதைத் தொடர்ந்து அடுத்த போட்டியாளர் சிபி புவனச் சந்திரன். இவர் திரைப்பட நடிகராக அறிமுகமான படம் வஞ்சகர் உலகம். அதை தொடர்ந்து இவர் பிளாக்பஸ்டர் மூவியான மாஸ்டர் படத்தில் முக்கியமான வேடத்தில் நடித்து கலக்கியிருப்பார். இவரின் புகைப்படமும் வெளியாகி இணையதளத்தில் வைரலாகி வருகிறது. சென்சார் செய்யாத செய்திகள், வீடியோக்கள் பார்க்க சினிமாபேட்டை Youtube ல் Subscribe பண்ணுங்க. | tamil |
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టీడీపీతో జనసేన పొత్తు ఖాయమేనా? పరిషత్ ఎన్నికలతో క్లారిటీ వచ్చినట్టేనా? ఆంధ్రప్రదేశ్ లో ప్రస్తుతం భారతీయ జనతా పార్టీతో జనసేన పొత్తు పెట్టుకుంది. 2014 ఎన్నికల్లో ఈ రెండు పార్టీలో టీడీపీతో కలిసి పోటీ చేశాయి. 2019 ఎన్నికల్లో మాత్రం మూడు పార్టీలు విడివిడిగానే బరిలో నిలిచాయి. ఎన్నికల తర్వాత బీజేపీ, జనసేన మధ్య సయోధ్య కుదిరింది. అయితే బీజేపీతో పొత్తు విషయంలో జనసేన హ్యాపీగా లేదనే ప్రచారం కొంత కాలంగా సాగుతోంది. బీజేపీతో కటీఫ్ చెప్పడానికి జనసేనాని సిద్ధమవుతున్నారనే చర్చ కూడా ఉంది. తాజాగా అందుకు బలాన్నిచ్చేలా రాజకీయ సమీకరణలు ఏపీలో జరుగుతున్నాయి. బీజేపీతో కటీఫ్ చెప్పి టీడీపీతో కలిసి పనిచేసేందుకు పవన్ కల్యాణ్ పార్టీ పావులు కదుపుతున్నట్లు స్పష్టమైంది. ఏపీలో జరిగిన స్థానిక సంస్థల ఎన్నికల్లో పలు ప్రాంతాల్లో టీడీపీ, జనసేన మధ్య స్థానికంగా పొత్తులు కుదిరాయి. గోదావరి జిల్లాలో ఇవి మంచి ఫలితాలనే ఇచ్చాయి. ఇటీవల జరిగిన ఎంపీపీ ఎన్నికల్లో ఇది మరింత బలపడింది. రెండు పార్టీలు కలిసి పలు మండలాల్లో అధికార పార్టీకి షాకిచ్చాయి. గుంటూరు జిల్లా పరిధిలోని మంగళగిరి నియోజకవర్గంలోని దుగ్గిరాల మండలంలో అధికార వైసీపీకి టీడీపీ చుక్కలు చూపిస్తుండగా.. తూర్పు గోదావరి జిల్లా రాజమహేంద్రవరం రూరల్ నియోజకవర్గ పరిధిలోని కడియం మండలంలో ఏకంగా ఎంపీపీ పదవినే కైవసం చేసుకుంది. ఇక్కడ కేవలం నాలుగు స్థానాలను దక్కించుకున్న టీడీపీకి.. 8 స్థానాలు గెలుచుకున్న జనసేన మద్దతు పలకడంతో పాటుగా ఎంపీపీ పదవిని టీడీపీకి కట్టబెట్టింది జనసేన. కడియం మండలంలో మొత్తం 22 ఎంపీటీసీ స్థానాలున్నాయి. నామినేషన్ల సమయంలోనే వైసీపీ, జనసేన ఒక్కో స్థానాన్ని ఏకగ్రీవంగా దక్కించుకున్నాయి. మిగిలిన 20 స్థానాలకు ఎన్నికలు జరగగా.. వైసీపీ, జనసేన 8 స్థానాల చొప్పున గెలుచుకోగా.. టీడీపీకి 4 స్థానాలు మాత్రమే దక్కాయి. ఈ క్రమంలో ఎంపీపీ స్థానం వైసీపీకి దక్కకుండా టీడీపీ, జనసేనలు ఎన్నికలకు ముందు నుంచే వ్యూహాత్మకంగా కలిసి సాగాయి. జనసేన బరిలో నిలిచిన స్థానాల్లో టీడీపీ మద్దతు పలికితే.. టీడీపీ బరిలో నిలిచిన చోట జనసేన మద్దతు పలికింది. రెండు పార్టీలు కలిసి వైసీపీకి చుక్కలు చూపాయి. అయితే ఎంపీపీ పదవిని దక్కించుకునేందుకు వైసీపీ రచించిన వ్యూహాన్ని జనసేన తిప్పికొట్టింది. తాను టీడీపీతోనే సాగుతానని తేల్చి చెప్పింది. కడియం జడ్పీటీసీని తాను గెలిచేలా సాయం చేసిన టీడీపీకే కడియం ఎంపీపీని ఇచ్చేస్తున్నట్లుగా జనసేన సంచలన నిర్ణయం తీసుకుంది. జనసేన ప్రస్తుతం బీజేపీతో మిత్రపక్షంగా సాగుతున్నా తిరుపతి పార్లమెంటుకు జరిగిన ఉప ఎన్నికల నాటి నుంచి ఇరు పార్టీల మధ్య విభేదాలు కనిపిస్తున్నాయి. ఏపీపై కేంద్ర ప్రభుత్వ వైఖరి సరిగా లేదనే అభిప్రాయంతో ఉన్నారు పవన్ కల్యాణ్. ప్రత్యేక హోదా విషయంలో మాట మార్చడంపై గుర్రుగా ఉన్నారు. ఇక విశాఖ స్టీల్ ప్లాంట్ ప్రైవేటీకరణ అంశం ఇరు పార్టీల మధ్య మరింత గ్యాప్ పెచ్చింది. తాజాగా విశాఖ స్టీల్ ప్లాంట్ కోసం ఉద్యమం చేస్తానని ప్రకటించారు పవన్ కల్యాణ్. విశాఖ స్టీల్ ప్లాంట్ ఉద్యమం చేయడమంటే కేంద్ర ప్రభుత్వాన్ని వ్యతిరేకించడమే. ఈ లెక్కన బీజేపీతో తెగతెంపులకు పవర్ స్టార్ దాదాపుగా సిద్దమైపోయారని చెబుతున్నారు. అందులో భాగంగానే పరిషత్ ఎన్నికల్లో టీడీపీతో కలిసి ముందుకు సాగారన అంటున్నారు. జనసేనాని ప్రస్తుతానికి బయటకు చెప్పకున్నా.. 2014 సార్వత్రిక ఎన్నికల మాదిరిగా.. 2024లోనూ టీడీపీతోనే జట్టు కట్టడం ఖాయమన్న వాదనలు వినిపిస్తున్నాయి. ఇందుకు నిదర్శనంగానే జనసేనకు బలమున్న చోటల్లా బీజేపీతో కాకుండా టీడీపీతోపొత్తు పెట్టుకునే ఆ పార్టీ ముందుకు సాగుతోంది. కడియంలో టీడీపీ కంటే తన బలం రెట్టింపుగా ఉన్నా కూడా టీడీపీకే ఎంపీపీ పీఠాన్ని వదిలేసిన వైనం కూడా టీడీపీ, జనసేనల మధ్య బలం మరింతగా బలోపేతాన్ని సూచిస్తున్నదేనని చెప్పాలి. టీడీపీ వెంట జనసేన సాగితే.. 2024లో వైసీపీకి చుక్కలు ఖాయమన్న చర్చ రాజకీయ వర్గాల్లోనూ సాగుతోంది. | telegu |
Drawing power through a kundi connection proved too costly for a labourer in the EWS colony here when a fire caused allegedly by a short circuit in the illegal connection badly burnt his two minor sons and a son-in-law, besides gutting his one room apartment late this afternoon. Kuldip Singh, 3, and Lucky, 6, both sons of labourer Kartar Singh, are battling for life.
While city residents are paying for their electricity bills through their nose, slum dwellers of Shaheed Bhagat Singh Nagar are enjoying power free of cost by stealing it. The Punjab State Electricity Board (PSEB) is turning a blind eye to the problem though residents have complained to it on numerous occasions.
The Ludhiana Architects’ Association has expressed serious concern over the attitude of the US-based software company Auto Cad for accusing them of using pirated software.
The bail application filed by Delhi-based businessman, Chetan Gupta, who was arrested in connection with the City Centre Scam, would come for hearing before Special Judge Gurbir Singh on June 2.
Two persons were reported murdered in the city in the last 24 hours. Jagdish Kumar, an ice cream vendor was murdered with sharp-edged weapons by unidentified robbers near Jagraon bridge sometime after midnight. It is believed that he was also looted as no money was found in his cash box.
The Central Jail authorities here have asked the city police to register a case against a man convicted under the NDPS Act and undergoing life sentence for falsely accusing another convict and some jail staff of tattooing ‘chor’ on his back.
When Maya Nagar-based grocery shop owner Amrik Singh took on the might of a strong police lobby to get the cops punished, who murdered his son in January 2001, even his relatives forsook him. His neighbours turned their backs towards him. Witnesses turned hostile and politicians advised him to compromise with the killers of his son.
Radio India managing director Maninder Singh Gill honours Amrik Singh Gill in Surrey, Canada.
After causing much hullabaloo with their claims to stick to the P Ram Committee’s deadline regarding the Common Effluent Treatment Plant (CETP) all that was done today in the name of inaugurating the plant was transportation of untreated water of a unit from Focal Point Phase-VI to Focal Point Phase-VIII where the plant is located.
Demanding the cancellation of the Electricity Act, 2003, employees of the Punjab State Electricity Board (PSEB), on a call given by the Technical Services Union, held a dharna here today.
The Bhagwan Mahavir Sewa Sansthan will hold a camp for the distribution of artificial limbs, crutches and wheel chairs to physically challenged persons free of cost at the Viklang Sahayata Kendra at Rishi Nagar here on June 3. State president of the BJP Rajinder Bhandari will inaugurate the camp while minister for tourism, jails, printing and stationery Hira Singh Gabria will be the chief guest.
Bharti AXA is planning to diversify its portfolio from life insurance to offering a range of financial services including general insurance and mutual funds, vice-chairman, Bharti Enterprises, Rakesh Bharti Mittal, said here today. "By the second half of this financial we would come up with more financial services," Mittal said.
The onion yield of 70 quintal from a half acre of land has not only taken people by surprise but has also set the vegetable market believing as only five onions can weigh 2 kg.
Despite the instructions of Agriculture University to avoid the sapling of paddy crop, farmers have started ploughing the paddy crop.
Sophie Dhaliwal has been crowned as Miss New Zealand Panjaban at an event organised by the NZI Culture Centre and Sabhyacharak Satth Punjab at the Telstra Pacific Event Centre, Manukau, New Zealand.
An interactive session organised by the Ludhiana branch of the National Integrated Medical Association (NIMA) to mark "World No Tobacco Day" here last evening, called for creating a tobacco-free society to save the people from life-threatening diseases like tuberculosis, cancer and asthma.
District health administration is observing the month of June as anti-malaria month. In this connection, an elaborate month-long programme has been chalked out to educate the people about preventive measures against malaria and other diseases of the summer season.
Holders Punjab lads proved too good for Andhra Pradesh team, whom they overcame easily 14-7 to retain the title in the 25th Junior National Softball Championship that concluded at the Punjab Agricultural University ground here today.
The unabated depletion of water resources, if left unchecked, would spell doom for Punjab's economy. These sentiments were expressed by director of research, Punjab Agricultural University, Ludhiana, Dr B S Dhillon.
Notwithstanding the notice of suspension served by the district unit of SAD, Ajmer Singh Bhagpur, chairman of Milk Plant, Ludhiana, received a warm welcome in Milk Bar at Bija, near here, yesterday.
Vice-Chancellor of Panjab University, Chandigarh, Dr R.C. Sobti, has nominated Dr Pawan Kaushal,senior lectuer in the postgraduate department of English of Government College, Ludhiana, member of the Undergraduate Board of Studies in English for two years in recognition of his services in the field of his subject. | english |
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पंजाब : मुख्यमंत्री चन्नी के भतीजे को ईडी ने किया गिरफ्तार, आठ घंटे तक की पूछताछ प्रवर्तन निदेशालय ईडी ने पंजाब के मुख्यमंत्री चरणजीत सिंह चन्नी के रिश्तेदार भूपिंदर सिंह हनी को सीमावर्ती राज्य में कथित अवैध रेत खनन से जुड़े धन शोधन के एक मामले में गिरफ्तार किया है। अधिकारियों ने शुक्रवार को यह जानकारी दी। 18 जनवरी को उनके परिसरों पर छापा मारा था उन्होंने बताया कि हनी को धन शोधन निवारण अधिनियम पीएमएलए के प्रावधानों के तहत बृहस्पतिवार को देर रात गिरफ्तार किया गया। गिरफ्तारी से पहले हनी से एजेंसी के जालंधर स्थित कार्यालय में कई घंटे तक पूछताछ हुई थी। सूत्रों ने दावा किया कि पूछताछ के दौरान हनी जवाब देने में टालमटोल कर रहे थे और इसलिए उन्हें हिरासत में लिया गया। ईडी हनी को शुक्रवार को मोहाली में विशेष पीएमएलए अदालत के समक्ष पेश करेगा और उसकी रिमांड की मांग करेगा। हनी, चन्नी की पत्नी की बहन के बेटे हैं। एजेंसी ने 18 जनवरी को उनके परिसरों पर छापा मारा था और लगभग आठ करोड़ रुपये नकद और आपत्तिजनक दस्तावेज जब्त करने का दावा किया था। कुछ अन्य लोगों के यहां भी छापेमारी की गई। पंजाब में विधानसभा चुनाव के लिए 20 फरवरी को मतदान यह घटनाक्रम ऐसे वक्त में हुआ है जब कुछ दिन पहले कांग्रेस नेता राहुल गांधी ने चुनावी राज्य में पार्टी के मुख्यमंत्री पद के उम्मीदवार की घोषणा करने की संभावना जतायी थी। गांधी के रविवार को लुधियाना में अपनी डिजिटल रैली के दौरान यह घोषणा करने की उम्मीद है और चन्नी को मुख्यमंत्री पद के उम्मीदवार में सबसे आगे बताया जा रहा है। विधानसभा चुनाव के लिए पंजाब में 20 फरवरी को मतदान होना है। पिछले महीने छापेमारी के बाद ईडी के सूत्रों ने दावा किया था कि एजेंसी ने 10 करोड़ रुपये से अधिक नकद राशि और कई दस्तावेज बरामद किए थे, जिनमें से आठ करोड़ रुपये और अधिकतर कागजात अकेले हनी से जुड़े परिसरों से जब्त किए गए थे। संदीप कुमार नामक व्यक्ति से जुड़े परिसर से लगभग दो करोड़ रुपये नकद जब्त किए गए। ईडी ने पिछले साल पीएमएलए के तहत आपराधिक मामला दर्ज किया था ईडी ने तब एक बयान जारी कर कहा था कि छापेमारी जिनके यहां की गई, उनमें कुदरतदीप सिंह, पिंजौर रॉयल्टी कंपनी और उसके सहयोगीशेयरधारक कंवरमहीप सिंह, मनप्रीत सिंह, सुनील कुमार जोशी, जगवीर इंदर सिंह, रणदीप सिंह, प्रोवाइडर्स ओवरसीज कंसल्टेंट्स प्राइवेट लिमिटेड और हनी और संदीप कुमार सहित इसके अन्य निदेशक, शेयरधारक शामिल हैं। छापे मोहाली, लुधियाना, रूपनगर, फतेहगढ़ साहिब तथा पठानकोट में मारे गए थे। चन्नी ने संवाददाताओं से कहा था कि पश्चिम बंगाल में विधानसभा चुनाव के दौरान मुख्यमंत्री ममता बनर्जी के रिश्तेदारों के यहां राज्य में जिस तरह से छापे मारे गए थे, उसी तरह ईडी पंजाब में उन पर, उनके मंत्रियों और कांग्रेस पार्टी के सदस्यों पर दबाव डालने के लिए वही तरीका आजमा रहा है। ईडी ने पिछले साल नवंबर में पीएमएलए के तहत आपराधिक मामला दर्ज किया था। 2018 को मलिकपुर खनन स्थल पर औचक निरीक्षण किया यह मामला शहीद भगत सिंह एसबीएस नगर पुलिस थाना में 2018 में दर्ज प्राथमिकी पर आधारित है, जिसमें भारतीय दंड संहिता और खान एवं खनिज विकास का नियमन अधिनियम, 1957 के तहत आरोप लगाए गए थे। प्राथमिकी में ईडी ने कहा था कि एसबीएस नगर थाना अंतर्गत राहोन में अवैध रेत खनन के संबंध में मिली एक शिकायत के आधार पर खनन विभाग, नागरिक प्रशासन और पुलिस के अधिकारियों की एक टीम ने सात मार्च, 2018 को मलिकपुर खनन स्थल पर औचक निरीक्षण किया था। इसके बाद मलिकपुर में खनन कार्य रोक दिया गया। ईडी ने प्राथमिकी का हवाला देते हुए कहा कि बुर्जतहल दास, बरसल, लालेवाल, मंडला और खोसा में भी अवैध खनन गतिविधियां हुईं। | hindi |
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موسیٖقی چھُ اَکھ فَن یَتھ مَنٛز آوازَن چھُ مٓخسوٗص تَرتیٖب یِوان دِینہٕ تاکہِ آخرس پؠٹھ بَنہٕ اَکھ اَصل آواز. | kashmiri |
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<a href="/2017/03/01/android面试题day1/">
android面试一天一题 day1
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<span class="date">2017-03-01</span>
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<a href="/categories/android面试/">android面试</a>
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<blockquote>
<p>感觉大四还是找工作的概率大，感觉考研没多大吸引力，也许是我没多大概念吧。与其寄希望于考研，不如把握现在。<br>参考一师兄的建议，每天看下面试题，总结衍生android知识框架。</p>
</blockquote>
<h1 id="面试题：知道Service吗，它有几种启动方式？"><a href="#面试题：知道Service吗，它有几种启动方式？" class="headerlink" title="面试题：知道Service吗，它有几种启动方式？"></a>面试题：知道Service吗，它有几种启动方式？</h1><p>原文链接：<a href="http://www.jianshu.com/p/7a7db9f8692d?utm_campaign=haruki&utm_content=note&utm_medium=reader_share&utm_source=qq" target="_blank" rel="external">http://www.jianshu.com/p/7a7db9f8692d?utm_campaign=haruki&utm_content=note&utm_medium=reader_share&utm_source=qq</a></p>
<blockquote>
<p>要我现在回答，我可能说我只知道,它没有界面，运行在后台，一直在处理一些耗时长的任务，比后台播放音乐，一些IM框架也会启动服务。两种启动方式，因为我好像在平时开发中从来没有用过它。既然这里要问，好好补补吧。</p>
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<a id="more"></a>
<h1 id="Service"><a href="#Service" class="headerlink" title="Service"></a>Service</h1><blockquote>
<p>Service是一个专门在后台处理长时间任务的android组件，它没有UI,一旦Service被启动起来，它就跟Activity一样，它完全具有自己的生命周期。他有两种启动方式，startService和bindService.</p>
<p>扩：开发Service的步骤和开发Activity的步骤很像，开发Service组件需要先开发一个Service子类，然后在AndroidManifest.xml文件中配置该Service，配置时可通过<intent-filter...>元素指定它可被那些intent启动。服务可以处理网络事务、播放音乐，执行文件 I/O 或与内容提供程序交互，而所有这一切均可在后台进行。android系统本身提供了大量的Service组件，开发者可通过这些系统Service来操作android系统本身。</intent-filter...></p>
</blockquote>
<h1 id="两种启动方式的区别"><a href="#两种启动方式的区别" class="headerlink" title="两种启动方式的区别"></a>两种启动方式的区别</h1><blockquote>
<p><strong>startService</strong> 只是启动Service，启动它的组件（如Activity）和Service并没有关联，只有当Service调用stopSelf或者其他组件调用stopService服务才会终止。</p>
<p><strong>bindService</strong>方法启动Service，其他组件可以通过回调获取Service的代理对象和Service交互，而这两方也进行了绑定，当启动方销毁时，Service也会自动进行unBind操作，当发现所有绑定都进行了unBind时才会销毁Service.</p>
<p><strong>对生命周期的影响</strong><br><img src="http://upload-images.jianshu.io/upload_images/1685558-5b9c3263c0af2ea2.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/1240" alt=""></p>
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<h2 id="Service的onCreate回调函数可以做耗时的操作吗？"><a href="#Service的onCreate回调函数可以做耗时的操作吗？" class="headerlink" title="Service的onCreate回调函数可以做耗时的操作吗？"></a>Service的onCreate回调函数可以做耗时的操作吗？</h2><blockquote>
<p>不能，看上面的生命周期图，onCreate回调在主线程里调用的，耗时操作会拥塞UI。</p>
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<h2 id="如果需要做耗时的操作，你会怎么做？"><a href="#如果需要做耗时的操作，你会怎么做？" class="headerlink" title="如果需要做耗时的操作，你会怎么做？"></a>如果需要做耗时的操作，你会怎么做？</h2><blockquote>
<p>这个问题作者也没给答案，大概就是另外开个子线程处理吧</p>
</blockquote>
<h1 id="应用"><a href="#应用" class="headerlink" title="应用"></a>应用</h1><blockquote>
<p>这个没咋弄，以后有空补上</p>
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</html> | code |
Lakshmi Manchu: మంచు వారమ్మాయి తన హాట్నెస్తో అదరగొట్టేస్తుందిగా..! Lakshmi Manchu: మోహన్ బాబు ముద్దుల కూతురు మంచు లక్ష్మీ బుల్లితెరతో పాటు వెండితెరపై అలరించిన విషయం తెలిసిందే. ఈ అమ్మడు ప్రస్తుతం సోషల్ మీడియాలో చాలా యాక్టివ్గా ఉంటుంది. ఆమె ఇటీవల వ్యక్తిగతంగా ఒక యూట్యూబ్ ఛానెల్ ను షురూ చేసింది. అందులో మై హోమ్ టూర్, మై మేకప్ అంటూ మంచు లక్ష్మి యూట్యూబ్ లో పలు వీడియోలు చేస్తోంది. ఇవి నెటిజన్స్ని ఎంతగానో అలరిస్తున్నాయి. ఇక సోషల్ మీడియాలోను చాలా యాక్టివ్గా ఉంటున్న The post Lakshmi Manchu: మంచు వారమ్మాయి తన హాట్నెస్తో అదరగొట్టేస్తుందిగా..! first appeared on The News Qube. Lakshmi Manchu: మోహన్ బాబు ముద్దుల కూతురు మంచు లక్ష్మీ బుల్లితెరతో పాటు వెండితెరపై అలరించిన విషయం తెలిసిందే. ఈ అమ్మడు ప్రస్తుతం సోషల్ మీడియాలో చాలా యాక్టివ్గా ఉంటుంది. ఆమె ఇటీవల వ్యక్తిగతంగా ఒక యూట్యూబ్ ఛానెల్ ను షురూ చేసింది. అందులో మై హోమ్ టూర్, మై మేకప్ అంటూ మంచు లక్ష్మి యూట్యూబ్ లో పలు వీడియోలు చేస్తోంది. ఇవి నెటిజన్స్ని ఎంతగానో అలరిస్తున్నాయి. Lakshmi Manchu Latest Hot Photos ఇక సోషల్ మీడియాలోను చాలా యాక్టివ్గా ఉంటున్న మంచు వారమ్మాయి.. హాట్ డ్రెస్లలో హీటెక్కిస్తుంది. మంచు లక్ష్మి ఎలాంటి డ్రెస్ ధరించినా గ్లామర్ గా కనిపించేందుకు ప్రాధాన్యత ఇస్తుంది. తాజాగా మంచు లక్ష్మి ఇన్స్టాగ్రామ్ లో కళ్ళు చెదిరేలా ఉన్న గ్లామరస్ పిక్స్ ని పోస్ట్ చేసింది. మోడరన్ డిజైనర్ డ్రెస్ లో హాట్ నెస్ తో కేక పెట్టిస్తోంది ఈ మంచు వారసురాలు. Lakshmi Manchu Latest Hot Photos అలాగే చీరకట్టు, సంప్రదాయ వస్త్ర ధారణలో కూడా మంచు లక్ష్మి అందంతో ఆకట్టుకుంటోంది. ముఖ్యంగా తన నడుము అందాలు హైలైట్ చేసేలా ఉన్న ఫోజులు మతిపోగొడుతున్నాయి. మంచు లక్ష్మి గ్లామర్ తో కుర్రాళ్లకు గిలిగింతలు తప్పవు. నాలుగు పదుల వయస్సులోను మంచు లక్ష్మీ తన క్యూట్నెస్తో కేక పెట్టిస్తుంది. Lakshmi Manchu Latest Hot Photos Lakshmi Manchu Latest Hot PhotosThe post Lakshmi Manchu: మంచు వారమ్మాయి తన హాట్నెస్తో అదరగొట్టేస్తుందిగా..! first appeared on The News Qube. | telegu |
/* Copyright (c) 2015-present, salesforce.com, inc. All rights reserved */
/* Licensed under BSD 3-Clause - see LICENSE.txt or git.io/sfdc-license */
export default {"viewBox":"0 0 52 52","xmlns":"http://www.w3.org/2000/svg","g":{"path":{"d":"M51.8 25.1c-1.6-3.2-3.7-6.1-6.3-8.4L37 25.1v.9c0 6.1-4.9 11-11 11h-.9l-5.4 5.4c2 .4 4.1.7 6.2.7 11.3 0 21.1-6.6 25.8-16.1.4-.7.4-1.3.1-1.9zM48.5 5.6l-2.1-2.1c-.6-.6-1.7-.5-2.4.3l-7.3 7.3C33.4 9.7 29.8 9 26 9 14.7 9 4.9 15.6.2 25.1c-.3.6-.3 1.3 0 1.8 2.2 4.5 5.5 8.2 9.6 11l-6 6.1c-.7.7-.8 1.8-.3 2.4l2.1 2.1c.6.6 1.7.5 2.4-.3L48.2 8c.8-.7.9-1.8.3-2.4zM15 26c0-6.1 4.9-11 11-11 2 0 3.8.5 5.4 1.4l-3 3c-.8-.2-1.6-.4-2.4-.4-3.9 0-7 3.1-7 7 0 .8.2 1.6.4 2.4l-3 3C15.5 29.8 15 28 15 26z"}}};
| code |
## INDICATION:
year old man with extensive LT IPH w/IVE now w/fever and
tachypnea please assess for pulmonary source.// year old man with extensive
LT IPH w/IVE now w/fever and tachypnea please assess for pulmonary source.
## HEART AND VASCULATURE:
The thoracic aorta is normal in caliber. The heart,
pericardium, and great vessels are within normal limits based on an unenhanced
scan. No pericardial effusion is seen. Marked coronary arterial calcification
is present.
## AXILLA, HILA, AND MEDIASTINUM:
No axillary or mediastinal lymphadenopathy is
present. No mediastinal mass or hematoma.
## PLEURAL SPACES:
There is a trace right pleural effusion with no pneumothorax
identified.
## LUNGS/AIRWAYS:
Breathing motion artifact limits the assessment for small
pulmonary nodules. There is mild centrilobular emphysema. Again noted is a
subpleural nodularity in the right upper lobe measuring 3.1 x 2.2 cm. This is
again adjacent to a small amount of loculated pleural fluid and likely
reflects rounded atelectasis. Since prior however the size of a similar
appearing consolidation in the posterior right lower lobe has increased and
now measures 5.0 x 3.1 cm. Increased patchy opacities throughout the right
lower lobe likely reflect aspiration and/or pneumonia.
## BASE OF NECK:
Visualized portions of the base of the neck show no abnormality.
## ABDOMEN:
Included portion of the unenhanced upper abdomen is notable for a
dense calcification in segment of the liver, unchanged. Gallstones are
present. There is a small hiatal hernia..
## BONES:
No suspicious osseous abnormality is seen.? There is no acute fracture.
## IMPRESSION:
Stable rounded atelectasis along the periphery of the right lower lobe and
increased size of the rounded atelectasis noted more posteriorly. New
scattered consolidations throughout the right lower lobe likely reflect
aspiration and/or pneumonia.
| medical |
ఆ మెషిన్ కావాలంటున్న ఆనంద్ మహీంద్రా.. ఎందుకోసమో మరి.. సోషల్ మీడియాలో ఎప్పుడూ ఫుల్ యాక్టివ్గా ఉండే ప్రముఖ పారిశ్రామికవేత్త ఆనంద్ మహీంద్రా Anand Mahindra గురించి తెలియని వారుండరు. ఆయన ట్విట్టర్ వేదికగా అప్ లోడ్ చేసే ఇంట్రెస్టింగ్, డిఫరెంట్ అండ్ యూనిక్ కంటెంట్ కోసం నెటిజనాలు ఎంతో ఆసక్తిగా ఎదురు చూస్తుంటారు. మండే మోటివేషన్ పేరిట ఆనంద్ మహీంద్రా షేర్ చేసే వీడియోస్ ఎంతో ఇన్స్పిరేషనల్గా ఉంటాయి. ఇకపోతే సాధారణ సందర్భాల్లోనూ ఆనంద్ మహీంద్రా మంచి వీడియోస్ అప్లోడ్ చేస్తుంటారు. తాజాగా ఆయన చేసిన ట్వీట్ ద్వారా పలు ఆసక్తికర విషయాలు బయటకు వచ్చాయి. ఇంతకీ ఆయన దేని గురించి ట్వీట్ చేశారంటే.. మహీంద్రా గ్రూప్ చైర్మన్ ఆనంద్ మహీంద్రా తన ట్విటర్ వేదికగా ఇంట్రెస్టింగ్ ట్వీట్ చేశారు. తనకు టైమ్ మెషిన్ కావాలంటూ ట్విట్టర్ పోస్టులో కోరారు. ఆ మెషిన్ ఉపయోగించి వెంటనే తనను గడిచిన కాలంలోకి తీసుకెళ్లాలని ఆనంద్ మహీంద్రా అభ్యర్థించారు. ఈ క్రమంలోనే ట్వీట్కు ఆయన 1903 నాటి ముంబై తాజ్ హోటల్ ఫొటోను జతపరిచారు. ఆయన ఎందుకు అలా తాజ్ ఫొటోను ట్యాగ్ చేశాడంటే.. ఆనాడున్న పరిస్థితుల్లో మన దేశంలోని ది బెస్ట్ హోటల్స్లో ఒకటి తాజ్ హోటల్ కాగా, 1903 డిసెంబర్ 1 దానిని ఓపెన్ చేశారు. ఆ సమయంలో తాజ్లో ఒక్కరోజు స్టే చేయడం కోసం అయ్యే ఖర్చు కేవలం ఆరు రూపాయలు మాత్రమే. ఈ సందర్భంగా తాజ్ హోటల్ ఓపెనింగ్ బ్రోచర్ను షేర్ చేసి తనను ఆ కాలంలోకి తీసుకెళ్లాలని కోరారు. అయితే, అప్పటి ధరల ప్రకారం అతి తక్కువగా కేవలం ఆరు రూపాయలు ఉండగా, ప్రజెంట్ కేవలం ఒక్క రోజుకు సుమారు ఇరవై వేల రూపాయల వరకు ఉంటుదని తెలుస్తోంది. ఈ నేపథ్యంలో దేశంలో ద్రవ్యోల్బణ పరిస్థితులను అధిగమించేందుకు తనను టైం మెషిన్ సాయంతో ఆనాటి కాలానికి తీసుకెళ్లాలని కోరారు. ధరల పెరుగుదలను ఆనంద్ మహీంద్రా ఈ ట్వీట్ ద్వారా చెప్పకనే చెప్తున్నారు. కాగా, నెటిజన్లు తమను కూడా ఆ కాలానికి తీసుకెళ్లాలని కామెంట్స్ చేస్తున్నారు. ఇవి కూడా చదవండి రాహుల్ గాంధీకి ట్విట్టర్ షాక్..ట్వీట్ డిలీట్ పీవీ సింధుకు థార్ వాహనం ఇవ్వాలన్న నెటిజన్.. ఆనంద్ మహీంద్రా రియాక్షన్ ఇదీ..! 70 మిలియన్ దాటిన ప్రధాని మోదీ ట్విట్టర్ ఫాలోవర్స్ | telegu |
// Copyright (C) 2014, Panagiotis Christopoulos Charitos.
// All rights reserved.
// Code licensed under the BSD License.
// http://www.anki3d.org/LICENSE
#ifndef ANKI_GL_GL_PROGRAM_PIPELINE_H
#define ANKI_GL_GL_PROGRAM_PIPELINE_H
#include "anki/gl/GlObject.h"
#include "anki/gl/GlProgramHandle.h"
namespace anki {
/// @addtogroup opengl_private
/// @{
/// Program pipeline
class GlProgramPipeline: public GlObject
{
public:
using Base = GlObject;
/// @name Constructors/Desctructor
/// @{
GlProgramPipeline()
{}
GlProgramPipeline(GlProgramPipeline&& b)
{
*this = std::move(b);
}
GlProgramPipeline(
const GlProgramHandle* progsBegin, const GlProgramHandle* progsEnd);
~GlProgramPipeline()
{
destroy();
}
/// @}
GlProgramPipeline& operator=(GlProgramPipeline&& b);
GlProgramHandle getAttachedProgram(GLenum type) const;
/// Bind the pipeline to the state
void bind();
private:
Array<GlProgramHandle, 6> m_progs;
/// Create pipeline object
void createPpline();
/// Attach all the programs
void attachProgramsInternal(const GlProgramHandle* progs, PtrSize count);
void destroy();
};
/// @}
} // end namespace anki
#endif
| code |
मेघालय में कांग्रेस के पांच विधायक भाजपा समर्थित एमडीए में शामिल हुए शिलांग, आठ फरवरी भाषा मेघालय में कांग्रेस के पांच विधायक मंगलवार को भाजपा समर्थित सत्तारूढ़ मेघालय जनतांत्रिक गठबंधन एमडीए में शामिल हो गए। उल्लेखनीय है कि पिछले साल पूर्व मुख्यमंत्री मुकुल संगमा सहित 12 विधायक कांग्रेस छोड़ तृणमूल कांग्रेस में शामिल हो गए थे। इसके बाद मेघालय विधानसभा में कांग्रेस के विधायकों की संख्या पांच रह गई थी, जबकि शुरुआत में विपक्षी पार्टी के सदन में 17 सदस्य थे। कांग्रेस विधायक दल सीएलपी ने औपचारिक रूप से मुख्यमंत्री कोनराड के संगमा को समर्थन का पत्र दिया है। पत्र में कहा गया, भारतीय राष्ट्रीय कांग्रेस के विधायकों ने एमडीए सरकार में आज आठ फरवरी 2022 को शामिल होने का फैसला किया है। हम सरकार के हाथ और फैसलों को मजबूत करने के लिए आपका मुख्यमंत्रीऔर एमडीए का समर्थन करने की इच्छा व्यक्त करते हैं ताकि सुनिश्चित हो सके कि हमारे संयुक्त प्रयास से नागरिकों के हित में राज्य आगे बढ़े। इस पत्र पर कांग्रेस विधायक दल के नेता अमपरीन लिंगदोह, विधायक पीटी सॉक्मी, मायरलबोर्न सिएम, केएस मारबानियांग और मोहेंद्रो रापसांग ने हस्ताक्षर किए हैं। पत्र की एक प्रति कांग्रेस अध्यक्ष सोनिया गांधी को भी भेजी गई है। लिंगदोह ने इसके साथ ही कांग्रेस विधायकों की मुख्यमंत्री के साथ तस्वीर ट्विटर पर साझा की है और लिखा है, मेघालय कांग्रेस के पांच विधायकों ने राज्य के लोगों खासतौर पर हमारे निर्वाचन क्षेत्रों के लोगों के हित में मेघालय जनतांत्रिक गठबंधन प्रशासन में शामिल होने का फैसला किया है। उल्लेखनीय है नेशनल पीपुल्स पार्टी नीत एमडीए का भाजपा समर्थन कर रही है। भाजपा विधायक सोनबोर शुल्लाई मेघालय सरकार में मंत्री भी हैं। कांग्रेस विधायकों के सत्तारूढ़ गठबंधन में शामिल होने के बाद विधानसभा में विपक्षी पार्टी के रूप में केवल तृणमूल कांग्रेस बच गई है। भाषा धीरज दिलीप दिलीप यह खबर भाषा न्यूज़ एजेंसी से ऑटोफीड द्वारा ली गई है. इसके कंटेट के लिए दिप्रिंट जिम्मेदार नहीं है. | hindi |
बकाया मांगने गये दुकानदार पर गंदे आरोप लगाकर बनाया बंधक, की पिटाई, बगैर शिकायत के हाजत में गुजरी रात बांका में उधार मांगने गए एक दुकानदार पर अवैध संबंध का आरोप लगाकर रस्सी से बांध कर पिटाई Shopkeeper beaten up in Banka की गयी. घटना की सूचना पर पहुंची पुलिस उसे ले गयी और बगैर किसी शिकायत के ही दुकानदार की रात हाजत में गुजरी. सुबह तक कोई आवेदन नहीं मिलने पर उसे छोड़ दिया गया.बांका: बिहार के बांका जिले के चांदन प्रखंड Chandan Block of Banka District के एक दुकानदार को एक ग्राहक से उधार का पैसा मांगना काफी मंहगा पड़ गया. पहले तो उसे बंधक बनाकर जमकर उसकी पिटाई Shopkeeper hostage beaten up in Banka की गयी. उसके बाद लोगों की सूचना पर पहुंची दुकानदार को छु़ड़ाकर ले तो गयी लेकिन उसके खिलाफ कोई शिकायत थाने में दर्ज नहीं थी. इसके बावजूद पूरी रात थाने के हाजत में गुजारनी पड़ी.मामला चांदन प्रखंड प्रखंड के बिरनिया पंचायत Birnia Panchayat of Chandan Block Block अंतर्गत कटोन की है. यहां के निवासी निरंजन पंडित की दुकान प्रखंड कार्यालय के पास है. उसकी दुकान से ग्रामीण दिलीप दास ने सामान उधार लिया था. बुधवार की शाम जब निरंजन अपना उधारी का पैसा मांगने उसके घर गया. तभी उसी गांव के कुछ लोगों ने निरंजन पर एक महिला से अवैध संबंध का आरोप लगाकर उसे पकड़ लिया और मारपीट करने लगे. देखें वीडियो: बांका में मिट्टी लदे ट्रैक्टर ने हवलदार को रौंदा, मौके पर हुई मौतइसकी जानकारी मिलते ही दर्जनों वहां लोग जमा हो गए. उसे रस्सी से बांध दिया गया. बाद में किसी ने घटना की जानकारी पुलिस को दी. पुलिस घटनास्थल पर पहुंची और निरंजन को थाने लेकर गयी. वहां पर उसे हाजत में बंद कर दिया जबकि उसके खिलाफ किसी ने शिकायत नहीं की थी. सुबह तक कोई आवेदन नहीं आने और उस महिला के साफ इनकार करने के बाद पुलिस को मामला समझ मे आया.: बांका के शंभूगंज में यूको बैंक में दबंगों ने किया हंगामा, बैंककर्मियों ने की सुरक्षा की मांगबाद में पुलिस ने बांड भरवाकर निरंजन पंडित को छोड़ दिया. उक्त युवक ने कहा कि उसके गांव के ही कुछ लोगों ने झूठे आरोप लगाकर उसके साथ ऐसा किया है. उसने ग्रामीणों के साथ ही पुलिस को भी पूरी बातें बतायी थीं लेकिन किसी ने उसकी नहीं सुनी. थानाध्यक्ष रविशंकर कुमार ने बताया कि ग्रामीणों का गुस्सा चरम पर था. इसलिए उसे बचाने के लिए रात को थाने में रखना पड़ा. सुबह जांच के बाद उसे निर्दोष पाकर छोड़ दिया गया. | hindi |
ಪಕ್ಷ ತೊರೆಯುವುದಿಲ್ಲ ಎಂದ ಟಿಎಂಸಿ ಸಂಸದ, ಬಿಜೆಪಿ ಎದುರು ಹೋರಾಡಲು ಕರೆ ಕೋಲ್ಕತ್ತ: ಅಸಮಾಧಾನಗೊಂಡಿದ್ದ ಸಂಸದ ಪ್ರಸೂನ್ ಬ್ಯಾನರ್ಜಿ ಟಿಎಂಸಿಯನ್ನು ತೊರೆಯುತ್ತಿಲ್ಲ ಎಂದು ಸ್ಪಷ್ಟಪಡಿಸಿದ್ದಾರೆ. ಇದೇ ವೇಳೆ ಪಕ್ಷದೊಳಗೆ ಯಾವುದೇ ಬಿನ್ನಾಭಿಪ್ರಾಯಗಳಿದ್ದರೂ ಕೂಡ ಬಿಜೆಪಿ ವಿರುದ್ಧ ಒಗ್ಗಟ್ಟಿನಿಂದ ಹೋರಾಡುವಂತೆ ಮನವಿ ಮಾಡಿದ್ದಾರೆ. ತೃಣಮೂಲ ಕಾಂಗ್ರೆಸ್ನ ಯುವ ಘಟಕದ ಅಧ್ಯಕ್ಷ ಅಭಿಷೇಕ್ ಬ್ಯಾನರ್ಜಿ ಅವರೊಂದಿಗೆ ಚರ್ಚಿಸಿದ ಬಳಿಕ ಈ ನಿರ್ಧಾರ ಪ್ರಕಟಿಸಿದ್ದಾರೆ. ಭಾರತದ ಫುಟ್ಬಾಲ್ ತಂಡದ ಮಾಜಿ ನಾಯಕರಾಗಿರುವ ಹೌರಾದ ಸಂಸದ, ಹೌರಾ ಜಿಲ್ಲೆಯಲ್ಲಿನ ತಮ್ಮ ಕುಂದುಕೊರತೆಗಳ ಬಗ್ಗೆ ಪಕ್ಷದ ನಡವಳಿಕೆ ಮತ್ತು ಪ್ರಮುಖ ವಿಚಾರಗಳಲ್ಲಿ ತಮ್ಮನ್ನು ಗಣನೆಗೆ ತೆಗೆದುಕೊಳ್ಳುತ್ತಿಲ್ಲ ಎಂದು ಬಹಿರಂಗವಾಗಿಯೇ ಅಸಮಾಧಾನ ವ್ಯಕ್ತಪಡಿಸಿದ್ದರು. ಮುಖ್ಯಮಂತ್ರಿ ಮಮತಾ ಬ್ಯಾನರ್ಜಿಯ ಸೋದರಳಿಯ ಅಭಿಷೇಕ್ ಬ್ಯಾನರ್ಜಿ ಅವರೊಂದಿಗೆ ಸಭೆ ನಡೆಸಿದ ಅರ್ಜುನ ಪ್ರಶಸ್ತಿ ಪುರಸ್ಕೃತ, ನಾನು ಪಕ್ಷವನ್ನು ತೊರೆದು ಎಲ್ಲಿಗೂ ಹೋಗುತ್ತಿಲ್ಲ. ಯಾವುದೇ ಭಿನ್ನಾಭಿಪ್ರಾಯಗಳನ್ನು ಹೊಂದಿದ್ದರೂ ಕೂಡ ಎಲ್ಲರೂ ಒಗ್ಗಟ್ಟಿನಿಂದ ಬಿಜೆಪಿ ವಿರುದ್ಧ ಹೋರಾಡಬೇಕು ಎಂದು ಕರೆ ನೀಡಿದ್ದಾರೆ. ಸಭೆಯಲ್ಲಿ ಪಾಲ್ಗೊಂಡಿದ್ದ ಟಿಎಂಸಿ ವಕ್ತಾರ ಕುನಾಲ್ ಘೋಷ್ ಮಾತನಾಡಿ, ಪಕ್ಷದಲ್ಲಿ ಪ್ರಸೂನ್ ಅವರು ಹಿರಿಯರು ಮತ್ತು ಈ ದೇಶದ ಹೆಮ್ಮೆ. ಅವರು ಈಗಾಗಲೇ ತಮ್ಮ ಕ್ಷೇತ್ರದಲ್ಲಿ ಸಾಕಷ್ಟು ಕೆಲಸ ಮಾಡಿದ್ದಾರೆ ಎಂದು ಹೇಳಿದ್ದಾರೆ. ಡೊಮ್ಜೂರ್ ಶಾಸಕ ರಾಜೀಬ್ ಬ್ಯಾನರ್ಜಿ ಮತ್ತು ಬ್ಯಾಲಿ ಶಾಸಕ ಬೈಶಾಲಿ ದಾಲ್ಮಿಯಾ ಅವರೊಂದಿಗೆ ಸೇರಿಕೊಂಡ ಪ್ರಸೂನ್ ಬ್ಯಾನರ್ಜಿ ಅವರು, ಹೌರಾ ಜಿಲ್ಲೆಯಲ್ಲಿನ ಪಕ್ಷದ ಕೆಲವು ವಿಚಾರಗಳ ಬಗ್ಗೆ ಬಹಿರಂಗವಾಗಿಯೇ ಅಸಮಾಧಾನ ವ್ಯಕ್ತಪಡಿಸಿದ್ದರು. ಮೂರು ದಿನಗಳ ಹಿಂದಷ್ಟೇ ಆರಂಭದಲ್ಲಿ ಬಿರ್ಭುಮ್ ಜಿಲ್ಲೆಯ ಪಕ್ಷದ ನಾಯಕತ್ವದ ಬಗ್ಗೆ ಅಸಮಾಧಾನ ವ್ಯಕ್ತಪಡಿಸಿದ್ದ ನಟಿಯಾಗಿದ್ದು ರಾಜಕಾರಣದತ್ತ ಹೊರಳಿದ್ದ ಶತಾಬ್ದಿ ರಾಯ್ ಕೂಡ, ಪಕ್ಷದಲ್ಲಿ ನಂಬಿಕೆ ಇಟ್ಟಿರುವುದಾಗಿ ತಿಳಿಸಿದ್ದರು. ಶುಕ್ರವಾರ ದೆಹಲಿಗೆ ಹಾರಲು ಯೋಜಿಸಿದ್ದ ಬಿರ್ಭಮ್ ಸಂಸದೆ ರಾಯ್ ಅವರು, ಅಭಿಷೇಕ್ ಬ್ಯಾನರ್ಜಿಯನ್ನು ಭೇಟಿಯಾದ ನಂತರ ಪಕ್ಷವನ್ನು ತೊರೆಯುವುದಿಲ್ಲ ಎಂದು ಘೋಷಿಸಿದರು. | kannad |
4 राशियां जो बहस से करती हैं नफरत जाने क्यों जनता से रिश्ता वेबडेस्क कुछ लोग ऐसे भी होते हैं जो अपने विचारों पर अडिग रहना पसंद करते हैं. वे सही साबित होने तक उनके बारे में बहस करते हैं. वहीं कुछ लोग ऐसे भी होते हैं जिन लोगों को बहस करना बिलकुल पसंद नहीं होता है. ये लोग सही होते हुए भी कई बार बहस और झगड़े वाली स्थिति से बचना पसंद करते हैं. हालांकि अक्सर, जो लोग तर्कवितर्क से बचते हैं, उन्हें राय या तथ्यों की कमी वाले लोगों के रूप Astro Tips में माना जाता है. लेकिन ऐसा सभी मामलों में नहीं है. ज्योतिष astrology के अनुसार हर राशि zodiac signs का स्वभाव अलगअलग होता है. इसमें कुछ राशि के लोग भी शामिल हैं जिन्हें बहस करना बिलकुल भी पसंद नहीं होता है.धनु राशिजिन लोगों को चीजों के बारे में ज्यादा जानकारी नहीं होती है, उनके साथ बहस करने के बजाए धनु राशि के लोग मौन रहना पसंद करते हैं. जब लोग सिर्फ अपनी बात साबित करने के लिए झगड़ों में पड़ जाते हैं तो उन्हें इससे नफरत होती है. धनु राशि के लोग ऐसी स्थिति से दूर जाना पसंद करते हैं. कई बार लोगों को उनकी ये आदत पसंद भी नहीं आती है.मेष राशिमेष राशि वाले भी बहस करने से नफरत करते हैं, चाहे वह दोस्तों के साथ हो या अजनबियों के साथ. इस राशि के लोग उन स्थितियों से दूर रहते हैं जहां विचारधारा या सोच का टकराव उत्पन्न हो सकता है. वे आमतौर पर शांत रहते हैं. इस राशि के लोग दूसरे पर कभी भी नहीं भड़ते भले ही दूसरा व्यक्ति गलत तथ्य के लिए बहस कर रहा हो.तुला राशिलाइब्रस भी बहस से नफरत करते हैं. लेकिन अगर ये उनकी डिग्निटी की बात है या ऐसा कुछ है जो दूसरों को खतरे में डाल सकता है तो वे जरूर बहस करेंगे. लेकिन अक्सर इस राशि के लोग बहस करना पसंद नहीं करते हैं.सिंह राशिसिंह राशि के लोगों को बहस करना बिलकुल भी पसंद नहीं है. सिंह राशि अपने बारे में भलीभांती जानते हैं कि वो क्या कर रहें हैं. वे उन लोगों के सामने अपने आप को साबित करने में समय बर्बाद नहीं करेंगे जो पहले से ही उन्हें नीचे लाना चाहते हैं. वे बहस की स्थिति से दूर जाना पसंद करेंगे. लेकिन अगर आप कभी भी इस राशि के लोगों को किसी से बहस करते हुए देखते है तो इसका मतलब है कि आपने किसी संवेदनशील विषय को छुआ होगा. | hindi |
Kaali Controversy : পোস্টার বিতর্কের মাঝেই নতুন বিতর্ক, নরেন্দ্র মোদিকে লীনা মনিমেকলাইয়ের পুরনো টুইট ভাইরাল মহানগর ডেস্ক : বর্তমানে কালি পরিচালক লীনা মনিমেকলাই রয়েছেন সমালোচনার কেন্দ্রবিন্দুতে তিনি তার আগাম ছবি কালির পোস্টারকেKaali Controversy ঘিরে সারা দেশজুড়ে শুরু হয়েছে বিতর্ক সেখানে এক মহিলাকে কালির পোশাক পড়ে ধুমপান করতে দেখা গেছে যার জেরে শোরগোল গোটা দেশে কেউ কেউ একে হিন্দু ধর্মীয় অনুভূতিতে আঘাত দেওয়া হয়েছে বলে দাবি করেছেন একই সঙ্গে পুরো ঘটনা ইচ্ছাকৃত বলে দাগিয়ে দিয়েছেন নেটিজেনরা তবে এর মাঝেই কালি পরিচালকের পুরনো টুইট ঘিরে নতুন করে জল্পনা শুরু হয়েছে ১৩ সেপ্টেম্বর ২০১৩ মনিমেকলাই ওই টুইটে মনিমেকলাই লিখেছিলেন, আমি আমার পাসপোর্ট,রেশন কার্ড ,প্যান কার্ড এবং নাগরিকত্ব সমর্পণ করব যদি মোদি আমার জীবদ্দশায় প্রধানমন্ত্রী হন এই শপথ করছি আমি পুরনো টুইট সোশ্যাল মাধ্যমে ভাইরাল হতেই সমালোচনা বেড়েছে দ্বিগুণ কেউ কেউ তাকে সোশ্যাল মাধ্যমে হিন্দু বিরোধী বলে দাগিয়ে দিয়েছেন এমনকি তাকে গ্রেপ্তার করার দাবিতে দিল্লি এবং উত্তরপ্রদেশের পুলিশের কাছে জমা পড়েছে একাধিক এফআইআর আরও পড়ুন, সাক্ষী নাকি আসামি?স্পষ্ট করুক সিবিআই,আবু তাহের প্রসঙ্গত, কানাডার আগাখান মিউজিয়ামে আন্ডার দ্য টেন্ট প্রকল্পের একটি অংশ হিসেবে এই ছবির পোস্টার প্রথম প্রদর্শন করা হয়েছিল তারপর থেকেই ছবিকে ঘিরে বিতর্ক উঠতে শুরু করে বর্তমানে যার রেশ ভয়াবহ আকার ধারণ করেছে এমনকি ওই প্রদর্শনী থেকে বাতিল করা হয়েছে এই ছবি | bengali |
1. For dough. Put the warm water in a bowl and sprinkle the yeast into the water. Whisk to dissolve the yeast. Cover and place in a warm place for 5 minutes.
2. Add 2 tspn olive oil, salt, and 83 grams of bread flour to the yeast mixture. Stir with a wooden spoon for about 5 minutes to form a wet dough.
3. Place the remaining 63 grams of flour on a flat worksurface and add the wet dough. Knead for 8 minutes to form a slightly sticky dough. If the dough is impossibly sticky at the end of the kneading, add the remaining bread flour one tablespoon at a time as necessary.
4. Coat the insides of a large bowl with olive oil. Form the dough into a ball and place in the oiled bowl, rolling the dough around to coat the dough in oil. Cover with a damp towel and place in a warm, draft-free place to rise for 1 hour.
5. For baking and toppings. Preheat oven to 450° F with a rack in the lower-third of the oven. Peel and mash the garlic cloves. Combine 3 of the garlic cloves with 3 Tbspn olive oil in a bowl and set aside.
6. Spread cornmeal on the back of a baking pan or a pizza peel. Take the dough and press it into a small round. Cover and let rest for 20 minutes.
7. Meanwhile, make the sauce. In a saucepan, heat a small amount of olive oil. Crush the peperoncino. Add the peperoncino and the remaining garlic cloves to the oil and saute briefly. Add the tomato paste and 1 - 2 tablespoons of water to loosen the paste, if necessary. Stir briefly to combine the tomato paste, water, garlic, and peperoncino. Remove from heat and set aside.
8. Uncover the dough and press it into its final shape. Cover with sauce, mozzarella, pecorino romano, and two cracked eggs. Place the pizza on a baking sheet in the lower third of the oven. Bake for 12 minutes. If using a pizza stone, transfer the pizza from the baking sheet to the stone after 8 minutes of baking.
9. Once the crust is golden, remove from the oven and immediately brush the exposed crust with the prepared garlic oil.
Note: if you don't have peperoncino, substitute with a 1/2 tspn of chili pepper flakes.
1. In a pot of boiling water, blanch the broccoli rabe for a few minutes, until it turns vibrant green. Remove, drain, and rinse with cold water to halt the cooking.
2. In a saucepan, heat a small amount of olive oil to coat. Saute the broccoli rabe for short few minutes with lemon juice, a small amount of red wine vinegar, and salt. Adjust amounts to taste.
3. Serve with shredded pecorino romano cheese, if desired.
i want to jump into that pizza and eat it completely!
Ooooh I love egg on pizza....it marries my two favorite foods!
Lovely photographs and an absolutely gorgeous recipe! Love your site, take care!
This sounds freaking fantastic! Looove that cheese!
S, this is my favorite post! I'm blown away with the beautiful light in the pictures and gorgeousness of it all. And now, pass me that pizza please!
There's hardly anything in the world I love more than homemade pizza. Normally I make a big batch of dough and freeze some, but there's something very indulgent about just making this pizza for one. Love the egg on top and spicy greens on the side. Delicious!
I looks so incredible! I definitely have to make this!
i LOVE the plate in the last photo! so cute!
wow looks amazing. and korean b/c koreans love putting egg and other items on their pizza.
Simple and beautiful. Love the shots!
Love this recipe and the way you describe the eggs seeping in the crevices between the spikes of cheese....I don't know how I am going to hold out til breakfast. Oh, and btw, don't think I am not going to point out to my children what the "other mothers" get when they visit their daughters, ha!! What a good girl you obviously are! | english |
Actress Jessica Alba has admitted that pregnancy second time around is much easier on the body and the mind. Already a mum to 2-year-old Honor, Jessica has revealed that the insecurities of first-time pregnancy have disappeared.
“Every moment was so new [the first time around] and kind of terrifying and now I know what to expect. It’s like, ‘it’s fine. I’ve been there before.’ With Honor, I was constantly like, ‘is she moving? Is her heart beating?’ I’d worry about everything and with this baby; I don’t have the same anxieties,” Jessica told Latina magazine.
One thing about Jessica’s pregnancies has stayed the same – her cravings.
“Sometimes you can’t get food out of your mind. I could always eat watermelon. With Honor I loved fruit, too. You still eat cheeseburgers and pickles. I don’t deprive myself of anything. I eat whatever,” Jessica said.
Jessica also took her daughter to enjoy some Easter treats this weekend. After helping Honor search for eggs around the garden of her family home, she tweeted a cute picture of herself and Honor with the Easter bunny.
To match the looks of mum and daughter, check out our Jessica and Honor steal their style. | english |
அக்டோபர் 4ம் தேதி முதல் பள்ளிகள் திறப்பு.. 7ம் தேதி முதல் மத வழிப்பாட்டு தலங்களுக்கு செல்லலாம்.. மகாராஷ்டிரா அரசு மகாராஷ்டிராவில் அக்டோபர் 4ம் தேதி முதல் பள்ளிகள் மீண்டும் திறக்கப்படும் என்றும், 7ம் தேதி முதல் மத வழிபாட்டு தலங்களுக்கு பக்தர்கள் செல்லலாம் என்று அம்மாநில அரசு தெரிவித்துள்ளது.கோவிட் பற்றிய அனைத்து லேட்டஸ்ட் அப்டேட்களை இங்கே படியுங்கள்மகாராஷ்டிராவில் அக்டோபர் 7ம் தேதி முதல் அனைத்து மத வழிபாட்டு தலங்களுக்கு பக்தர்களுக்கு திறக்கப்படும் என்று அம்மாநில முதல்வர் உத்தவ் தாக்கரே தெரிவித்துள்ளார். இது தொடர்பாக மகாராஷ்டிரா அலுவலகம் வெளியிட்டுள்ள அறிக்கையில் கூறப்பட்டுள்ளதாவது: இரண்டாவது அலையை வெற்றிகரமாக எதிர்த்து போராடிய பிறகு நாங்கள் 3வது அலையை சமாளிக்க ஆயத்தங்களை செய்துள்ளோம்.உத்தவ் தாக்கரேநாங்கள் மெதுவாக தளர்வு திறக்கிறோம். வழக்குகளின் எண்ணிக்கையில் சரிவு உள்ளது. நாம் இன்னும் முன்னெச்சரிக்கைகள் எடுக்க வேண்டும். மத வழிப்பாட்டு தலங்கள் பக்தர்களுக்காக திறக்கப்படும். மாஸ்க், சமூக இடைவெளி மற்றும் கைகளை சுத்திகரித்தல் போன்ற கோவிட் நெறிமுறைகள் பின்பற்ற வேண்டும். இவ்வாறு அதில் தெரிவிக்கப்பட்டுள்ளது. மகாராஷ்டிராவில் எதிர்க்கட்சியான பா.ஜ.க. மத வழிப்பாட்டு தலங்களை பக்தர்களுக்காக திறக்க வேண்டும் பல போராட்டங்கள் நடத்தி வரும் வேளையில், அக்டோபர் 7ம் தேதி முதல் மத வழிப்பாட்டு தலங்கள் திறக்கும் என்று மகாராஷ்டிரா அரசு அறிவித்துள்ளது குறிப்பிடத்தக்கது.மீண்டும் பள்ளிகள் திறப்பு?தற்போது மகாராஷ்டிராவில் அக்டோபர் 4ம் தேதி முதல் பள்ளிகளை திறக்கவும் அம்மாநில அரசு அனுமதி அளித்துள்ளது. இது தொடர்பாக அம்மாநில பள்ளி கல்வித்துறை அமைச்சர் வர்ஷா கெய்க்வாட் கூறுகையில், கிராமப்புறங்களில் உள்ள அனைத்து பள்ளிகளிலும் 5 முதல் 12ம் வகுப்பு வரையிலான மாணவர்களுக்கு நேரடி வகுப்புகள் தொடங்கும். நகர்புறங்களில் 8 முதல் 12ம் வகுப்பு வரையிலான மாணவர்களுக்கு நேரடி வகுப்புகள் தொடங்கும் என்று தெரிவித்தார். | tamil |
Recipe: गुणों से भरपूर होता है बथुआ, जानें Bathua Boondi रायता की रेसिपी Recipe: सर्दियों Winters में कई तरह के साग आते हैं। जैसे बथुआ, सरसों, सोया आदि, ये सभी कई तरह के स्वास्थ्य लाभों से भरपूर होनें के साथसाथ टेस्ट में भी बेस्ट होते हैं। अपनी इस स्टोरी में हम आपको बथुआ बूंदी रायता Bathua Boondi Raita बनाना सिखाएंगे। बथुआ बूंदी रायता रेसिपी Bathua Boondi Raita Recipe बनाने के लिए हमें चाहिए... सामग्रीउबला बथुआ 500 ग्राम ताजा दही 500 ग्राम पानी 1 कप हरी मिर्च पेस्ट 12 टीस्पून बूंदी 100 ग्राम सरसों का तेल 14 टीस्पून हींग 1 चुटकी भर जीरा 14 टीस्पून काली मिर्च पावडर 12 टीस्पून काला नमक 12 टीस्पून चाट मसाला 12 टीस्पून विधि पहले उबले बथुए को मिक्सी में पीस लें। अलग बर्तन में दही को पानी और हरी मिर्च का पेस्ट मिलाकर अच्छी तरह फेंट लें। इसमें पिसा बथुआ और बूंदी मिलाकर 20 मिनट के लिए ढंककर रख दें ताकि बूंदी फूल जाए। 20 मिनट बाद सरसों के तेल को बघार कर पैन में गर्म करके हींग, जीरा तड़काकर दही में डालें। अब चाट मसाला, काला नमक और काली मिर्च डालकर अच्छी तरह चलाकर गरमगरम रोटी या परांठा के साथ सर्व करें। | hindi |
शादी कर लौटे आरपीएफ दरोगा व परिजनों से मारपीट पीडीडीयू नगर। संवाददातापीडीडीयू जंक्शन परिसर में शनिवार की देर रात साढ़े 11 बजे पार्किग स्थल पर कार के व्हील कैप गायब हो जाने पर पार्किंग कर्मियों से आरपीएफ दरोगा से झड़प हो गई। वही देखते ही देखते ही जमकर मारपीट होने लगी। इससे आरपीएफ दरोगा के साथ महिलाएं व रिस्तेदार चोटिल हो गये। इसके अलावा अलावा एक पार्किग कर्मी भी घायल हो गया। मौके पर पहुंची जीआरपी दोनों पक्ष को कोतवाली लेकर पहुंची। जहां भोर तक चले सुलह समझौता के बाद दोनों पक्ष को छोड़ दिया गया। वही विभागीय मामला होने के कारण आरपीएफ कमानडेंट आशीष मिश्रा सीसीटीवी फुटेज की जांच कराकर अगली कार्रवाई में जुटे है।बलिया के रहने वाले शुभम कुमार बिहार दानापुर स्टेशन पर स्थित आरपीएफ थाने में उपनिरीक्षक के पद पर कार्यरत है। आरपीएफ दरोगा अपनी बारात लेकर जोधपुर गया था। इस दौरान स्टेशन परिसर में अपनी कार रख दी थी। शनिवार की देर रात जोधपुर हावड़ा एक्सप्रेस से बारात पीडीडीयू जंक्शन पर पहुंची। इस दौरान सभी बराती बलिया जाने के लिए कार व बस में सवार होने लगे। लेकिन इसी दौरान एक कार के चक्के से व्हील कैप गायब होने पर पार्किंग कर्मियों से सभी लोग पूछताछ करने लगे। इस दौरान पार्किंग कर्मियों ने रशीद न लेने की बात कहकर नाराजगी जाहिर की। वही देखते ही देखते दोनों पक्ष में मारपीट होने लगी। मारपीट के दौरान स्टेशन परिसर में भगदड़ मच गई। आरपीएफ दरोगा का आरोप है कि पार्किंग कर्मियों ने महिलाओं को भी पीट दिया। घटना की जानकारी होते ही जीआरपी दोनों पक्ष को थोने लेकर पहुंची। वही दोनों पक्ष के तहरीर मिलने पर देर रात तक सुलह समझौता होता रहा। इसके बाद दोनों पक्ष को जीआरपी छोड़ दी। जीआरपी कोतवाल ने बताया कि दोनों पक्ष में सुलह हो गया था। वही आरपीएफ कमानडेंट आशीष मिश्रा ने बताया कि घटना के सभी पहलुओं की जांच कराई जा रही है। जांच के बाद कार्रवाई की जाएगी। For Hindustan : हिन्दुस्तान ईसमाचार पत्र के लिए क्लिक करें epaper.livehindustan.com | hindi |
குலாபி புடவையில் பார்ப்பதற்கு அம்மா ஸ்ரீதேவி போலவே மின்னும் ஜான்வி கபூர்! மறைந்த நடிகை ஸ்ரீதேவியின் மகளும், பிரபல பாலிவுட் நடிகையுமான ஜான்வி கபூர், பராம்பரிய புடவை அணிந்து எடுத்த புகைப்படங்கள் இணையத்தில் வைரலாகியுள்ளது. பெரும்பாலும் ஜான்வி கபூர், பளபளப்பான லெஹெங்காக்கள், பிரமிக்க வைக்கும் புடவைகள் மற்றும் சூட் செட்டுகளை அணிந்திருப்பார் இவை அனைத்தும் புக்மார்க் செய்ய வேண்டியவை. அவை பொதுவாக பிரபல டிசைனர் மணீஷ் மல்ஹோத்ரா வடிவமைத்த ஆடைகளாக தான் இருக்கும். இந்நிலையில் தற்போது, ஜான்வி கபூர் இலையுதிர்குளிர்கால ஃபேஷனின் நியூட்ரல் பேலட்டுக்கான சரியான அண்டிடோட்டாக இருக்கும் ஃப்ளோரல் புடவையில் மற்றொரு நேர்த்தியான தோற்றத்தைப் பகிர்ந்துள்ளார். பிரபல ஸ்டைலிஸ்ட் மோஹித் ராய் பாணியில், வெள்ளை நிற ஸ்லீவ்லெஸ் ரவிக்கையுடன், ஆர்கன்சாவில் இளஞ்சிவப்பு மலர் அச்சிடப்பட்ட, ரா மாம்பழப் புடவையில் ஜான்வி ரொமாண்டிக்காக இருக்கிறார். அதில் கூந்தலை அவிழ்த்துவிட்டு, தனது சிக்னேட்சர் லுக்கான, லேசான ஐ மேக்கப், நியூட் லிப்ஸ்டிக் உடன் ஒரு சிறிய கருப்பு பொட்டு வைத்து பார்ப்பதற்கு சிம்பிளாகவும், அதேநேரம் எலிகெண்ட் ஆகவும் இருந்தார். இதைப்பார்த்த ரசிகர்கள் சிலர், புடவையில் ஜான்வி கபூர் அவர் அம்மா ஸ்ரீதேவியை போன்று இருப்பதாக கூறிவருகின்றனர். இந்த தோற்றம், 90களின் பாலிவுட் கவர்ச்சிக்கு த்ரோபேக் ஆக இருந்தது. ஜான்வி, தனது பாரம்பரியத்தை எவ்வளவு சிரமமின்றி எடுத்துச் செல்கிறார் என்பதற்கு இது ஒரு சிறந்த எடுத்துக்காட்டு. ஜான்வியின் தந்தையும், தயாரிப்பாளருமான போனி கபூர், தனது அடுத்த படமான வலிமையை ஜனவரி 2022 இல் வெளியிட திட்டமிட்டுள்ளார். இதற்கு முன்பு ஒரு அழகான பிரமிக்க வைக்கும், சிக்கலான எம்ப்ராய்டரி செய்யப்பட்ட வயலிட் நிற அனாமிகா கண்ணா அனார்கலியில் ஜான்வி தேவதை போல இருந்தார். | tamil |
यूक्रेन सरकार और बैंकों की वेबसाइट पर साइबर हमला बोस्टन, 23 फरवरी एपी यूक्रेन की सरकार तथा बैंकों की वेबसाइट पर एक और साइबर हमला किया गया, जिससे वेबसाइट ऑफलाइन हो गईं। इन वेबसाइट पर जो हमला किया गया, उसे तकनीकी भाषा में डिस्ट्रिब्यूटेड डिनायल ऑफ सर्विस डीडीओएस हमला कहा जाता है, जिसका अर्थ है कि किसी सर्वर को लक्षित कर उस पर इंटरनेट डेटा की बाढ़ कर देना, ताकि सामान्य तौर पर आने वाला डेटा बाधित हो जाए। यूक्रेन पर हुए साइबर हमलों में बुधवार को जिन वेबसाइट को निशाना बनाया गया, उनमें रक्षा, विदेश एवं गृह मंत्रालयों की वेबसाइट के अलावा देश के सबसे बड़े वाणिज्यिक बैंक प्राइवेटबैंक की वेबसाइट भी शामिल है। इनमें से अधिकतर वेबसाइट पर 1314 फरवरी को भी इसी प्रकार के हमले किए गए थे, जिनके लिए अमेरिका और ब्रिटेन सरकारों ने रूस की जीआरयू सैन्य खुफिया एजेंसी को दोषी ठहराया था। एपी सिम्मी नेत्रपाल नेत्रपाल | hindi |
کیٛاہ ژٕ ہیٚکھٕ میٲنہِ خٲطرٕ الارم تھٲیِتھ | kashmiri |
\begin{document}
\title{Dynamic entanglement transfer in a double-cavity optomechanical system}
\author{Tiantian Huan}
\affiliation{College of Information Engineering, East China JiaoTong University,
Nanchang, China}
\affiliation{Institute of Applied Physics and Materials Engineering, FST, University
of Macau, Macau}
\author{Rigui Zhou}
\thanks{Corresponding author}
\affiliation{College of Information Engineering, East China JiaoTong University,
Nanchang, China}
\author{Hou Ian}
\affiliation{Institute of Applied Physics and Materials Engineering, FST, University
of Macau, Macau}
\begin{abstract}
We give a theoretical study of a double-cavity system in which a mechanical
resonator beam is coupled to two cavity modes on both sides through
radiation pressures. The indirect coupling between the cavities via
the resonator sets up a correlation in the optomechanical entanglements
between the two cavities with the common resonator. This correlation
initiates an entanglement transfer from the intracavity photon-phonon
entanglements to an intercavity photon-photon entanglement. Using
numerical solutions, we show two distinct regimes of the optomechanical
system, in which the indirect entanglement either builds up and eventually
saturates or undergoes a death-and-revival cycle, after a time lapse
for initiating the cooperative motion of the left and right cavity
modes.
\end{abstract}
\pacs{42.50.Wk, 03.65.Ud, 42.50.Lc}
\maketitle
\section{Introduction}
Cavity optomechanical systems~\cite{kippenberg08} arise from the
classical Fabry-Perot interferometer~\cite{vaughan89} by replacing
one of the fixed sidewalls with a cantilever or double-clamped beam~\cite{cleland96,meyer88,kleckner06}.
The one-dimensional degree of freedom introduced by the movable mechanical
element adds a free resonator mode to the cavity system and allows
this mode to interact with the cavity field through radiation pressure
on the reflectively coated mechanical resonator. Regarded as a micromirror,
this resonator can be feedback-controlled through the cavity field,
on which numerous cooling protocols have been conceived and experimentally
demonstrated in the last decade~\cite{metzger04,naik06,arcizet06,ian08-1,liu13}.
The degree of control in this hybrid cavity-micromirror system can
be further enhanced when the micromirror is replaced by a double-face
reflective membrane~\cite{thompson08,jayich08}. If a second optical
cavity is coupled to it on the opposite side of the existing cavity,
a two-mode or double-cavity optomechanical system with enhanced nonlinearity
is formed~\cite{pinard05,miao09,naeini11,ludwig12}. Entanglement-wise,
though it was observed that the enhanced squeezing resulted from the
nonlinear coupling helps generate static entangled state of distant
mirrors\cite{pinard05}, the dynamic property of entanglement between
the two cavities is less well-understood.
Recent studies reveal that the dynamics of phonon-photon entanglement
plays an important role in defining the system characteristics, such
as the transitions between oscillation modes~\cite{wang14,ying14},
robustness against noisy environment~\cite{tian13}, sudden death
and revival of states~\cite{ian08,chang09,lin14}, and optimal entanglement~\cite{ydwang13}.
In this article, we study the dynamics of the entanglements in a double-cavity
optomechanical system where each photon mode in the two opposite cavities
is, structure-wise, symmetrically coupled to a common mechanical resonator
mode via radiation pressures, albeit asymmetric coupling strengths
and driving powers are generally assumed. Our main concern is to determine
how the cavity-resonator entanglements~\cite{vitali07} can be transferred
to the indirectly coupled cavities over time.
We show here such an entanglement transfer is possible in a double-cavity
optomechanical system through measuring the entanglements in logarithmic
negativities among the component pairs. In particular, the negativity
is computed through determining the symplectic eigenvalues of a covariance
matrix that relates the fluctuations of all six quadratures of the
system's main components. This method is standard in the literature
of dynamic entanglement but we have generalized it to apply on a $6\times6$
covariance matrix. We observe that the successful generation of entanglement
transfer only requires a single-sided driving laser and that the transfer
patterns can be distinctively categorized into two groups for the
different operating regimes assumed by optomechanical system.
Moreover, all the logarithmic negativities computed exhibit a time
delay before the first appearance of a non-zero value. This time point
signifies the initiation of cooperative motions among the three components
in the optomechanical system, showing the transient response of the
system to the external driving lasers as a whole. Nonetheless, the
indirect entanglement between the left and the right cavity is apparent
in all cases, thereby facilitating a mechanism for entanglement relay
through cascaded cavities although the cavities are physically not
directly coupled. Such a mechanism would be useful to quantum information
processing, especially in terms of non-adiabatic quantum state transfer~\cite{palomaki13,zhang03},
and would provide a physical means to realize cavity arrays or resonator
waveguides for transmitting information encoded in a quantum state~\cite{zhou08,gong08,xuereb12}.
In Sec.~\ref{sec:model}, we give a detailed description of the double-cavity
model. The equations of motions are derived under the Heisenberg picture
in Sec.~\ref{sec:dynamics} and the steady-state solutions are calculated
to give proof of the sufficiency of single-sided driving. After the
covariance matrix of the fluctuations is introduced, the entanglements
among all component pairs are computed numerically and analyzed in
Sec.~\ref{sec:entanglement_transfer}. The conclusions are given
finally in Sec.~\ref{sec:conclusions}.
\section{Double optomechanical cavity\label{sec:model}}
The proposed double-cavity optomechanical system is illustrated in
Fig.~\ref{fig:model}, in which a mechanical resonator with reflective
coatings on both sides receives the radiation pressures from both
the cavity on the left side (L) and the cavity on the right side (R).
The total Hamiltonian $H=H_{0}+H_{\mathrm{rad}}+H_{\mathrm{ext}}$
thus consists of three parts, which reads ($\hbar=1$), respectively,
\begin{eqnarray}
H_{0} & = & \omega_{L}a_{L}^{\dagger}a_{L}+\omega_{R}a_{R}^{\dagger}a_{R}+\frac{p^{2}}{2m}+\frac{1}{2}m\Omega_{M}^{2}q^{2},\label{eq:Ham_0}\\
H_{\mathrm{rad}} & = & \left(\eta_{L}a_{L}^{\dagger}a_{L}-\eta_{R}a_{R}^{\dagger}a_{R}\right)q,\label{eq:Ham_rad}\\
H_{\mathrm{ext}} & = & i\varepsilon_{L}\left(a_{L}^{\dagger}e^{-i\omega_{d,L}t}-\mathrm{h.c.}\right)+i\varepsilon_{R}\nonumber \\
& & \times\left(a_{R}^{\dagger}e^{-i\omega_{d,R}t}-\mathrm{h.c.}\right)\label{eq:Ham_ext}
\end{eqnarray}
The part $H_{0}$ accounts for the free Hamiltonians of the resonator
and the cavities, the latter being regarded as bosonic modes of frequencies
$\omega_{L}$ and $\omega_{R}$. We associate a pair of annihilation
and creation operators $a_{\sigma}$ and $a_{\sigma}^{\dagger}$ for
each bosonic mode, where $\sigma$ indexes the cavity side, either
left $L$ or right $R$. We assume the frequencies $\omega_{L}$ and
$\omega_{R}$ to be different in general according to the asymmetric
cavity lengths $\ell_{\sigma}$ and finesses $F_{\sigma}$ assumed.
The leakage rates are defined correspondingly from these parameters:
$\kappa_{\sigma}=\pi c/2F_{\sigma}\ell_{\sigma}$. The mechanical
resonator is described by the conjugate pair $q$ and $p$, along
with its oscillation mode frequency of $\text{\ensuremath{\Omega}}_{M}$
and its mechanical damping rate of $\Gamma_{M}$.
\begin{figure}
\caption{(Color online) Model schematic of the double-cavity optomechanical
system: a mechanical element with reflective coatings on both sides
serves as a double-face mirror that experiences radiation pressures
from both the left-side cavity and the right-side cavity. An incident
driving laser enters the double-cavity system from the left side.~\label{fig:model}
\label{fig:model}
\end{figure}
The part $H_{\mathrm{rad}}$ accounts for the phonon-photon interactions
derived from the radiation pressures. The radiation pressure from
each cavity side results from the deformation of the cavity volume
due to the displacement $q$ of the middle resonator, which shifts
the resonance frequencies of each cavity modes. Expending this frequency
shift to first order, i.e. $g_{L}\simeq\omega_{L}/\ell_{L}$, the
radiation pressure term sets the optomechanical coupling on the left
side with strength $\eta_{L}=g_{L}/\sqrt{2m\Omega_{M}}$, where $m$
is the effective mass of the resonator mode. The same derivation applies
to the right cavity, giving the coupling strength $\eta_{R}=g_{R}/\sqrt{2m\Omega_{M}}$
but the leading sign would be opposite to $\eta_{L}$ as the common
resonator has its displacement $q$ follow opposite directions for
the two radiation pressures. Between the two cavities, there is no
direct coupling.
The part $H_{\mathrm{ext}}$ accounts for the two external driving
lasers with frequency $\omega_{d,L}$ and frequency $\omega_{d,R}$.
The driving strength $\varepsilon_{\sigma}$ of each laser is related
to the input laser power $P_{\sigma}$ and the leakage $\kappa_{\sigma}$
by $|\varepsilon_{\sigma}|^{2}=2\kappa_{\sigma}P_{\sigma}/\hbar\omega_{d,\sigma}$.
Note that we assume an asymmetric setting for the double-cavity system:
the radiation pressures from the two sides are not identical and the
cavities are unequally driven.
To study the indirect entanglement across the two cavity modes, we
begin with the dynamics of the three components in the double-cavity
optomechanical system through deriving a set of nonlinear Langevin
equations. We carry out this step by finding the Heisenberg equations
of the operators from the Hamiltonian in E.~(\ref{eq:Ham_0})-(\ref{eq:Ham_ext})
and introducing phenomenologically the relaxation terms and their
associative Brownian noise terms. The Langevin equations under the
rotating frames of reference read
\begin{eqnarray}
\overset{.}{q} & = & \frac{p}{m},\nonumber \\
\overset{.}{p} & = & -m\Omega_{M}^{2}q-\Gamma_{M}p-\eta_{L}a_{L}^{\dagger}a_{L}+\eta_{R}a_{R}^{\dagger}a_{R}+\xi,\nonumber \\
\overset{.}{a_{L}} & = & -(\kappa_{L}+i\Delta_{L})a_{L}-i\eta_{L}a_{L}q+\varepsilon_{L}+\sqrt{2\kappa_{L}}a_{L}^{\mathrm{in}},\nonumber \\
\overset{.}{a_{R}} & = & -(\kappa_{R}+i\Delta_{R})a_{R}+i\eta_{R}a_{R}q+\varepsilon_{R}+\sqrt{2\kappa_{R}}a_{R}^{\mathrm{in}},\label{eq:Langevin}
\end{eqnarray}
where $\Delta_{0,L}=\omega_{L}-\omega_{d,L}$ ($\Delta_{0,R}=\omega_{R}-\omega_{d,R}$)
is the static detuning of the left (right) cavity field from the left
(right) driving laser. The zero-mean fluctuation terms $a_{\sigma}^{\mathrm{in}}$
obey the correlation relation $\langle a_{\sigma}^{\mathrm{in}}(t)a_{\sigma}^{\mathrm{in}\dagger}(t')\rangle=\delta(t-t').$
The mechanical mode is under the influence of stochastic Brownian
noise that satisfies in general the non-Markovian auto-correlation
relation with a colored spectrum:
\begin{equation}
\left\langle \xi(t)\xi(t')\right\rangle =\frac{\Gamma_{M}}{\Omega_{M}}\int d\omega\frac{\omega}{2\pi}e^{-i\omega(t-t')}\left\{ \coth\left(\frac{\omega}{2k_{B}T}\right)+1\right\} ,
\end{equation}
where $k_{B}$ is the Boltzmann constant and $T$ is the temperature
of the mechanical bath. However, for a high quality mechanical resonator
with $Q=\Omega_{M}/\Gamma_{M}\gg1$, this non-Markovian process can
be approximated as a Markovian one, where its fluctuation-dissipation
relation can be asymptotically simplified to~\cite{Giovannetti01,Fabre94}:
\begin{equation}
\left\langle \xi(t)\xi(t')+\xi(t')\xi(t)\right\rangle /2=\Gamma_{M}(2\bar{n}+1)\delta(t-t'),\label{eq:correlation}
\end{equation}
where $\bar{n}=\left(\exp\{\Omega_{M}/k_{B}T\}-1\right)^{-1}$ is
the mean occupation number of the mechanical mode. This simplified
Markovian relation will be assumed in the calculation of the entanglements.
\section{Dynamics and entanglement\label{sec:dynamics}}
\subsection{Steady states}
In a single-cavity optomechanical system, the radiation pressure contributes
the nonlinear photon number term in the Langevin equation of the mirror
momentum $p$ in Eq.~(\ref{eq:Langevin}), leading to a multistability
of the coordinate $p$ with three nonzero steady states. For a double-cavity
case here, the second radiation pressure by the other cavity contributes
a similar term in the equation. Under the asymmetric setting, the
two pressure terms are not commensurate and the number of steady states
of $p$ increases to five. The steady states are given by
\begin{eqnarray}
\langle q\rangle & = & \frac{-\eta_{L}\left|\left\langle a_{L}\right\rangle \right|^{2}+\eta_{R}\left|\left\langle a_{R}\right\rangle \right|^{2}}{m\Omega_{M}^{2}},\label{eq:steady_q}\\
\langle a_{\sigma}\rangle & = & \frac{\varepsilon_{\sigma}}{\kappa_{\sigma}+i(\Delta_{0,\sigma}\pm\eta_{\sigma}\left\langle q\right\rangle )},\label{eq:steady_a}
\end{eqnarray}
where the plus (minus) signs in the second equation refers to the
left (right) cavity.
For entanglement generation, it is necessary for the equation set
(\ref{eq:steady_q})-(\ref{eq:steady_a}) to have non-zero steady
states. Therefore, a single-cavity optomechanical system usually requires
an external driving laser (i.e., non-zero value of $\varepsilon$)
to drive the mechanical resonator out of its zero steady states at
equilibrium position. However, for optomechanical systems with double-sided
cavities, one external driving laser at either end of the cavities
is sufficient to drive the mechanical resonator out of its zero position,
in which case Eq.~(\ref{eq:steady_q}) would fall back to the single-cavity
case of three roots.
In addition, we can observe that even when the double cavities have
exactly symmetrical setup, i.e. identical laser driving amplitudes
($\varepsilon_{L}=\varepsilon_{R}=\varepsilon$), radiation pressures
$(\eta_{L}=\eta_{R}=\eta)$, and cavity lengths, the differing signs
before $\eta_{\sigma}\left\langle q\right\rangle $ to be taken by
$\left\langle a_{L}\right\rangle $ and $\left\langle a_{R}\right\rangle $
in Eq.~(\ref{eq:steady_a}) allows the cavities to admit non-zero
steady states. This is because the two cavity modes are constructively
interfering with each other at the interface of the mechanical resonator
through their indirect interactions of radiation pressures. In other
words, even though the radiation pressures are exerted along opposite
directions, the dynamic $\pi$-phase difference between the cavities
fields, reflected in the Hamiltonian Eq.~(\ref{eq:Ham_rad}) as the
generator of the cavity motion, render the radiation pressures out
of phase to favor the generation of entanglement. Given the symmetric
setting where $\kappa_{L}=\kappa_{R}=\kappa$ and $\Delta_{0,L}=\Delta_{0,R}=\Delta_{0}$
in addition to the identities in driving amplitudes and radiation
pressures, the condition for the steady-state equations to admit real
roots is the inequality among the system parameters
\begin{equation}
\eta\varepsilon\geq\sqrt{\frac{m\Omega_{M}^{2}}{4\Delta_{0}}}(\kappa^{2}+\Delta_{0}^{2}).
\end{equation}
Its derivation is given in Appendix A. Finding $m\Omega_{M}^{2}$
as the Young's modulus of the resonator ($m\Omega_{M}^{2}<\Delta_{0}$)
and that the cavities have sufficient finesses ($\kappa\leq\Delta_{0}$),
the above criterion is met in most scenarios and the validity of entanglement
generation is almost guaranteed.
For the symmetric setting, we expect the patterns of entanglement
generations between either end of the cavity modes and the mechanical
resonator to be qualitatively similar and differ only quantitatively
in their variations over time. Deviating from this setting, the increase
in asymmetry among the system parameters would increase the qualitative
difference between the patterns of entanglements. We demonstrate these
effect later in Sec.~\ref{sec:entanglement_transfer}.
\subsection{Entanglement measure}
Theoretically, the entanglements in terms of logarithmic negativity
are computed through the fluctuations of the cavity quadratures about
the steady states obtained from Eqs.~(\ref{eq:steady_q})-(\ref{eq:steady_a}).
That is, we define the dimensionless quadratures of the two cavity
fields as
\begin{eqnarray}
X_{\sigma} & = & \frac{1}{\sqrt{2}}\left(a_{\sigma}+a_{\sigma}^{\dagger}\right),\\
Y_{\sigma} & = & \frac{1}{i\sqrt{2}}(a_{\sigma}-a_{\sigma}^{\dagger}).
\end{eqnarray}
and the corresponding input noise operators accordingly. Then taking
$\mathcal{O}\equiv(q,p,X_{L},Y_{L},X_{R},Y_{R})$ as the vector operator
for all the quadratures in the optomechanical system, we expand it
to first-order using a c-number steady-state value and a zero-mean
fluctuation operator $\mathcal{O}(t)=\left\langle \mathcal{O}\right\rangle +\delta O(t)$.
In addition, the nonlinear terms are linearized assuming $|\left\langle a\right\rangle |\gg1$
in the expansion: $\left\langle a^{\dagger}a\right\rangle \simeq|\left\langle a\right\rangle |^{2}$
and $\left\langle aq\right\rangle \simeq\left\langle a\right\rangle \left\langle q\right\rangle $,
while the higher-order products of the fluctuations are ignored.
The Langevin equations in Eq.~(\ref{eq:Langevin}) with the first-order
expansion gives a coupled system of differential equations about the
noise operators, enabling the coupling between the fluctuations of
the two cavity fields and the mechanical resonator and thus the generation
of entanglement between the two optical modes. Note that even though
we have linearized the equations for these operators, eliminating
the mechanical quadratures $q$ and $p$ in Eq.~(\ref{eq:Langevin})
will lead to equations of $a_{L}$ and $a_{L}^{\dagger}$ nonlinearly
related to $a_{R}$ and $a_{R}^{\dagger}$. This implies that the
indirect entanglement between the quadratures of the left and the
right cavities follow a nonlinear form in time.
In the following, instead of solving the coupled equations analytically,
we follow the standard numerical approach adopted by the current researches
on dynamic entanglement~\cite{wang14,ying14,vitali07}. The difference
here is that we have a 6-component vector $u=(\delta q,\delta p,\delta X_{L},\delta Y_{L},\delta X_{R},\delta Y_{R})$
over the six quadratures of the tripartite optomechanical system instead
of the usual 4-component vector. Similarly extending the input-noise
vector to the 6-component $n=(0,\xi,\sqrt{2\kappa_{L}}X_{L}^{\mathrm{in}},\sqrt{2\kappa_{L}}Y_{L}^{\mathrm{in}},\sqrt{2\kappa_{R}}X_{R}^{\mathrm{in}},\sqrt{2\kappa_{R}}Y_{R}^{\mathrm{in}}$),
we write the time-dependent inhomogeneous equations of motion as $\overset{.}{u}(t)=A(t)u(t)+n(t)$,
where $A(t)=$
\begin{equation}
\left[\begin{array}{cccccc}
0 & 1/m & 0 & 0 & 0 & 0\\
-m\Omega_{M}^{2} & -\Gamma_{M} & -G_{xL}(t) & -G_{yL}(t) & G_{xR}(t) & G_{yR}(t)\\
G_{yL}(t) & 0 & -\kappa_{L} & \Delta_{L}(t) & 0 & 0\\
-G_{xL}(t) & 0 & -\Delta_{L}(t) & -\kappa_{L} & 0 & 0\\
-G_{yR}(t) & 0 & 0 & 0 & -\kappa_{R} & \Delta_{R}(t)\\
G_{xR}(t) & 0 & 0 & 0 & -\Delta_{R}(t) & -\kappa_{R}
\end{array}\right].
\end{equation}
In the matrix, $G_{x\sigma}(t)=\eta_{\sigma}\left\langle x(t)\right\rangle $
and $G_{y\sigma}(t)=\eta_{\sigma}\left\langle y(t)\right\rangle $
are the real and the imaginary parts of the scaled coupling constants
$G_{\sigma}(t)=\sqrt{2}\langle a_{\sigma}(t)\rangle\eta_{\sigma}$.
Along with the oscillation of the mechanical resonator, the dynamic
detunings of the two cavities are defined as
\begin{eqnarray}
\Delta_{\sigma}(t) & = & \Delta_{0,\sigma}\pm\eta_{\sigma}\langle q(t)\rangle,
\end{eqnarray}
where the plus (minus) sign corresponds to the left (right) cavity.
When the tripartite system is stable, it reaches a unique steady state,
independently from the initial condition. Then given any arbitrary
steady state, the fluctuations about it is fully characterized by
its $6\times6$ covariance matrix $V$ of the pairwise correlations
among the quadratures, which obeys the equation $\dot{V}(t)=A(t)V(t)+V(t)A^{T}(t)+D$.
The diagonal elements of the $V$ are, in order, auto-correlations
of the quadratures of the resonator, the left, and the right cavity
mode. Hence, $D=\mathrm{diag}(0,\Gamma_{M}(2\bar{n}+1),\kappa_{L},\kappa_{L},\kappa_{R},\kappa_{R})$
is the diagonal matrix for the corresponding damping and leakage rates
responsible for the fluctuations. The multiple fluctuation-dissipation
relations defined in Sec.~\ref{sec:model} are therefore encapsulated
in the relation $\left\langle n_{i}(t)n_{j}(t')+n_{j}(t')n_{i}(t)\right\rangle /2=\delta(t-t')D_{ij}$.
From its evolution equation, the covariance matrix $V$ can be written
as a block-matrix
\begin{equation}
V=\left[\begin{array}{ccc}
V_{M} & V_{ML} & V_{MR}\\
V_{ML}^{T} & V_{L} & V_{LR}\\
V_{MR}^{T} & V_{LR}^{T} & V_{R}
\end{array}\right],\label{eq:matrix_V}
\end{equation}
where each block represents $2\times2$ matrix. The blocks on the
diagonal indicate the variance within each subsystem (the resonator
$M$, the left cavity mode $L$, and the right cavity mode $R$),
while the off-diagonal blocks indicate covariance across different
subsystems, i.e. the correlations between two components that describe
their entanglement property.
To compute the pairwise entanglements, we reduce the $6\times6$ covariance
matrix $V$ to a $4\times4$ submatrix $V_{S}$. There are three such
cases of the submatrix $V_{S}$: (i) if the indices $i$ and $j$
for the element $V_{ij}$ are confined to the set $\{1,2,3,4\}$,
the submatrix $V_{S}=[V_{ij}]$ is formed by the first four rows and
columns of $V$ and corresponds to the covariance between the resonator
mode and the left cavity mode. Similarly, (ii) if the indices run
over $\{1,2,5,6\}$, $V_{S}$ is the covariance matrix of the resonator
and the right cavity mode. (iii) If the indices run over $\{3,4,5,6\}$,
$V_{S}$ designates the covariance between the two opposite cavity
modes. Summarizing, the submatrix can be written as
\begin{equation}
V_{S}=\left[\begin{array}{cc}
V_{\alpha} & V_{\alpha\beta}\\
V_{\alpha\beta}^{T} & V_{\beta}
\end{array}\right],\label{eq:matrix_subV}
\end{equation}
where $\alpha$, $\beta$, and $\gamma$ index the subsystems $\{M,L,R\}$
in the optomechanical cavity. The entanglement measured by logarithmic
negativity is computed through a process known as symplectic diagonalization
of each submatrix $V_{S}$, where the entanglement properties are
contained in the symplectic eigenvalues of the diagonalized matrix.
If we write the diagonalized matrix as $\mathrm{diag}(v_{-},v_{-},v_{+},v_{+})$,
then the eigenvalues along the diagonal read~\cite{plenio07}
\begin{equation}
v_{\mp}=\sqrt{\frac{1}{2}\left[\Sigma(V_{S})\mp\sqrt{\Sigma(V_{S})^{2}-4\det V_{S}}\right]},
\end{equation}
where $\Sigma(V_{S})=\det(V_{\alpha})+\det(V_{\beta})-2\det(V_{\alpha\beta})$.
Denoting the state of a bipartite subsystem in the tripartite optomechanical
cavity as $\rho$, the negativity is defined as
\begin{equation}
N(\rho)=\frac{\left\Vert \text{\ensuremath{\rho}}^{T}\right\Vert _{1}-1}{2},\label{eq:negativity}
\end{equation}
where $\parallel\rho^{T}\parallel_{1}$ indicates the trace norm of
the partial transposition of $\rho$~\cite{Vidal02}. Taking $v_{-}$
as the minimum symplectic eigenvalue of the covariance matrix, $\left\Vert \text{\ensuremath{\rho}}^{T}\right\Vert _{1}$
is equivalent to $1/v_{-}$ after the diagonalization. Hence, the
negativity is a decreasing function of $v_{-}$ and we usually write
$N(\rho)=\max\{0,(1-v_{-})/2v_{-}\}$ and take its logarithmic value
$E_{N}=\ln\left\Vert \text{\ensuremath{\rho}}^{T}\right\Vert _{1}$
as a measure of the entanglement~\cite{Adesso04}. This logarithmic
negativity has the expression $E_{N}=\max\{0,-\ln(v_{-})\}.$
In other words, the symplectic eigenvalue $v_{-}$ completely quantifies
the quantum entanglement between each pair of components in the system.
The necessary condition for showing a bipartite subsystem is entangled
is that the symplectic eigenvalue retains a value less than one, which
is equivalent to the inequality $4\det V_{S}<\Sigma(V_{S})-1/4$~\cite{Simon00}.
\section{Entanglement transfer\label{sec:entanglement_transfer}}
\subsection{Delayed build-up}
To measure the entanglements, the noise terms $\xi$, $X_{L}^{\mathrm{in}}$,
$Y_{L}^{\mathrm{in}}$, $X_{R}^{\mathrm{in}}$, and $Y_{R}^{\mathrm{in}}$
that appear in the variance matrix of Eq.~(\ref{eq:matrix_V}) are
taken as random variables of zero-mean Gaussian processes. The entanglements
measured in logarithmic negativities $E_{N}$ are plotted against
time for each of submatrices given in Eq.~(\ref{eq:matrix_subV})
to discern the entanglement transfer. We found similar transfer patterns
over a range of parameters close to the experiments\cite{Zhang10}.
One typical case is shown here in Fig.~\ref{fig:comparison}, where
from top to bottom we plot, respectively, $E_{N}$ between the left
cavity and the resonator, between the right cavity and the resonator,
and finally between the left and the right cavities.
\begin{figure}
\caption{(Color online) Time evolution of the tripartite optomechanical system
characterized by the logarithmic negativities between (a) the left
cavity mode and the mechanical resonator, (b) the right cavity mode
and the mechanical resonator, and (c) the left and the right cavity
modes. Two cases are shown with different colors: (i) the blue curves
show the symmetric case where the parameters of the left and the right
cavities are set identical; and, in contrast, (ii) the red curves
show the asymmetric case where some parameters of the two cavities
are set distinct. The parameter values taken for the plots are given
in the text.~\label{fig:comparison}
\label{fig:comparison}
\end{figure}
For comparison, two cases are plotted for each entanglement pair:
the blue ones denote the symmetric case and the red ones denote the
asymmetric case. For the symmetric case, we adopt for the mechanical
resonator a quality factor $Q=20000$, resonance frequency $\omega_{M}=1$MHZ,
and effective mass $m=10$ ng~; for the cavities, we take cavity
length at $22$ mm with finesse $F=2.6\times10^{5}$ and cavity mode
wavelength of $1064$ nm. We set the power of the driving lasers at
70$\mu\mathrm{W}$, which is detuned from the cavity mode at $\Delta=6.5\omega_{M}$.
For the asymmetric case plotted in red, we have adjusted the right
cavity to a length of $19$ mm, which consequently affects the cavity
leakage and the coupling amplitude between the driving and the cavity,
while the length of the left cavity and other parameters remain unchanged.
We observe from Fig.~\ref{fig:comparison} that there are two phases
in the entanglement evolution. The initial phase is a period of zero
$E_{N}$, showing a delay in the formation of entanglement. The latter
phase is a gradual build-up until certain saturation is reached. While
the entanglement generations between either cavity and the mechanical
resonator are smooth, that between the two cavities are oscillating
or quasi-oscillating because of the nonlinear nature of the radiation
pressure coupling~\cite{wang14}. Averaging out the oscillation,
we see the patterns in the build-up of entanglement are identical
to those between the cavity and the resonator. In addition, the delay
periods among all three pairs coincide, demonstrating the transfer
of cavity-resonator entanglement to intercavity entanglement and showing
that distant entanglement is possible if the distant objects are indirectly
coupled.
The delay in the entanglement build-up, during which $E_{N}$ assumes
zero value, corresponds to the negativity in Eq.~(\ref{eq:negativity})
taking a nonphysical negative value. We can interpret this delay period
as the time duration when the three components in the tripartite system
spend to establish their cooperation, which like the effect of superradiance
depends strongly on the resonance linewidths. Comparing the delays
for the symmetric and the asymmetric cases from Fig.~\ref{fig:comparison}(a)
and (b), we see the similar inverse proportionality in the entanglement
delay $T_{D}$ on the cavity leakage rates $\kappa_{\sigma}$, i.e.,
$T_{D}\propto\kappa_{\sigma}^{-1}$ . When the cavities are setup
symmetrically, we measure the delays in both Fig.~\ref{fig:comparison}(a)
and (b) at about $89\mu\mathrm{s}$; when they are setup asymmetrically
with $\kappa_{L}<\kappa_{R}$, we observe $T_{D}$ for the left cavity
being greater than its counterpart at the right side, at a difference
of $15.7\mu\mathrm{s}$ in time for a difference about $2.3\mathrm{kHz}$
in cavity linewidths.
\subsection{Death and revival}
The influences of asymmetric parameter setup for the cavities are
not only reflected in the delays of entanglement generation, but also
in the entanglement pattern itself. In Fig.~\ref{fig:death-revival},
we show a typical example with entanglements generated in a pattern
distinctly differently from those in Fig.~\ref{fig:comparison}.
The entanglements measured in logarithmic negativity are again plotted
from top to bottom, respectively, for the three component pairs discussed
above, but with driving laser powers increased to $80\mu\mathrm{W}$
and cavity finesses decreased to $F=1.0\times10^{5}$. The left and
the right cavity lengths remain in an asymmetric setup of $22$mm
and $20$mm, respectively, and the rest of parameters are kept identical
to those in Sec.~\ref{sec:entanglement_transfer}A.
\begin{figure}
\caption{Time evolution of the logarithmic negativity $E_{N}
\label{fig:death-revival}
\end{figure}
While the cavity-resonator entanglements for the two cavities follow
the pattern of build-up to saturation after a time delay, which is
similar to those of Fig.~\ref{fig:comparison}, the intercavity entanglement
does not but otherwise oscillate over a death-revival cycle. Because
of the inverse proportionality of the time delay to the cavity linewidths,
the plots show a shortened delay and a reduced discrepancy between
the delays in the left and the right cavity-resonator entanglements
due to the decrease in cavity finesses.
On closer inspection, we can see the build-up in (a) and (b) are sharper
and less gradual than their counterparts in Sec.~\ref{sec:entanglement_transfer}A
and the absolute negativity they can obtain are much smaller, especially
for the left cavity. Even for the right cavity, its entanglement with
the resonator declines shortly after a peak value, making all three
plots assume essentially different characteristics than those of Fig.~\ref{fig:comparison}.
This distinction can be attributed to the strong dependence of the
operating regimes of optomechanical systems on external driving power
and cavity finesse. In a single optomechanical cavity, it is reflected
as periodic and quasiperiodic motions of the resonator~\cite{wang14};
in the double optomechanical cavity here, it is reflected as the resonator
being driven monotonically in-phase (Fig.~\ref{fig:comparison}(c))
and driven periodically in-phase and out-of-phase (Fig.~\ref{fig:death-revival}(c))
with the left and right cavities.
\section{Conclusions\label{sec:conclusions}}
To summarize, we have studied the dynamic transfer of quantum entanglement
from those within two cavity-resonator pairs to that between these
two cavities inside a double-cavity optomechanical system. We numerically
solved a coupled set of Heisenberg-Langevin equations to show the
generation of quantum entanglements between each pair of the components
under an experimentally accessible set of parameters. We find that
the entanglement of the indirectly coupled cavities is built up over
time in a pattern similar to those of the directly entangled cavity-resonator
pairs, verifying the entanglement transfer. The similarities are accentuated
by the almost identical characteristic delays and rising patterns
but the entanglement transfer would be suppressed by the asymmetries
in the two cavities. The asymmetries also differentiates the initiation
times of the cavity-resonator entanglements, which leads to our speculation
that the tripartite system is undergoing a cooperation process similar
to that of superradiance before the emergence of the entanglement.
To understand such a transient effect in a multipartite system demands
a detailed analysis of the Heisenberg-Langevin equation set, which
we shall leave to future studies, but we have seen here that dynamic
entanglement is not only a measure of quantum information, but also
a useful tool to dissect the cooperative motions of microscopic systems.
\begin{acknowledgments}
R.~Z. is supported by the National Natural Science Foundation of
China under Grant No.~61463016 and 61340029, Program for New Century
Excellent Talents in University under Grant No.~NCET-13-0795, Landing
project of science and technique of colleges and universities of Jiangxi
Province under Grant No. KJLD14037, Project of International Cooperation
and Exchanges of Jiangxi Province under Grant No.~20141BDH80007.
H.~I. is supported by the FDCT of Macau under grant 013/2013/A1,
University of Macau under grants MRG022/IH/2013/FST and MYRG2014-00052-FST,
and National Natural Science Foundation of China under Grant No.~11404415.
\end{acknowledgments}
\appendix
\section{Steady states of symmetrical double cavity optomechanical system}
Substituting Eq.~(\ref{eq:steady_a}) into Eq.~(\ref{eq:steady_q})
and cancelling the factor $\left\langle q\right\rangle $ on both
sides of the equation, which implies the trivial solution being one
of the steady state in the symmetrical cavity setup, we arrive at
the quartic equation
\begin{equation}
\left\langle q\right\rangle ^{4}+2\frac{\kappa^{2}-\Delta_{0}^{2}}{\eta^{2}}\left\langle q\right\rangle ^{2}+\left(\frac{\kappa^{2}+\Delta_{0}^{2}}{\eta^{2}}\right)^{2}-\frac{4\Delta_{0}\varepsilon^{2}}{m\eta^{2}\Omega_{M}^{2}}=0.\label{eq:quartic_eq}
\end{equation}
Lacking the odd-order terms in $\left\langle q\right\rangle $, the
roots $\left\langle q\right\rangle ^{2}$ of the equation can be solved
directly through quadratic formula. Since $\kappa^{2}+\Delta_{0}^{2}>0$,
the real roots $\left\langle q\right\rangle $ exist only when:
i) $\left\langle q\right\rangle ^{2}$ is real, i.e. the discriminant
being non-negative, which gives
\begin{equation}
(\eta\varepsilon)^{2}>m\Omega_{M}^{2}\kappa^{2}\Delta_{0},\label{eq:cond_i}
\end{equation}
and ii) the quadratic root $\left\langle q\right\rangle ^{2}$ to
Eq.~(\ref{eq:quartic_eq}) is non-negative.
To satisfy the latter, we have to consider two cases:
ii-1) when $\kappa^{2}-\Delta_{0}^{2}<0$, the square root of the
determinant could take either the positive or the negative value.
For the negative case, it is required that
\begin{equation}
(\eta\varepsilon)^{2}<m\Omega_{M}^{2}\frac{(\kappa^{2}+\Delta_{0}^{2})^{2}}{4\Delta_{0}}\label{eq:cond_ii_x}
\end{equation}
or ii-2) for the postive case or when $\kappa^{2}-\Delta_{0}^{2}>0$,
it is required that
\begin{equation}
(\eta\varepsilon)^{2}\geq m\Omega_{M}^{2}\frac{(\kappa^{2}+\Delta_{0}^{2})^{2}}{4\Delta_{0}}.\label{eq:cond_ii}
\end{equation}
When two cases of condition (ii) are combined with condition (i),
we see case (ii-1) impose a very stringent constraint on the admissible
values of $(\eta\varepsilon)^{2}$: between zero and $m\Omega_{M}^{2}(\kappa^{2}-\Delta_{0}^{2})^{2}/4\Delta_{0}$.
Case (ii-2) is more inclusive, which is what we are interested in
here. Since it always holds that $(\kappa^{2}+\Delta_{0}^{2})>4\kappa^{2}\Delta_{0}^{2}$,
when the inequality of Eq.~(\ref{eq:cond_ii}) holds, the first condition
in Eq.~(\ref{eq:cond_i}) is automatically satisfied.
To simplify the study, we confine our investigation in the positive
domain of the detuning $\Delta_{0}$, for which Eq.~(\ref{eq:cond_ii})
can be further reduced to
\begin{equation}
\eta\varepsilon\geq\sqrt{\frac{m\Omega_{M}^{2}}{4\Delta_{0}}}(\kappa^{2}+\Delta_{0}^{2}).
\end{equation}
\end{document} | math |
//
// PrefWindow.h
// SunX
//
// Created by Peter Pearson on 04/06/2009.
// Copyright 2009 __MyCompanyName__. All rights reserved.
//
#import <Cocoa/Cocoa.h>
@interface PrefWindow : NSWindow {
}
@end
| code |
ریو ڈی جنیرو 10 اگست اردو پوائنٹ اخبارتازہ ترین اے پی پی10 اگست2016ء ریو اولمپکس میں امریکا سب سے زیادہ تمغوں کے ساتھ بدستور برقرار ہے امریکہ طلائی چاندی اور کانسی تمغوں کے ساتھ ٹاپ پوزیشن پر براجمان ہے چین دوسرے اور ہنگری تیسرے نمبر پر ہے جبکہ سٹریلیا تیسرے سے چوتھے نمبر پر چلا گیا ہے تفصیلات کے مطابق برازیل میں سمر اولمپکس کے سنسنی خیز مقابلوں کا سلسلہ جاری ہے اور امریکا نو سونے ٹھ چاندی اور نو کانسی کے تمغے جیت چکا ہے اور وہ مجموعی طور پر 26 میڈلز کے ساتھ پہلے نمبر پر براجمان ہے چین بھی طلائی تمغے حاصل کر چکا ہے اور وہ پوائٹنس ٹیبل پر مجموعی طور پر 17 تمغوں کے ساتھ دوسرے نمبر پر ہے جبکہ چین چاندی اور کانسی کے تمغے جیتے ہیں اس طرح وہ 17 میڈلز کے ساتھ دوسرے نمبر پر ہے ہنگری چار طلائی ایک چاندی اور ایک کانسی کے تمغوں کے ساتھ تیسرے نمبر پر ہے سٹریلیا چار سونے اور پانچ کانسی کے تمغوں کے ساتھ چوتھے نمبر پر ہے روس تین سونے چھ چاندی اور تین کانسی کے تمغوں کے ساتھ پانچویں نمبر پر ہے اور اسکے مجموعی تمغوں کی تعداد 12 ہے اٹلی تین سونے چار چاندی اور دو کانسی کے تمغوں کے ساتھ چھٹے نمبر پر ہے جنوبی کوریا تین سونے دو چاندی اور ایک کانسی کے تمغے کے ساتھ ساتویں نمبر پر ہے جاپان تین سونے ایک چاندی اور دس کانسی کے تمغے کے ساتھ ٹھویں نمبر پر ہے فرانس دو طلائی تین چاندی اور ایک کانسی کے تمغے کے ساتھ نویں نمبر پر ہے تھائی لینڈ دو طلائی ایک چاندی اور ایک کانسی کے ساتھ دسویں نمبر پر ہے انگلینڈ گیارہویں جرمنی بارہویں سویڈن 13ویں میزبان برازیل 14ویں چائنیز تائپے 15 ویں بیلجیئم یونان ہالینڈ 16ویں ارجنٹائن کولمبیا کروشیا کوسوو سلوانیہ اور ویتنام پوائنٹس ٹیبل پر 19 ویں نمبر پر ہیں اور یہ ملک ایک ایک طلائی تمغہ اپنے نام کرچکے ہیں | urdu |
ಪಾಲಕರಿಗೆ ಕೀರ್ತಿ ತನ್ನಿ: ಡಿವೈಎಸ್ಪಿ ಬಸವೇಶ್ವರ ಹೀರಾ ಸಲಹೆ ಬೀದರ್: ಮಕ್ಕಳು ವಿವಿಧ ಕ್ಷೇತ್ರಗಳಲ್ಲಿ ಉತ್ತುಂಗದ ಸಾಧನೆ ಮಾಡುವ ಮೂಲಕ ಪಾಲಕರಿಗೆ ಕೀರ್ತಿ ತರಬೇಕು ಎಂದು ಡಿವೈಎಸ್ಪಿ ಬಸವೇಶ್ವರ ಹೀರಾ ಸಲಹೆ ಮಾಡಿದರು. ನಗರದ ವಿ.ಕೆ. ಇಂಟರ್ನ್ಯಾಷನಲ್ನಲ್ಲಿ ಶುಕ್ರವಾರ 2021ನೇ ಸಾಲಿನ ದಿನದರ್ಶಿಕೆ, ದಿನಚರಿ ಬಿಡುಗಡೆ ಹಾಗೂ ವಿ.ಕೆ. ಇಂಟರ್ನ್ಯಾಷನಲ್ನಲ್ಲಿ ಪ್ರಶಸ್ತಿ ಪ್ರದಾನ ಸಮಾರಂಭ ಉದ್ಘಾಟಿಸಿ ಮಾತನಾಡಿದ ಅವರು, ಛಲವಿದ್ದರೆ ಏನನ್ನು ಬೇಕಾದರೂ ಸಾಧನೆ ಮಾಡಬಹುದು ಎಂದು ತಿಳಿಸಿದರು. ಬಸವ ತತ್ವ ಶಿಕ್ಷಣ ಸಂಸ್ಥೆ ಮಕ್ಕಳಿಗೆ ಸಂಸ್ಕಾರಯುತ ಶಿಕ್ಷಣ ನೀಡುತ್ತಿದೆ. ಸಂಸ್ಥೆಯ ಶಾಲಾ ಕಾಲೇಜುಗಳಲ್ಲಿ ವ್ಯಾಸಂಗ ಮಾಡಿದ ಬಹಳಷ್ಟು ವಿದ್ಯಾರ್ಥಿಗಳು ಉನ್ನತ ಹುದ್ದೆಗಳಲ್ಲಿ ಇದ್ದಾರೆ ಎಂದು ಮೆಚ್ಚುಗೆ ವ್ಯಕ್ತಪಡಿಸಿದರು. ಬಸವ ತತ್ವ ಶಿಕ್ಷಣ ಸಂಸ್ಥೆಯ ಅಧ್ಯಕ್ಷ ವೈಜಿನಾಥ ಕಮಠಾಣೆ ಮಾತನಾಡಿ, ಮಹಿಳಾ ಶಿಕ್ಷಣಕ್ಕೆ ಉತ್ತೇಜನ ನೀಡಲು 38 ವರ್ಷಗಳ ಹಿಂದೆ ಶುರು ಮಾಡಿದ ಸಂಸ್ಥೆ ಇಂದು ಬೃಹತ್ತಾಗಿ ಬೆಳೆದಿದೆ. ಸಂಸ್ಥೆಯ ಅಡಿಯಲ್ಲಿ ನರ್ಸರಿಯಿಂದ ಹಿಡಿದು ಪದವಿ, ವಿವಿಧ ವೃತ್ತಿಪರ ಕೋರ್ಸ್ಗಳ ಶಾಲಾ ಕಾಲೇಜುಗಳು ಇವೆ ಎಂದು ತಿಳಿಸಿದರು. ಮಕ್ಕಳು ನೈತಿಕತೆ ಹಾಗೂ ಮಾನವೀಯ ಮೌಲ್ಯಗಳನ್ನು ಬೆಳೆಸಿಕೊಳ್ಳಬೇಕು ಎಂದು ಹೃದಯ ರೋಗ ತಜ್ಞ ಡಾ. ಚಂದ್ರಕಾಂತ ಗುದಗೆ ನುಡಿದರು. ಕೊರೊನಾ ಸೋಂಕು ತಡೆಗೆ ಪ್ರತಿಯೊಬ್ಬರು ಮುಂಜಾಗ್ರತಾ ಕ್ರಮಗಳನ್ನು ಅನುಸರಿಸಬೇಕು ಎಂದರು. ಸಂಚಾರ ಠಾಣೆ ಸಿಪಿಐ ವಿಜಯಕುಮಾರ ಬಿರಾದಾರ ಅವರು ಸಂಚಾರ ನಿಯಮಗಳ ಕುರಿತು ಉಪನ್ಯಾಸ ನೀಡಿದರು. ಡಿವೈಎಸ್ಪಿ ಬಸವೇಶ್ವರ ಹೀರಾಪೊಲೀಸ್ ಸೇವೆ, ಹೃದಯ ರೋಗ ತಜ್ಞ ಡಾ. ಚಂದ್ರಕಾಂತ ಗುದಗೆಆರೋಗ್ಯ ಸೇವೆ ಹಾಗೂ ಪತ್ರಕರ್ತ ಮಲ್ಲಿಕಾರ್ಜುನ ನಾಗರಾಳೆಮಾಧ್ಯಮ ಸೇವೆ ಅವರಿಗೆ ವಿ.ಕೆ. ಇಂಟರ್ ನ್ಯಾಷನಲ್2021 ಪ್ರಶಸ್ತಿ ನೀಡಿ ಗೌರವಿಸಲಾಯಿತು. ಇದೇ ಸಂದರ್ಭದಲ್ಲಿ ಕೇಕ್ ಕತ್ತರಿಸಿ ಬಸವ ತತ್ವ ಶಿಕ್ಷಣ ಸಂಸ್ಥೆಯ ಕಟ್ಟಡ ದಾನಿ ಲಕ್ಷ್ಮೀಬಾಯಿ ಕಮಠಾಣೆ ಅವರ 76ನೇ ಜನ್ಮದಿನ ಆಚರಿಸಲಾಯಿತು. ವಿದ್ಯಾರ್ಥಿಗಳು, ಪಾಲಕರು, ಸಿಬ್ಬಂದಿ ಹಾಗೂ ಸಾರ್ವಜನಿಕರಿಗೆ ಸಿಹಿ, ಟೀ ಮಗ್, ದಿನದರ್ಶಿಕೆ ಹಾಗೂ ದಿನಚರಿ ವಿತರಿಸಲಾಯಿತು. ಮಾರ್ಕೇಟ್ ಠಾಣೆ ಸಿಪಿಐ ಮಲ್ಲಮ್ಮ ಚೌಬೆ, ಮಹಿಳಾ ಠಾಣೆ ಸಿಪಿಐ ಯಶವಂತ, ಬೀದರ್ ಗ್ರಾಮೀಣ ಠಾಣೆ ಸಿಪಿಐ ಶ್ರೀಕಾಂತ ಅಲ್ಲಾಪುರ, ಟೌನ್ ಪೊಲೀಸ್ ಠಾಣೆ ಸಿಪಿಐ ಬಿ.ಎನ್. ರಾಜಣ್ಣ, ಮುಖಂಡ ಶರಣಪ್ಪ ಬಲ್ಲೂರ್, ಬಸವ ತತ್ವ ಶಿಕ್ಷಣ ಸಂಸ್ಥೆಯ ಕಾರ್ಯದರ್ಶಿ ಡಾ.ದಿಲೀಪ್ ಕಮಠಾಣೆ, ನಿರ್ದೇಶಕಿ ವೈಶಾಲಿ ಕಮಠಾಣೆ, ದೀಕ್ಷಾ ಕಮಠಾಣೆ, ಪದವಿ ಕಾಲೇಜು ಪ್ರಾಚಾರ್ಯೆ ಶಿವಲೀಲಾ ಟೊಣ್ಣೆ, ಶಾಲಾ ಆಡಳಿತಾಧಿಕಾರಿ ಜಿನ್ಸ್ ಕೆ. ಥಾಮಸ್, ಮುಖ್ಯ ಶಿಕ್ಷಕಿ ರೋಶನಿ ಕೆ. ಥಾಮಸ್, ಶಿವರಾಜ ರೊಟ್ಟೆ, ವೈಜಿನಾಥ ಬಾಬಶೆಟ್ಟಿ, ಜಗದೀಶ ಹಿಬಾರೆ, ವೀರೇಂದ್ರ ಜಿಂದೆ, ರವಿ ದೇವಾ, ಪ್ರದೀಪ್ ಗಾಜಲ್, ಝರಣಪ್ಪ ಹೊಸಳ್ಳಿ, ರಾಜೇಶ್ವರಿ ಕುದರೆ, ಪರಶುರಾಮ ಸಿಂಧೆ ಇದ್ದರು. ಲಕ್ಷ್ಮೀಬಾಯಿ ಕಮಠಾಣೆ ಬಿ.ಎಡ್. ಕಾಲೇಜು ಪ್ರಾಚಾರ್ಯ ಧನರಾಜ ಪಾಟೀಲ ಸ್ವಾಗತಿಸಿದರು. ಉಪನ್ಯಾಸಕ ಮಹಮ್ಮದ್ ಯುನೂಸ್ ನಿರೂಪಿಸಿದರು. ಉಪ ಪ್ರಾಚಾರ್ಯ ನಾಗೇಶ ಬಿರಾದಾರ ವಂದಿಸಿದರು. | kannad |
"Mayfair Practice delivers industry leading outcomes by expert Private GPs and Aesthetic Practitioners in a family environment in the heart of London's Mayfair."
Our skin is under constant attack from the sun, environmental and lifestyle factors. The way in which our skin shows signs of ageing also depends on genetics, weight and daily facial movement.
We carefully assess your needs and design a treatment regime aimed to repair, renew and invigorate the skin.
Mesotherapy is essentially injecting vitamins, serums and natural extracts into the skin itself to stimulate cell activity. Depending on the ingredients used, Mesotherapy can rejuvenate skin and stimulate hair growth in the scalp. This medical speciality can also be used to treat cellulite, stretch-marks and scars. Here at the Mayfair Practice we use the MCT injector, which is a clever device that rapidly delivers nutrients comfortably into the skin. The MCT injector also incorporates CO2 carboxy-therapy which has the additional benefit of stimulating cell repair and improves microcirculation.
The sub-dermal vitamin injections rejuvenate the cells, making them more active, and thereby stimulating the production of collagen and elastin. You can begin anti-ageing treatments in your mid twenties to promote skin health.
A series of treatments is required depending on the condition being treated. For skin rejuvenation we cleanse the face, perform the mesotherapy, then complete the treatment with a soothing and hydrating Crystal Fiber Mask. To finish we apply a foundation with an SPF to ensure you leave the clinic looking photo ready.
The results do last, especially when combined with exercise and proper nutrition. However, we cannot stop the natural ageing that affects your appearance, therefore we recommend regular maintenance visits.
As we age, blood circulation in the dermis is reduced; this means less oxygen gets to the cells. As a result, the process of creating new cells, along with collagen production slows down over time. Injecting natural carbon dioxide gas under the skin tricks the body into believing it needs more oxygen. This kick starts your body’s own natural restorative processes, resulting in an increase in blood flow and new collagen and cell growth. Carboxy therapy has also been clinically shown to destroy fat cells, while making the dermis look renewed and firmer. Rioblush has received CE mark in Europe and FDA approval in the US.
During the treatment heated carbon-dioxide is administered via micro-injections to the treatment area, some individuals may experience mild discomfort or a slight burning, itching, or tingling sensation followed by a feeling of warmth in the treated area.
The treatment requires on average between 4 and 12 treatments depending on the condition and the area being treated. The treatment does not stop the ageing process, therefore maintenance treatments will extend the benefits.
We offer expert aesthetic treatments at a reasonable price and never compromise safety or quality of products.
*Consultation required to assess: scar, cellulite, stretch-marks or hair loss in terms of designing a treatment regime of combined treatments.
Within a Skin Consultation at the Mayfair Practice we can identify your needs, assess your skin and create a bespoke treatment plan. All of your questions will be answered and all treatment options fully explained.
New Patients, a £50 deposit required to secure your appointment, fully redeemable against any treatment or skincare product.
Please note 24 hours notice is required to change or cancel an appointment to avoid a cancellation charge.
We are discreetly located in Mayfair, with Bond Street and Marble Arch Tube stations only a few minutes walk. Nestled between Selfridges and Grosvenor Square, we are neighbours to Harley Street’s Private Medical District.
Please reach out by phone or email and we look forward to welcoming you to the clinic to assist in any medical or aesthetic need you may have.
To provide quick and easy access to expert medical services and aesthetic treatments when you need them.
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Perfectly aligned aesthetic beauty and well-being.
2019 © All Rights Reserved by The Mayfair Practice. | english |
کَاڑرموہ چھُ جۆم تہٕ کٔشیٖر ہُنٛد پلوۄم ضِلُک اَکھ گام۔
== حَوالہٕ == | kashmiri |
பெரியாரை ஞாபகப்படுத்த மட்டுமே முடியும்.. அவமானப்படுத்த முடியாது.. கமல் ஹாசன் ட்வீட் சென்னை: தமிழ்நாட்டில் சமீப காலமாகத் தந்தை பெரியாரின் சிலைகள் அவமதிக்கப்படும் நிகழ்வுகள் ஆங்காங்கே நடந்து கொண்டு வருகிறது. கும்மிடிப்பூண்டியில் இருந்த பெரியார் சிலை கடந்த மாதம் இறுதியில் மர்ம நபர்களால் தேசப்படுத்தப்பட்டது. அதேபோல சென்னை பெரியார் ஈ.வெ.ரா. நெடுஞ்சாலையில் உள்ள மணியம்மையார் சிலையும் அவமதிக்கப்பட்டது. இதுபோன்ற சம்பவங்கள் தொடர்ந்து வரும் நிலையில், பல்வேறு அரசியல் கட்சித் தலைவர்களும் இதற்கு கடும் கண்டனம் தெரிவித்து வருகின்றனர். இதற்கிடையே நேற்று அதிகாலை கோவை அருகே வெள்ளலூரில் உள்ள தந்தை பெரியார் சிலை அவமதிக்கப்பட்டுள்ளது. வெள்ளலூர் பகுதியில் உள்ள திராவிடர் கழகத்தின் படிப்பகம் முன்பாக பெரியார் சிலை உள்ளது. இந்த சிலைக்கு மர்ம நபர்கள் செருப்பு மாலை அணிவித்து, காவி நிற பொடியை வீசி சென்றுள்ளனர். கொரோனாவை கட்டுப்படுத்த ஞாயிறு ஊரடங்கு அமல்படுத்தப்பட்டுள்ள நிலையில், அதைப் பயன்படுத்தி சிலர் இந்த விஷம செயலில் ஈடுபட்டுள்ளனர். இந்தச் சம்பவம் அங்குப் பரபரப்பை ஏற்படுத்தியுள்ளது. பெரியார் சிலையை அவமதித்த நபர்கள் மீது நடவடிக்கை எடுக்க வேண்டும் என்பதை வலியுறுத்தி தி.க, திமுக நிர்வாகிகள் மற்றும் பொதுமக்கள் பெரியார் சிலை அருகே திரண்டு முழக்கம் எழுப்பினர். திக தலைவர் வீரமணி, அமமுக பொதுச்செயலாளர் டிடிவி தினகரன் உள்ளிட்ட பல்வேறு தலைவர்களும் இந்தச் சம்பவத்திற்குக் கண்டனம் தெரிவித்துள்ளார். இந்நிலையில், மக்கள் நீதி மய்ய தலைவர் கமலும் இந்தச் சம்பவத்திற்குக் கண்டம் தெரிவித்துள்ளார். இது தொடர்பாக அவர் தனது ட்விட்டர் பக்கத்தில், ஒவ்வொரு முறை பெரியார் சிலையை அவமதிக்கும்தோறும் பெரியார் இன்னமும் வீச்சுடனும்,வீரியத்துடனும் இன்றைய தலைமுறையிடம் சென்று சேருவார். பெரியாரை ஞாபகப்படுத்த மட்டுமே முடியும் அவமானப்படுத்த முடியாது என்று பதிவிட்டுள்ளார். source: oneindia.com | tamil |
Well hello there, foxy! This adorable mini card will certainly bring a smile to the loved one in your life. Add it to a lunch, coat pocket, or car window--the creative ways to partner with this charming little fox are endless, and will undoubtedly delight the recipient! | english |
پی ایس ایل نے پاکستان کرکٹ کو متعدد اسٹارز دیے اور کھلاڑیوں کو اضافی پیسے فراہم کیے ہیں سابق فاسٹ بولر فوٹو فائل لاہور پاکستان کرکٹ ٹیم کے سابق فاسٹ بولر شعیب اختر کا کہنا ہے کہپی ایس ایل ایک برانڈ بن چکا ہے اور یہ پاکستان کرکٹ کیلیے بہترین ہے شعیب اختر نے کہا کہ پی ایس ایل کی ٹیموں کی تعداد بھی بڑھ رہی ہے اور انھیں حیرت نہیں ہوگی کہ ائندہ انے والے سالوں میں پی ایس ایل میں 10 ٹیمیں مدمقابل نظر ائیں تاہم پی ایس ایل ایک برانڈ بن چکا ہے اور یہ پاکستان کرکٹ کیلیے بہترین ہے ایک انٹرویو کے دوران ان کا کہنا تھا کہ پی ایس ایل نے پاکستان کرکٹ کو متعدد اسٹارز دیے اور کھلاڑیوں کو اضافی پیسے فراہم کیے ہیں انھوں نے کہا کہ عمر اکمل اچھے فارم میں ہیں کامران اکمل بے خوف ہوکر کرکٹ کھیل رہے ہیں جبکہ شاہین افریدی ابھرتے ہوئے باصلاحیت فاسٹ بولر ہیںپی ایس ایل تھری میں عمر اکمل کامران اکمل اور شاہین افریدی اچھا پرفارم کریں گے | urdu |
## HISTORY:
woman status post fall with left acetabular fracture.
## FINDINGS:
There is a comminuted intra-articular fracture involving the
anterior, posterior, and roof of the left acetabulum extending slightly into
the superior pubic ramus. No fracture of the proximal femur is identified.
There is a hematoma along the medial soft tissues measuring up to 5 cm.
Additional pubic fractures are identified on the left adjacent to the pubic
symphysis and in the inferior pubic ramus. The SI and right hip joints are
unremarkable. No sacral fracture is identified. There are degenerative
changes of the lower lumbar spine at L4-5 with disc space narrowing and
prominent anterior osteophytes.
There is marked distention of the bladder. A small amount of pelvic free
fluid is noted. No free air is seen. Vascular calcifications are seen in the
aorta and iliac vessels.
## IMPRESSION:
Pelvic fractures as described above including comminuted intra-
articular fracture of the left acetabulum.
| medical |
விஜயதசமி: பந்தல்குடி ஸ்ரீசீரடி சாய்பாபா கோவிலில் 1,008 தீபங்கள் ஏற்றி சிறப்பு வழிபாடு அருப்புக்கோட்டை அருகே பந்தல்குடி ஸ்ரீசீரடி சாய்பாபா கோவிலில் விஜயதசமியை முன்னிட்டு வெள்ளிக்கிழமை 1008 தீபங்கள் வைத்து சிறப்பு வழிபாடும் மேலும் பாபாவின் 103ஆவது குருபூஜையை முன்னிட்டு சிறப்பு வழிபாடும் நடைபெற்றது. விருதுநகர் மாவட்டம், பந்தல்குடி அருகே செட்டிப்பட்டியில் அமைந்துள்ள அருள்மிகு ஸ்ரீசீரடி சாய்பாபா கோவிலில் விஜயதசமியை முன்னிட்டு கோவில் உள்வளாகத்தில் 1008 தீபங்கள் ஏற்றியும், அழகிய வண்ண, வண்ண மலர்களால் பாபாவின் திருஉருவச்சிலை, நந்தி தேவர், உற்சவர் ஆகியவற்றைச் சுற்றி அலங்கரித்தும் விஜயதசமி வழிபாடு நடைபெற்றது. இதையும் படிக்க பாலதோஷம் போக்கும் திருமாந்துறை ஆம்ரவனேசுவரர் திருக்கோயில் அதையடுத்து அருள்மிகு பாபாவின் 103ஆவது முக்தி தினத்தை முன்னிட்டு சிறப்பு தீப, தூப ஆரத்தி வழிபாடும் நடைபெற்றது. இதையடுத்து, உலக நன்மை வேண்டியும், கரோனாவிலிருந்து உலக மக்கள் விடுபட்டு நிலைபெற்ற நலம்பெறவும் சிறப்பு சங்கல்பத்துடன் அர்ச்சனை நடைபெற்றது. பின்னர் வழிபாட்டிற்கு வந்திருந்த பெண் பக்தர்களுக்கு மங்களப் பொருட்களான குங்குமம், மஞ்சள், வெற்றிலை, வளையல், இனிப்புகள், மாங்கல்யகயிறு, சட்டைத்துணி ஆகிய பொருள்கள் தானமாக வழங்கப்பட்டன. அதைத்தொடர்ந்து அன்னதானம் நடைபெற்றது. இந்நிகழ்ச்சிகள் அனைத்தையும் கோவில் நிர்வாகியும், அன்பு ரியல் எஸ்டேட் நிறுவனரும் மனிதத்தேனீ என மக்களால் அழைக்கப்படுபவருமான வி.சுந்தரமூர்த்தி செய்திருந்தார். | tamil |
கண்மாய்க்குள் பாய்ந்த கார் தத்தளித்த குடும்பம் உடனே இறங்கி காப்பாற்றிய சிவகங்கை இளைஞர்! சிவகங்கை மாவட்டம் திருப்புவனம் அருகே கட்டுப்பாட்டை இழந்து கண்மாய்க்குள் பாய்ந்த காரில் இருந்த 5 பேரை இளைஞர் ஒருவர் காப்பாற்றி கரை சேர்த்த சம்பவம், தற்போது தெரியவந்து அனைவரும் அவரை பாராட்டி வருகிறார்கள்.கண்மாய்க்குள் கார்சிவகங்கை மாவட்டம் திருப்புவனம் வடகரையைச் சேர்ந்த முத்துகிருஷ்ணன் மதுரையிலுள்ள தனியார் நிறுவனத்தில் பணியாற்றி வருகிறார். கடந்த 7ம் தேதி மாலை நிறுவனத்தின் வேலைக்காக காரில் ராமநாதபுரம் சென்று கொண்டிருந்தவர், திருப்புவனம் தாண்டி சாலையை ஒட்டியுள்ள மாரநாடு கண்மாய்க்குள் ஒரு கார் மூழ்கிக்கொண்டிருப்பதை பார்த்து அதிர்ச்சியானார். உடனே காரை நிறுத்தி அருகில் சென்று பார்த்தார்.காருக்குள் இருந்து, காப்பாற்றுங்கள்... காப்பாற்றுங்கள்! என்று கதறல் சத்தம் கேட்கவே, எதைப்பற்றியும் யோசிக்காமல், கண்மாய்க்குள் இறங்கி காரிலிருந்த இரண்டு குழந்தைகள், ஒரு பெரியவருடன் இருந்த தம்பதி என 5 பேரை மீட்டு கரைக்கு கொண்டு வந்தார்.கண்மாய்க்குள் மூழ்கிய கார் இனி உயிர் பிழைக்க மாட்டோம்னு நினைச்சேன்! ஆனைவாரி நீர்வீழ்ச்சியின் திக்... திக்... நிமிடங்கள்!அதன் பின்பு அவர்களை வேறு வாகனத்தில் மானாமதுரைக்கு அனுப்பி வைத்தார். இந்த சம்பவத்தை அவருடன் சென்றவர் போட்டோ எடுத்து சமூக ஊடகத்தில் பகிர்ந்த பின்புதான் எல்லோரும் இதை அறிந்து முத்துகிருஷ்ணனை பாராட்டி வருகிறார்கள்.நாமும் வாழ்த்தி விட்டு, முத்து கிருஷ்ணனிடம் பேசினோம். அலுவலக வேலையா அன்னைக்கு ராம்நாட்டுக்கு கார்ல போய்க்கிட்டிருக்கும்போது தூரத்துல ஒரு வண்டி டிவைடரைத் தாண்டி எதிர்ல வர்ற மாதிரி தெரிஞ்சது. அப்புறம் கொஞ்ச நேரத்துல அந்த கார் கண்மய்க்குள் பாஞ்சிருச்சு. பிஸியான அந்த ரோட்டுல இதை யாரும் கவனிக்கல. பதறிப்போய் உடனே வண்டிய நிறுத்திட்டேன். அவங்க காப்பாத்தச் சொல்லி சத்தம் போட்டாங்க. நல்ல வேளை, ரோட்டுல இருந்து அந்த கண்மாய் பக்கம். கரைக்கும் காருக்கும் கொஞ்ச தூரம்தான் டிஸ்டன்ஸ் இருந்ததால உடனே நான் போய் ஒவ்வொருத்தரா கீழே இறக்கி கரைக்கு கொண்டு வந்துட்டேன். பாவம் அவங்க ரொம்ப பதற்றமா இருந்தாங்க.முத்துகிருஷ்ணன்காருல வந்தது ரயில்வே ஸ்டாஃபோட குடும்பம். மானாமதுரையிலிருந்து மதுரைக்கு வரும்போது இப்படி ஆயிடுச்சு. உடனே அவங்களை பஸ்ஸுல ஏத்தி மானாமதுரைக்கு அனுப்பிட்டேன். அவங்க யார் என்னன்கிற விவரம் ஏதும் கேட்கல. என் போன் நம்பரை வாங்கிட்டு போனாங்க. அவங்க குழந்தைங்க போன் பண்ணி நன்றி சொன்னாங்க. மின்சாரம் தாக்கி உயிருக்குப் போராடிய இளைஞர் முதலுதவி செய்து காப்பாற்றிய காவலர்!பரபரப்பா இருக்குற ரோடுங்கிறதால காருல போறவங்க யாரும் சைடுல சரியா கவனிக்க மாட்டாங்க. நான் அந்த பகுதியை சேர்ந்தவங்கிறதால எல்லா பக்கமும் உன்னிப்பா கவனிப்பேன். நல்லவேளை அவங்க காரு கண்மாயில மூழ்கினது என் கண்ணுல பட்டுச்சு. அவங்க குடும்பம் இந்த சம்பவத்தை மறந்துட்டு நல்லா இருக்கணும் என்றார்.விபத்தைக் கண்டதும் தயங்காமல் கண்மாயில் இறங்கி குடும்பத்தினரைக் காப்பாற்றிய முத்துகிருஷ்ணனின் செயலை கேள்விப்பட்டு அனைவரும் பாராட்டுகிறார்கள். | tamil |
అసమానతలపై పాశుపతాస్త్రం జాషువా ఖమ్మం సాంస్కృతికం, న్యూస్టుడే: సమాజంలోని అసమానతలపై పాశుపతాస్త్రంలా తనదైన కవితా విలక్షణతో సంస్కరించి తెలుగు సాహిత్యాన్ని సుసంపన్నం చేసిన నవయుగ కవి గుర్రం జాషువా అని ప్రముఖ సినీ హాస్యనటుడు డా.బ్రహ్మానందం అన్నారు. జాషువా సాహిత్య వేదిక అధ్యక్షుడు మువ్వా శ్రీనివాసరావు అధ్యక్షతన శనివారం ఆన్లైన్ వేదికగా మహాకవి గుర్రం జాషువా వర్ధంతి సభను నిర్వహించారు. ఈ కార్యక్రమానికి ముఖ్యఅతిథిగా బ్రహ్మానందం హాజరై మాట్లాడారు. ప్రపంచానికి లభించిన అపురూప వరం జాషువా అని కొనియాడారు. తనదైన హాస్య చతురతతో చేసిన వ్యాఖ్యానం ఆకట్టుకుంది. అనంతరం ప్రముఖ సామాజిక విశ్లేషకుడు ఆచార్య మాడభూషి శ్రీధర్ మాట్లాడుతూ.. జాషువా అద్భుత సంఘసంస్కర్త అని, తన కవితా వైదుష్యంతో సమాజ మార్పునకు కారణమయ్యారని తెలిపారు. తన జీవిత గమనానికి స్ఫూర్తిగా పేర్కొన్నారు. కార్యక్రమంలో కవులు బండ్ల మాధవరావు, అట్లూరి వెంకటరమణ, పగిడిపల్లి వెంకటేశ్వర్లు, అనిల్డ్యానీ, రచయితలు, సాహితీవేత్తలు పాల్గొన్నారు. | telegu |
कुसुम विहार में आईजी मानवाधिकार के ससुर के घर चोरी का प्रयास धनबाद मुख्य संवाददातासरायढेला थाना क्षेत्र के कोयला नगर कुसुम विहार बी10 में मंगलवार की रात चोर ने चोरी का प्रयास किया। यह घर झारखंड मानवाधिकार आईजी अखिलेश झा के ससुर डॉ दिनेश मिश्रा का है। वे पत्नी का इलाज कराने हैदराबाद गए हैं। घर की देखरेख के लिए उन्होंने उदय धोबी नामक गार्ड को रखा था। चार दिन पहले गार्ड बिना किसी को सूचना दिए अपने गांव मधुबनी बिहार चला गया।मामले की शिकायत रांची ध्रुवा के सिपाही महेंद्र भंडारी ने सरायढेला थाना में की है। पुलिस को दिए आवेदन में बताया कि चोर ने घर के मुख्य दरवाजे पर लगे ग्रिल का ताला काट दिया था। अंदर कमरे में घुसने के लिए चोर ने लकड़ी के इंटरलॉक को तोड़ने का प्रयास किया, लेकिन सफलता नहीं मिली। पड़ोसियों ने ग्रिल गेट टूटा हुआ देखा तो मामले की जानकारी पुलिस के साथसाथ मकान मालिक को दी। डॉ दिनेश ने इसकी जानकारी अपने दामाद अखिलेश झा को दी। आईजी को खबर मिलते ही धनबाद पुलिस रेस हो गई। सिटी एसपी आर रामकुमार और एएसपी मनोज स्वर्गियारी के साथ सरायढेला थाना प्रभारी किशोरी तिर्की दलबल के साथ मौके पर पहुंचे। प्राथमिकी दर्ज कर पुलिस छानबीन में जुट गई है।रात 12.39 में आए चोर, सुबह 3.20 बजे भागेडॉ दिनेश के घर पर सीसीटीवी कैमरा नहीं लगा हुआ है। मौके पर पहुंची पुलिस ने आसपास के घरों का सीसीटीवी कैमरे का फुटेज खंगाला। पास के एक घर के कैमरे में रोशनी से बने चोर की छाया कैद हुई है। फुटेज में दिख रहा है कि चोर रात 12.39 बजे डॉ दिनेश के आवासीय परिसर में घुसा। सुबह 3.20 बजे उसके जाने की छाया भी सीसीटीवी कैमरे में कैद हुई है। फुटेज में दिख रहा है कि एक गाड़ी आने के बाद चोर ओट में छिप रहा है। For Hindustan : हिन्दुस्तान ईसमाचार पत्र के लिए क्लिक करें epaper.livehindustan.com | hindi |
// Copyright 2012 the V8 project authors. All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above
// copyright notice, this list of conditions and the following
// disclaimer in the documentation and/or other materials provided
// with the distribution.
// * Neither the name of Google Inc. nor the names of its
// contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
#include "src/v8.h"
#include "test/cctest/cctest.h"
#include "src/arm/assembler-arm-inl.h"
#include "src/arm/simulator-arm.h"
#include "src/disassembler.h"
#include "src/factory.h"
using namespace v8::internal;
// Define these function prototypes to match JSEntryFunction in execution.cc.
typedef Object* (*F1)(int x, int p1, int p2, int p3, int p4);
typedef Object* (*F2)(int x, int y, int p2, int p3, int p4);
typedef Object* (*F3)(void* p0, int p1, int p2, int p3, int p4);
typedef Object* (*F4)(void* p0, void* p1, int p2, int p3, int p4);
#define __ assm.
TEST(0) {
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
Assembler assm(isolate, NULL, 0);
__ add(r0, r0, Operand(r1));
__ mov(pc, Operand(lr));
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F2 f = FUNCTION_CAST<F2>(code->entry());
int res = reinterpret_cast<int>(CALL_GENERATED_CODE(f, 3, 4, 0, 0, 0));
::printf("f() = %d\n", res);
CHECK_EQ(7, res);
}
TEST(1) {
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
Assembler assm(isolate, NULL, 0);
Label L, C;
__ mov(r1, Operand(r0));
__ mov(r0, Operand::Zero());
__ b(&C);
__ bind(&L);
__ add(r0, r0, Operand(r1));
__ sub(r1, r1, Operand(1));
__ bind(&C);
__ teq(r1, Operand::Zero());
__ b(ne, &L);
__ mov(pc, Operand(lr));
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F1 f = FUNCTION_CAST<F1>(code->entry());
int res = reinterpret_cast<int>(CALL_GENERATED_CODE(f, 100, 0, 0, 0, 0));
::printf("f() = %d\n", res);
CHECK_EQ(5050, res);
}
TEST(2) {
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
Assembler assm(isolate, NULL, 0);
Label L, C;
__ mov(r1, Operand(r0));
__ mov(r0, Operand(1));
__ b(&C);
__ bind(&L);
__ mul(r0, r1, r0);
__ sub(r1, r1, Operand(1));
__ bind(&C);
__ teq(r1, Operand::Zero());
__ b(ne, &L);
__ mov(pc, Operand(lr));
// some relocated stuff here, not executed
__ RecordComment("dead code, just testing relocations");
__ mov(r0, Operand(isolate->factory()->true_value()));
__ RecordComment("dead code, just testing immediate operands");
__ mov(r0, Operand(-1));
__ mov(r0, Operand(0xFF000000));
__ mov(r0, Operand(0xF0F0F0F0));
__ mov(r0, Operand(0xFFF0FFFF));
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F1 f = FUNCTION_CAST<F1>(code->entry());
int res = reinterpret_cast<int>(CALL_GENERATED_CODE(f, 10, 0, 0, 0, 0));
::printf("f() = %d\n", res);
CHECK_EQ(3628800, res);
}
TEST(3) {
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
int i;
char c;
int16_t s;
} T;
T t;
Assembler assm(isolate, NULL, 0);
Label L, C;
__ mov(ip, Operand(sp));
__ stm(db_w, sp, r4.bit() | fp.bit() | lr.bit());
__ sub(fp, ip, Operand(4));
__ mov(r4, Operand(r0));
__ ldr(r0, MemOperand(r4, OFFSET_OF(T, i)));
__ mov(r2, Operand(r0, ASR, 1));
__ str(r2, MemOperand(r4, OFFSET_OF(T, i)));
__ ldrsb(r2, MemOperand(r4, OFFSET_OF(T, c)));
__ add(r0, r2, Operand(r0));
__ mov(r2, Operand(r2, LSL, 2));
__ strb(r2, MemOperand(r4, OFFSET_OF(T, c)));
__ ldrsh(r2, MemOperand(r4, OFFSET_OF(T, s)));
__ add(r0, r2, Operand(r0));
__ mov(r2, Operand(r2, ASR, 3));
__ strh(r2, MemOperand(r4, OFFSET_OF(T, s)));
__ ldm(ia_w, sp, r4.bit() | fp.bit() | pc.bit());
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F3 f = FUNCTION_CAST<F3>(code->entry());
t.i = 100000;
t.c = 10;
t.s = 1000;
int res = reinterpret_cast<int>(CALL_GENERATED_CODE(f, &t, 0, 0, 0, 0));
::printf("f() = %d\n", res);
CHECK_EQ(101010, res);
CHECK_EQ(100000/2, t.i);
CHECK_EQ(10*4, t.c);
CHECK_EQ(1000/8, t.s);
}
TEST(4) {
// Test the VFP floating point instructions.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
double a;
double b;
double c;
double d;
double e;
double f;
double g;
double h;
int i;
double j;
double m;
double n;
float x;
float y;
} T;
T t;
// Create a function that accepts &t, and loads, manipulates, and stores
// the doubles and floats.
Assembler assm(isolate, NULL, 0);
Label L, C;
if (CpuFeatures::IsSupported(VFP3)) {
CpuFeatureScope scope(&assm, VFP3);
__ mov(ip, Operand(sp));
__ stm(db_w, sp, r4.bit() | fp.bit() | lr.bit());
__ sub(fp, ip, Operand(4));
__ mov(r4, Operand(r0));
__ vldr(d6, r4, OFFSET_OF(T, a));
__ vldr(d7, r4, OFFSET_OF(T, b));
__ vadd(d5, d6, d7);
__ vstr(d5, r4, OFFSET_OF(T, c));
__ vmla(d5, d6, d7);
__ vmls(d5, d5, d6);
__ vmov(r2, r3, d5);
__ vmov(d4, r2, r3);
__ vstr(d4, r4, OFFSET_OF(T, b));
// Load t.x and t.y, switch values, and store back to the struct.
__ vldr(s0, r4, OFFSET_OF(T, x));
__ vldr(s31, r4, OFFSET_OF(T, y));
__ vmov(s16, s0);
__ vmov(s0, s31);
__ vmov(s31, s16);
__ vstr(s0, r4, OFFSET_OF(T, x));
__ vstr(s31, r4, OFFSET_OF(T, y));
// Move a literal into a register that can be encoded in the instruction.
__ vmov(d4, 1.0);
__ vstr(d4, r4, OFFSET_OF(T, e));
// Move a literal into a register that requires 64 bits to encode.
// 0x3ff0000010000000 = 1.000000059604644775390625
__ vmov(d4, 1.000000059604644775390625);
__ vstr(d4, r4, OFFSET_OF(T, d));
// Convert from floating point to integer.
__ vmov(d4, 2.0);
__ vcvt_s32_f64(s31, d4);
__ vstr(s31, r4, OFFSET_OF(T, i));
// Convert from integer to floating point.
__ mov(lr, Operand(42));
__ vmov(s31, lr);
__ vcvt_f64_s32(d4, s31);
__ vstr(d4, r4, OFFSET_OF(T, f));
// Convert from fixed point to floating point.
__ mov(lr, Operand(2468));
__ vmov(s8, lr);
__ vcvt_f64_s32(d4, 2);
__ vstr(d4, r4, OFFSET_OF(T, j));
// Test vabs.
__ vldr(d1, r4, OFFSET_OF(T, g));
__ vabs(d0, d1);
__ vstr(d0, r4, OFFSET_OF(T, g));
__ vldr(d2, r4, OFFSET_OF(T, h));
__ vabs(d0, d2);
__ vstr(d0, r4, OFFSET_OF(T, h));
// Test vneg.
__ vldr(d1, r4, OFFSET_OF(T, m));
__ vneg(d0, d1);
__ vstr(d0, r4, OFFSET_OF(T, m));
__ vldr(d1, r4, OFFSET_OF(T, n));
__ vneg(d0, d1);
__ vstr(d0, r4, OFFSET_OF(T, n));
__ ldm(ia_w, sp, r4.bit() | fp.bit() | pc.bit());
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F3 f = FUNCTION_CAST<F3>(code->entry());
t.a = 1.5;
t.b = 2.75;
t.c = 17.17;
t.d = 0.0;
t.e = 0.0;
t.f = 0.0;
t.g = -2718.2818;
t.h = 31415926.5;
t.i = 0;
t.j = 0;
t.m = -2718.2818;
t.n = 123.456;
t.x = 4.5;
t.y = 9.0;
Object* dummy = CALL_GENERATED_CODE(f, &t, 0, 0, 0, 0);
USE(dummy);
CHECK_EQ(4.5, t.y);
CHECK_EQ(9.0, t.x);
CHECK_EQ(-123.456, t.n);
CHECK_EQ(2718.2818, t.m);
CHECK_EQ(2, t.i);
CHECK_EQ(2718.2818, t.g);
CHECK_EQ(31415926.5, t.h);
CHECK_EQ(617.0, t.j);
CHECK_EQ(42.0, t.f);
CHECK_EQ(1.0, t.e);
CHECK_EQ(1.000000059604644775390625, t.d);
CHECK_EQ(4.25, t.c);
CHECK_EQ(-4.1875, t.b);
CHECK_EQ(1.5, t.a);
}
}
TEST(5) {
// Test the ARMv7 bitfield instructions.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
Assembler assm(isolate, NULL, 0);
if (CpuFeatures::IsSupported(ARMv7)) {
CpuFeatureScope scope(&assm, ARMv7);
// On entry, r0 = 0xAAAAAAAA = 0b10..10101010.
__ ubfx(r0, r0, 1, 12); // 0b00..010101010101 = 0x555
__ sbfx(r0, r0, 0, 5); // 0b11..111111110101 = -11
__ bfc(r0, 1, 3); // 0b11..111111110001 = -15
__ mov(r1, Operand(7));
__ bfi(r0, r1, 3, 3); // 0b11..111111111001 = -7
__ mov(pc, Operand(lr));
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F1 f = FUNCTION_CAST<F1>(code->entry());
int res = reinterpret_cast<int>(
CALL_GENERATED_CODE(f, 0xAAAAAAAA, 0, 0, 0, 0));
::printf("f() = %d\n", res);
CHECK_EQ(-7, res);
}
}
TEST(6) {
// Test saturating instructions.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
Assembler assm(isolate, NULL, 0);
if (CpuFeatures::IsSupported(ARMv7)) {
CpuFeatureScope scope(&assm, ARMv7);
__ usat(r1, 8, Operand(r0)); // Sat 0xFFFF to 0-255 = 0xFF.
__ usat(r2, 12, Operand(r0, ASR, 9)); // Sat (0xFFFF>>9) to 0-4095 = 0x7F.
__ usat(r3, 1, Operand(r0, LSL, 16)); // Sat (0xFFFF<<16) to 0-1 = 0x0.
__ add(r0, r1, Operand(r2));
__ add(r0, r0, Operand(r3));
__ mov(pc, Operand(lr));
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F1 f = FUNCTION_CAST<F1>(code->entry());
int res = reinterpret_cast<int>(
CALL_GENERATED_CODE(f, 0xFFFF, 0, 0, 0, 0));
::printf("f() = %d\n", res);
CHECK_EQ(382, res);
}
}
enum VCVTTypes {
s32_f64,
u32_f64
};
static void TestRoundingMode(VCVTTypes types,
VFPRoundingMode mode,
double value,
int expected,
bool expected_exception = false) {
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
Assembler assm(isolate, NULL, 0);
if (CpuFeatures::IsSupported(VFP3)) {
CpuFeatureScope scope(&assm, VFP3);
Label wrong_exception;
__ vmrs(r1);
// Set custom FPSCR.
__ bic(r2, r1, Operand(kVFPRoundingModeMask | kVFPExceptionMask));
__ orr(r2, r2, Operand(mode));
__ vmsr(r2);
// Load value, convert, and move back result to r0 if everything went well.
__ vmov(d1, value);
switch (types) {
case s32_f64:
__ vcvt_s32_f64(s0, d1, kFPSCRRounding);
break;
case u32_f64:
__ vcvt_u32_f64(s0, d1, kFPSCRRounding);
break;
default:
UNREACHABLE();
break;
}
// Check for vfp exceptions
__ vmrs(r2);
__ tst(r2, Operand(kVFPExceptionMask));
// Check that we behaved as expected.
__ b(&wrong_exception,
expected_exception ? eq : ne);
// There was no exception. Retrieve the result and return.
__ vmov(r0, s0);
__ mov(pc, Operand(lr));
// The exception behaviour is not what we expected.
// Load a special value and return.
__ bind(&wrong_exception);
__ mov(r0, Operand(11223344));
__ mov(pc, Operand(lr));
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F1 f = FUNCTION_CAST<F1>(code->entry());
int res = reinterpret_cast<int>(
CALL_GENERATED_CODE(f, 0, 0, 0, 0, 0));
::printf("res = %d\n", res);
CHECK_EQ(expected, res);
}
}
TEST(7) {
CcTest::InitializeVM();
// Test vfp rounding modes.
// s32_f64 (double to integer).
TestRoundingMode(s32_f64, RN, 0, 0);
TestRoundingMode(s32_f64, RN, 0.5, 0);
TestRoundingMode(s32_f64, RN, -0.5, 0);
TestRoundingMode(s32_f64, RN, 1.5, 2);
TestRoundingMode(s32_f64, RN, -1.5, -2);
TestRoundingMode(s32_f64, RN, 123.7, 124);
TestRoundingMode(s32_f64, RN, -123.7, -124);
TestRoundingMode(s32_f64, RN, 123456.2, 123456);
TestRoundingMode(s32_f64, RN, -123456.2, -123456);
TestRoundingMode(s32_f64, RN, static_cast<double>(kMaxInt), kMaxInt);
TestRoundingMode(s32_f64, RN, (kMaxInt + 0.49), kMaxInt);
TestRoundingMode(s32_f64, RN, (kMaxInt + 1.0), kMaxInt, true);
TestRoundingMode(s32_f64, RN, (kMaxInt + 0.5), kMaxInt, true);
TestRoundingMode(s32_f64, RN, static_cast<double>(kMinInt), kMinInt);
TestRoundingMode(s32_f64, RN, (kMinInt - 0.5), kMinInt);
TestRoundingMode(s32_f64, RN, (kMinInt - 1.0), kMinInt, true);
TestRoundingMode(s32_f64, RN, (kMinInt - 0.51), kMinInt, true);
TestRoundingMode(s32_f64, RM, 0, 0);
TestRoundingMode(s32_f64, RM, 0.5, 0);
TestRoundingMode(s32_f64, RM, -0.5, -1);
TestRoundingMode(s32_f64, RM, 123.7, 123);
TestRoundingMode(s32_f64, RM, -123.7, -124);
TestRoundingMode(s32_f64, RM, 123456.2, 123456);
TestRoundingMode(s32_f64, RM, -123456.2, -123457);
TestRoundingMode(s32_f64, RM, static_cast<double>(kMaxInt), kMaxInt);
TestRoundingMode(s32_f64, RM, (kMaxInt + 0.5), kMaxInt);
TestRoundingMode(s32_f64, RM, (kMaxInt + 1.0), kMaxInt, true);
TestRoundingMode(s32_f64, RM, static_cast<double>(kMinInt), kMinInt);
TestRoundingMode(s32_f64, RM, (kMinInt - 0.5), kMinInt, true);
TestRoundingMode(s32_f64, RM, (kMinInt + 0.5), kMinInt);
TestRoundingMode(s32_f64, RZ, 0, 0);
TestRoundingMode(s32_f64, RZ, 0.5, 0);
TestRoundingMode(s32_f64, RZ, -0.5, 0);
TestRoundingMode(s32_f64, RZ, 123.7, 123);
TestRoundingMode(s32_f64, RZ, -123.7, -123);
TestRoundingMode(s32_f64, RZ, 123456.2, 123456);
TestRoundingMode(s32_f64, RZ, -123456.2, -123456);
TestRoundingMode(s32_f64, RZ, static_cast<double>(kMaxInt), kMaxInt);
TestRoundingMode(s32_f64, RZ, (kMaxInt + 0.5), kMaxInt);
TestRoundingMode(s32_f64, RZ, (kMaxInt + 1.0), kMaxInt, true);
TestRoundingMode(s32_f64, RZ, static_cast<double>(kMinInt), kMinInt);
TestRoundingMode(s32_f64, RZ, (kMinInt - 0.5), kMinInt);
TestRoundingMode(s32_f64, RZ, (kMinInt - 1.0), kMinInt, true);
// u32_f64 (double to integer).
// Negative values.
TestRoundingMode(u32_f64, RN, -0.5, 0);
TestRoundingMode(u32_f64, RN, -123456.7, 0, true);
TestRoundingMode(u32_f64, RN, static_cast<double>(kMinInt), 0, true);
TestRoundingMode(u32_f64, RN, kMinInt - 1.0, 0, true);
TestRoundingMode(u32_f64, RM, -0.5, 0, true);
TestRoundingMode(u32_f64, RM, -123456.7, 0, true);
TestRoundingMode(u32_f64, RM, static_cast<double>(kMinInt), 0, true);
TestRoundingMode(u32_f64, RM, kMinInt - 1.0, 0, true);
TestRoundingMode(u32_f64, RZ, -0.5, 0);
TestRoundingMode(u32_f64, RZ, -123456.7, 0, true);
TestRoundingMode(u32_f64, RZ, static_cast<double>(kMinInt), 0, true);
TestRoundingMode(u32_f64, RZ, kMinInt - 1.0, 0, true);
// Positive values.
// kMaxInt is the maximum *signed* integer: 0x7fffffff.
static const uint32_t kMaxUInt = 0xffffffffu;
TestRoundingMode(u32_f64, RZ, 0, 0);
TestRoundingMode(u32_f64, RZ, 0.5, 0);
TestRoundingMode(u32_f64, RZ, 123.7, 123);
TestRoundingMode(u32_f64, RZ, 123456.2, 123456);
TestRoundingMode(u32_f64, RZ, static_cast<double>(kMaxInt), kMaxInt);
TestRoundingMode(u32_f64, RZ, (kMaxInt + 0.5), kMaxInt);
TestRoundingMode(u32_f64, RZ, (kMaxInt + 1.0),
static_cast<uint32_t>(kMaxInt) + 1);
TestRoundingMode(u32_f64, RZ, (kMaxUInt + 0.5), kMaxUInt);
TestRoundingMode(u32_f64, RZ, (kMaxUInt + 1.0), kMaxUInt, true);
TestRoundingMode(u32_f64, RM, 0, 0);
TestRoundingMode(u32_f64, RM, 0.5, 0);
TestRoundingMode(u32_f64, RM, 123.7, 123);
TestRoundingMode(u32_f64, RM, 123456.2, 123456);
TestRoundingMode(u32_f64, RM, static_cast<double>(kMaxInt), kMaxInt);
TestRoundingMode(u32_f64, RM, (kMaxInt + 0.5), kMaxInt);
TestRoundingMode(u32_f64, RM, (kMaxInt + 1.0),
static_cast<uint32_t>(kMaxInt) + 1);
TestRoundingMode(u32_f64, RM, (kMaxUInt + 0.5), kMaxUInt);
TestRoundingMode(u32_f64, RM, (kMaxUInt + 1.0), kMaxUInt, true);
TestRoundingMode(u32_f64, RN, 0, 0);
TestRoundingMode(u32_f64, RN, 0.5, 0);
TestRoundingMode(u32_f64, RN, 1.5, 2);
TestRoundingMode(u32_f64, RN, 123.7, 124);
TestRoundingMode(u32_f64, RN, 123456.2, 123456);
TestRoundingMode(u32_f64, RN, static_cast<double>(kMaxInt), kMaxInt);
TestRoundingMode(u32_f64, RN, (kMaxInt + 0.49), kMaxInt);
TestRoundingMode(u32_f64, RN, (kMaxInt + 0.5),
static_cast<uint32_t>(kMaxInt) + 1);
TestRoundingMode(u32_f64, RN, (kMaxUInt + 0.49), kMaxUInt);
TestRoundingMode(u32_f64, RN, (kMaxUInt + 0.5), kMaxUInt, true);
TestRoundingMode(u32_f64, RN, (kMaxUInt + 1.0), kMaxUInt, true);
}
TEST(8) {
// Test VFP multi load/store with ia_w.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
double a;
double b;
double c;
double d;
double e;
double f;
double g;
double h;
} D;
D d;
typedef struct {
float a;
float b;
float c;
float d;
float e;
float f;
float g;
float h;
} F;
F f;
// Create a function that uses vldm/vstm to move some double and
// single precision values around in memory.
Assembler assm(isolate, NULL, 0);
__ mov(ip, Operand(sp));
__ stm(db_w, sp, r4.bit() | fp.bit() | lr.bit());
__ sub(fp, ip, Operand(4));
__ add(r4, r0, Operand(OFFSET_OF(D, a)));
__ vldm(ia_w, r4, d0, d3);
__ vldm(ia_w, r4, d4, d7);
__ add(r4, r0, Operand(OFFSET_OF(D, a)));
__ vstm(ia_w, r4, d6, d7);
__ vstm(ia_w, r4, d0, d5);
__ add(r4, r1, Operand(OFFSET_OF(F, a)));
__ vldm(ia_w, r4, s0, s3);
__ vldm(ia_w, r4, s4, s7);
__ add(r4, r1, Operand(OFFSET_OF(F, a)));
__ vstm(ia_w, r4, s6, s7);
__ vstm(ia_w, r4, s0, s5);
__ ldm(ia_w, sp, r4.bit() | fp.bit() | pc.bit());
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F4 fn = FUNCTION_CAST<F4>(code->entry());
d.a = 1.1;
d.b = 2.2;
d.c = 3.3;
d.d = 4.4;
d.e = 5.5;
d.f = 6.6;
d.g = 7.7;
d.h = 8.8;
f.a = 1.0;
f.b = 2.0;
f.c = 3.0;
f.d = 4.0;
f.e = 5.0;
f.f = 6.0;
f.g = 7.0;
f.h = 8.0;
Object* dummy = CALL_GENERATED_CODE(fn, &d, &f, 0, 0, 0);
USE(dummy);
CHECK_EQ(7.7, d.a);
CHECK_EQ(8.8, d.b);
CHECK_EQ(1.1, d.c);
CHECK_EQ(2.2, d.d);
CHECK_EQ(3.3, d.e);
CHECK_EQ(4.4, d.f);
CHECK_EQ(5.5, d.g);
CHECK_EQ(6.6, d.h);
CHECK_EQ(7.0, f.a);
CHECK_EQ(8.0, f.b);
CHECK_EQ(1.0, f.c);
CHECK_EQ(2.0, f.d);
CHECK_EQ(3.0, f.e);
CHECK_EQ(4.0, f.f);
CHECK_EQ(5.0, f.g);
CHECK_EQ(6.0, f.h);
}
TEST(9) {
// Test VFP multi load/store with ia.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
double a;
double b;
double c;
double d;
double e;
double f;
double g;
double h;
} D;
D d;
typedef struct {
float a;
float b;
float c;
float d;
float e;
float f;
float g;
float h;
} F;
F f;
// Create a function that uses vldm/vstm to move some double and
// single precision values around in memory.
Assembler assm(isolate, NULL, 0);
__ mov(ip, Operand(sp));
__ stm(db_w, sp, r4.bit() | fp.bit() | lr.bit());
__ sub(fp, ip, Operand(4));
__ add(r4, r0, Operand(OFFSET_OF(D, a)));
__ vldm(ia, r4, d0, d3);
__ add(r4, r4, Operand(4 * 8));
__ vldm(ia, r4, d4, d7);
__ add(r4, r0, Operand(OFFSET_OF(D, a)));
__ vstm(ia, r4, d6, d7);
__ add(r4, r4, Operand(2 * 8));
__ vstm(ia, r4, d0, d5);
__ add(r4, r1, Operand(OFFSET_OF(F, a)));
__ vldm(ia, r4, s0, s3);
__ add(r4, r4, Operand(4 * 4));
__ vldm(ia, r4, s4, s7);
__ add(r4, r1, Operand(OFFSET_OF(F, a)));
__ vstm(ia, r4, s6, s7);
__ add(r4, r4, Operand(2 * 4));
__ vstm(ia, r4, s0, s5);
__ ldm(ia_w, sp, r4.bit() | fp.bit() | pc.bit());
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F4 fn = FUNCTION_CAST<F4>(code->entry());
d.a = 1.1;
d.b = 2.2;
d.c = 3.3;
d.d = 4.4;
d.e = 5.5;
d.f = 6.6;
d.g = 7.7;
d.h = 8.8;
f.a = 1.0;
f.b = 2.0;
f.c = 3.0;
f.d = 4.0;
f.e = 5.0;
f.f = 6.0;
f.g = 7.0;
f.h = 8.0;
Object* dummy = CALL_GENERATED_CODE(fn, &d, &f, 0, 0, 0);
USE(dummy);
CHECK_EQ(7.7, d.a);
CHECK_EQ(8.8, d.b);
CHECK_EQ(1.1, d.c);
CHECK_EQ(2.2, d.d);
CHECK_EQ(3.3, d.e);
CHECK_EQ(4.4, d.f);
CHECK_EQ(5.5, d.g);
CHECK_EQ(6.6, d.h);
CHECK_EQ(7.0, f.a);
CHECK_EQ(8.0, f.b);
CHECK_EQ(1.0, f.c);
CHECK_EQ(2.0, f.d);
CHECK_EQ(3.0, f.e);
CHECK_EQ(4.0, f.f);
CHECK_EQ(5.0, f.g);
CHECK_EQ(6.0, f.h);
}
TEST(10) {
// Test VFP multi load/store with db_w.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
double a;
double b;
double c;
double d;
double e;
double f;
double g;
double h;
} D;
D d;
typedef struct {
float a;
float b;
float c;
float d;
float e;
float f;
float g;
float h;
} F;
F f;
// Create a function that uses vldm/vstm to move some double and
// single precision values around in memory.
Assembler assm(isolate, NULL, 0);
__ mov(ip, Operand(sp));
__ stm(db_w, sp, r4.bit() | fp.bit() | lr.bit());
__ sub(fp, ip, Operand(4));
__ add(r4, r0, Operand(OFFSET_OF(D, h) + 8));
__ vldm(db_w, r4, d4, d7);
__ vldm(db_w, r4, d0, d3);
__ add(r4, r0, Operand(OFFSET_OF(D, h) + 8));
__ vstm(db_w, r4, d0, d5);
__ vstm(db_w, r4, d6, d7);
__ add(r4, r1, Operand(OFFSET_OF(F, h) + 4));
__ vldm(db_w, r4, s4, s7);
__ vldm(db_w, r4, s0, s3);
__ add(r4, r1, Operand(OFFSET_OF(F, h) + 4));
__ vstm(db_w, r4, s0, s5);
__ vstm(db_w, r4, s6, s7);
__ ldm(ia_w, sp, r4.bit() | fp.bit() | pc.bit());
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F4 fn = FUNCTION_CAST<F4>(code->entry());
d.a = 1.1;
d.b = 2.2;
d.c = 3.3;
d.d = 4.4;
d.e = 5.5;
d.f = 6.6;
d.g = 7.7;
d.h = 8.8;
f.a = 1.0;
f.b = 2.0;
f.c = 3.0;
f.d = 4.0;
f.e = 5.0;
f.f = 6.0;
f.g = 7.0;
f.h = 8.0;
Object* dummy = CALL_GENERATED_CODE(fn, &d, &f, 0, 0, 0);
USE(dummy);
CHECK_EQ(7.7, d.a);
CHECK_EQ(8.8, d.b);
CHECK_EQ(1.1, d.c);
CHECK_EQ(2.2, d.d);
CHECK_EQ(3.3, d.e);
CHECK_EQ(4.4, d.f);
CHECK_EQ(5.5, d.g);
CHECK_EQ(6.6, d.h);
CHECK_EQ(7.0, f.a);
CHECK_EQ(8.0, f.b);
CHECK_EQ(1.0, f.c);
CHECK_EQ(2.0, f.d);
CHECK_EQ(3.0, f.e);
CHECK_EQ(4.0, f.f);
CHECK_EQ(5.0, f.g);
CHECK_EQ(6.0, f.h);
}
TEST(11) {
// Test instructions using the carry flag.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
int32_t a;
int32_t b;
int32_t c;
int32_t d;
} I;
I i;
i.a = 0xabcd0001;
i.b = 0xabcd0000;
Assembler assm(isolate, NULL, 0);
// Test HeapObject untagging.
__ ldr(r1, MemOperand(r0, OFFSET_OF(I, a)));
__ mov(r1, Operand(r1, ASR, 1), SetCC);
__ adc(r1, r1, Operand(r1), LeaveCC, cs);
__ str(r1, MemOperand(r0, OFFSET_OF(I, a)));
__ ldr(r2, MemOperand(r0, OFFSET_OF(I, b)));
__ mov(r2, Operand(r2, ASR, 1), SetCC);
__ adc(r2, r2, Operand(r2), LeaveCC, cs);
__ str(r2, MemOperand(r0, OFFSET_OF(I, b)));
// Test corner cases.
__ mov(r1, Operand(0xffffffff));
__ mov(r2, Operand::Zero());
__ mov(r3, Operand(r1, ASR, 1), SetCC); // Set the carry.
__ adc(r3, r1, Operand(r2));
__ str(r3, MemOperand(r0, OFFSET_OF(I, c)));
__ mov(r1, Operand(0xffffffff));
__ mov(r2, Operand::Zero());
__ mov(r3, Operand(r2, ASR, 1), SetCC); // Unset the carry.
__ adc(r3, r1, Operand(r2));
__ str(r3, MemOperand(r0, OFFSET_OF(I, d)));
__ mov(pc, Operand(lr));
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F3 f = FUNCTION_CAST<F3>(code->entry());
Object* dummy = CALL_GENERATED_CODE(f, &i, 0, 0, 0, 0);
USE(dummy);
CHECK_EQ(0xabcd0001, i.a);
CHECK_EQ(static_cast<int32_t>(0xabcd0000) >> 1, i.b);
CHECK_EQ(0x00000000, i.c);
CHECK_EQ(0xffffffff, i.d);
}
TEST(12) {
// Test chaining of label usages within instructions (issue 1644).
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
Assembler assm(isolate, NULL, 0);
Label target;
__ b(eq, &target);
__ b(ne, &target);
__ bind(&target);
__ nop();
}
TEST(13) {
// Test VFP instructions using registers d16-d31.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
if (!CpuFeatures::IsSupported(VFP32DREGS)) {
return;
}
typedef struct {
double a;
double b;
double c;
double x;
double y;
double z;
double i;
double j;
double k;
uint32_t low;
uint32_t high;
} T;
T t;
// Create a function that accepts &t, and loads, manipulates, and stores
// the doubles and floats.
Assembler assm(isolate, NULL, 0);
Label L, C;
if (CpuFeatures::IsSupported(VFP3)) {
CpuFeatureScope scope(&assm, VFP3);
__ stm(db_w, sp, r4.bit() | lr.bit());
// Load a, b, c into d16, d17, d18.
__ mov(r4, Operand(r0));
__ vldr(d16, r4, OFFSET_OF(T, a));
__ vldr(d17, r4, OFFSET_OF(T, b));
__ vldr(d18, r4, OFFSET_OF(T, c));
__ vneg(d25, d16);
__ vadd(d25, d25, d17);
__ vsub(d25, d25, d18);
__ vmul(d25, d25, d25);
__ vdiv(d25, d25, d18);
__ vmov(d16, d25);
__ vsqrt(d17, d25);
__ vneg(d17, d17);
__ vabs(d17, d17);
__ vmla(d18, d16, d17);
// Store d16, d17, d18 into a, b, c.
__ mov(r4, Operand(r0));
__ vstr(d16, r4, OFFSET_OF(T, a));
__ vstr(d17, r4, OFFSET_OF(T, b));
__ vstr(d18, r4, OFFSET_OF(T, c));
// Load x, y, z into d29-d31.
__ add(r4, r0, Operand(OFFSET_OF(T, x)));
__ vldm(ia_w, r4, d29, d31);
// Swap d29 and d30 via r registers.
__ vmov(r1, r2, d29);
__ vmov(d29, d30);
__ vmov(d30, r1, r2);
// Convert to and from integer.
__ vcvt_s32_f64(s1, d31);
__ vcvt_f64_u32(d31, s1);
// Store d29-d31 into x, y, z.
__ add(r4, r0, Operand(OFFSET_OF(T, x)));
__ vstm(ia_w, r4, d29, d31);
// Move constants into d20, d21, d22 and store into i, j, k.
__ vmov(d20, 14.7610017472335499);
__ vmov(d21, 16.0);
__ mov(r1, Operand(372106121));
__ mov(r2, Operand(1079146608));
__ vmov(d22, VmovIndexLo, r1);
__ vmov(d22, VmovIndexHi, r2);
__ add(r4, r0, Operand(OFFSET_OF(T, i)));
__ vstm(ia_w, r4, d20, d22);
// Move d22 into low and high.
__ vmov(r4, VmovIndexLo, d22);
__ str(r4, MemOperand(r0, OFFSET_OF(T, low)));
__ vmov(r4, VmovIndexHi, d22);
__ str(r4, MemOperand(r0, OFFSET_OF(T, high)));
__ ldm(ia_w, sp, r4.bit() | pc.bit());
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F3 f = FUNCTION_CAST<F3>(code->entry());
t.a = 1.5;
t.b = 2.75;
t.c = 17.17;
t.x = 1.5;
t.y = 2.75;
t.z = 17.17;
Object* dummy = CALL_GENERATED_CODE(f, &t, 0, 0, 0, 0);
USE(dummy);
CHECK_EQ(14.7610017472335499, t.a);
CHECK_EQ(3.84200491244266251, t.b);
CHECK_EQ(73.8818412254460241, t.c);
CHECK_EQ(2.75, t.x);
CHECK_EQ(1.5, t.y);
CHECK_EQ(17.0, t.z);
CHECK_EQ(14.7610017472335499, t.i);
CHECK_EQ(16.0, t.j);
CHECK_EQ(73.8818412254460241, t.k);
CHECK_EQ(372106121, t.low);
CHECK_EQ(1079146608, t.high);
}
}
TEST(14) {
// Test the VFP Canonicalized Nan mode.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
double left;
double right;
double add_result;
double sub_result;
double mul_result;
double div_result;
} T;
T t;
// Create a function that makes the four basic operations.
Assembler assm(isolate, NULL, 0);
// Ensure FPSCR state (as JSEntryStub does).
Label fpscr_done;
__ vmrs(r1);
__ tst(r1, Operand(kVFPDefaultNaNModeControlBit));
__ b(ne, &fpscr_done);
__ orr(r1, r1, Operand(kVFPDefaultNaNModeControlBit));
__ vmsr(r1);
__ bind(&fpscr_done);
__ vldr(d0, r0, OFFSET_OF(T, left));
__ vldr(d1, r0, OFFSET_OF(T, right));
__ vadd(d2, d0, d1);
__ vstr(d2, r0, OFFSET_OF(T, add_result));
__ vsub(d2, d0, d1);
__ vstr(d2, r0, OFFSET_OF(T, sub_result));
__ vmul(d2, d0, d1);
__ vstr(d2, r0, OFFSET_OF(T, mul_result));
__ vdiv(d2, d0, d1);
__ vstr(d2, r0, OFFSET_OF(T, div_result));
__ mov(pc, Operand(lr));
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F3 f = FUNCTION_CAST<F3>(code->entry());
t.left = BitCast<double>(kHoleNanInt64);
t.right = 1;
t.add_result = 0;
t.sub_result = 0;
t.mul_result = 0;
t.div_result = 0;
Object* dummy = CALL_GENERATED_CODE(f, &t, 0, 0, 0, 0);
USE(dummy);
const uint32_t kArmNanUpper32 = 0x7ff80000;
const uint32_t kArmNanLower32 = 0x00000000;
#ifdef DEBUG
const uint64_t kArmNanInt64 =
(static_cast<uint64_t>(kArmNanUpper32) << 32) | kArmNanLower32;
ASSERT(kArmNanInt64 != kHoleNanInt64);
#endif
// With VFP2 the sign of the canonicalized Nan is undefined. So
// we remove the sign bit for the upper tests.
CHECK_EQ(kArmNanUpper32, (BitCast<int64_t>(t.add_result) >> 32) & 0x7fffffff);
CHECK_EQ(kArmNanLower32, BitCast<int64_t>(t.add_result) & 0xffffffffu);
CHECK_EQ(kArmNanUpper32, (BitCast<int64_t>(t.sub_result) >> 32) & 0x7fffffff);
CHECK_EQ(kArmNanLower32, BitCast<int64_t>(t.sub_result) & 0xffffffffu);
CHECK_EQ(kArmNanUpper32, (BitCast<int64_t>(t.mul_result) >> 32) & 0x7fffffff);
CHECK_EQ(kArmNanLower32, BitCast<int64_t>(t.mul_result) & 0xffffffffu);
CHECK_EQ(kArmNanUpper32, (BitCast<int64_t>(t.div_result) >> 32) & 0x7fffffff);
CHECK_EQ(kArmNanLower32, BitCast<int64_t>(t.div_result) & 0xffffffffu);
}
TEST(15) {
// Test the Neon instructions.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
uint32_t src0;
uint32_t src1;
uint32_t src2;
uint32_t src3;
uint32_t src4;
uint32_t src5;
uint32_t src6;
uint32_t src7;
uint32_t dst0;
uint32_t dst1;
uint32_t dst2;
uint32_t dst3;
uint32_t dst4;
uint32_t dst5;
uint32_t dst6;
uint32_t dst7;
uint32_t srcA0;
uint32_t srcA1;
uint32_t dstA0;
uint32_t dstA1;
uint32_t dstA2;
uint32_t dstA3;
uint32_t dstA4;
uint32_t dstA5;
uint32_t dstA6;
uint32_t dstA7;
} T;
T t;
// Create a function that accepts &t, and loads, manipulates, and stores
// the doubles and floats.
Assembler assm(isolate, NULL, 0);
if (CpuFeatures::IsSupported(NEON)) {
CpuFeatureScope scope(&assm, NEON);
__ stm(db_w, sp, r4.bit() | lr.bit());
// Move 32 bytes with neon.
__ add(r4, r0, Operand(OFFSET_OF(T, src0)));
__ vld1(Neon8, NeonListOperand(d0, 4), NeonMemOperand(r4));
__ add(r4, r0, Operand(OFFSET_OF(T, dst0)));
__ vst1(Neon8, NeonListOperand(d0, 4), NeonMemOperand(r4));
// Expand 8 bytes into 8 words(16 bits).
__ add(r4, r0, Operand(OFFSET_OF(T, srcA0)));
__ vld1(Neon8, NeonListOperand(d0), NeonMemOperand(r4));
__ vmovl(NeonU8, q0, d0);
__ add(r4, r0, Operand(OFFSET_OF(T, dstA0)));
__ vst1(Neon8, NeonListOperand(d0, 2), NeonMemOperand(r4));
// The same expansion, but with different source and destination registers.
__ add(r4, r0, Operand(OFFSET_OF(T, srcA0)));
__ vld1(Neon8, NeonListOperand(d1), NeonMemOperand(r4));
__ vmovl(NeonU8, q1, d1);
__ add(r4, r0, Operand(OFFSET_OF(T, dstA4)));
__ vst1(Neon8, NeonListOperand(d2, 2), NeonMemOperand(r4));
__ ldm(ia_w, sp, r4.bit() | pc.bit());
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F3 f = FUNCTION_CAST<F3>(code->entry());
t.src0 = 0x01020304;
t.src1 = 0x11121314;
t.src2 = 0x21222324;
t.src3 = 0x31323334;
t.src4 = 0x41424344;
t.src5 = 0x51525354;
t.src6 = 0x61626364;
t.src7 = 0x71727374;
t.dst0 = 0;
t.dst1 = 0;
t.dst2 = 0;
t.dst3 = 0;
t.dst4 = 0;
t.dst5 = 0;
t.dst6 = 0;
t.dst7 = 0;
t.srcA0 = 0x41424344;
t.srcA1 = 0x81828384;
t.dstA0 = 0;
t.dstA1 = 0;
t.dstA2 = 0;
t.dstA3 = 0;
t.dstA4 = 0;
t.dstA5 = 0;
t.dstA6 = 0;
t.dstA7 = 0;
Object* dummy = CALL_GENERATED_CODE(f, &t, 0, 0, 0, 0);
USE(dummy);
CHECK_EQ(0x01020304, t.dst0);
CHECK_EQ(0x11121314, t.dst1);
CHECK_EQ(0x21222324, t.dst2);
CHECK_EQ(0x31323334, t.dst3);
CHECK_EQ(0x41424344, t.dst4);
CHECK_EQ(0x51525354, t.dst5);
CHECK_EQ(0x61626364, t.dst6);
CHECK_EQ(0x71727374, t.dst7);
CHECK_EQ(0x00430044, t.dstA0);
CHECK_EQ(0x00410042, t.dstA1);
CHECK_EQ(0x00830084, t.dstA2);
CHECK_EQ(0x00810082, t.dstA3);
CHECK_EQ(0x00430044, t.dstA4);
CHECK_EQ(0x00410042, t.dstA5);
CHECK_EQ(0x00830084, t.dstA6);
CHECK_EQ(0x00810082, t.dstA7);
}
}
TEST(16) {
// Test the pkh, uxtb, uxtab and uxtb16 instructions.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
uint32_t src0;
uint32_t src1;
uint32_t src2;
uint32_t dst0;
uint32_t dst1;
uint32_t dst2;
uint32_t dst3;
uint32_t dst4;
} T;
T t;
// Create a function that accepts &t, and loads, manipulates, and stores
// the doubles and floats.
Assembler assm(isolate, NULL, 0);
__ stm(db_w, sp, r4.bit() | lr.bit());
__ mov(r4, Operand(r0));
__ ldr(r0, MemOperand(r4, OFFSET_OF(T, src0)));
__ ldr(r1, MemOperand(r4, OFFSET_OF(T, src1)));
__ pkhbt(r2, r0, Operand(r1, LSL, 8));
__ str(r2, MemOperand(r4, OFFSET_OF(T, dst0)));
__ pkhtb(r2, r0, Operand(r1, ASR, 8));
__ str(r2, MemOperand(r4, OFFSET_OF(T, dst1)));
__ uxtb16(r2, Operand(r0, ROR, 8));
__ str(r2, MemOperand(r4, OFFSET_OF(T, dst2)));
__ uxtb(r2, Operand(r0, ROR, 8));
__ str(r2, MemOperand(r4, OFFSET_OF(T, dst3)));
__ ldr(r0, MemOperand(r4, OFFSET_OF(T, src2)));
__ uxtab(r2, r0, Operand(r1, ROR, 8));
__ str(r2, MemOperand(r4, OFFSET_OF(T, dst4)));
__ ldm(ia_w, sp, r4.bit() | pc.bit());
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F3 f = FUNCTION_CAST<F3>(code->entry());
t.src0 = 0x01020304;
t.src1 = 0x11121314;
t.src2 = 0x11121300;
t.dst0 = 0;
t.dst1 = 0;
t.dst2 = 0;
t.dst3 = 0;
t.dst4 = 0;
Object* dummy = CALL_GENERATED_CODE(f, &t, 0, 0, 0, 0);
USE(dummy);
CHECK_EQ(0x12130304, t.dst0);
CHECK_EQ(0x01021213, t.dst1);
CHECK_EQ(0x00010003, t.dst2);
CHECK_EQ(0x00000003, t.dst3);
CHECK_EQ(0x11121313, t.dst4);
}
TEST(17) {
// Test generating labels at high addresses.
// Should not assert.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
// Generate a code segment that will be longer than 2^24 bytes.
Assembler assm(isolate, NULL, 0);
for (size_t i = 0; i < 1 << 23 ; ++i) { // 2^23
__ nop();
}
Label target;
__ b(eq, &target);
__ bind(&target);
__ nop();
}
#define TEST_SDIV(expected_, dividend_, divisor_) \
t.dividend = dividend_; \
t.divisor = divisor_; \
t.result = 0; \
dummy = CALL_GENERATED_CODE(f, &t, 0, 0, 0, 0); \
CHECK_EQ(expected_, t.result);
TEST(18) {
// Test the sdiv.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
typedef struct {
uint32_t dividend;
uint32_t divisor;
uint32_t result;
} T;
T t;
Assembler assm(isolate, NULL, 0);
if (CpuFeatures::IsSupported(SUDIV)) {
CpuFeatureScope scope(&assm, SUDIV);
__ mov(r3, Operand(r0));
__ ldr(r0, MemOperand(r3, OFFSET_OF(T, dividend)));
__ ldr(r1, MemOperand(r3, OFFSET_OF(T, divisor)));
__ sdiv(r2, r0, r1);
__ str(r2, MemOperand(r3, OFFSET_OF(T, result)));
__ bx(lr);
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), Handle<Code>());
#ifdef DEBUG
code->Print();
#endif
F3 f = FUNCTION_CAST<F3>(code->entry());
Object* dummy;
TEST_SDIV(1073741824, kMinInt, -2);
TEST_SDIV(kMinInt, kMinInt, -1);
TEST_SDIV(5, 10, 2);
TEST_SDIV(3, 10, 3);
TEST_SDIV(-5, 10, -2);
TEST_SDIV(-3, 10, -3);
TEST_SDIV(-5, -10, 2);
TEST_SDIV(-3, -10, 3);
TEST_SDIV(5, -10, -2);
TEST_SDIV(3, -10, -3);
USE(dummy);
}
}
#undef TEST_SDIV
TEST(code_relative_offset) {
// Test extracting the offset of a label from the beginning of the code
// in a register.
CcTest::InitializeVM();
Isolate* isolate = CcTest::i_isolate();
HandleScope scope(isolate);
// Initialize a code object that will contain the code.
Handle<Object> code_object(isolate->heap()->undefined_value(), isolate);
Assembler assm(isolate, NULL, 0);
Label start, target_away, target_faraway;
__ stm(db_w, sp, r4.bit() | r5.bit() | lr.bit());
// r3 is used as the address zero, the test will crash when we load it.
__ mov(r3, Operand::Zero());
// r5 will be a pointer to the start of the code.
__ mov(r5, Operand(code_object));
__ mov_label_offset(r4, &start);
__ mov_label_offset(r1, &target_faraway);
__ str(r1, MemOperand(sp, kPointerSize, NegPreIndex));
__ mov_label_offset(r1, &target_away);
// Jump straight to 'target_away' the first time and use the relative
// position the second time. This covers the case when extracting the
// position of a label which is linked.
__ mov(r2, Operand::Zero());
__ bind(&start);
__ cmp(r2, Operand::Zero());
__ b(eq, &target_away);
__ add(pc, r5, r1);
// Emit invalid instructions to push the label between 2^8 and 2^16
// instructions away. The test will crash if they are reached.
for (int i = 0; i < (1 << 10); i++) {
__ ldr(r3, MemOperand(r3));
}
__ bind(&target_away);
// This will be hit twice: r0 = r0 + 5 + 5.
__ add(r0, r0, Operand(5));
__ ldr(r1, MemOperand(sp, kPointerSize, PostIndex), ne);
__ add(pc, r5, r4, LeaveCC, ne);
__ mov(r2, Operand(1));
__ b(&start);
// Emit invalid instructions to push the label between 2^16 and 2^24
// instructions away. The test will crash if they are reached.
for (int i = 0; i < (1 << 21); i++) {
__ ldr(r3, MemOperand(r3));
}
__ bind(&target_faraway);
// r0 = r0 + 5 + 5 + 11
__ add(r0, r0, Operand(11));
__ ldm(ia_w, sp, r4.bit() | r5.bit() | pc.bit());
CodeDesc desc;
assm.GetCode(&desc);
Handle<Code> code = isolate->factory()->NewCode(
desc, Code::ComputeFlags(Code::STUB), code_object);
F1 f = FUNCTION_CAST<F1>(code->entry());
int res = reinterpret_cast<int>(CALL_GENERATED_CODE(f, 21, 0, 0, 0, 0));
::printf("f() = %d\n", res);
CHECK_EQ(42, res);
}
#undef __
| code |
कर्नाटक हिजाब विवाद: गाजियाबाद में मुस्लिम महिलाओं ने किया प्रदर्शन, पुलिस ने बल प्रयोग कर खदेड़ा, धक्कामुक्की विस्तार कर्नाटक हिजाब मामले की आंच अब गाजियाबाद भी पहुंच गई है। खोड़ा क्षेत्र के नवनीत विहार की मुस्लिम महिलाओं ने विरोध प्रदर्शन किया। सूचना पर पहुंची पुलिस ने महिलाओं से पोस्टर छीनने का प्रयास किया। इस बीच महिला और कुछ लोगों ने पुलिस चौकी पर धक्कामुक्की की। प्रदर्शन के दौरान इलाके में शांति व्यवस्था बनाने के लिए पुलिस ने हल्का बल प्रयोग कर प्रदर्शनकारियों को खदेड़ दिया। एसपी सिटी सेकंड ज्ञानेंद्र सिंह का कहना है कि कुछ महिलाएं पोस्टर बैनर लेकर हिजाब के लिए प्रदर्शन कर रही थी। आचार संहिता लगने की वजह से उनसे प्रदर्शन की अनुमति मांगी गई, जिसे वह नहीं दिखा सकी। वीडियो फुटेज के आधार पर महिला और प्रदर्शनकारियों की पहचान कर कार्रवाई की जाएगी। | hindi |
रूस ने यूक्रेन मुद्दे पर पश्चिम से और बातचीत का दिया संकेत मॉस्को। यूक्रेन को लेकर चल रहे तनाव के बीच रूस के शीर्ष राजनयिक ने सोमवार को राष्ट्रपति व्लादिमीर पुतिन को रूसी सुरक्षा मांगों पर पश्चिम के साथ बातचीत जारी रखने का सुझाव दिया। इसे संकेत माना जा रहा है कि क्रेमलिन का इरादा यूक्रेन पर रूसी आक्रमण की आशंका को लेकर अमेरिकी चेतावनी के बीच राजनयिक प्रयासों को जारी रखने का है। : यूक्रेन संकट : बारबार झगड़े में क्यों फंसती है नॉर्ड स्ट्रीम2 गैस पाइपलाइन रूस, पश्चिमी देशों से गारंटी चाहता है कि नाटो गठबंधन यूक्रेन और अन्य पूर्व सोवियत देशों को सदस्य नहीं बनाएगा, गठबंधन यूक्रेन में हथियारों की तैनाती रोक देगा और पूर्वी यूरोप से अपनी सेना वापस ले लेगा। हालांकि इन मांगों को पश्चिमी देशों ने सिरे से खारिज कर दिया है। पुतिन के साथ एक बैठक में विदेश मंत्री सर्गेई लावरोव ने सुझाव दिया कि रूस को अमेरिका और उसके सहयोगियों के साथ बातचीत जारी रखनी चाहिए, भले ही उन देशों ने प्रमुख रूसी सुरक्षा मांगों को खारिज कर दिया है। लावरोव ने कहा कि अमेरिका ने यूरोप में मिसाइल तैनाती की सीमा, सैन्य अभ्यास पर प्रतिबंध और विश्वास बहाली के लिए अन्य उपायों पर बातचीत करने की पेशकश की है। उन्होंने कहा कि बातचीत अनिश्चित काल तक नहीं चल सकती, लेकिन इस स्तर पर मैं बातचीत जारी रखने और उनका विस्तार करने का सुझाव दूंगा। पुतिन द्वारा यह पूछे जाने पर कि राजनयिक प्रयासों को जारी रखने का कोई तुक है, लावरोव ने जवाब दिया कि बातचीत की संभावनाएं समाप्त नहीं हुई हैं और उन्होंने वार्ता जारी रखने का प्रस्ताव रखा। पुतिन ने कहा कि पश्चिम बिना किसी निर्णायक नतीजे के रूस को अंतहीन वार्ता में उलझाने की कोशिश कर सकता है। लावरोव ने कहा कि हमेशा एक मौका होता है। उनका मंत्रालय अमेरिका और उसके सहयोगियों को रूस की मुख्य मांगों को रोकने की अनुमति नहीं देगा। यह बैठक तब हुई, जब जर्मन चांसलर ओलाफ शॉल्त्स रूसी हमले के बढ़ते डर के बीच यूक्रेन पहुंचे। उनके यूक्रेन से मॉस्को जाने की योजना है, जहां वे राष्ट्रपति व्लादिमीर पुतिन को इस मामले में पीछे हटने के लिए समझाने का प्रयास करेंगे। | hindi |
கெட்டிக்காரன் புளுகு 8 நாளைக்கு நாடாளுமன்றத்தில் மாஸ் காட்டிய ப.சிதம்பரம் பேச்சு! காங்கிரஸ் மூத்த தலைவர் ப.சிதம்பரம் இன்று மாநிலங்களவையில் பேசுகையில், நாட்டில் வளர்ச்சிக்கான தேவையைத் தூண்டுவதில் மத்திய அரசு தவறிவிட்டது. அரசு இன்னும் பாடங்களைக் கற்கவில்லை. நீங்கள் பாடங்களைக் கற்காததன் விளைவாக, இன்னும் 12 மாதங்கள் ஏழைகள் கஷ்டப்பட்டு, பெரிதும் பாதிக்கப்படுவார்கள் என்று நான் பயப்படுகிறேன். நாட்டின் ஒட்டுமொத்த உற்பத்தி மதிப்பு ரூ.130 கோடி லட்சம் கோடியாக சரிந்துள்ளது. கெட்டிக்காரன் புளுகு 8 நாளைக்கு என்பதற்கு மாறாக 3 நாட்களிலேயே பெட்ரோல் விலை உயர்ந்துவிட்டது. நாட்டின் 70 சதவீதம் வளங்கள் ஒரு சதவீதம் பணக்காரர்களிடமே உள்ளது. அந்த ஒரு சதவீத மக்களுக்காகவே நீங்கள் செயல்படுகிறீர்கள். பணக்காரர்களுக்காக, பணக்காரர்களால், பணக்காரர்களே நடத்தும் ஆட்சியாக தற்போதைய ஆட்சி உள்ளது என கூறினார். | tamil |
سعد بن عبید ٲسؠ اَکھ صُحابی.
زٲتی زِندگی
== حَوالہٕ == | kashmiri |
નાઇટ ક્લબમાં દારૂ પીતો જાેવા મળ્યો આર્યન ખાન મુંબઈ, બોલીવુડ સુપરસ્ટાર શાહરૂખ ખાનનો પુત્ર આર્યન ખાન જ્યારથી ડ્રગ્સ કેસમાં ફસાયો છે. સોશિયલ મીડિયા પર લોકોની નજર તેના પર રહે છે. તેને આ કેસમાં ક્લીન ચિટ પણ મળી ચુકી છે પરંતુ આજે પણ તેને કોઈ કારણને લીધે ટ્રોલ કરવામાં આવે છે. ગવે આર્યનનો એક વીડિયો ઇન્ટરનેટ પર વિવાદોમાં આવી ગયો છે, જેમાં દાવો કરવામાં આવી રહ્યો છે કે આર્યને કોઈ નાઇટ ક્લબમાં જઈને દારૂ પીધો છે. આ વીડિયો ઘણા લોકો શેર કરી રહ્યાં છે. હકીકતમાં શાહરૂખ ખાનના પુત્ર આર્યનનો આ વીડિયો ખુબ શેર થઈ રહ્યો છે. આ વીડિયોમાં આર્યન ખાન ભીડની વચ્ચે નાઇટ ક્લબમાં જાેવા મળી રહ્યો છે. તેણે બ્લેક કલરની ટીશર્ટ પહેરી છે અને ચહેરા પર બ્લેક માસ્ક લગાવ્યું છે. આ વીડિયોમાં જાેવા મળી રહ્યું છે કે તે પોતાનું માસ્ક નીચુ કરે છે અને સામે કાઉન્ટર પર રાખેલો દારૂનો ગ્લાસ ઉઠાવીને પી જાય છે. તે ફરી પોતાનું માસ્ક ઉપર કરે છે અને ત્યાંથી જતો રહે છે. આર્યનની સાથે આ વીડિયોમાં કેટલાક અન્ય લોકો પણ જાેવા મળી રહ્યાં છે. જશ્ન ભર્યા માહોલમાં ડ્રિંક કરતો આર્યન ખાનનો વીડિયો જાેઈ ઘણા લોકો નારાજ થઈ ગયા છે. વીડિયો પર મળી રહેલી કોમેન્ટમાં લોકોનું કહેવું છે કે આર્યન રેવ પાર્ટીમાં પકડાયો હતો, ત્યારબાદ તે ડ્રગ્સ કેસમાં ફસાયો હતો. ક્લીન ચિટ મળ્યા બાદ પણ તે નશામાં ડૂબનારી વસ્તુનું સેવન કેમ કરી રહ્યો છે? તો કેટલાક લોકોનું કહેવું છે કે આ તેનો અંગત ઈચ્છે છે, જેની રિસ્પેક્ટ કરવી જાેઈએ. | gujurati |
ত্রিপুরা জুড়ে পালিত খুশির ঈদ দেশ এবং বিদেশের সঙ্গে তাল মিলিয়ে এক মাসের রোজা শেষে মঙ্গলবার ত্রিপুরা রাজ্যে বসবাসরত ইসলাম ধর্মাবলম্বী মানুষ খুশির ঈদ পালনে মেতে ওঠেন এদিন সকালে নতুন জামা কাপড় পড়ে নানা বয়সী লোকজন একে অপরকে শুভেচ্ছা বিনিময় করেন ঈদ উপলক্ষে রাজধানী আগরতলা শহর রাজ্যের অন্যান্য জায়গায় মসজিদগুলোতে বিশেষ নামাজের আয়োজন করা হয় রাজ্যের সবচেয়ে বড় নামাজ অনুষ্ঠিত হয় আগরতলার চিত্তরঞ্জন রোড এলাকার গেদুমিয়া মসজিদের ঈদগা ময়দানে এখানে কয়েকশো মানুষ একসঙ্গে নামাজ আদায় করেন এছাড়াও রাজধানীর শান্তি পাড়া মসজিদ রামনগর মসজিদ সহ সব মসজিদে বিশেষ নামাজের আয়োজন করা হয় বিভিন্ন বয়সী মানুষ মসজিদে এসে একে অপরকে কুশল বিনিময় করেন এবং ঈদের শুভেচ্ছা জ্ঞাপন করেনএ বছর ঈদকে ঘিরে বাড়তি আনন্দ লক্ষ্য করা যায় কারণ গত দুই বছর করোনা মহামারীর কারণে বাইরে বড় করে আয়োজন করা যায়নি এবছর তেমন কোনো বিধিনিষেধ না থাকায় অবাধে মানুষ মসজিদে এসে নামাজ আদায় করেন তবে নামাজের সময় বৃষ্টির আসায় কিছুটা সমস্যার সৃষ্টি হয় তবে বৃষ্টিকে উপেক্ষা করেই ঈদের নামাজে অংশ নেন | bengali |
சிங்கப்பூருக்குச் செல்வதைத் தவிர்க்குமாறு அமெரிக்கா பயண ஆலோசனை அமெரிக்கா, சிங்கப்பூருக்குப் பயணம் மேற்கொள்வதைத் தவிர்க்குமாறு கேட்டுக்கொண்டுள்ளது. இங்கு பதிவாகும் கிருமித்தொற்றுச் சம்பவங்கள் காரணமாக, சிங்கப்பூருக்கான அமெரிக்கப் பயண ஆலோசனை உச்ச நிலைக்கு உயர்த்தப்பட்டுள்ளது. தற்போதுள்ள சூழலில், முழுமையாகத் தடுப்பூசி போட்டுக்கொண்டோர், சிங்கப்பூருக்குச் சென்றால், கிருமித்தொற்றுக்கு ஆளாகக்கூடும் என்று அமெரிக்க நோய் கட்டுப்பாட்டு, தடுப்பு நிலையம் தெரிவித்தது. சிங்கப்பூருக்குச் சென்றே வேண்டும் என்று நிலையில் இருப்போர், முழுமையாகத் தடுப்பூசி போட்டிருக்க வேண்டும். நாட்டின் பரிந்துரைகளையும் விதிமுறைகளையும் பின்பற்ற வேண்டும் என்றும் அமெரிக்கா கேட்டுக்கொண்டது. | tamil |
The special guest on the January 18, 2014 edition of Michael Collins Piper’s nightly forum on the Republic Broadcasting Network was veteran political activist and traditionalist Catholic James Condit, Jr.
Condit joined Piper to discuss the outrageous intrigues of the late Father Malachi Martin who was the subject of a chapter in Piper’s new book THE JUDAS GOATS which analyzes Zionist infiltration of the American nationalist movement and which detailed (based on Condit’s research and that of others) the little-known story of how Father Martina priest working high up in the Vatican acted as an agent of Zionist interests during the Vatican II “reform” conference of the early 1960s bending the doctrines of the Catholic Church to accord with the demands of the Zionist interests.
However LOOK did not identify Martin as the Zionist agent. It did mention though that the Zionist agent had written a book under a pseudonym Michael Serafian. It was some years later that that pseudonym was revealed to be a pen-name for none other than Malachi Martin. So there is no question that Martin was a Zionist agent.
Michael Collins Piper (RIP) was assassinated for telling the truth about the JFK assassination, the Numec Coverup, and all aspects of Zionist infiltration into American culture, Christianity, and politics.
For information about Zionist infiltration into American society read: Freud’s Mafia: Sigmund Freud’s Crimes Against Christianity by Christian scholar and author/publisher Paul Boggs.
A sayanim (sing. Sayan; Hebrew: helpers, assistants) is a Jew living outside Israel who volunteers (or more appropriately is emotionally blackmailed) to provide assistance to Israel and/or the Israeli Mossad utilizing the capacity of their own nationality to procure assistance. This assistance includes facilitating medical care, money, logistics, and even overt intelligence gathering. Estimates put the number of sayanim in the hundreds of thousands.
In order to preserve the research of Michael Collins Piper, we have mirrored the long version of the Jim Condit, Jr. radio show.
Who controls the Catholic church? | english |
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[' \n \n [ਇਹ ਯੁੱਧ/ਦਹਿਸ਼ਤਗਰਦੀ ਬਾਰੇ ਕੀਤੇ ਗਏ ਟਵੀਟਾਂ ਦੀਆਂ ਕੁੱਝ ਉਦਾਹਰਣਾਂ ਹਨਃ \\n-\\n-\\ \'ਆਰਟੀ @USER: ਇਸਲਾਮਿਕ ਇਨਕਲਾਬ ਦਿਵਸ #Iran ਵਿੱਚਃ "ਨਾਮ ਦਾ ਧੰਨਵਾਦ, ਸੱਚਾ ਚਿਹਰਾ ਪ੍ਰਗਟ ਕਰਨ ਲਈ।ਅਮਰੀਕਾ ਦਾ "#الله_اکبر HTTPURL...\\\'\\n-\\\' RT @USER: #Libya: #UAE ਹਵਾਈ ਹਮਲੇ \\n #Serbia: ਜਨਤਕ ਵਿਰੋਧ ਪ੍ਰਦਰਸ਼ਨ \\n #Armenia ਅਤੇ ਵਿਚਕਾਰ ਹਡ਼ਤਾਲਾਂ ਦਾ ਆਦਾਨ-ਪ੍ਰਦਾਨ#Azerbaijan\\\\n ਵਿੱਚ ਅਸ਼ਾਂਤੀ #Mali\\\\n...\\\'\\n-\\\' ਕਾਫ਼ਰ-ਨੁਬੁਦ ਦੇ ਅੱਤਵਾਦੀਆਂ ਨੇ ਸਰਕਾਰੀ ਸੈਨਿਕਾਂ ਦੀ ਨਿਰੀਖਣ ਚੌਕੀ ਉੱਤੇ ਇੱਕ ਮਸ਼ੀਨ ਗੰਨ ਅਤੇ ਇੱਕ ਬੰਦੂਕ ਨਾਲ ਗੋਲੀਬਾਰੀ ਕੀਤੀ।ਗ੍ਰਨੇਡ ਲਾਂਚਰ। ਐੱਸ. ਏ. ਏ. ਦੇ ਪੰਜ ਜਵਾਨ ਜ਼ਖ਼ਮੀ ਹੋਏ। ਐੱਚ. ਟੀ. ਟੀ. ਪੀ. ਯੂ. ਆਰ. ਐੱਲ.\\\'\\n\\n "1" ਨਾਲ ਜਵਾਬ ਦਿਓ ਜੇਕਰ ਤੁਹਾਨੂੰ ਲਗਦਾ ਹੈ ਕਿ ਹੇਠ ਦਿੱਤਾ ਟਵੀਟ ਯੁੱਧ ਜਾਂ ਦਹਿਸ਼ਤ ਬਾਰੇ ਹੈ, "0" ਨਹੀਂ ਤਾਂਃ\\"ਆਰ. ਟੀ.@USER: #Idlib ਸੂਬੇ ਵਿੱਚ NAME _ 3 ਨਾਲ ਲਡ਼ਾਈ ਵਿੱਚ ਜ਼ਖਮੀ ਹੋਏ ਹਯਾਤ ਤਹਰੀਰ ਅਲ-ਨਾਮ _ 2 ਅੱਤਵਾਦੀਆਂ ਨੂੰ ਬਾਹਰ ਕੱਢ ਲਿਆ ਗਿਆ... "] ', 'ਯੁੱਧ/ਦਹਿਸ਼ਤਗਰਦੀ ਬਾਰੇ ਕੀਤੇ ਗਏ ਟਵੀਟਾਂ ਲਈ ਇਹ ਕੁੱਝ ਉਦਾਹਰਣਾਂ ਹਨਃ-\'ਆਰਟੀ @USER: ਇਸਲਾਮਿਕ ਇਨਕਲਾਬ ਦਿਵਸ #Iran: "ਧੰਨਵਾਦ ਨਾਮ _ 1, ਯੁੱਧ/ਦਹਿਸ਼ਤਗਰਦੀ ਦਾ ਸੱਚਾ ਚਿਹਰਾ ਪ੍ਰਗਟ ਕਰਨ ਲਈ।ਯੂਐੱਸ "#الله_اکبر HTTPURL... \'-\' ਆਰਟੀ @USER: #Libya: #UAE ਹਵਾਈ ਹਮਲੇ \\n #Serbia: ਜਨਤਕ ਵਿਰੋਧ ਪ੍ਰਦਰਸ਼ਨ \\n #Armenia ਅਤੇ #Azerbaijan \\n ਦਰਮਿਆਨ ਹਡ਼ਤਾਲਾਂ ਦਾ ਆਦਾਨ-ਪ੍ਰਦਾਨ\'-\' ਕਾਫ਼ਰ-ਨੁਬੁਦ ਦੇ ਅੱਤਵਾਦੀਆਂ ਨੇ ਸਰਕਾਰੀ ਸੈਨਿਕਾਂ ਦੀ ਨਿਰੀਖਣ ਚੌਕੀ ਉੱਤੇ ਇੱਕ ਮਸ਼ੀਨ ਗੰਨ ਅਤੇ ਇੱਕ ਗ੍ਰਨੇਡ ਲਾਂਚਰ ਨਾਲ ਗੋਲੀਬਾਰੀ ਕੀਤੀ। ਪੰਜਐੱਸ. ਏ. ਏ. ਸੈਨਿਕ ਜ਼ਖਮੀ ਹੋ ਗਏ। ਐੱਚ. ਟੀ. ਟੀ. ਪੀ. ਯੂ. ਆਰ. ਐੱਲ. \'1 ਨਾਲ ਜਵਾਬ ਦਿਓ\' ਜੇ ਤੁਹਾਨੂੰ ਲਗਦਾ ਹੈ ਕਿ ਹੇਠ ਦਿੱਤਾ ਟਵੀਟ ਯੁੱਧ ਜਾਂ ਦਹਿਸ਼ਤ ਬਾਰੇ ਹੈ, \'0\' ਨਹੀਂ ਤਾਂਃ \'ਆਰ. ਟੀ. @USER: ਹਯਾਤ ਤਹਰੀਰ ਅਲ-ਨਾਮ _ 2#Idlib ਪ੍ਰਾਂਤ ਵਿੱਚ NAME _ 3 ਨਾਲ ਲਡ਼ਾਈ ਵਿੱਚ ਜ਼ਖਮੀ ਹੋਏ ਅੱਤਵਾਦੀਆਂ ਨੂੰ ਬਾਹਰ ਕੱਢਿਆ ਗਿਆ ਸੀ... \' \n '] | punjabi |
سری لنکن فاسٹ بالر دھمیکا پرساد فٹنس مسائل کی وجہ سے دورہ انگلینڈ سے باہر ہوگئے انہیں بحالی صحت کےلئے انگلینڈ سے وطن واپس بھیج دیا گیا ہے دھمیکا پرساد ایسکس کے خلاف پریکٹس میچ میں کندھے کی تکلیف میں مبتلا ہوگئے تھےٹیم مینجر چاریتھ سینانائیکے کا کہنا ہے کہ دھمیکا پرساد کا فٹنس ٹیسٹ لیا مگر وہ فٹنس ثابت کرنے میں ناکام رہے انہیں بحالی صحت کےلئے وطن واپس بھیجنے کا فیصلہ کیا گیا ہے اس طرح وہ انگلینڈکے خلاف ٹیسٹ سیریز نہیں کھیل سکیں گے انہوں نے کہا کہ پرساد کی انجری سنجیدہ نوعیت کی ہے اور ان کی ون ڈے سیریز میں بھی شرکت مشکل ہے | urdu |
सपा ने अब्दुल कलाम और जयराम पांडेय पर जताया भरोसा सपा ने अब्दुल कलाम और जयराम पांडेय पर जताया भरोसा खलीलाबाद और मेंहदावल से प्रत्याशी घोषित संवाद न्यूज एजेंसी संतकबीरनगर। समाजवादी पार्टी ने सोमवार शाम को खलीलाबाद और मेंहदावल विधानसभा क्षेत्र से प्रत्याशी घोषित कर दिया। खलीलाबाद से पूर्व विधायक अब्दुल कलाम और मेंहदावल से जयराम पांडेय को प्रत्याशी बनाया गया है। धनघटा विधानसभा क्षेत्र से प्रत्याशी घोषित नहीं किया गया है। खलीलाबाद विधानसभा क्षेत्र से पूर्व विधायक अब्दुल कलाम को प्रत्याशी घोषित किया गया है। बघौली ब्लॉक के आटाकला निवासी पूर्व विधायक अब्दुल कलाम मेंहदावल विधानसभा से तीन बार विधायक रहे हैं। वह 1996, 2002 और 2007 में सपा के टिकट पर विधायक चुने गए थे। इसके बाद 2012 में खलीलाबाद विधानसभा से टिकट मिला था, लेकिन वह चुनाव हार गए थे। 2019 के लोकसभा चुनाव में उनको उम्मीदवार बनाया गया था, बाद में उनका नाम वापस ले लिया गया। वह लगातार क्षेत्र में सक्रिय रहे। जिसका उन्हें लाभ मिला और 2022 के विधानसभा चुनाव में पार्टी ने उम्मीदवार बनाया है। इसी तरह से मेंहदावल विधानसभा से सपा ने पूर्व प्रत्याशी रहे जयराम पांडेय पर फिर से भरोसा जताया है। खलीलाबाद के रौरापार निवासी जयराम पांडेय 2017 में सपा के टिकट पर मेंहदावल विधानसभा क्षेत्र से चुनाव लड़ चुके हैं। वह तीसरे स्थान पर रहे। उसके बाद वह लगातार क्षेत्र में सक्रिय रहे। वहीं, पार्टी ने अब तक धनघटा विधानसभा से प्रत्याशी घोषित नहीं किया है। जिसको लेकर ऊहापोह की स्थिति बनी हुई है। सपा जिलाध्यक्ष गौहर अली खां ने कहा कि धनघटा विधानसभा से जल्द ही प्रत्याशी घोषित कर दिया जाएगा। | hindi |
بٔہ اوسُس چانہِ خٲطرٕ بییٚہِ رۄپیہِ اَننہٕ خٲطرٕ پَنہٕ نِس مُلکس گوٚمُت أمۍ ووٚنُس | kashmiri |
सौभाग्य के तहत सौर विद्युतीकरण के मामले में राजस्थान सबसे आगे: केंद्र नयी दिल्ली केंद्र सरकार ने बृहस्पतिवार को कहा कि सौभाग्य योजना के तहत सौर ऊर्जा आधारित सिस्टम के माध्यम से सबसे ज्यादा घरो में बिजली पहुंचाने के मामले में राजस्थान सबसे आगे है। ऊर्जा मंत्री आर के सिंह ने लोकसभा में प्रश्नकाल में यह जानकारी दी। उन्होंने बताया कि सौभाग्य योजना के तहत राजस्थान में 1,23,682 घरों में सौर आधारित सिस्टम के जरिये विद्युतीकरण किया गया। इसके अलावा छत्तीसगढ़ में 65,373, उत्तर प्रदेश में 53,234 और असम में 50,754 घरों का सौर विद्युतीकरण किया गया। मंत्री ने यह भी बताया कि हिमाचल प्रदेश, सिक्किम और केंद्रशासित प्रदेश जम्मू कश्मीर में इस योजना के तहत कोई लाभार्थी नहीं है। | hindi |
UPTET Answer Key 2022: यूपीटीईटी फाइनल आंसरकी आज जारी होना मुश्किल उत्तर प्रदेश शिक्षक पात्रता परीक्षा यूपीटीईटी की अंतिम उत्तरकुंजी बुधवार को जारी होना मुश्किल है। 22 दिसंबर को जारी समय सारिणी के अनुसार 25 फरवरी को परिणाम घोषित होना है। उससे दो दिन पहले 23 फरवरी.Follow Us: Google News Dailyhunt News Facebook Instagram Twitter Pinterest Tumblr esarkariresult.info | hindi |
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\begin{equation}gin{document}
\begin{equation}gin{titlepage}
\thetaitle{Robust Phase Transitions for Heisenberg and Other Models
on General Trees}
\author{Robin Pemantle\thetahanks{Research partially
supported by a Presidential Faculty Fellowship and a Sloan Foundation
Fellowship.}
\and Jeffrey E. Steif\thetahanks{Research supported by
grants from the Swedish Natural Science Research Council and from
the Royal Swedish Academy of Sciences.}
\and \\
\it University of Wisconsin-Madison
and Chalmers University of Technology }
\bar{d}ate{}
\title{Robust Phase Transitions for Heisenberg and Other Models
on General Trees}
\begin{equation}gin{abstract}
We study several statistical mechanical models on a general tree.
Particular attention is devoted to the classical
Heisenberg models, where the state
space is the $d$--dimensional unit sphere
and the interactions are proportional to
the cosines of the angles between neighboring spins. The phenomenon of
interest here is the classification of phase transition
(non-uniqueness of the Gibbs state) according to whether it is {\it robust}.
In many cases, including all of the Heisenberg and Potts models,
occurrence of robust phase transition is determined by the geometry
(branching number) of
the tree in a way that parallels the situation with independent
percolation and usual phase transition for the Ising model. The critical
values for robust phase transition for the Heisenberg and Potts
models are also calculated exactly. In some cases, such as the $q\ge 3$ Potts
model, robust phase transition and usual phase transition do not coincide,
while in other cases, such as the Heisenberg models, we conjecture that robust
phase transition and usual phase transition are equivalent. In addition,
we show that symmetry breaking is equivalent to the existence of a phase
transition, a fact believed but not known for the rotor model on $Z\!\!\!Z^2$.
\mbox{\rm \small e}nd{abstract}
\noindent
AMS 1991 subject classifications. Primary 60K35, 82B05, 82B26. \\
Key words and phrases. phase transitions, symmetry breaking, Heisenberg
models.\\
Running head: Phase transitions for Heisenberg models.
\mbox{\rm \small e}nd{titlepage}
\setcounter{equation}{0}
\section{Definition of the model and main results} \labelel{sec:one}
Particle systems on trees have produced the first and most tractable
examples of certain qualitative phenomena. For example, the
contact process on a tree has multiple phase transitions,
(\cite{Pem,Lig2,Sta}) and the critical temperature for the
Ising model on a tree is determined by its branching number or Hausdorff
dimension (\cite{Ly1,EKPS,PP}), which makes the Ising model
intimately related to independent percolation whose critical value is also
determined by the branching number (see \cite{Ly2}). In this paper
we study several models on general infinite trees,
including the classical Heisenberg and Potts models.
Our aim is to exhibit a distinction between two kinds of phase transitions,
{\it robust} and {\it non-robust}, as well as to investigate conditions
under which robust phase transitions occur.
In many cases, including the Heisenberg and Potts models,
the existence of a robust phase transition is determined
by the branching number. However, in some cases (including
the $q > 2$ Potts model), the critical temperature for
the existence of usual phase transition is not determined by the
branching number. Thus robust phase transition
behaves in a more universal manner than non-robust phase transition,
being a function of the branching number alone,
as it is for usual phase transition for independent percolation and
the Ising model. Although particle systems on trees do not always
predict the qualitative behavior of the same particle system on
high-dimensional lattices, it seems likely that there is a
lattice analogue of non-robust phase transition, which would make
an interesting topic for further research. Another unresolved question
is whether there is ever a non-robust phase transition for the Heisenberg
models (see Conjecture~\ref{conj:PS}).
We proceed to define the general statistical ensemble
on a tree and to state the main results of the paper.
Let $G$ be a compact metrizable group acting transitively by isometries on
a compact metric space $({\bf S},d)$.
It is well known that there exists a unique
$G$--invariant probability measure on ${\bf S}$, which we denote by $\bar{d}x$.
An {\bf energy function} is any nonconstant function
$H : {\bf S} \thetaimes {\bf S} \rightarrow \overline{h}ox{I\kern-.2em\overline{h}ox{R}}$ that is symmetric, continuous,
and $d$--invariant in that $H(x,y)$ depends only on $d(x,y)$. This implies that
$$
H(x,y)=H(gx,gy) \,\,\bar{d}eltasiorall \, x,y\in {\bf S}, \,g\in G.
$$
${\bf S}$ together with its $G$--action and the function $H$ will be called a
{\bf statistical ensemble}.
Several examples with which we will be concerned are as follows.
\begin{equation}gin{eg} \labelel{eg:ising}
The Ising model. Here ${\bf S} = \{ 1 , -1 \}$
acted on by itself (multiplicatively), $d$ is the usual discrete metric,
$\bar{d}x$ is uniform on ${\bf S}$, and $H (x , y) = - xy$.
\mbox{\rm \small e}nd{eg}
\begin{equation}gin{eg} \labelel{eg:potts}
The Potts model. Here ${\bf S} = \{ 0 , 1 , \ldots ,
q-1 \}$ for some integer $q > 1$, $G$ is the symmetric group $S_q$ with its
natural action, $d$ is the usual discrete metric,
$\bar{d}x$ is uniform on ${\bf S}$, and $H (x , y) = 1 - 2 \bar{d}eltata_{x,y}$.
This reduces to the Ising model when $q = 2$.
\mbox{\rm \small e}nd{eg}
\begin{equation}gin{eg} \labelel{eg:rotor}
The rotor model. Here ${\bf S}$ is the unit
circle, acted on by itself by translations,
$d(\thetaheta , \bar{d}eltahi) = 1- \cos (\thetaheta - \bar{d}eltahi)$,
$\bar{d}x$ is normalized Lebesgue measure, and
$H (\thetaheta , \bar{d}eltahi) = - \cos (\thetaheta - \bar{d}eltahi)$.
\mbox{\rm \small e}nd{eg}
\begin{equation}gin{eg} \labelel{eg:spherical}
The Heisenberg models for $d \ge 1$.
In the $d$--dimensional
Heisenberg model, ${\bf S}$ is the unit sphere $S^d$, $G$ is
the special orthogonal group with its natural action; $d(x,y)$ is $1-x\cdot y$,
$\bar{d}x$ is normalized surface measure,
and $H (x , y)$ is again the negative of the dot product of $x$ and $y$.
When $d=1$, we recover the rotor model.
\mbox{\rm \small e}nd{eg}
Let $A$ be any finite graph, with vertex and edge sets denoted by
$V(A)$ and $E(A)$ respectively, and let ${\cal J} : E (A) \rightarrow \overline{h}ox{I\kern-.2em\overline{h}ox{R}}^+$
be a function mapping the edge set of $A$ to the nonnegative reals which
we call {\bf interaction strengths}.
We now assume that ${\bf S}$, $G$ and $H$ are given and fixed.
\begin{equation}gin{defn} \labelel{defn:Gibbs}
The {\bf Gibbs measure} with interaction strengths ${\cal J}$ is
the probability measure $\mu=\mu^{{\cal J}}$ on ${\bf S}^{V(A)}$ whose density
with respect to product measure $\bar{d}x^{V(A)}$ is given by
$$ { \mbox{\rm \small e}xp (- H^{\cal J} (\mbox{\rm \small e}ta)) \over Z},\,\,\,\, \mbox{\rm \small e}ta\in {\bf S}^{V(A)} $$
where
$$ H^{\cal J}(\mbox{\rm \small e}ta) = \sum_{e = \overline{xy} \in E(A)}
{\cal J} (e) H(\mbox{\rm \small e}ta (x) , \mbox{\rm \small e}ta (y)) ,$$
and $Z = \int \mbox{\rm \small e}xp (- H^{\cal J}(\mbox{\rm \small e}ta)) \, \bar{d}x^{V(A)}$ is a normalization.
\mbox{\rm \small e}nd{defn}
In statistical mechanics, one wants to define Gibbs measures on infinite
graphs $A$ in which case the above definition of course does not make sense.
We follow the usual approach (see~\cite{Ge}), in which one introduces
boundary conditions and takes a weak limit of finite subgraphs
increasing to $A$. Since the precise nature of the boundary conditions
play a role here (we know this to be true at least for the Potts model
with $q > 2$), we handle boundary conditions with extra care and,
unfortunately, notation. We give definitions in the case of a rooted
tree, though the extensions to general locally finite graphs are immediate.
By a {\bf tree}, we mean any connected loopless graph $\Gamma$ where
every vertex has finite degree. One fixes a vertex $o$ of $\Gamma$
which we call the {\bf root}, obtaining a {\bf rooted tree}.
The vertex set of $\Gamma$ is denoted by $V(\Gamma)$. If $x$ is a vertex,
we write $|x|$ for the number of edges on the shortest
path from $o$ to $x$ and for two vertices $x$ and $y$, we
write $|x-y|$ for the number of edges on the shortest
path from $x$ to $y$. For vertices $x$ and $y$, we write $x \le y$
if $x$ is on the shortest path from $o$ to $y$, $x < y$
if $x \le y$ and $x \ne y$, and $x \thetao y$ if $x \le y$ and
$|y|=|x|+1$. For $x \in V(\Gamma)$, the tree $\Gamma (x)$ denotes
the subtree of $\Gamma$ rooted at $x$ consisting of $x$ and all of its
descendents. We also define $\bar{d}eltaartial\Gamma$, which we refer to as the
boundary of $\Gamma$, to be the set of infinite
self-avoiding paths starting from $o$.
Throughout the paper, the following assumption is in force.
\noindent{\bf ASSUMPTION:} For all trees considered in this paper,
the number of children of the vertices will be assumed bounded
and we will denote this bound by $B$.
A {\bf cutset} $C$ is a finite set of vertices not including $o$ such that
every self-avoiding infinite path from $o$ intersects $C$ and such that there
is no pair $x , y \in C$ with $x < y$. Given a cutset $C$,
$\Gamma \begin{equation}gin{array}ckslash C$ has one finite component (which contains $o$)
which we denote by $C^i$ (``i'' for inside) and we let
$C^o$ (``o'' for outside) denote the union of the infinite components
of $\Gamma \begin{equation}gin{array}ckslash C$. We say that a sequence
$\{ C_n \}$ of cutsets approaches $\infty$ if for all $v \in \Gamma$,
$v \in C_n^i$ for all sufficiently large $n$.
Boundary conditions will take the form of specifications of the
value of $\mbox{\rm \small e}ta$ at some cutset $C$.
Let $\bar{d}eltata$ be any element of ${\bf S}^C$. The Gibbs measure with boundary
condition $\bar{d}eltata$ is the probability
measure $\mu^\bar{d}eltata_C = \mu^{{\cal J} , \bar{d}eltata}_C$ on ${\bf S}^{C^i}$
whose density with respect to product measure $\bar{d}x^{C^i}$ is given by
\begin{equation}gin{equation} \labelel{eq:Gibbs}
{ \mbox{\rm \small e}xp (- H^{{\cal J} , \bar{d}eltata}_C (\mbox{\rm \small e}ta)) \over Z},\,\,\,\, \mbox{\rm \small e}ta\in {\bf S}^{C^i}
\mbox{\rm \small e}nd{equation}
where
$$ H^{{\cal J} , \bar{d}eltata}_C (\mbox{\rm \small e}ta) = \sum_{e = \overline{xy} \in E(\Gamma)
\atop x,y \in C^i} {\cal J} (e) H(\mbox{\rm \small e}ta (x) , \mbox{\rm \small e}ta (y))
+ \sum_{e = \overline{xy} \in E(\Gamma) \atop x \in C^i, y \in C}
{\cal J} (e) H(\mbox{\rm \small e}ta (x) , \bar{d}eltata (y)) $$
and
$Z = \int \mbox{\rm \small e}xp (- H^{{\cal J} , \bar{d}eltata}_C (\mbox{\rm \small e}ta)) \, \bar{d}x^{C^i}$ is a normalization.
When we don't include the second summand above,
we call this the {\it free} Gibbs measure on $C^i$, denoted by $\mu^{\rm free}_C$,
where ${\cal J}$ is suppressed in the notation.
As we will see in Lemma~\ref{lem:free}, the free measure
does not depend on $C$ except for its domain of definition,
so we can later also suppress $C$ in the notation.
\begin{equation}gin{defn} \labelel{defn:gibbstree}
A probability measure $\mu$ on ${\bf S}^{V(\Gamma)}$ is called a {\bf Gibbs state}
for the interactions ${\cal J}$ if for each cutset $C$, the
conditional distribution on $C^i$ given the configuration $\bar{d}eltata'$
on $C\cup C^o$ is given by $\mu_C^{{\cal J} , \bar{d}eltata}$ where $\bar{d}eltata$
is the restriction of $\bar{d}eltata'$ to $C$. (A similar definition is used for
general graphs.)
Both in the case of lattices and trees (or for any graph), we say that
a statistical ensemble {\bf exhibits a phase transition (PT) for the
interaction strengths ${\cal J}$} if there is more than one Gibbs state
for the interaction strengths ${\cal J}$.
\mbox{\rm \small e}nd{defn}
In the next section we will prove
\begin{equation}gin{lem} \labelel{lem:free}
Fix interaction strengths ${\cal J}$ and let
$C$ and $D$ be any two cutsets of $\Gamma$. Then the projections
of $\mu^{\rm free}_C$ and $\mu^{\rm free}_D$ to ${\bf S}^{C^i \cap D^i}$ are equal. Hence the
measures $\mu^{\rm free}_C$ have a weak limit as $C \rightarrow \infty$,
denoted $\mu^{\rm free}$.
\mbox{\rm \small e}nd{lem}
For general graphs, the measures $\mu^{\rm free}_C$ are not compatible
in this way. Also, one has the following fact, which follows from
Theorems~4.17 and~7.12 in \cite{Ge}.
\begin{equation}gin{lem} \labelel{lem:limits}
If $\{C_n\}$ is a sequence of cutsets approaching $\infty$ and if for each
$n$, $\bar{d}eltata_n\in {\bf S}^{C_n}$, then any weak subsequential limit of the sequence
$\{\mu_{C_n}^{{\cal J},\bar{d}eltata_n}\}_{n\ge 1}$
is a Gibbs state for the interactions ${\cal J}$.
In addition, if all such possible limits are the same,
then there is no phase transition. (A similar statement holds for
graphs other than trees.)
\mbox{\rm \small e}nd{lem}
We pause for a few remarks about more general graphs, before restricting
our discussion to trees for the rest of the paper. Lemma~\ref{lem:free}
does not apply to graphs with cycles, so the existence of a unique
weak limit $\mu^{\rm free}$ is not guaranteed there, but Lemma~\ref{lem:limits}
together with compactness tells us that there always is at least one Gibbs
state. The state of knowledge about the rotor model (Example~\ref{eg:rotor})
on more general graphs is somewhat interesting. It is known
(see~\cite{Ge}, p.178 and p.434)
that for $Z\!\!\!Z^d$, $d \leq 2$, all Gibbs states are rotationally invariant
when ${\cal J}\mbox{\rm \small e}quiv J$ for any $J$
(and it is believed but not known that there is a unique Gibbs state for the
rotor model in this case) while for $d \geq 3$, there are values of $J$
for which the rotor model with ${\cal J}\mbox{\rm \small e}quiv J$ has a Gibbs state whose
distribution at the origin is not
rotationally invariant (and hence there is
more than one Gibbs state). In statistical mechanics,
this latter phenomenon is referred to as a {\it continuous
symmetry breaking} since we have a continuous state space (the circle) where
the interactions are invariant under a certain continuous symmetry
(rotations) but there are Gibbs states which are not invariant under this
symmetry. We also mention that it is proved in~\cite{C} that
for the rotor model with ${\cal J}\mbox{\rm \small e}quiv J$ for any $J$
on any graph of bounded degree
for which simple random walk is recurrent, all
the Gibbs states are rotationally invariant. (This was then extended
in~\cite{MW} where the condition of boundedness of the degree is dropped
and the group involved is allowed to be more general than the circle.)
This however is not a sharp criterion: in~\cite{E},
a graph (in fact a tree) is constructed for which simple random walk
is transient but such that there is no phase transition in the
rotor model when ${\cal J}\mbox{\rm \small e}quiv J$ for any $J$. (This will also follow from
Theorem~\ref{th:0hd} below together with the easy fact that
there are trees with branching number 1 for which
simple random walk is transient.)
However, Y.\ Peres has conjectured a sharp criterion,
Conjecture~\ref{conj:peres} below, for which our Corollary~\ref{cor:perestree}
together with the discussion following it provides some corroboration.
For the rest of this paper, we will restrict to trees. It is usually
in this context that the most explicit results can be obtained and our
basic goal is to determine whether there is a phase transition by comparing
the interaction strengths with the ``size'' (branching number) of our tree.
It turns out that we can only
partially answer this question but the question which we can answer more
completely is whether there is a {\it robust} phase transition, a concept
which we will introduce shortly.
\begin{equation}gin{defn} \labelel{defn:notation}
Given ${\cal J},C$ and $\bar{d}eltata$ defined on $C$, let
$f^{{\cal J},\bar{d}eltata}_{C , o}$
(or $f^{\bar{d}eltata}_{C , o}$ if ${\cal J}$ is understood)
denote the marginal density of $\mu^{{\cal J} , \bar{d}eltata}_{C}$ at the root $o$.
\mbox{\rm \small e}nd{defn}
For any tree, recall that $\Gamma (v)$ denotes the subtree
rooted at $v$, so that the tree $\Gamma(v)$ has vertex set
$\{ w \in \Gamma : v \leq w\}$. If $v\in C^i$ and
we intersect $C$ with $\Gamma (v)$, we obtain a cutset $C(v)$ for $\Gamma(v)$.
We now extend Definition~\ref{defn:notation} to other marginals as follows.
\begin{equation}gin{defn} \labelel{defn:marginals}
With ${\cal J},C$ and $\bar{d}eltata$ as in Definition~\ref{defn:notation} and $v \in C^i$,
define $f_{C,v}^{{\cal J} , \bar{d}elta}$
by replacing $\Gamma$ by $\Gamma (v)$, $C$ with $C(v)$, ${\cal J}$ with
${\cal J}$ restricted to $E (\Gamma (v))$, $\bar{d}eltata$ with $\bar{d}eltata$ restricted
to $C(v)$ and $o$ with $v$ in Definition~\ref{defn:notation}.
\mbox{\rm \small e}nd{defn}
It is important to note that $f_{C,v}^{{\cal J},\bar{d}elta}$ is not the density
of the projection of $\mu_C^{{\cal J},\bar{d}elta}$ onto vertex $v$, but rather
the density of a Gibbs measure with similar boundary conditions
on the smaller graph $\Gamma (v)$.
\begin{equation}gin{defn} \labelel{defn:SB}
A statistical ensemble on a tree $\Gamma$ exhibits a
{\bf symmetry breaking (SB) for the interactions ${\cal J}$}
if there exists a Gibbs state such that the marginal distribution at some
vertex $v$ is not $G$--invariant (or equivalently is not $\bar{d}x$).
\mbox{\rm \small e}nd{defn}
The following proposition which will be proved in Section~\ref{sec:prelims}
is interesting since it establishes the equivalence of PT and SB for
general trees and general statistical ensembles, something not known for
general graphs, see the remark below.
\begin{equation}gin{prop} \labelel{prop:SB=}
Consider a statistical ensemble on a tree $\Gamma$ with interactions ${\cal J}$.
The following four conditions are equivalent. \\
(i) There exists a vertex $v$ such that for
any sequence of cutsets $C_n\thetao\infty$, there exist boundary
conditions $\bar{d}elta_n$ on $C_n$ such that
$$
\inf_n \|f_{C_n,v}^{\bar{d}elta_n}-1\|_\infty \neq 0.
$$
(ii) There exists a vertex $v$, a
sequence of cutsets $C_n\thetao\infty$ and boundary
conditions $\bar{d}elta_n$ on $C_n$ such that
$$
\inf_n \|f_{C_n,v}^{\bar{d}elta_n}-1\|_\infty \neq 0.
$$
(iii) The system satisfies SB. \\
(iv) The system satisfies PT.
\mbox{\rm \small e}nd{prop}
We now fix a distinguished element in ${\bf S}$, hereafter denoted ${\hat{0}}$.
The notation $\mu^{{\cal J} , +}_C$ denotes $\mu^{{\cal J} , \bar{d}eltata}_C$ when
$\bar{d}eltata$ is the constant function ${\hat{0}}$. In the case ${\cal J} \mbox{\rm \small e}quiv J$, we
denote this simply $\mu^{J,+}_C$. We will be particularly concerned
about whether $\mu^{{\cal J} , +}_C \rightarrow \mu^{\rm free}$ weakly, as
$C \rightarrow \infty$.
\begin{equation}gin{defn} \labelel{defn:SB+}
A statistical ensemble on a tree $\Gamma$ exhibits a
{\bf symmetry breaking with plus boundary conditions (SB+) for the
interactions ${\cal J}$} if there exists a vertex $v$ and a sequence of
cutsets $C_n\thetao\infty$ such that
$$
\inf_n \|f_{C_n,v}^{{\cal J},+}-1\|_\infty \neq 0.
$$
\mbox{\rm \small e}nd{defn}
Note that by symmetry, SB+ does not depend on which point of ${\bf S}$
is chosen to be ${\hat{0}}$.
In Section~\ref{sub:spherical} we will prove:
\begin{equation}gin{pr} \labelel{pr:rotor equiv}
For the rotor model on a tree, SB is equivalent to SB+.
\mbox{\rm \small e}nd{pr}
We conjecture but cannot prove the stronger statement:
\begin{equation}gin{conj} \labelel{conj:SB}
For any Heisenberg model on any graph, SB is equivalent to SB+.
\mbox{\rm \small e}nd{conj}
\noindent{\mbox{\rm \small e}m Remarks:} $(i)$ By Proposition~\ref{prop:SB=}, we have that
SB+ implies SB for any statistical ensemble on a tree. While
Proposition~\ref{prop:SB=} tells us that PT and SB are equivalent for any
statistical ensemble
on a tree, we note that such a result is not even known for the rotor model
on $Z\!\!\!Z^2$ where it has been established that for all
$J$, all Gibbs states are rotationally invariant for ${\cal J}\mbox{\rm \small e}quiv J$
but where it has not been established that there is no phase transition.
A weaker form of the above conjecture would be that SB+ and SB are
equivalent for all Heisenberg models on trees. This is
Problem~\ref{pblm:all spheres} in~Section~\ref{sec:anal}.
An extension to graphs with cycles would seem to entail a different kind
of reasoning, perhaps similar to the inequalities of Monroe and
Pearce~\cite{MP} which fall just short of proving
Conjecture~\ref{conj:SB} for the rotor model. \\
\noindent{$(ii)$} The fact that PT and SB+
are equivalent when the rotor model is replaced by the Ising model
is an immediate consequence of the fact that the probability measure is
stochastically increasing in the boundary conditions. More generally,
it is also the case that PT and SB+ are equivalent for the Potts models
(see \cite{ACCN}).
We now consider the idea of a {\it robust phase transition} where we
investigate if the boundary conditions on a cutset have a nontrivial effect
on the root even when the interactions along the cutset are made
arbitrarily small but fixed.
Given parameters $J>0$ and $J' \in (0,J]$ and
a cutset $C$ of $\Gamma$, let $ {\cal J} ( J', J , C)$ be the function
on $E(\Gamma)$ which is $J$ on edges in $C^i$ and
$J'$ on edges connecting $C^i$ to $C$ (the values elsewhere being
irrelevant).
Let $f^{J',J , +}_{C_n , o}$ denote the marginal at the root $o$ of the
measure $\mu^{J',J, +}_C:=\mu^{{\cal J} (J', J , C) , +}_C$.
\begin{equation}gin{defn} \labelel{defn:robustPT}
The statistical ensemble on the tree $\Gamma$ has a {\bf robust phase
transition (RPT) for the parameter $J>0$} if for every $J'\in (0,J]$
$$
\inf_C \|f^{J',J , +}_{C , o} - 1\|_\infty \neq 0 \,
$$
where the $\inf$ is taken over all cutsets $C$.
\mbox{\rm \small e}nd{defn}
\noindent{\mbox{\rm \small e}m Remarks:}
In the case ${\cal J} \mbox{\rm \small e}quiv J$, by taking $J'=J$, it is clear
that a RPT implies SB+ (which in turn implies SB and PT). Note that
in this case, RPT is
stronger than SB+ not only because $J'$ can be any number in $(0,J]$
and the root $o$ must play the role of $v$
but also because in SB+, we only require that for {\it some} sequence
of cutsets going to infinity, the marginal at the vertex $v$ stays away from
uniform while in RPT, we require this for {\it all} cutsets going to
infinity.
We note also that with some care, this definition makes sense for general
graphs, and that the issue of robustness of phase transition on general graphs
is worth investigating, although we do not do so here.
Our first theorem gives criteria based on $J$ and the branching number
of $\Gamma$ (which will now be defined) for robust phase transition to
occur for the Heisenberg models. A little later on, we will have an analogous
result for the Potts models. In \cite{F}, Furstenberg introduced the notion
of the Hausdorff dimension of a tree (or more accurately of the boundary of
the tree). This was further investigated by Lyons~(\cite{Ly2}) using the
term branching number instead.
The {\bf branching number} of a tree $\Gamma$, denoted
$\thetaextstyle {br} (\Gamma)$, is a real number greater than or equal to one
that measures the average number of branches per vertex of the
tree. More precisely, the {\bf branching number} of $\Gamma$ is defined by
$$\thetaextstyle{br}\,\Gamma:=\inf\left\{\lambda>0;\inf\limits_{C}
\sum_{x \in C}\lambda^{-|x|} = 0 \right \} \;$$
where the second infimum is over all cutsets $C$.
The branching number is a measure of the average number of
branches per vertex of $\Gamma$.
It is less than or equal to $\liminf_{n \thetao \infty} M_n^{1/n}$, where
$M_n := | \left \{x \in \Gamma ; |x| = n \right \}|$,
and takes more of the structure of $\Gamma$ into account
than does this latter growth rate.
For sufficiently regular trees, such as homogeneous trees or, more generally,
Galton-Watson trees, $\thetaextstyle{br}\, \Gamma = \lim_{n\thetao\infty}
M_n^{1/n}$ (\cite{Ly2}). We also mention that the branching number is the
exponential of the Hausdorff dimension of $\bar{d}eltaartial\Gamma$ where the latter
is endowed with the
metric which gives distance $e^{-k}$ to two paths which split off after $k$
steps. As indicated earlier, the branching number has been an important
quantity in previous investigations. More specifically, in \cite{Ly1} and
\cite{Ly2}, the critical values for independent percolation and
for phase transition in the Ising model on general trees
are explicitly computed in terms of the branching number.
For each $J\ge 0$, define a continuous strictly positive
probability density function
$K_J : {\bf S} \rightarrow \overline{h}ox{I\kern-.2em\overline{h}ox{R}}^+$ by
\begin{equation}gin{equation} \labelel{eq:KJ}
K_J (u): = C(J)^{-1} \mbox{\rm \small e}xp (- J H (u , {\hat{0}}))
\mbox{\rm \small e}nd{equation}
where $C(J) = \int \mbox{\rm \small e}xp (- J H(w,{\hat{0}})) \, \bar{d}x (w)$ is a normalizing
constant, and more generally let
$K_{J,y} : {\bf S} \rightarrow \overline{h}ox{I\kern-.2em\overline{h}ox{R}}^+$ be given by
\begin{equation}gin{equation} \labelel{eq:KJy}
K_{J,y} (u): = C(J)^{-1} \mbox{\rm \small e}xp (- J H (u , y))
\mbox{\rm \small e}nd{equation}
(noting that $K_{J,{\hat{0}}}=K_{J}$).
Let ${\cal K}J$ denote the convolution operator on the space
$L^2 ({\bf S} , \bar{d}x)$ given by the formula
\begin{equation}gin{equation} \labelel{eq:conv}
{\cal K}J f (u) : = \int_{{\bf S}} f(x) K_{J,x} (u) \bar{d}x(x) \,\, .
\mbox{\rm \small e}nd{equation}
Note that by the assumed invariance $\int_{{\bf S}} \mbox{\rm \small e}xp (- J H(w,y)) \, \bar{d}x (w)$
is independent of $y$ and that $f\ge 0$ and $\int_{{\bf S}} f(x) \bar{d}x(x)=1$ imply
that ${\cal K}J f\ge 0$ and $\int_{{\bf S}} {\cal K}J f(x) \bar{d}x(x)=1$.
We extend the above notation to cover the case where $f$ is a pointmass $\bar{d}elta_y$
at $y$ by defining in that case
\begin{equation}gin{equation} \labelel{eq:pointconv}
{\cal K}J \bar{d}elta_y (u) : = K_{J , y}(u) .
\mbox{\rm \small e}nd{equation}
We will now give the exact critical
parameter $J$ for RPT for the Heisenberg models. For any $d\ge 1$, let
$$
{\cal R}dJ:= {\int_{-1}^1 r e^{Jr}(1-r^2)^{{d \over 2}-1} dr \over
\int_{-1}^1 e^{Jr}(1-r^2)^{{d \over 2}-1} dr }.
$$
When $d=1$ (rotor model), this is (by a change of variables)
the first Fourier coefficient of $K_J$
($\int_{{\bf S}} K_J(\thetaheta) \cos (\thetaheta) d\thetaheta$) which is perhaps
more illustrative.
When $d=2$, this is the first Legendre coefficient
of $e^{Jr}$ (properly normalized) and for $d\ge 3$,
this is the first so-called ultraspherical coefficient of $e^{Jr}$
(properly normalized).
\begin{equation}gin{th} \labelel{th:main} Let $d\ge 1$. \\
(i) If $\thetaextstyle {br} (\Gamma) {\cal R}dJ <1$,
then the $d$--dimensional Heisenberg model on $\Gamma$ with
parameter $J$ does not exhibit a robust phase transition. \\
(ii) If $\thetaextstyle{br}(\Gamma) {\cal R}dJ >1$, then the $d$--dimensional
Heisenberg model on $\Gamma$ with parameter $J$ exhibits a robust phase
transition.
\mbox{\rm \small e}nd{th}
\noindent{\mbox{\rm \small e}m Remark:}
It is easy to see that $\lim_{d\thetao\infty} {\cal R}dJ=0$ which says that
it is harder to obtain a robust phase transition on higher dimensional
spheres. This is consistent with the fact that it is in some sense harder to
have a phase transition for the rotor model than in the Ising
model (0-dimensional sphere); this
latter fact can be established using the ideas in \cite{PS}.
A simple computation shows that the derivative of ${\cal R}dJ$ with respect to
$J$ is the variance of a random variable whose density function is
proportional to $e^{Jr}(1-r^2)^{d/2 -1}$ on $[-1,1]$, thereby obtaining
the following lemma.
\begin{equation}gin{lem} \labelel{lem:inc}
For any $d\ge 1$,
we have that ${\cal R}dJ$ is a strictly increasing function of $J$.
\mbox{\rm \small e}nd{lem}
Theorem \ref{th:main} and Lemma \ref{lem:inc} together with the
fact that for any $d\ge 1$,
${\cal R}dJ$ is a continuous function of $J$ which approaches
0 as $J\thetao 0$ and approaches 1 as $J\thetao \infty$ give us
the following corollary.
\begin{equation}gin{cor} \labelel{cor:critical}
For any Heisenberg model with $d\ge 1$ and any
tree $\Gamma$ with branching number larger than 1, let $J_c=J_c(\Gamma, d)$
be such that $\thetaextstyle{br}(\Gamma) \rho^d(J_c)=1$. Then
there is a robust phase transition for the $d$--dimensional Heisenberg
model on $\Gamma$ if $J> J_c$ and
there is no such robust phase transition for $J< J_c$.
\mbox{\rm \small e}nd{cor}
For the Heisenberg models, we believe that phase transition and
robust phase transition coincide and therefore we have the
following conjecture.
\begin{equation}gin{conj} \labelel{conj:PS}
For any $d\ge 1$, if $\thetaextstyle {br} (\Gamma) {\cal R}dJ <1$,
then the $d$--dimensional Heisenberg
model on $\Gamma$ with parameter $J$ does not exhibit a phase
transition.
\mbox{\rm \small e}nd{conj}
We can however obtain the following weaker form of this conjecture which is
valid for all statistical ensembles.
\begin{equation}gin{th} \labelel{th:0hd}
If $\thetaextstyle {br} (\Gamma) = 1$, then there is no phase transition
for any statistical ensemble on $\Gamma$ with bounded ${\cal J}$.
\mbox{\rm \small e}nd{th}
Theorems \ref{th:main}(ii) and \ref{th:0hd} together with the facts that
RPT implies PT and that for any $d\ge 1$,
$\lim_{J\thetao\infty} {\cal R}dJ = 1$ immediately yield the following corollary.
\begin{equation}gin{cor} \labelel{cor:perestree}
For any Heisenberg model with $d\ge 1$ and for any tree $\Gamma$,
there is a \bar{d}eltat for the tree $\Gamma$ for some
value of the parameter $J$ if and only if $\thetaextstyle {br} (\Gamma)>1$.
\mbox{\rm \small e}nd{cor}
Since it is known (see \cite{Ly2}) that $\thetaextstyle {br} (\Gamma)>1$
if and only if there is some $p< 1$ with the property that when
performing independent percolation on $\Gamma$ with parameter $p$, there
exists a.s.\ an infinite cluster on which simple random walk is transient, the
above corollary yields the following conjecture of Y. Peres for the
special case of trees of bounded degree.
\begin{equation}gin{conj} \labelel{conj:peres}
For any graph $A$, the rotor model exhibits a \bar{d}eltat for some $J$ if and only
if there is some $p< 1$ with the property
that performing independent bond percolation on $A$ with parameter $p$, there
exists a.s.\ an infinite cluster on which simple random walk is transient.
\mbox{\rm \small e}nd{conj}
Recall that the rotor model on the graph $A$ exhibits
no SB for any parameter $J$ if $A$ is recurrent for simple random walk,
which is of course consistent with the above conjecture.
Note that, on the other hand, the standard Ising model does exhibit a
\bar{d}eltat on $Z\!\!\!Z^2$, a graph which is recurrent (as are its subgraphs)
for simple random walk.
The next result states the critical value for RPT for the Potts models.
\begin{equation}gin{th} \labelel{th:potts}
Consider the Potts model with $q \ge 2$ and let
$$\alphapha_J = {e^J - e^{-J} \over e^J + (q-1) e^{-J}} \, .$$
(i) If $\thetaextstyle {br} (\Gamma) \alphapha_J <1$,
then the Potts model on $\Gamma$ with
parameter $J$ does not exhibit a robust phase transition. \\
(ii) If $\thetaextstyle{br}(\Gamma) \alphapha_J >1$, then the
Potts model on $\Gamma$ with parameter $J$ exhibits a robust phase
transition.
\mbox{\rm \small e}nd{th}
\noindent{\mbox{\rm \small e}m Remarks:}\\
$(i)$ $d\alphapha_J/dJ >0$ and so there is a critical value of $J$ depending
on $\thetaextstyle{br}(\Gamma)$ analogous to in Corollary~\ref{cor:critical}
for the Heisenberg models. \\
\noindent{$(ii)$}
Note that when $q=2$ (the Ising model), this formula agrees
with the formula for the Heisenberg models when one formally sets $d=0$
in the formula
$$
{\cal R}dJ=\int_{S^d} (x \cdot {\hat{0}}) K_J (x) \, \bar{d}x(x),
$$
the latter being obtained by a change of variables.
To point out the subtlety involved in Conjecture \ref{conj:PS},
we continue to discuss the Potts model, a case in which the analogue of
Conjecture~\ref{conj:PS} fails. Our final result tells us that
phase transitions (unlike robust phase transitions) in the Potts model with
$q > 2$ cannot be determined by the branching number.
\begin{equation}gin{th} \labelel{th:2trees} Given any integer $q >2$,
there exist trees $\Gamma_1$ and $\Gamma_2$ and a nontrivial interval $I$ such
that $\thetaextstyle {br} (\Gamma_1) < \thetaextstyle {br} (\Gamma_2)$
and for any $J\in I$, there is a phase transition for the $q$--state
Potts model with parameter $J$ on $\Gamma_1$ but
no such phase transition on $\Gamma_2$.
\mbox{\rm \small e}nd{th}
\noindent{\mbox{\rm \small e}m Remarks:}\\
$(i)$ $\Gamma_1$ and $\Gamma_2$ can each be taken to
be spherically symmetric which means that for all $k$, all vertices at the
$k$th generation have the same number of children. \\
\noindent{$(ii)$}
In the case $q=2$, more is known. In \cite{Ly1}, the critical value
for phase transition in the Ising model is found and corresponds to
what is obtained in Theorem~\ref{th:potts} above. It follows that
there is never
a non-robust phase transition except possibly at the critical value. However,
a sharp capacity criterion exists~\cite{PP} for phase transition for the
Ising model (settling the issue of phase transition at the critical parameter)
and using this criterion, one can show that phase transition and robust
phase transition correspond even at criticality.
The arguments of~\cite{PP} cannot be extended to the Potts model for $q > 2$
because the operator ${\cal K}J$, acting on a certain likelihood function,
when conjugated by the logarithm is not concave in this case.
Theorems~\ref{th:potts} and~\ref{th:2trees}
together tell us that there is indeed a non-robust phase
transition when $q > 2$ for a nontrivial interval of $J$.
The rest of the paper is devoted to the proofs of the above results.
In Section~\ref{sec:prelims}, we collect several lemmas that apply to
general statistical ensembles, including the basic recursion
formula (Lemma~\ref{lem:rec}) that allows us to analyze general statistical
ensembles on trees, prove Lemma~\ref{lem:free} and
Proposition~\ref{prop:SB=} as well as provide some background
concerning Heisenberg models (showing that they satisfy the more
general hypotheses of Theorems~\ref{th:gen ii} and~\ref{th:gen i} given
later on) and the more general notion of distance
regular spaces. Section~\ref{sec:proofs} is devoted to the proofs of
Theorems~\ref{th:gen ii} and~\ref{th:gen i}. In
Section~\ref{sec:anal}, we use these theorems to find the critical
parameters for robust phase transition in the Heisenberg and
Potts models, Theorems~\ref{th:main} and~\ref{th:potts}, as well as
prove Proposition~\ref{pr:rotor equiv}.
Section~\ref{sec:zero} discusses the special case of trees of
branching number 1, proving Theorem~\ref{th:0hd}. Finally, in
Section~\ref{sec:potts}, Theorem~\ref{th:2trees} is proved.
\setcounter{equation}{0}
\section{Basic background results} \labelel{sec:prelims}
In this section, we collect various background results which
will be needed to prove the results described in the introduction.
We begin with a subsection describing results pertaining to trees that
hold for general statistical ensembles.
After discussing the concept of a distance
regular space in Section~\ref{sub:drs}, we specialize
to Heisenberg models (the most relevant family of continuous distance
regular models) in Section~\ref{sub:sphere}
and then to distance regular graphs in Section~\ref{sub:finite}.
\subsection{The fundamental recursion and other lemmas} \labelel{sub:rec}
We start off with two lemmas exploiting the recursive structure
of trees.
Let ${\bf S},G$ and $H$ be a statistical ensemble.
Let $A_1$ and $A_2$ be two disjoint finite graphs, with distinguished
vertices $v_1 \in V(A_1)$ and $v_2 \in V(A_2)$. Let ${\cal J}_1$ and ${\cal J}_2$
be interaction functions for $A_1$ and $A_2$,
i.e., positive functions on $E(A_1)$
and $E(A_2)$ respectively. For any $C_1 \subseteq V(A_1) \setminus
\{ v_1 \}$ (possibly empty) and any $C_2 \subseteq V(A_2)$, and for any
$\bar{d}eltata_1 \in {\bf S}^{C_1}$ and $\bar{d}eltata_2 \in {\bf S}^{C_2}$,
we have measures $\mu_i := \mu^{{\cal J}_i , \bar{d}eltata_i}_{C_i}$, $i = 1, 2$
on ${\bf S}^{V(A_i)\setminus C_i}$ defined (essentially) by~(\ref{eq:Gibbs}).
Abbreviate $H_{C_i}^{{\cal J}_i,\bar{d}elta_i}$ (which has the obvious meaning) by $H_i$.
Let $A$ be the union of $A_1$
and $A_2$ together with an edge connecting $v_1$ and $v_2$. Let
$C = C_1 \cup C_2$, ${\cal J}$ extend each ${\cal J}_i$ and the value of the
new edge be given the value $J$, $\bar{d}eltata$
extend each $\bar{d}eltata_i$ and denote $\mu^{{\cal J} , \bar{d}eltata}_C$
(a probability measure on
${\bf S}^{(V(A_1)\setminus C_1)\cup (V(A_2)\setminus C_2)}$)
by $\mu$ and $H^{{\cal J} , \bar{d}eltata}_C$ (again having the obvious meaning) by $H$.
The identity \begin{equation}gin{equation} \labelel{eq:Hdecomp}
H = H_1 + H_2 + J H (\mbox{\rm \small e}ta (v_1) , \mbox{\rm \small e}ta (v_2))
\mbox{\rm \small e}nd{equation}
leads to the following lemma.
\begin{equation}gin{lem} \labelel{lem:decomps}
The measure $\mu$ satisfies
\begin{equation}gin{equation} \labelel{eq:mudecomp}
{d\mu \over d (\mu_1 \thetaimes \mu_2)} = c \mbox{\rm \small e}xp [- J H(\mbox{\rm \small e}ta_1 (v_1) ,
\mbox{\rm \small e}ta_2 (v_2))] ,
\mbox{\rm \small e}nd{equation}
where
$$c = \left [ \int \int \mbox{\rm \small e}xp (- J H (\mbox{\rm \small e}ta_1 (v_1) , \mbox{\rm \small e}ta_2 (v_2)))
\, d\mu_1 (\mbox{\rm \small e}ta_1) \, d\mu_2 (\mbox{\rm \small e}ta_2) \right ]^{-1}$$
is a normalizing constant. Let $f_i$ denote the marginal density
of $\mu_i$ at $v_i$, $i = 1 , 2$, and $f$ denotes the marginal
density of $\mu$ at $v_1$. Then the projection $\mu^{(1)}$ of
$\mu$ onto ${\bf S}^{V(A_1)\setminus C_1}$ satisfies
\begin{equation}gin{equation} \labelel{eq:mudecomp2}
\mu^{(1)} = c \int \int \mu_{1 , y} f_1 (y) f_2 (z) \mbox{\rm \small e}xp (- J H(y,z))
\, \bar{d}x (z) \, \bar{d}x (y)
\mbox{\rm \small e}nd{equation}
for some normalizing constant $c$, where $\mu_{1 , y}$ denotes the
conditional distribution of $\mu_1$ given $\mbox{\rm \small e}ta (v_1) = y$. Consequently,
\begin{equation}gin{equation} \labelel{eq:fdecomp}
f (y) = c f_1 (y) \int f_2 (z) \mbox{\rm \small e}xp (- J H(y,z)) \, \bar{d}x (z) \, ,
\mbox{\rm \small e}nd{equation}
where $c$ normalizes $f$ to be a probability density.
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.} The relation~(\ref{eq:mudecomp}) follows
from~(\ref{eq:Hdecomp}) and the defining equation~(\ref{eq:Gibbs}). From
this it follows that the measure $\mu$ on pairs $(\mbox{\rm \small e}ta_1 , \mbox{\rm \small e}ta_2)$
makes $\mbox{\rm \small e}ta_1$ and $\mbox{\rm \small e}ta_2$ conditionally independent given $\mbox{\rm \small e}ta_1 (v_1)$
and $\mbox{\rm \small e}ta_2 (v_2)$. Hence the conditional distribution of $\mu^{(1)}$
given $\mbox{\rm \small e}ta_1 (v_1) = y$ and $\mbox{\rm \small e}ta_2 (v_2) = z$ is just $\mu_{1 , y}$.
Next, (\ref{eq:mudecomp}) and the last fact
yield~(\ref{eq:mudecomp2}). The marginal of
$\mu_{1, y}$ at $v_1$ is just $\bar{d}eltata_y$, and
so~(\ref{eq:mudecomp2}) yields~(\ref{eq:fdecomp}).
$
\Box$
A tree $\Gamma$ may be built up from isolated vertices by the joining
operation described in the previous lemma. The decompositions in
Lemma~\ref{lem:decomps} may be applied inductively
to derive a fundamental recursion for marginals. This recursion,
Lemma~\ref{lem:rec} below, expresses the marginal distribution
at the root of $\Gamma$ as a pointwise product of marginals at
the roots of each of the generation 1 subtrees, each convolved
with a kernel $K_J$. The normalized pointwise product will be
ubiquitous throughout what follows, so we introduce notation for it.
\begin{equation}gin{defn}
If $f_1 , \ldots , f_k$ are nonnegative functions on ${\bf S}$ with
$\int f_i \, \bar{d}x = 1$ for each $i$,
let
\\ $\bar{d}eltaoi_k (f_1 , \ldots , f_k)$
denote the normalized pointwise product,
$$\bar{d}eltaoi_k (f_1 , \ldots , f_k) (x) = {\bar{d}eltarod_{i=1}^k f_i (x) \over
\int \bar{d}eltarod_{i=1}^k f_i (y) \, \bar{d}x (y)}$$
whenever this makes sense, e.g., when each $f_i$ is in $L^k (\bar{d}x)$
and the product is not almost everywhere zero. Let $\bar{d}eltaoi$ denote
the operator which for each $k$ is $\bar{d}eltaoi_k$ on each $k$-tuple of functions.
There is an obvious associativity property, namely $\bar{d}eltaoi (\bar{d}eltaoi (f,g) , h)
= \bar{d}eltaoi (f,g,h)$, which may be extended to arbitrarily many arguments.
\mbox{\rm \small e}nd{defn}
\begin{equation}gin{lem}[Fundamental recursion] \labelel{lem:rec}
Given a tree $\Gamma$, a cutset $C$, interactions ${\cal J}$, boundary condition
$\bar{d}eltata$ and $v\in C^i$,
let $\{ w_1 , \ldots , w_k \}$ be the children of $v$. Let $J_1 , \ldots ,
J_k$ denote the values of ${\cal J} (v , w_1) , \ldots , {\cal J} (v , w_k)$. Then
\begin{equation}gin{equation} \labelel{eq:recurse}
f_{C,v}^{{\cal J},\bar{d}elta} = \bar{d}eltaoi ({\cal K}_{J_1} f^{{\cal J} , \bar{d}eltata}_{C , w_1} ,
\ldots , {\cal K}_{J_k} f^{{\cal J} , \bar{d}eltata}_{C , w_k}) \, ,
\mbox{\rm \small e}nd{equation}
where when $w_i\in C$, $f^{{\cal J} , \bar{d}eltata}_{C , w_i}$ is taken to be the point
mass at $\bar{d}eltata(w_i)$ and convention~(\ref{eq:pointconv}) is in effect.
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.}
Passing to the subtree $\Gamma (v)$, we may assume without loss of
generality that $v = o$. Also assume without loss of generality that
$w_1 , \ldots , w_k$ are numbered so that
for some $s$, $w_i \in C^i$ for $i \leq s$ and $w_i \in C$ for $i > s$.
For $i\le s$, let $C(w_i) = C \cap \Gamma (w_i)$. For such $i$, by
definition, $f_i := f^{{\cal J} , \bar{d}elta}_{C,w_i}$ is the marginal at $w_i$
of the measure $\mu_i := \mu^{{\cal J}, \bar{d}elta}_{C(w_i) , w_i}$ on
configurations on $\Gamma (w_i)\cap C^i$, where ${\cal J}$ and $\bar{d}elta$
are restricted to $E (\Gamma (w_i))$ and $C(w_i)$ respectively.
Let $\Gamma_r$ denote the induced subgraph of $\Gamma$ whose vertices
are the union of $\{ o \}$, $\Gamma (w_1) , \ldots , \Gamma (w_r)$.
We prove by induction on $r$ that the density $g_r$ at the root of
$\Gamma_r$ of the analogue of $\mu^{{\cal J} , \bar{d}eltata}_C$ for $\Gamma_r$ is equal to
$$\bar{d}eltaoi ({\cal K}_{J_1} f^{{\cal J} , \bar{d}eltata}_{C , w_1} , \ldots ,
{\cal K}_{J_r} f^{{\cal J} , \bar{d}eltata}_{C , w_r}) \, ;$$
The case $r = k$ is the desired conclusion.
To prove the $r=1$ step, use~(\ref{eq:fdecomp}) with $v_1 = o$,
$A_1 = \{ o \}$, $C_1 = \mbox{\rm \small e}mptyset$, $v_2 = w_1$, $A_2 = \Gamma (w_1)$
and $C_2 = C(w_1)$. If $w_1 \in C$, the $r=1$ case is
trivially true, so assume $s \geq 1$.
The measure $\mu_1$ is uniform on ${\bf S}$ since $C(v) = \mbox{\rm \small e}mptyset$.
Thus from~(\ref{eq:fdecomp}) we find that
$$g_1 (y) = c \int e^{-J_1 H (y,z)} f_1 (z) \, dz
= ({\cal K}_{J_1} f_1) (y)$$
which proves the $r = 1$ case.
For $1 < r \leq s$, use~(\ref{eq:fdecomp}) with $A_1 = \Gamma_{r-1}$,
$v_1 = o$, $C_1 = \Gamma_{r-1} \cap C$, $A_2 = \Gamma (w_r)$,
$v_2 = w_r$ and $C_2 = \Gamma (w_r) \cap C$.
Using~(\ref{eq:fdecomp}) we find that
\begin{equation}gin{eqnarray*}
g_r (y) & = & c g_{r-1} (y) \int e^{-J_r H (y,z)}
f_r (z) \, \bar{d}x (z) \\[1ex]
& = & c g_{r-1} (y) ({\cal K}_{J_r} f_r) (y) \\[1ex]
& = & (\bar{d}eltaoi (g_{r-1} , {\cal K}_{J_r} f_r)) (y) \, .
\mbox{\rm \small e}nd{eqnarray*}
By associativity of $\bar{d}eltaoi$ the induction step is completed for $r \leq s$.
Finally, if $r > s$, then the difference between $H (\mbox{\rm \small e}ta)$ on
$\Gamma_{r-1}$ and $H (\mbox{\rm \small e}ta)$ on $\Gamma_r$ is just $- J_r
H(\mbox{\rm \small e}ta (o) , \bar{d}eltata (w_r))$, so
$$g_r (y) = c g_{r-1} (y) \mbox{\rm \small e}xp (- J_r
H(y , \bar{d}eltata (w_r))) = \left ( \bar{d}eltaoi
(g_{r-1} , {\cal K}_{J_r} f_r) \right ) (y)$$
by the convention~(\ref{eq:pointconv}), and associativity of $\bar{d}eltaoi$
completes the induction as before.
$
\Box$
Another consequence of Lemma~\ref{lem:decomps} is Lemma~\ref{lem:free},
giving the existence of a natural and well defined free boundary measure.
\noindent{\bf Proof of Lemma~\bar{d}eltarotect{\ref{lem:free}}.}
Observe that in~(\ref{eq:mudecomp2}), if $f_2 \mbox{\rm \small e}quiv 1$ then
the integral against $z$ is independent of $y$, so one has
$\mu^{(1)} = \mu_1$. Let $F$ be any cutset and $w \in F^i$ be
chosen so each of its children $v_1 , \ldots , v_k$ is in $F$.
Applying our observation inductively to eliminate each child
of $w$ in turn, we see that the projection of $\mu^{\rm free}_F$ onto
${\bf S}^{F^i \setminus \{ w \}}$ is just $\mu^{\rm free}_{F'}$ where
$F' = F \cup \{ w \} \setminus \{ v_1 , \ldots , v_k \}$.
Given cutsets $C$ and $D$ with $D \cap C^i \neq \mbox{\rm \small e}mptyset$, choose
$v \in D \cap C^i$ and $w \geq v$ maximal in $C^i$. Then all
children of $w$ are in $C$. Applying the previous paragraph
with $F = C$, we see that $\mu^{\rm free}_C$ agrees with $\mu^{\rm free}_{F'}$.
Continually reducing in this way, we conclude that on $C^i \cap D^i$
$\mu^{\rm free}_C$ agrees with $\mu^{\rm free}_Q$ where $Q$ is the
exterior boundary of $C^i \cap D^i$. The same argument shows
that $\mu^{\rm free}_D$ agrees with $\mu^{\rm free}_Q$, which finishes the
proof of the lemma.
$
\Box$
According to Lemma~\ref{lem:rec}, if, for $J>0$, we define ${\bf P}P (J)$ to be
the smallest class of densities containing each $K_{J' , y}$ for
$J' \in (0,J]$ and $y \in {\bf S}$ and closed under ${\cal K}_{J'}$ for $J' \in (0,J]$
and $\bar{d}eltaoi$, then, when ${\cal J}$ is strictly positive and
bounded by $J$, each density $f^{{\cal J} , \bar{d}elta}_{C , v}$ is an element of ${\bf P}P(J)$.
Similarly, if ${\bf P}P_+(J)$ is taken to be
the smallest class of densities containing each $K_{J'}$ for
$J' \in (0,J]$ and closed under ${\cal K}_{J'}$ for $J' \in (0,J]$
and $\bar{d}eltaoi$, then, when ${\cal J}$ is strictly positive and
bounded by $J$, each density
$f^{{\cal J} , +}_{C , v}$ is an element of ${\bf P}P_+(J)$. We also let
${\bf P}P:=\bigcup_{J> 0}{\bf P}P(J)$ and ${\bf P}P_+:=\bigcup_{J> 0}{\bf P}P_+(J)$.
This leads to the following lemma whose proof is left to the reader.
\begin{equation}gin{lem} \labelel{lem:unifbd}
Suppose the interaction strengths $\{ {\cal J} (e) \}$ are bounded above
by some constant.
Then there exist constants $0 < B_{\rm min} < B_{\rm max}$ such that
for every $C , \bar{d}eltata$ and $v \in C^i$, the one-dimensional marginal
of $\mu^{\bar{d}eltata}_C$ at $v$ is absolutely
continuous with respect to $\bar{d}x$ with a
density function in $[B_{\rm min} , B_{\rm max}]$.
It follows, since the above properties are closed under convex combinations,
that all one-dimensional marginals of any Gibbs state have densities
in $[B_{\rm min} , B_{\rm max}]$. Similarly, the $k$-dimensional marginals have
densities in the interval $[B_{\rm min}^{(k)} , B_{\rm max}^{(k)}]$
for some constants $0< B_{\rm min}^{(k)} < B_{\rm max}^{(k)}$.
In addition, the family of all one--dimensional densities which arise as
above is an equicontinuous family.
\mbox{\rm \small e}nd{lem}
The usefulness of the equicontinuity property is that the following
easily proved lemma (whose proof is also left to the reader) tells us that
in determining weak convergence to $\bar{d}x$, it is equivalent to look to see if
there is convergence in $L^\infty$ of the associated densities to 1.
\begin{equation}gin{lem} \labelel{lem:converge}
Let $(X,d)$ be a compact metric space and $\mu$ a probability measure on
$X$ with full support. If $\{f_n\}$ is an equicontinuous family of
probability densities (with respect to $\mu$), then
$$
\lim_{n\thetao\infty} \|f_n-1\|_{\infty} = 0 \mbox{ if and only if }
\lim_{n\thetao\infty} f_n d\mu = \mu \mbox{ weakly }.
$$
\mbox{\rm \small e}nd{lem}
Using this, we can prove the equivalence of phase transition and
symmetry breaking on trees (Proposition~\ref{prop:SB=}).
\noindent{\bf Proof of Proposition~\ref{prop:SB=}.}
(i) implies (ii) is trivial. For (ii) implying (iii), assume we have
a vertex $v$, a sequence of cutsets $C_n\thetao\infty$ and boundary
conditions $\bar{d}elta_n$ on $C_n$ such that
$$
\inf_n \|f_{C_n,v}^{\bar{d}elta_n}-1\|_\infty \neq 0.
$$
Clearly we obtain the same result if we change $\bar{d}elta_n$ on
$C_n\setminus \Gamma(v)$ to anything, in particular, if we take no (i.e.,
free) boundary condition there. We then take any weak limit of these
measures as $n\thetao\infty$. This will yield a Gibbs state and by the first line
of the proof of Lemma~\ref{lem:free}, together with
Lemma~\ref{lem:converge},
the marginal density at $v$ of this Gibbs state is not 1, which proves (iii).
(iii) implies (iv) is also trivial of course. To see that (iv) implies (i),
note that if there is PT, then there exists an extremal Gibbs state
$\mu\neq \mu^{\rm free}$. Choose a cutset $C$ such that
$\mu\neq \mu^{\rm free}$ when restricted to $C^i$. If (i) fails, then for all
$v\in C$, there exists a
sequence of cutsets $C_n\thetao\infty$ such that for all boundary
conditions $\bar{d}elta_n$ on $C_n$ we have that
\begin{equation}gin{equation} \labelel{eq:ivgivesi}
\inf_n \|f_{C_n,v}^{\bar{d}elta_n}-1\|_\infty = 0.
\mbox{\rm \small e}nd{equation}
Clearly, because of the geometry, $\{C_n\}$ can be chosen independent of $v$.
Since $\mu$ is extremal, it is known (see Theorem 7.12(b) in \cite{Ge}, p. 122)
that there exist boundary conditions
$\bar{d}elta_n'$ on $C_n$ so that $\mu_{C_n}^{\bar{d}elta_n'} \rightarrow \mu$ weakly.
However, by (\ref{eq:ivgivesi}) and Lemma~\ref{lem:rec}, $\mu$ must equal
$\mu^{\rm free}$ on $C^i$, a contradiction. $
\Box$
\subsection{Distance regular spaces} \labelel{sub:drs}
Our primary interest in this paper is in the Heisenberg models.
Nevertheless, it turns out that many of the properties of the Heisenberg model
hold in the more general context of distance regular spaces.
A {\bf distance regular graph} is a finite graph for
which the size of the set $\{ z : d(x,z) = a , d (y,z) = b \}$
depends on $x$ and $y$ only through the value of $d(x,y)$ where
$d(x,y)$ is the usual graph distance between $x$ and $y$.
We generalize this by saying that the metric space $({\bf S},d)$
with probability measure
$\bar{d}x$ is {\bf distance regular} if the law of the pair $(d(x,Z) , d(y,Z))$
when $Z$ has law $\bar{d}x$ depends only on $d(x,y)$.
In particular, when the action of $G$ on ${\bf S}$ is distance transitive
(in addition to preserving $d$ and $\bar{d}x$),
meaning that $(x,y)$ can be mapped to any $(x' , y')$ with
$d(x,y) = d(x' , y')$, it follows easily that $({\bf S},d, \bar{d}x)$ is
distance regular. All the examples we have mentioned so far are distance
transitive (and hence distance regular)
except for the rotor model which is still distance regular.
(For an example of a graph showing that the full automorphism group
acting distance transitively
is strictly stronger than the assumption of distance
regularity, see~\cite{AVLF} or
{\it Additional Result} {\bf 23b} of~\cite{Big}.)
We present some of the background in this generality not because
we are fond of gratuitous generalization but because we find the
reasoning clearer, and because it seems reasonable that
someone in the future might study a particle system whose
spin states are elements of some distance regular space,
such as real projective space or the discrete $n$-cube. The primary
consequence of distance regularity is that it allows one to define
a commutative convolution on a certain subspace of $L^2$.
\begin{equation}gin{defn}
Let $L^2 ({\bf S})$ denote the space $L^2 (\bar{d}x)$, and let $L^2 ({\bf S})g$ denote
the space of functions $f \in L^2 ({\bf S})$ for which $f(x)$ depends
only on $d(x , {\hat{0}})$. For $f \in L^2 ({\bf S})g$, define a function $\bar{d}eltasib$
on $\{d({\hat{0}},y)\}_{y\in {\bf S}}$
by $\bar{d}eltasib (r) := f(x)$ where $x$ is such that $d({\hat{0}},x) = r$.
\mbox{\rm \small e}nd{defn}
\begin{equation}gin{defn}
If $({\bf S},\bar{d}x)$ is distance regular,
define a commutative convolution operation on $L^2 ({\bf S})g \thetaimes L^2 ({\bf S})g$ by
$$f * h (x) := \int_{{\bf S}} h(y) \bar{d}eltasib (d(x,y)) \, \bar{d}x (y) =
\int_{[0,\infty)^2} \bar{d}eltasib (u) \overline{h} (v) \, d\bar{d}eltai_x(u,v)$$
where $\bar{d}eltai_x$ is the law of $(d(x,Z) , d({\hat{0}} , Z))$ for a variable
$Z$ with law $\bar{d}x$. It is clear from the definition of a
distance regular space that $(d(x,Z) , d({\hat{0}},Z))$ and
$(d({\hat{0}},Z) , d(x,Z))$ are equal in distribution implying
that $f * h =h * f$ and that, since $\bar{d}eltai_x$ only depends on $d(x,{\hat{0}})$,
$f,h\in L^2 ({\bf S})g$ implies that $f * h \in L^2 ({\bf S})g$.
\mbox{\rm \small e}nd{defn}
The following lemma is straightforward and left to the reader.
\begin{equation}gin{lem} \labelel{lem:dt}
For all $J\ge 0$, $K_J\in L^2 ({\bf S})g$ and for all $h\in L^2 ({\bf S})$,
${\cal K}_J(h)(x)$ (defined in~(\ref{eq:conv})) is equal to
$\int_{{\bf S}} h(y) \overline{K_J} (d(x,y)) \, \bar{d}x (y)$.
In particular, if $({\bf S} , \bar{d}x)$ is distance regular,
then the operators ${\cal K}_J$ map $L^2 ({\bf S})g$ into itself and
${\cal K}_J(h) =K_J * h$ for all $h \in L^2 ({\bf S})g$.
\mbox{\rm \small e}nd{lem}
We believe that for most distance regular spaces, one can verify the
necessary hypotheses of Theorems~\ref{th:gen ii} and~\ref{th:gen i}
below in the same way as
we will do for the Heisenberg models in detail
in the next section. Doing this however
would take us too far afield and so we content ourselves with pointing out
to the reader that much of this probably can be done, and after analyzing
the Heisenberg models in Section~\ref{sub:sphere},
explain how to carry much of this out in the context of distance regular
graphs in Section~\ref{sub:finite}.
\subsection{Heisenberg models} \labelel{sub:sphere}
In this subsection, we consider Example \ref{eg:spherical} in
Section~\ref{sec:one}
and so we have ${\bf S} = S^d$, $d \geq 1$, the unit sphere in
$(d+1)$--dimensional Euclidean space with the corresponding
$G, d, \bar{d}x$ and $H$.
Recall that this is distance transitive for $d\ge 2$ (and hence
distance regular) and distance regular for $d=1$.
The following lemma allows us to set up coordinates in which our bookkeeping
will be manageable. It is certainly well known.
\begin{equation}gin{lem} \labelel{lem:spherical} For any $d\ge 1$,
there exist real--valued functions $\bar{d}eltasi_0 , \bar{d}eltasi_1 , \bar{d}eltasi_2 , \ldots \in L^2 ({\bf S})g$
$({\bf S}=S^d)$,
orthogonal under the inner product
$\langle f,g \rangle = \int_{{\bf S}} f \overline{g} \, \bar{d}x$,
such that $\bar{d}eltasi_n$ is a polynomial of degree exactly $n$ in $x\cdot {\hat{0}}$,
and such that the following properties hold. \\
(1) $\bar{d}eltasi_0 (x) \mbox{\rm \small e}quiv 1$ and $\bar{d}eltasi_1 (x) = x \cdot {\hat{0}}$. \\
(2) $1 = \bar{d}eltasi_j ({\hat{0}}) = \sup_{x \in {\bf S}} |\bar{d}eltasi_j (x)|$, for all $j$. \\
(3) $\bar{d}eltasi_i \bar{d}eltasi_j = \sum_{r\ge 0} q^r_{ij} \bar{d}eltasi_r$, where the coefficients
$q^r_{ij}$ are nonnegative and $\sum_r q^r_{ij} = 1$. \\
(4) $\bar{d}eltasi_i * \bar{d}eltasi_j = \gamma_j \bar{d}eltata_{ij} \bar{d}eltasi_j$, where
$\gamma_j := \bar{d}eltasi_j * \bar{d}eltasi_j ({\hat{0}}) = \int \bar{d}eltasi_j^2(x) \, \bar{d}x(x)$. \\
(5) The functions $\bar{d}eltasi_j$ are eigenfunctions of any convolution
operator, that is, $f * \bar{d}eltasi_j = c \bar{d}eltasi_j$ for any $f \in L^2 ({\bf S})g$. \\
(6) Any $f \in L^2 ({\bf S})g$ can be written as a convergent series
$f(x) = \sum_{j\ge 0} a_j (f) \bar{d}eltasi_j(x)$ (in the $L^2$ sense),
where the complex numbers $a_j(f)$
are given by $a_j(f) : = \gamma_j^{-1} \int f(x) \bar{d}eltasi_j (x) \, \bar{d}x (x) .$ \\
(7) For $f,g \in L^2 ({\bf S})g$, we have $a_j(f * g)= \gamma_j a_j(f) a_j(g)$.
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.} For each $\alphapha, \begin{equation}ta >-1$, define the
Jacobi polynomials $\{{\bf P}^{(\alphapha , \begin{equation}ta)}_n(r)\}_{n\ge 0}$ by
\begin{equation}gin{equation} \labelel{eq:rod}
(1 - r)^\alphapha (1 + r)^\begin{equation}ta {\bf P}_n^{(\alphapha , \begin{equation}ta)} (r) =
{(-1)^n \over 2^n n!} {d^n \over dr^n} \left [ (1 - r)^{n + \alphapha}
(1 + r)^{n + \begin{equation}ta} \right ] \, .
\mbox{\rm \small e}nd{equation}
(The Jacobi polynomials are usually defined differently in which
case~(\ref{eq:rod}) becomes what is known as Rodrigues' formula but we shall
use~(\ref{eq:rod}) as our definition; when $\alphapha=\begin{equation}ta$, which is the case
relevant to us, these are the ultraspherical polynomials.)
For any given $d\ge 1$, we let, for $n\ge 0$,
$$
\bar{d}eltasi_n(x):=
{{\bf P}^{({d \over 2}-1 ,{d \over 2}-1)}_n (x\cdot {\hat{0}})
\over
{\bf P}^{({d \over 2}-1 ,{d \over 2}-1)}_n (1)}.
$$
By p.254 in \cite{R}, ${\bf P}^{(\alphapha , \begin{equation}ta)}_n$ is a polynomial of degree
exactly $n$.
By p.259 in \cite{R}, the collection $\{{\bf P}^{(\alphapha , \begin{equation}ta)}_n\}_{n\ge 0}$
are orthogonal on $[-1,1]$ with respect to the weight function
$(1-r)^\alphapha (1+r)^\begin{equation}ta$. A change of variables then shows that the $\bar{d}eltasi_n$'s
are orthogonal in $L^2 ({\bf S})$.
(1) is then an easy calculation, the first equality in (2) is trivial
while the second equality is in \cite{R}, p.278 and 281.
(3) is in~\cite{Askey74},
p.41. (4) and (5) follow from the Funk--Hecke Theorem (\cite{N}, p.195)
(the calculation of $\gamma_j$ being trivial).
Since the subspace generated by the
$\{{\bf P}^{({d \over 2}-1 ,{d \over 2}-1)}_n(r)\}$'s are uniformly dense
in $C([-1,1])$ by the Stone-Weierstrass Theorem, it easily follows that the
subspace generated by the $\bar{d}eltasi_n$'s are uniformly dense in $L^2 ({\bf S})g\cap C({\bf S})$.
Hence the $\bar{d}eltasi_n$'s are a basis for $L^2 ({\bf S})g$ and (6) follows.
Finally, (4) and (6) together yield (7). $
\Box$
Note that for all $f,g\in L^2 ({\bf S})g$, we have that
$fg\in L^2 ({\bf S})g$ provided $fg\in L^2 ({\bf S})$.
Since $\bar{d}eltasi_n$ is a polynomial of degree exactly $n$ in $x\cdot {\hat{0}}$,
the greatest $r$ for which
$q^r_{ij} \neq 0$ must be $i + j$. From this and the nonnegativity
of the $q^r_{ij}$'s, it follows that for $\lambda > 0$ the function
$e^{\lambda \bar{d}eltasi_1(x)} = \sum_{n \geq 0} \lambda^n \bar{d}eltasi_1 (x)^n / n!$ has
\begin{equation}gin{equation} \labelel{eq:viii}
a_j (e^{\lambda \bar{d}eltasi_1}) > 0 , \mbox{ for all } j\ge 0.
\mbox{\rm \small e}nd{equation}
It follows from Lemmas~\ref{lem:rec}, \ref{lem:dt}
and \ref{lem:spherical}(3,4) that ${\bf P}P_+\subseteq L^2 ({\bf S})g$ and that
for all $g \in {\bf P}P_+$,
\begin{equation}gin{equation} \labelel{eq:ix}
a_j (g) > 0, \mbox{ for all } j\ge 0.
\mbox{\rm \small e}nd{equation}
\begin{equation}gin{defn}
Define the $A$ norm on $L^2 ({\bf S})g$ by
$$||f||_A = \sum_{j\ge 0} |a_j (f)| ,$$
provided it is finite.
\mbox{\rm \small e}nd{defn}
From the fact that $\sum_{r\ge 0} q^r_{ij} = 1$, one can easily show
that for all $f,g\inL^2 ({\bf S})g$ with $fg\inL^2 ({\bf S})g$,
\begin{equation}gin{equation} \labelel{eq:submult}
||fg||_A \leq ||f||_A ||g||_A ,
\mbox{\rm \small e}nd{equation}
and that equality holds if $f , g \in {\bf P}P_+$. An easy computation also
shows that $||e^{\lambda \bar{d}eltasi_1(x)}||_A =e^{\lambda} <\infty$
for all $\lambda \ge 0$
and hence by Lemmas~\ref{lem:rec} and~\ref{lem:spherical}(4)
and~(\ref{eq:submult}), $||f||_A<\infty$ for all $f\in{\bf P}P_+$.
Also, it follows from~(\ref{eq:ix}), Lemma~\ref{lem:spherical}(2,6),
the fact that $\int f \, \bar{d}x = 1$ for all $f \in {\bf P}P_+$ and the fact
that ${\bf P}P_+\subseteq L^2 ({\bf S})g$ that for $f \in {\bf P}P_+$,
\begin{equation}gin{equation} \labelel{eq:x}
1 + ||f - 1||_A = ||f||_A = f ({\hat{0}}) = ||f||_\infty =
1 + ||f - 1||_\infty .
\mbox{\rm \small e}nd{equation}
The last equality is obtained by observing that $\le$ is clear while
$ ||g||_\infty \le ||g ||_A $ for all $g\in L^2 ({\bf S})g$ is also clear.
\begin{equation}gin{lem} \labelel{lem:taylor}
There exists a function $o$ with $\bar{d}isplaystyle{\lim_{h \thetao 0} {o(h) \over h}
= 0}$ such that for all $h_1 , \ldots , h_k \in {\bf P}P_+$
with $k \leq B$,
\begin{equation}gin{equation} \labelel{eq:xi}
|| \bar{d}eltaoi (h_1 , \ldots , h_k) - 1 - \sum_{i=1}^k (h_i - 1)||_A
\leq o(\max_i ||h_i - 1||_A) ,
\mbox{\rm \small e}nd{equation}
provided $\max_i ||h_i - 1||_A\le 1$.
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.} Write
\begin{equation}gin{equation} \labelel{eq:new01}
|| \bar{d}eltarod_{i=1}^k h_i - 1 - \sum_{i=1}^k (h_i - 1)||_A =
|| \sum_{{A\subseteq\{1,\ldots,k\}\atop |A|\ge 2}} \bar{d}eltarod_{i\in A}(h_i-1)||_A.
\mbox{\rm \small e}nd{equation}
Then $\max_i ||h_i - 1|| \leq 1$ and
submultiplicativity~(\ref{eq:submult})
of $|| \cdot ||_A$ implies this is at most
$$ 2^k (\max_i ||h_i - 1||_A)^2 .$$
Next, since $\int (h_i - 1) \, \bar{d}x = 0$ for $1 \leq i \leq k$,
we similarly obtain
$$\left|\int \bar{d}eltarod_{i=1}^k h_i - 1\right| \leq 2^k (\max_i ||h_i - 1||_A)^2.$$
We then have
$$
|| \bar{d}eltaoi (h_1 , \ldots , h_k) - \bar{d}eltarod_{i=1}^k h_i||_A =
{1\over \int \bar{d}eltarod_{i=1}^k h_i}\left|\int \bar{d}eltarod_{i=1}^k h_i - 1\right|
|| \bar{d}eltarod_{i=1}^k h_i ||_A
\leq 4^k (\max_i ||h_i - 1||_A)^2 ,$$
since $|| \bar{d}eltarod_{i=1}^k h_i ||_A\le 2^k$ and
$\int \bar{d}eltarod_{i=1}^k h_i\ge 1$ by
the positivity of the $q^r_{ij}$ and~(\ref{eq:ix}).
A use of the triangle inequality completes the proof. $
\Box$
We note five facts that follow easily from the above, but
which will be useful later on in generalizing our results.
Let $ spherically symmetric p$ be the linear subspace of $L^2 ({\bf S})g$ spanned by ${\bf P}P_+$,
$ spherically symmetric pj$ be the linear subspace of $L^2 ({\bf S})g$ spanned by ${\bf P}P_+(J)$
and $|| {\cal K}_{J'} ||_A$ denote the operator norm of ${\cal K}_{J'}$ on
$( spherically symmetric p,||\,\,||_A)$.
\begin{equation}gin{equation} \labelel{eq:xii}
\lim_{J' \thetao 0} ||K_{J'} - 1||_A = 0 ;
\mbox{\rm \small e}nd{equation}
\begin{equation}gin{equation} \labelel{eq:present iii}
c_1:=\sup_{f\in spherically symmetric p ,f \neq 1} {||f - 1||_\infty \over ||f - 1||_A} < \infty ;
\mbox{\rm \small e}nd{equation}
\begin{equation}gin{equation} \labelel{eq:present iii'}
c_2:=\inf_{f\in{\bf P}P_+,f\neq 1} {||f - 1||_\infty \over ||f - 1||_A} > 0 ;
\mbox{\rm \small e}nd{equation}
\begin{equation}gin{equation} \labelel{eq:xiii}
\mbox{ For all } J' \geq 0, \,\,\, || {\cal K}_{J'} ||_A \leq 1;
\mbox{\rm \small e}nd{equation}
There exist $a,b\in {\bf S}$ such that for all $f\in {\bf P}P_+$,
\begin{equation}gin{equation} \labelel{eq:xiiii}
f(a)=\sup_{x\in{\bf S}} f(x) \mbox{ and } f(b)=\inf_{x\in{\bf S}} f(x).
\mbox{\rm \small e}nd{equation}
(\ref{eq:xiii}), for example, follows immediately from Lemmas~\ref{lem:dt}
and~\ref{lem:spherical}(7) and the fact that $|\gamma_n a_n(g)|\le 1$ for any
probability density function $g\in L^2 ({\bf S})g$.
The results on Heisenberg models presented thus far are parallel to
the results obtainable for any finite distance regular graph (see
the next subsection). One useful result that is not true for general
distance regular models depends on the following obvious geometric property
of the sphere:
$$|\{ z : d(x,z) \leq a , d(y,z) \leq b \}|$$
is a nonincreasing function of $d(x,y)$ for any fixed $a$ and $b$ where
$|\,\,|$ denotes surface measure.
[Proof: For $S^1$, this is obvious. For $S^d$, $d\ge 2$, by symmetry, we can
assume that $x=(0,\ldots,0,1)$ and $y=(\cos\thetaheta,0,\ldots, 0, \sin\thetaheta)$
(both vectors with $d+1$ coordinates). Write $S^d$ as
$$
\cup_{u\in [-1,1]^{d-1}} A_u
$$
where
$$
A_u:=S^d\cap\{(a_1,\ldots,a_{d+1}):(a_2,\ldots,a_{d})=u\}.
$$
Each $A_u$ is a circle (or is empty) and so essentially by the 1--dimensional
case, we have the desired behaviour on each $A_u$ (using 1--dimensional
Lebesgue measure) and by Fubini's Theorem, we obtain the desired result
on $S^d$.]
Calling a function $f\inL^2 ({\bf S})g$ nonincreasing if the corresponding $\bar{d}eltasib$ is
nonincreasing, the latter can be seen to be
equivalent to the property that ${\bf 1}_{d(x , {\hat{0}}) \leq a} *
{\bf 1}_{d(x , {\hat{0}}) \leq b}$
is nonincreasing, and by taking linear combinations, this is equivalent
to $f * g$ being nonincreasing for all nonincreasing $f$ and $g$ in $L^2 ({\bf S})g$.
Since $K_J$ is nonincreasing for all $J$,
it follows from the fundamental recursion that
\begin{equation}gin{equation} \labelel{eq:xiv}
f \in {\bf P}P_+ \overline{h}ox{I\kern-.2em\overline{h}ox{R}}ightarrow f \mbox{ is nonincreasing} .
\mbox{\rm \small e}nd{equation}
\begin{equation}gin{lem} \labelel{lem:incr}
For any positive nonincreasing $f \in L^2 ({\bf S})g$,
$$
\left|\int_{{\bf S}} f \bar{d}eltasi_n \, \bar{d}x\right| \le \int_{{\bf S}} f \bar{d}eltasi_1 \, \bar{d}x
$$
for all $n \ge 1 $.
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.} It suffices to prove this for functions of the form
$f(x) = {\bf 1}_{\{x \cdot {\hat{0}} \geq t\}}$ with $t\in [-1,1]$.
We rely on explicit formulae for the functions $\{ \bar{d}eltasi_n \}$.
Letting $\alphapha = d/2 - 1$, a change of variables yields
$$\int_{{\bf S}} f \bar{d}eltasi_n \, \bar{d}x
= s_d^{-1}\int_t^1 {P_n^{(\alphapha , \alphapha)} (r) \over P_n^{(\alphapha ,
\alphapha)} (1)} (1 - r^2)^\alphapha \, dr,$$
where
$$
s_d=\int_{-1}^1 (1-r^2)^\alphapha dr
$$
and
${\bf P}_n^{(\alphapha , \alphapha)}$ is the Jacobi polynomial defined earlier.
Taking the indefinite integral of each side in~(\ref{eq:rod})
with $\begin{equation}ta = \alphapha$ yields
\begin{equation}gin{eqnarray*}
\int (1 - r)^\alphapha (1 + r)^\alphapha P_n^{(\alphapha , \alphapha)} (r) \, dr & = &
{(-1)^n \over 2^n n!} {d^{n-1} \over dr^{n-1}} \left [ (1 - r)^{n + \alphapha}
(1 + r)^{n + \alphapha} \right ] \\[2ex]
& = & {- 1 \over 2n} (1 - r^2)^{\alphapha + 1} P_{n-1}^{(\alphapha + 1 ,
\alphapha + 1)} (r)\, .
\mbox{\rm \small e}nd{eqnarray*}
Evaluating at 1 and $t$ gives
\begin{equation}gin{eqnarray*}
\int_{{\bf S}} f \bar{d}eltasi_n \, \bar{d}x
& = & s_d^{-1}\int_t^1 {P_n^{(\alphapha , \alphapha)} (r) (1 - r^2)^\alphapha \over
P_n^{(\alphapha , \alphapha)} (1)} \, dr \\[2ex]
& = & s_d^{-1}
{P_{n-1}^{(\alphapha + 1 , \alphapha + 1)} (t) (1 - t^2)^{\alphapha + 1} \over
2 n P_n^{(\alphapha , \alphapha)} (1)} .
\mbox{\rm \small e}nd{eqnarray*}
When $n = 1$, using~(\ref{eq:rod}),
this is just $s_d^{-1}(1 - t^2)^{\alphapha + 1} / 2(1+\alphapha)$. Dividing, we get
$${ \int_{{\bf S}} f \bar{d}eltasi_n \, \bar{d}x \over \int_{{\bf S}} f \bar{d}eltasi_1 \, \bar{d}x }
= {P_{n-1}^{(\alphapha + 1 , \alphapha + 1)} (t) (1+\alphapha)
\over n P_n^{(\alphapha , \alphapha)} (1)} =
{P_{n-1}^{(\alphapha + 1 , \alphapha + 1)} (t) \over
P_{n-1}^{(\alphapha + 1 , \alphapha + 1)} (1)} \cdot
{P_{n-1}^{(\alphapha + 1 , \alphapha + 1)} (1) \over
n P_n^{(\alphapha , \alphapha)} (1)}\cdot(1+\alphapha).$$
The first term in the product is bounded in absolute value by 1.
By \cite{Askey74}, p.7,
$$P_n^{(\alphapha , \alphapha)} (1) = {\alphapha + n \choose n} ,$$
and so we see that the second term is $1 / (\alphapha + 1)$, completing the
proof of the lemma. $
\Box$
\noindent{\mbox{\rm \small e}m Remark:}
The case $d = 1$ can also be handled by a rearrangement lemma.
\begin{equation}gin{defn} \labelel{defn:op}
Define a linear functional $L$ on $L^2 ({\bf S})g$ by
$L (g):= \int_{{\bf S}}g(x)\bar{d}eltasi_1(x) \bar{d}x(x)$ $(= \gamma_1 a_1 (g))$
and set ${\bf Op}_J = L(K_J)$. (Recall that $\bar{d}eltasi_1,\gamma_1$ and $a_1$ are defined
in Lemma~\ref{lem:spherical}.)
\mbox{\rm \small e}nd{defn}
It follows from Lemmas~\ref{lem:dt},~\ref{lem:spherical}(7)
and~\ref{lem:incr},~(\ref{eq:xiv}) and an easy computation that
\begin{equation}gin{equation} \labelel{eq:ixix}
||{\cal K}_J f-1||_A\le {\bf Op}_J ||f-1||_A \mbox{ for all } f\in{\bf P}P_+(J).
\mbox{\rm \small e}nd{equation}
In the following inequalities, we denote
$\rho := {\bf Op}_J$. For $f \in {\bf P}P_+(J)$, it also follows easily that
\begin{equation}gin{equation} \labelel{eq:(a)}
L ({\cal K}_J f - 1 ) \geq \rho L (f - 1)
\mbox{\rm \small e}nd{equation}
and that there is a constant $c_3$ such that for all $f\in\,\, spherically symmetric pj$,
\begin{equation}gin{equation} \labelel{eq:(c)}
|L(f)| \leq c_3 ||f||_A .
\mbox{\rm \small e}nd{equation}
(We can of course take $c_3$ to be 1, but we leave the condition written
in this more general form for use as a hypothesis in Theorem~\ref{th:gen i}.)
Putting together the results of Lemmas~\ref{lem:spherical} and~\ref{lem:incr},
as well as~(\ref{eq:viii}),~(\ref{eq:ix}) and~(\ref{eq:xiv}),
gives the following corollary.
\begin{equation}gin{cor} \labelel{cor:(b)}
For all $J\ge 0$,
there is a constant $c_4 > 0$ such that for all $f \in {\bf P}P_+(J)$,
\begin{equation}gin{equation} \labelel{eq:(b)}
L (f) \geq c_4 ||f - 1||_A .
\mbox{\rm \small e}nd{equation}
\mbox{\rm \small e}nd{cor}
\noindent{\bf Proof.} Fix $f \in {\bf P}P_+(J)$. If $f = K_{J'}$ for
some $J' \in (0, J]$, we argue as follows. As
$||e^{\lambda \bar{d}eltasi_1(x)}||_A =e^{\lambda}$ (which we mentioned earlier)
and $K_{J'}(x)=e^{J'\bar{d}eltasi_1(x)}/\int e^{J'\bar{d}eltasi_1(x)}\bar{d}x(x)$, we have
\begin{equation}gin{eqnarray*}
||K_{J'} - 1||_A & = & ||K_{J'} ||_A -1
\\[2ex]
& = & {e^{J'}\over \int e^{J'\bar{d}eltasi_1(x)}\bar{d}x(x)} -1
\\[2ex]
& \le & e^{2J'} -1.
\mbox{\rm \small e}nd{eqnarray*}
Next,
\begin{equation}gin{eqnarray*}
L (K_{J'}) & = & {1\over \int e^{J'\bar{d}eltasi_1(x)}\bar{d}x(x)}
\int e^{J'\bar{d}eltasi_1(x)}\bar{d}eltasi_1(x)\bar{d}x(x) \\[2ex]
& = & {1\over \int e^{J'\bar{d}eltasi_1(x)}\bar{d}x(x)}
\sum_{k=0}^\infty {(J')^k\over k!} \int \bar{d}eltasi_1^{k+1}(x)\bar{d}x(x).
\mbox{\rm \small e}nd{eqnarray*}
By Lemma~\ref{lem:spherical}(3), all terms in the sum are nonnegative and
by Lemma~\ref{lem:spherical}(4), the $k=1$ term is $J'\gamma_1$.
Hence $L (K_{J'})\ge J'\gamma_1/e^{J'}$.
Since
$$
\inf_{J'\in (0,J]} {J'\gamma_1 \over e^{J'}(e^{2J'} -1) } >0,
$$
we can find a $c_4$ in this case.
Otherwise, by the fundamental recursion, we may represent $f$ as
$\bar{d}eltaoi ({\cal K}_{J_1} h_1 , \ldots , {\cal K}_{J_k} h_k)$ with each
$h_i$ either in ${\bf P}P_+(J)$ or equal to $\bar{d}eltata_{{\hat{0}}}$ and each
$J_i\in (0,J]$. Define $g_i = {\cal K}_{J_i} h_i - 1$.
Let $m :=\inf_{0< J'\le J} a_1 (K_{J'}) / \sum_{n > 0} a_n (K_{J'})$ which is
strictly positive by the above. It follows that if
$h_i\in {\bf P}P_+(J)$ (the case $h_i=\bar{d}eltata_{{\hat{0}}}$ is already done),
$${L (g_i) \over ||g_i ||_A} = {a_1 (K_{J_i}) a_1 (h_i) \gamma_1^2\over
\sum_{n > 0} a_n (K_{J_i}) a_n (h_i) \gamma_n} \geq m\gamma_1$$
by Lemma~\ref{lem:spherical}(7) and
since $a_1(h_i)\gamma_1 \ge a_n(h_i)\gamma_n$ for all $n\ge 1$ by
Lemma~\ref{lem:incr} and~(\ref{eq:xiv}).
Let $h = \bar{d}eltarod_{i=1}^k {\cal K}_{J_i} h_i$. Then
$L (h) = L(1 + \sum_{i=1}^k g_i + Q)$, where $Q$ is a sum
of monomials in $\{ g_i \}$. Using $q^r_{ij} \ge 0$
and~(\ref{eq:ix}), we have that $L(Q) \geq 0$, and hence
\begin{equation}gin{equation} \labelel{eq:new02}
L(h) \geq \sum_{i=1}^k L(g_i) \geq m \gamma_1\sum_{i=1}^k ||g_i ||_A .
\mbox{\rm \small e}nd{equation}
On the other hand, for any $B$ and $M$, there is $C = C(M,B)$ such that
if $x_1 , \ldots , x_k \in (0,M)$ with $k\le B$, then
$$ -1 + \bar{d}eltarod_{i=1}^k (1 + x_i) \leq C \sum_{i=1}^k x_i .$$
Next,
the positivity of the $q^r_{ij}$ implies
$\int_{{\bf S}} h(x) \, \bar{d}x(x) = a_0 (h) \geq 1$. It follows that
$$||h - 1||_A = -1+ ||h ||_A =
-1 + \bar{d}eltarod_{i=1}^k ||g_i + 1||_A \leq C \sum_{i=1}^k
||g_i||_A $$
for some constant $C$ since $||g_i+1 ||_A=||g_i ||_A +1$ and
$||g_i+1 ||_A$ clearly has a universal upper bound. [To see the latter
statement, one notes that
$$
\sup_{0<J' \le J} ||K_{J'}||_A <\infty,
$$
$$
||K_{J'} *f||_A \le ||K_{J'} ||_A
$$
for any probability density function $f\in L^2 ({\bf S})g$
(by Lemma~\ref{lem:spherical}(7)),~(\ref{eq:submult}) and the fact that we
never have more than $B$ terms in our pointwise products imply that
$$
\sup_{f\in {\bf P}P_+(J)}||f||_A \le
\left(\sup_{0<J' \le J} ||K_{J'}||_A \right)^B <\infty.]
$$
Putting this together with~(\ref{eq:new02}) gives
$${L(h) \over ||h - 1||_A} \geq {m \gamma_1\over C} \, .$$
Finally, letting $f = h / \left(\int_{{\bf S}} h(x) \, \bar{d}x(x)\right)$, we obtain
\begin{equation}gin{eqnarray*}
||h - 1||_A & \ge & \sum_{n\ge 1} a_n(h)
\\[2ex]
& = & \sum_{n\ge 1} \left[\int_{{\bf S}} h(x)\bar{d}x(x)\right] a_n(f) \\[2ex]
& = & \left[\int_{{\bf S}} h(x)\bar{d}x(x)\right] ||f - 1||_A.
\mbox{\rm \small e}nd{eqnarray*}
Hence
$$
{L(f)\over ||f - 1||_A} \ge {L(h)\over ||h - 1||_A} \ge {m \gamma_1\over C}
$$
and we're done. $
\Box$
\subsection{Distance regular graphs} \labelel{sub:finite}
For the remainder of this section, we suppose that ${\bf S}$ is the vertex
set of a finite, connected, distance regular graph, that $d(x,y)$ is
the graph distance, and that the energy $H (x,y)$ depends only
on $d(x,y)$. The Potts models fit into this
framework, with the respective graphs being
the complete graph $K_q$ on $q$ vertices.
All the results we need follow
in fact from an even weaker assumption, namely that ${\bf S}$ is an
{\it association scheme}. For the definition of association schemes
and the proofs of the relevant results, see~\cite{BCN} or~\cite{Ter98}.
By developing
the analogue of Lemma~\ref{lem:spherical} for distance regular graphs,
we will illustrate the extent to which our results are independent of
the special properties of the Heisenberg model.
We have a distinguished element ${\hat{0}} \in {\bf S}$ and the measure $\bar{d}x$ will of
course be normalized counting measure $|{\bf S}|^{-1} \sum_{x \in {\bf S}} \bar{d}eltata_x$.
The spaces $L^2 ({\bf S})$ and $L^2 ({\bf S})g$ are then simply finite dimensional vector
spaces with respective dimensions $|{\bf S}|$ and $1+D$, where $D$ is the
diameter of the graph ${\bf S}$.
Denote by $M({\bf S})$ the space of matrices with rows and columns
indexed by ${\bf S}$, thought of as linear maps from $L^2 ({\bf S})$ to $L^2 ({\bf S})$.
Associated with each function $f \in L^2 ({\bf S})g$ is the matrix $M_f \in M({\bf S})$
whose $(x,y)$ entry is $\bar{d}eltasib (d(x,y))$, whence the matrix $M_f$
corresponds to the linear operator $h \mapsto h * f$ given in
Section~\ref{sub:drs}. The following
analogue of Lemma~\ref{lem:spherical} is derived from Section~2.4
of~\cite{Ter98}; a published reference is Section~2.3 of~\cite{BCN}.
\begin{equation}gin{lem} \labelel{lem:scheme}
There exists a basis of real--valued functions
$\bar{d}eltasi_0 , \ldots , \bar{d}eltasi_D$ of $L^2 ({\bf S})g$
orthogonal under the inner product
$\langle f , g\rangle = |{\bf S}|^{-1} \sum_x f(x)
\overline{g(x)}$ with the following properties. \\
(1) $\bar{d}eltasi_0 (x) \mbox{\rm \small e}quiv 1$. \\
(2) $\bar{d}eltasi_j ({\hat{0}}) = 1 = \sup_x |\bar{d}eltasi_j (x)|$ for all $j$. \\
(3) $\bar{d}eltasi_i \bar{d}eltasi_j = \sum_{r=0}^D q^r_{ij} \bar{d}eltasi_r$ for some nonnegative coefficients
$q^r_{ij}$ with $\sum_r q^r_{ij} = 1$. \\
(4) $\bar{d}eltasi_i * \bar{d}eltasi_j = \gamma_j \bar{d}eltata_{ij} \bar{d}eltasi_j$, where $\gamma_j : = \bar{d}eltasi_j * \bar{d}eltasi_j
({\hat{0}}) = |{\bf S}|^{-1} \sum_x \bar{d}eltasi_j (x)^2$. \\
(5) The functions $\bar{d}eltasi_j$ are eigenfunctions of any convolution
operator, that is, $M_f \bar{d}eltasi_j = c \bar{d}eltasi_j$ for any $f \in L^2 ({\bf S})g$. \\
(6) For $f \in L^2 ({\bf S})g$, we have $f = \sum_{j=0}^D a_j(f) \bar{d}eltasi_j$, where
$a_j : = \gamma_j^{-1} |{\bf S}|^{-1} \sum_x f(x) \bar{d}eltasi_j (x)$. \\
(7) For $f,g \in L^2 ({\bf S})g$, we have $a_j(f * g)= \gamma_j a_j(f) a_j(g)$. \\
(8) For $f\in L^2 ({\bf S})g$ which is positive and nonincreasing,
$|\langle f , \bar{d}eltasi_i\rangle|\le \langle f , \bar{d}eltasi_1\rangle $
for each $i\ge 1$.
\mbox{\rm \small e}nd{lem}
If we place the norm $\sum_{j=0}^D |a_j(f)|$ on $ spherically symmetric pj$, essentially all of the
hypotheses in Theorems~\ref{th:gen ii} and~\ref{th:gen i} (to come later) are
immediate noting that all norms are equivalent on finite dimensional spaces.
If the analogue of~(\ref{eq:xiv}) holds, then letting
$L (g):= |S|^{-1}\sum_{x\in{\bf S}}g(x)\bar{d}eltasi_1(x)$ and both ${\bf Op}_J $ and $\rho$ to
be $L(K_J)$, then one can easily show that {\it all} of the
hypotheses in Theorems~\ref{th:gen ii} and~\ref{th:gen i} hold.
As far as~(\ref{eq:xiv}), it trivially holds for the complete graph where the
diameter $D$ is equal to 1 and in any case, the reader is left with only one
condition to check.
\setcounter{equation}{0}
\section{Two Technical Theorems} \labelel{sec:proofs}
We now state two general results from which
Theorems~\ref{th:main} and~\ref{th:potts} will follow.
\begin{equation}gin{th} \labelel{th:gen ii}
Let $\Gamma$ be any tree (with bounded degree).
For the $d$--dimensional Heisenberg model with $d\ge 1$,
if $J > 0$ and $$\thetaextstyle {br} (\Gamma) \cdot {\bf Op}_J < 1,$$
then there is no robust phase transition for the parameter $J$, where ${\bf Op}_J$ is
given in Definition~\ref{defn:op} (${\bf Op}_J$ implicitly depends on $d$).
More generally, if $J>0$ and
if $({\bf S} , G , H)$ is any statistical ensemble with a norm
$|| \cdot ||$ on $ spherically symmetric pj$
satisfying~(\ref{eq:xi}),~(\ref{eq:xii}),~(\ref{eq:present iii})
and~(\ref{eq:xiii}) and there exists a number ${\bf Op}_J \in (0,1)$ satisfying
(\ref{eq:ixix}) and
$\thetaextstyle {br} (\Gamma) \cdot {\bf Op}_J < 1$, then there is no robust
phase transition for the parameter $J$.
\mbox{\rm \small e}nd{th}
\begin{equation}gin{th} \labelel{th:gen i}
Let $\Gamma$ be any tree (with bounded degree).
For the $d$--dimensional Heisenberg model with $d\ge 1$,
if $J > 0$ and $$\thetaextstyle {br} (\Gamma) \cdot {\bf Op}_J > 1,$$
then there is a robust phase transition for the parameter $J$, where
${\bf Op}_J$ is as above. More generally, if $J>0$ and
if $({\bf S} , G , H)$ is any statistical ensemble with a norm
$|| \cdot ||$ on $ spherically symmetric pj$
satisfying~(\ref{eq:xi}),~(\ref{eq:present iii}),
(\ref{eq:present iii'}),~(\ref{eq:xiii}) and~(\ref{eq:xiiii}),
and if $L$ is a linear
functional on $ spherically symmetric pj$ which vanishes
on the constants and
satisfies~(\ref{eq:(a)}),~(\ref{eq:(c)}) and~(\ref{eq:(b)})
for a constant $\rho > 0$, then
$\thetaextstyle {br} (\Gamma) \cdot \rho > 1$ implies
a robust phase transition for the parameter $J$.
\mbox{\rm \small e}nd{th}
To prove these results,
we begin with a purely geometric lemma on the existence of
cutsets of uniformly small content below the branching number.
\begin{equation}gin{lem} \labelel{lem:globalcut}
Assume that $\thetaextstyle {br} (\Gamma) < d$.
Then for all $\mbox{\rm \small e}psilonsilon >0$, there exists a cutset $C$ such that
$$
\sum_{x\in C}({1 \over d})^{|x|} \le \mbox{\rm \small e}psilonsilon
$$
and
for all $v\in C^i\cup C$,
\begin{equation}\label{eqn:goodcut}
\sum_{x\in C\cap \Gamma (v)}({1 \over d})^{|x|-|v|} \le 1.
\mbox{\rm \small e}nd{equation}
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.}
Since $\thetaextstyle {br} (\Gamma) < d$, for any given $\mbox{\rm \small e}psilonsilon >0$, there exists
a cutset $C$ such that
$$
\sum_{x\in C}({1 \over d})^{|x|} \le \mbox{\rm \small e}psilonsilon.
$$
We can assume that $C$ is a minimal cutset with this property with respect
to the partial order $C_1 \bar{d}eltareceq C_2$ if for all $v\in C_1$, there exists
$w\in C_2$ such that $v\le w$. We claim that this cutset
satisfies~(\ref{eqn:goodcut}). If this property failed for some $v$,
we let $C'$ be the modified cutset obtained by replacing $C\cap \Gamma (v)$
by $v$ (and leaving $C\cap \Gamma^c_v$ unchanged).
As~(\ref{eqn:goodcut}) clearly holds for $w\in C$, we must
have that $v\not\in C$ in which case $C'\neq C$.
We then have
\begin{equation}gin{eqnarray*}
\sum_{x\in C'}({1 \over d})^{|x|} & = &
\sum_{x\in C\cap \Gamma (v)^c}({1 \over d})^{|x|}+({1 \over d})^{|v|} \\[1ex]
& < & \sum_{x\in C\cap \Gamma (v)^c}({1 \over d})^{|x|}+
({1 \over d})^{|v|} \sum_{x\in C\cap \Gamma (v)}({1 \over d})^{|v-x|} \\[1ex]
& = & \sum_{x\in C\cap \Gamma (v)^c}({1 \over d})^{|x|}+
\sum_{x\in C\cap \Gamma (v)}({1 \over d})^{|x|} \\[1ex]
& = & \sum_{x\in C}({1 \over d})^{|x|} \\[1ex]
& \le & \mbox{\rm \small e}psilonsilon,
\mbox{\rm \small e}nd{eqnarray*}
contradicting the minimality of $C$ since clearly $C'\bar{d}eltareceq C$.
$
\Box$
We now proceed with the proofs of Theorems~\ref{th:gen ii} and~\ref{th:gen i}.
\noindent{\bf Proof of Theorem \ref{th:gen ii}.}
Since in Section~\ref{sub:sphere}
the Heisenberg models have been shown to satisfy all of
the more general hypotheses of this theorem, we need only prove the last
statement of the theorem where we have a given $J>0$, a given $\|\,\,\|$
on $ spherically symmetric pj$ and a given ${\bf Op}_J$ satisfying the required conditions.
By~(\ref{eq:xi}), for any $\mbox{\rm \small e}psilonsilon > 0$, there is
an $\mbox{\rm \small e}psilonsilon_0 > 0$ such that for all $k \leq B$ and all $h_1 , \ldots ,
h_k \in {\bf P}P_+(J)$ with $\|h_i - 1\| \leq \mbox{\rm \small e}psilonsilon_0$ for all $i$, we have that
\begin{equation}gin{equation} \labelel{eq:star2}
\| \bar{d}eltaoi_k (h_1 , \ldots , h_k) - 1 \| \leq (1 + \mbox{\rm \small e}psilonsilon) \sum_{i=1}^k
\|h_i - 1\| \, .
\mbox{\rm \small e}nd{equation}
Choose $\mbox{\rm \small e}psilonsilon > 0$ so that
$(1 + \mbox{\rm \small e}psilonsilon)^{-1} > \thetaextstyle {br} (\Gamma) \cdot {\bf Op}_J$ and
choose $\mbox{\rm \small e}psilonsilon_0$ as above.
By~(\ref{eq:xii}), we can choose $J'>0$ small enough
so that $\| K_{J'} -1 \| \leq \mbox{\rm \small e}psilonsilon_0 {\bf Op}_J$.
Use Lemma~\ref{lem:globalcut} to choose
a sequence of cutsets $\{ C_n \}$ for which
$$\lim_{n \rightarrow \infty} \sum_{x \in C_n} [(1 + \mbox{\rm \small e}psilonsilon)
{\bf Op}_J ]^{|x|} = 0$$
and for all $n$ and all $v \in C_n^i \cup C_n$,
\begin{equation}gin{equation} \labelel{eq:star43}
\sum_{x \in C_n \cap \Gamma (v)}
[(1 + \mbox{\rm \small e}psilonsilon) {\bf Op}_J ]^{|x| - |v|} \leq 1.
\mbox{\rm \small e}nd{equation}
We now show by induction that for all $n$ and all $v \in C_n^i$,
\begin{equation}gin{equation} \labelel{eq:ind}
\|f^{J' ,J, +}_{C_n , v} - 1\| \leq \mbox{\rm \small e}psilonsilon_0 \sum_{x \in C_n \cap \Gamma (v)}
[(1 + \mbox{\rm \small e}psilonsilon) {\bf Op}_J ]^{|x| - |v|} \, .
\mbox{\rm \small e}nd{equation}
Indeed, from Lemma~\ref{lem:rec}, letting $w_1 , \ldots , w_k$
be the children of $v$,
$$\|f^{J',J , +}_{C_n , v} - 1\|
= \| \bar{d}eltaoi ({\cal K}_{J_1''} f^{J',J , +}_{C_n , w_1},
\ldots , {\cal K}_{J_k''} f^{J',J , +}_{C_n , w_k}) - 1 \| \, $$
where $J_i''$ is $J$ if $w_i\in C_n^i$ and $J'$ otherwise.
When $w_i \in C_n$, the choice of $J'$ guarantees that
$\|{\cal K}_{J_i''} f^{J',J , +}_{C_n , w_i} - 1\| \leq \mbox{\rm \small e}psilonsilon_0{\bf Op}_J\leq \mbox{\rm \small e}psilonsilon_0$,
while when $w_i \notin C_n$,
the induction hypothesis together with~(\ref{eq:star43}) guarantees that
$\|f^{J',J , +}_{C_n , w_i} - 1\| \le \mbox{\rm \small e}psilonsilon_0$ which implies that
$\|{\cal K}_{J_i''} f^{J',J , +}_{C_n , w_i} - 1\| \le \mbox{\rm \small e}psilonsilon_0$
by~(\ref{eq:xiii}). Hence, from~(\ref{eq:star2}),
$$\|f^{J',J , +}_{C_n , v} - 1\| \leq
(1 + \mbox{\rm \small e}psilonsilon) \sum_{w_i \in C_n} \| {\cal K}JP f^{J',J , +}_{C_n , w_i} - 1 \|
+ (1 + \mbox{\rm \small e}psilonsilon) \sum_{w_i \notin C_n}
\|{\cal K}_J f^{J',J , +}_{C_n , w_i} - 1\|.$$
The summands in the first sum are at most
$\mbox{\rm \small e}psilonsilon_0 {\bf Op}_J$ while those in the second sum are by~(\ref{eq:ixix}) at
most ${\bf Op}_J \|f^{J',J , +}_{C_n , w_i} - 1\| $.
Therefore using the induction hypothesis on the second term, we obtain
\begin{equation}gin{eqnarray*}
\|f^{J',J , +}_{C_n , v} - 1\|
& \leq & \sum_{i=1}^k (1 + \mbox{\rm \small e}psilonsilon) \mbox{\rm \small e}psilonsilon_0 {\bf Op}_J \sum_{x \in C_n \cap
\Gamma (w_i)} \left [ (1 + \mbox{\rm \small e}psilonsilon ) {\bf Op}_J \right ]^{|x| - |w_i|} \\[2ex]
& = & \mbox{\rm \small e}psilonsilon_0 \sum_{x \in C_n \cap \Gamma (v)} \left [ (1 + \mbox{\rm \small e}psilonsilon)
{\bf Op}_J \right ]^{|x| - |v|} ,
\mbox{\rm \small e}nd{eqnarray*}
completing the induction.
Finally, the theorem follows by taking $v = o$, letting $n \rightarrow
\infty$, and using~(\ref{eq:present iii}). $
\Box$
For the proof of Theorem~\ref{th:gen i}, it is easiest to isolate the
following two lemmas.
\begin{equation}gin{lem} \labelel{lem:first}
Under the more general hypotheses of Theorem~\ref{th:gen i}
(with a given $J >0$, a given $\|\,\,\|$ on $ spherically symmetric pj$, a given $L$ and
a given $\rho$ satisfying the required conditions),
for all $\alphapha>0$,
there exists $\begin{equation}ta>0$ so that if $h_1,\ldots, h_k\in {\bf P}P_+(J)$ with
$k\le B$ and $\|h_i-1\| < \begin{equation}ta$ for each $i$, then
$$
L \left [ (\bar{d}eltaoi_k ({\cal K}J h_1 , \ldots , {\cal K}J h_k)) - 1 \right ]
\geq {1 \over 1 + \alphapha} \sum_{i=1}^k L ({\cal K}J h_i - 1)
$$
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.}
In~(\ref{eq:xi}), choose $\begin{equation}ta<1$ so that
$$o(h)\le h \left(1-{1 \over (1+\alphapha)}\right) {c_4 \over c_3} $$
for all $h\in (0,\begin{equation}ta)$, with $c_3$ and $c_4$ as in~(\ref{eq:(c)})
and~(\ref{eq:(b)}). If $h_1,\ldots, h_k\in {\bf P}P_+(J)$ are such that
$\|h_i-1\| < \begin{equation}ta$, then $\|{\cal K}J h_i-1\| < \begin{equation}ta$ by~(\ref{eq:xiii}).
We can now write
\begin{equation}gin{equation} \labelel{eq:U1}
\bar{d}eltaoi_k({\cal K}J h_1,\ldots,{\cal K}J h_k)-1-
{1 \over (1+\alphapha)}\sum_{i=1}^k ({\cal K}J h_i-1)
\mbox{\rm \small e}nd{equation}
as
\begin{equation}gin{equation} \labelel{eq:U2}
\left(1-{1 \over (1+\alphapha)}\right)\sum_{i=1}^k ({\cal K}J h_i-1) +U
\mbox{\rm \small e}nd{equation}
where by assumption,
\begin{equation}gin{eqnarray} \labelel{eq:new03}
\|U\| & \le & o(\max_i \|{\cal K}J h_i-1 \|) \\[2ex]
& \le & \left(1-{1 \over (1+\alphapha)}\right) {c_4 \over c_3}
\max_i \|{\cal K}J h_i-1 \| \nonumber \\[2ex]
& \le & \left(1-{1 \over (1+\alphapha)}\right){c_4 \over c_3}
\sum_{i=1}^k \|{\cal K}J h_i-1 \|. \nonumber
\mbox{\rm \small e}nd{eqnarray}
Letting $a$ be the quantity~(\ref{eq:U1}), we see that
\begin{equation}gin{eqnarray*}
L(a) & = & L \left [ \left ( 1 - {1 \over (1+\alphapha)} \right )
\sum_{i=1}^k ({\cal K}J h_i-1) \right ] + L(U) \\
& \ge & \left ( 1 - {1 \over (1+\alphapha)} \right ) c_4 \sum_{i=1}^k
\|{\cal K}J h_i-1\| -c_3 \|U\| \\
& \geq & 0
\mbox{\rm \small e}nd{eqnarray*}
by~(\ref{eq:(c)}),~(\ref{eq:(b)}) and~(\ref{eq:new03}),
which is the conclusion of the lemma. $
\Box$
The next lemma tells us that in ``one step'', we can't move from being ``far
away'' from uniform to being ``very close'' to uniform.
\begin{equation}gin{lem} \labelel{lem:second}
Under the more general hypotheses of Theorem~\ref{th:gen i}
(with a given $J >0$, a given $\|\,\,\|$ on $ spherically symmetric pj$, a given $L$ and
a given $\rho$ satisfying the required conditions),
for all $\begin{equation}ta>0$ and $J'\in (0,J]$, there exists a $\gamma<\begin{equation}ta$ such that if
$\| \bar{d}eltaoi_k ( {\cal K}_{J_1''} h_1 , \ldots , {\cal K}_{J_k''} h_k) - 1 \| <\gamma$
with $h_1,\ldots, h_k\in {\bf P}P_+(J)\cup \{\bar{d}elta_{{\hat{0}}}\}$ and $k\le B$
and with $J_i''$ being $J$ if $h_i\in {\bf P}P_+(J)$ and $J'$ if $h_i=\bar{d}elta_{{\hat{0}}}$,
then each $h_i$ is not $\bar{d}elta_{{\hat{0}}}$ and $\sum_{i=1}^k \| h_i - 1\| < \begin{equation}ta$.
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.} Choose $\gamma\in (0,\min\{\begin{equation}ta,1/c_1\})$ so that
$$
{2c_1 c_3 B\gamma \over\rho c_2 c_4 (1-c_1\gamma)} < \begin{equation}ta
$$
and
$$
\min\{||K_J-1||,||K_{J'}-1||\} > {2c_1 \gamma \over (1-c_1\gamma)c_2}
$$
where $c_1,c_2,\rho,c_3$ and $c_4$ come
from~(\ref{eq:present iii}),~(\ref{eq:present iii'}),~(\ref{eq:(a)}),~(\ref{eq:(c)}) and~(\ref{eq:(b)}) respectively.
We first show that if $h_1,\ldots,h_k\in{\bf P}P_+(J)$, with $k\le B$, then
$\| \bar{d}eltaoi_k (h_1 , \ldots , h_k) - 1 \| <\gamma< 1/c_1$ implies that for all
$i$
$$
\| h_i - 1 \| <{2c_1\gamma \over (1-c_1\gamma)c_2}.
$$
[Proof:
$$
||h_i-1||\le c_2^{-1}||h_i-1||_\infty
\le c_2^{-1}\left({\max h_i\over \min h_i}-1\right)
$$
$$
\le c_2^{-1}\left({\max \bar{d}eltarod_i h_i\over \min \bar{d}eltarod_i h_i}-1\right)
= c_2^{-1}\left({\max \bar{d}eltaoi_k (h_1 , \ldots , h_k)\over\min \bar{d}eltaoi_k
(h_1 , \ldots , h_k) }-1\right)
$$
where the second inequality is straightforward and the
third inequality comes from~(\ref{eq:xiiii}).
Next, $\| \bar{d}eltaoi_k (h_1 , \ldots , h_k) - 1 \| <\gamma< 1/c_1$ implies
$|| \bar{d}eltaoi_k (h_1 , \ldots , h_k) - 1 ||_\infty\le c_1\gamma$
which implies the last expression is at most
$$
c_2^{-1}\left({1+c_1\gamma\over 1-c_1\gamma}-1\right)=
c_2^{-1}{2c_1\gamma\over 1-c_1\gamma}.]
$$
It follows that if
$\| \bar{d}eltaoi_k ( {\cal K}_{J_1''} h_1 , \ldots , {\cal K}_{J_k''} h_k) - 1 \| <\gamma$,
then
$$
\| {\cal K}_{J_i''} h_i-1 \| <{2c_1 \gamma \over (1-c_1\gamma)c_2}
$$
for each $i$ which implies that $h_i\in{\bf P}P_+(J)$
(as opposed to being $\bar{d}elta_{{\hat{0}}}$). Hence $J_i''$ is $J$ for all $i$.
Now from~(\ref{eq:(a)})--(\ref{eq:(b)}) we have
$$||{\cal K}_{J} h_i - 1|| \geq {\rho c_4 ||h_i - 1|| \over c_3}$$
and we obtain the conclusion of the lemma.
$
\Box$
\noindent{\bf Proof of Theorem~\ref{th:gen i}.}
Since in Section~\ref{sub:sphere}
the Heisenberg models have been shown to satisfy all of
the more general hypotheses of this theorem, we need only prove the last
statement of the theorem, where we have
a given $J >0$, a given $\|\,\,\|$ on $ spherically symmetric pj$, a given $L$ and
a given $\rho$ satisfying the required conditions.
Choose an $\alphapha > 0$ so that
$\thetaextstyle {br} (\Gamma) \cdot \rho > 1 + \alphapha$.
Choosing $\begin{equation}ta$ from Lemma \ref{lem:first}, we have, under
our assumptions, that for all $h_1 , \ldots , h_k \in {\bf P}P_+(J)$ with
$k\le B$ and $\|h_i-1\| < \begin{equation}ta$ for each $i$,
\begin{equation}gin{equation} \labelel{eq:star4old}
L \left [ (\bar{d}eltaoi_k ({\cal K}J h_1 , \ldots , {\cal K}J h_k)) - 1 \right ]
\geq {1 \over 1 + \alphapha} \sum_{i=1}^k L ({\cal K}J h_i - 1)
\geq {\rho \over 1 + \alphapha} \sum_{i=1}^k L (h_i - 1).
\mbox{\rm \small e}nd{equation}
Now, if there is no robust phase transition, then by~(\ref{eq:present iii'})
there must exist $J'\in (0,J]$
and a sequence of cutsets $\{ C_n \}$ going to infinity
such that $\lim_{n \rightarrow \infty} \|f^{J',J , +}_{C_n , o} - 1\| = 0$.
Using Lemma \ref{lem:second}, choose $\gamma<\begin{equation}ta$
corresponding to $\begin{equation}ta$ and $J'$. Next, by our choice of $\alphapha$, we have
$$I := \inf_C \sum_{x \in C} \left ( {\rho \over 1 + \alphapha} \right)^{|x|}
> 0$$
where the infimum is over all cutsets.
We now choose $n$ so that
$$
\|f^{J',J , +}_{C_n , o} - 1\| < \min \{ \gamma , {c_4 \gamma I \over c_3} \}.
$$
where $c_3$ and $c_4$ come from~(\ref{eq:(c)}) and~(\ref{eq:(b)}) respectively.
We then define $\Gamma'$ to be the component of the set
$$\{ v \in C_n^i : \|f^{J',J , +}_{C_n , v} - 1\| < \gamma \}$$
that contains $o$
and let $C$ be the exterior boundary of $\Gamma'$
(that is, the set of $x \notin \Gamma'$ neighboring some $y \in \Gamma'$).
By the choice of $\gamma$, $C \subseteq C_n^i$ and
for each $v\in C^i\cup C$, the density $f^{J',J , +}_{C_n , v}$ is in
$$ {\bf P}P_+(J) \cap \{f: \|f-1\| < \begin{equation}ta\}. $$
Using~(\ref{eq:star4old}) and induction, we see that
$$L (f^{J',J , +}_{C_n , o} - 1) \geq \sum_{x \in C} \left (
{\rho \over 1 + \alphapha} \right )^{|x|} L (f^{J',J , +}_{C_n , x} - 1) .$$
By definition of $\Gamma' , C$ and $I$ and the fact that $L (f-1) \geq c_4
\|f - 1\|$ on ${\bf P}P_+(J)$, we see that
$$L (f^{J',J , +}_{C_n , o} - 1) \geq c_4 \gamma I .$$
Hence
$$\|f^{J',J , +}_{C_n , o} - 1\| \geq {c_4 \over c_3} \gamma I .$$
This contradicts the choice of $n$, proving that there is indeed
a robust phase transition.
$
\Box$
\setcounter{equation}{0}
\section{Analysis of specific models} \labelel{sec:anal}
\subsection{Heisenberg models} \labelel{sub:spherical}
For the Heisenberg models, recall that ${\bf S} = S^d$, $d \geq 1$,
and $H(x,y) = - x \cdot y$. The operator ${\cal K}J$ is convolution
with the function $K_J (x) = c e^{ J x \cdot {\hat{0}}}$, where $c$ is
a normalizing constant.
\noindent{\bf Proof of Theorem~\bar{d}eltarotect{\ref{th:main}}.}
A change of variables shows that $L(K_J)={\cal R}dJ$ and so the result follows
from Theorems~\ref{th:gen ii} and~\ref{th:gen i}. $
\Box$
For the rotor model, we now prove the equivalence of SB and SB+.
\noindent{\bf Proof of Proposition~\bar{d}eltarotect{\ref{pr:rotor equiv}}.}
We have already seen the representation
$$f = \sum_{n \geq 0} a_n (f) \bar{d}eltasi_n, $$
for functions $f \in L^2 ({\bf S})g$. In the case of the rotor model, where
${\bf S} = S^1$ and we take ${\hat{0}}$ to be $(1,0)$,
the space $L^2 ({\bf S})g$ is the space of even functions of
$\thetaheta \in [-\bar{d}eltai , \bar{d}eltai]$ and $\bar{d}eltasi_n = \cos (n \thetaheta)$. We now
turn to the full Fourier decomposition $f = \sum_{n \in Z\!\!\!Z} b_n (f)
e^{i n \thetaheta}$, where $b_n (f) = \int_0^{2\bar{d}eltai} f(\thetaheta) e^{-i n \thetaheta} \,
d\thetaheta/ (2 \bar{d}eltai)$.
Let $C$ be any cutset and $\bar{d}elta$ be a set of boundary conditions on $C$.
Let ${\cal J}$ be any set of interaction strengths. It suffices to show that
$$||f^{{\cal J} , \bar{d}elta}_{C,w} - 1||_\infty \leq ||f^{{\cal J} , +}_{C,w}-1||_\infty$$
for all $w\in C^i$.
For $v \in C$ and $n\in Z\!\!\!Z$, let $x_{v,n} = b_n (K_{{\cal J}(x) , \bar{d}elta (v)})$
where $e$ is the edge from $v$ to its parent.
\noindent{\mbox{\rm \small e}m Claim}: For all $y\in C^i$, the
Fourier coefficients $\int_0^{2\bar{d}eltai} e^{i n \thetaheta}
\, d\mu^{{\cal J} , \bar{d}elta}_{C,y}(\thetaheta)$, which we denote by
$\{ u_{y , n} : n \in Z\!\!\!Z \}$, are sums of monomials in
$\{ x_{v,n} \}_{v\in C, n\inZ\!\!\!Z}$ with
nonnegative coefficients. {\it Proof:} Let $w \in C^i$ have children
$w_1 , \ldots , w_r \in C^i$ and $w_{r+1} , \ldots , w_k \in C$.
Then the Fourier coefficients $\{ u_{w,n} : n \in Z\!\!\!Z \}$
are the convolution of the $k - r$ series $\{ x_{v , n} : n \in Z\!\!\!Z \}$
as $v$ ranges over $w_{r+1} , \ldots , w_k$, also convolved with the
series $\{ b_n (K_{{\cal J} (\overline{wv})}) u_{v,n} : n \in Z\!\!\!Z \}$ as $v$
ranges over $w_1 , \ldots , w_r$. Since $b_n (K_J) \geq 0$, this
establishes the claim via induction and the fundamental recursion.
Now write $x_{v,n}^+$ for the Fourier coefficients $b_n (K_{{\cal J} (e)})$ where
$e$ is as before.
Since $K_{J , e^{i \alphapha}} (x) = K_J (e^{-i \alphapha} x)$, it follows that
$$|x_{v,n}| = |x_{v,n}^+| .$$
But $x_{v,n}^+$ is real because $K_J$ is even, and has been
shown to be nonnegative. Thus
$$|x_{v,n}| = x_{v,n}^+ ,$$
and it follows from the claim that each $u_{w,n}$ has modulus
bounded above by the corresponding $u_{w,n}^+$ when plus boundary
conditions are taken. Hence
$$
||f^{{\cal J} , \bar{d}elta}_{C,w} - 1||_\infty \le ||f^{{\cal J} , \bar{d}elta}_{C,w} - 1||_A
\leq \sum_{n \neq 0} |u_{w,n}|
\leq \sum_{n \neq 0} u_{w,n}^+ = ||f^{{\cal J} , +}_{C,w} - 1||_A
= ||f^{{\cal J} , +}_{C,w} - 1||_\infty,$$
proving the lemma. $
\Box$
\noindent{\mbox{\rm \small e}m Remark:} Although we have used special properties
of the Fourier decomposition on $L^2 (S^1)$, there exist similar
decompositions for $S^d$. We believe that a parallel argument
can probably be constructed, bounding the modulus of the sum of
the coefficients of spherical harmonics of a given order by the
coefficients one obtains for the analogous monomials in the values
$a_n (K_{{\cal J} (x)})$, whose coefficients are necessarily nonnegative
by the nonnegativity of the connection coefficients $q^r_{ij}$.
Thus we are led to state:
\begin{equation}gin{pblm} \labelel{pblm:all spheres}
Prove a version of Proposition~\ref{pr:rotor equiv} for general
Heisenberg models on trees.
\mbox{\rm \small e}nd{pblm}
\subsection{The Potts model} \labelel{sub:potts}
\noindent{\bf Proof of Theorem}~\ref{th:potts}.
We will obtain this result from Theorems~\ref{th:gen ii} and~\ref{th:gen i}.
For (i), letting $||\,\,||$ be the $L_\infty$ norm on $ spherically symmetric pj$ and
${\bf Op}_J=\alphapha_J$, all of the hypotheses in Theorem~\ref{th:gen ii}
except~(\ref{eq:ixix}) are clear. The function $K_J$ is given by
$$K_J (x) = c \mbox{\rm \small e}xp (J (2 \bar{d}eltata_{x,0} - 1))$$
where $c = (e^J + (q-1) e^{-J})^{-1}$. The operator ${\cal K}J$ is linear and
$${\cal K}J \bar{d}eltata_j = c e^J \bar{d}eltata_j + \sum_{i \neq j} c e^{-J} \bar{d}eltata_i \, .$$
Hence in the basis $\bar{d}eltata_0 , \ldots , \bar{d}eltata_{q-1}$, the
matrix representation of ${\cal K}J$ is $c (e^J - e^{-J}) I + c e^{-J} M$
where $M$ is the matrix of all ones. On the orthogonal complement
of the constant functions, ${\cal K}J$ is $c (e^J - e^{-J}) I$,
and~(\ref{eq:ixix}) follows, proving (i) by an application of
Theorem~\ref{th:gen ii}.
For (ii), let $||\,\,||$ be the same as above, $\rho=\alphapha_J$ and
$L(h)=h(0)-h(1)$. It is then immediate to check that
all of the hypotheses in Theorem~\ref{th:gen i} hold and we may conclude
(ii) by an application of Theorem~\ref{th:gen i}. $
\Box$
\setcounter{equation}{0}
\section{Proof of Theorem~\bar{d}eltarotect{\ref{th:0hd}}.} \labelel{sec:zero}
By Proposition~\ref{prop:SB=} and the fact that any subtree of
a tree with branching number 1 also has branching number 1,
it suffices to show:
\begin{equation}gin{quote}
For for any $\Gamma$ with $\thetaextstyle {br} (\Gamma) = 1$,
and any bounded ${\cal J}$, there is
a sequence of cutsets $\{ C_n \}$ such that for any sequence
$\{ \bar{d}eltata_n \}$ of boundary conditions on $\{ C_n \}$,
$$
\lim_{n\thetao\infty}\| f^{{\cal J} , \bar{d}eltata_n}_{C_n , o} - 1\|_\infty = 0 .
$$
\mbox{\rm \small e}nd{quote}
It is convenient to work with a different measure of size, the {\mbox{\rm \small e}m Max/Min}
measure, defined as follows. (This arose already in the proof of
Lemma~\ref{lem:second}.) For any continuous strictly positive
function $f$ on ${\bf S}$, let
$$\|f\|_M := {\max_{x \in {\bf S}} f(x) \over \min_{x \in {\bf S}} f(x)} \, .$$
It is immediate to see:
\begin{equation}gin{lem} \labelel{lem:mmequiv}
For any sequence $\{ h_n \}$ of continuous
probability densities, $\|h_n - 1\|_\infty \rightarrow 0$ if and only if
$\log \|h_n\|_M \rightarrow 0$.
\mbox{\rm \small e}nd{lem}
Next, we examine the effect of ${\cal K}J$ on $\|f\|_M$.
\begin{equation}gin{lem} \labelel{lem:unifmm}
For any statistical ensemble $({\bf S} , G , H)$,
any $J_{\rm max}$ and any $T > 0$ there
is an $\mbox{\rm \small e}psilonsilon > 0$ such that for any continuous strictly
positive function $f$ with
$\|f\|_M \leq T$, and any $J \leq J_{\rm max}$,
$$\log \|{\cal K}J f\|_M \leq (1 - \mbox{\rm \small e}psilonsilon) \log \| f \|_M \, .$$
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.} Fix $H, J$ and $f$ and assume without loss
of generality that $\int f \, \bar{d}x = 1$ since the
{\mbox{\rm \small e}m Max/Min} measure is unaffected by multiplicative constants.
Let $[a,b]$ be the smallest closed interval containing the range of $f$
and $[c,d]$ contain the range of $K_J$ with $a,c >0$.
Since $f$ is a probability density,
$a < 1 < b$ (we rule out the trivial case $f \mbox{\rm \small e}quiv 1$). Since
$K_J = c + (1-c) g$ for some probability density $g$, it follows that
for any $x \in {\bf S}$,
$$c + (1-c) a \leq {\cal K}J f(x) \leq c + (1-c) b .$$
As $J$ varies over $[0 , J_{\rm max}]$, $\min_x K_J (x)$ is bounded
below by some $c_0 > 0$, so for all such $J$,
$$c_0 + (1-c_0) a \leq {\cal K}J f(x) \leq c_0 + (1-c_0) b$$
and so
$$\| {\cal K}J f \|_M \leq {c_0 + (1 - c_0) b \over c_0 + (1 - c_0) a} \, .$$
Setting $R = \|f\|_M - 1$, we have $b = (1+R) a$ and so
$$\| {\cal K}J f\|_M \leq {c_0 + (1 - c_0) (1 + R) a \over c_0 + (1 - c_0) a}
= 1 + R {(1 - c_0) a \over c_0 + (1 - c_0) a}
\leq 1 + R (1 - c_0) \, .$$
Thus
\begin{equation}gin{equation} \labelel{eq:u}
\|{\cal K}J f\|_M \leq 1 + (1 - c_0) \left ( \|f\|_M - 1 \right ) \, .
\mbox{\rm \small e}nd{equation}
The function $\log (1 + (1 - c_0) u) / \log (1 + u)$ is bounded above
by some $1 - \mbox{\rm \small e}psilonsilon < 1$ as $u$ varies over $(0 , T-1]$, and setting
$u = \|f\|_M - 1$ in~(\ref{eq:u}) gives
$$\log \| {\cal K}J f\|_M \leq \log (1 + (1 - c_0) (\|f\|_M - 1)) \leq
(1 - \mbox{\rm \small e}psilonsilon) \log \|f\|_M \, ,$$
proving the lemma.
$
\Box$
Proceeding with the proof of Theorem~\ref{th:0hd}, let $C$ be a cutset
with no vertices in the first generation,
$$\bar{d}eltaartial C = \{ v \in C^i : \mbox{\rm \small e}xists w \in C~{\rm with }\,\, v \thetao w \}, $$
and $\bar{d}elta$ be defined on $C$. Clearly, for continuous strictly positive
functions $h_1 , \ldots , h_k$,
$$
\| \bar{d}eltaoi (h_1 , \ldots , h_k) \|_M \leq \bar{d}eltarod_{i=1}^k \| h_i \|_M \, .
$$
We have also previously seen (Lemma~\ref{lem:unifbd})
that all densities that arise are uniformly
bounded away from 0 and $\infty$ and hence there is a uniform bound on the
$\| \,\, \|_M $ that arise. We can therefore choose $\mbox{\rm \small e}psilonsilon$ from
Lemma~\ref{lem:unifmm}. Next for any $v\in C^i\setminus \bar{d}eltaartial C$,
applying the fundamental recursion gives
\begin{equation}gin{eqnarray*}
\log \|f^{{\cal J} , \bar{d}eltata}_{C,v} \|_M & = & \log \| \bar{d}eltaoi ({\cal K}_{{\cal J} (\overline{vw_1})}
f^{{\cal J} , \bar{d}eltata}_{C , w_1} , \ldots , {\cal K}_{{\cal J} (\overline{vw_k})}
f^{{\cal J} , \bar{d}eltata}_{C , w_k} \|_M \\[2ex]
& \leq & \sum_{i=1}^k \log \| {\cal K}_{{\cal J} (\overline{vw_i})}
f^{{\cal J} , \bar{d}eltata}_{C , w_i} \|_M \\[2ex]
& \leq & \sum_{i=1}^k (1 - \mbox{\rm \small e}psilonsilon) \log \| f^{{\cal J} , \bar{d}eltata}_{C , w_i} \|_M.
\mbox{\rm \small e}nd{eqnarray*}
Working backwards, we find that for any cutset $C$,
$$\log \|f^{{\cal J} , \bar{d}eltata}_{C , o}\|_M \leq \sum_{w \in \bar{d}eltaartial C}
(1 - \mbox{\rm \small e}psilonsilon)^{|w|} \log \|f^{{\cal J} , \bar{d}eltata}_{C , w}\|_M \, .$$
Since $\thetaextstyle {br} (\Gamma) = 1$
one can choose a sequence of cutsets $\{ C_n \}$
such that $\sum_{w \in \bar{d}eltaartial C_n} (1 - \mbox{\rm \small e}psilonsilon)^{|w|} \rightarrow 0$.
The uniform bound on
$\|f^{{\cal J} , \bar{d}eltata}_{C , w}\|_M$
implies that for any sequence of functions $\bar{d}elta_n$ on $C_n$,
$$
\lim_{n\thetao\infty}\log \|f^{{\cal J} , \bar{d}eltata_n}_{C_n , o} \|_M =0,
$$
which along with Lemma~\ref{lem:mmequiv} proves the theorem.
$
\Box$
Olle H\"aggstr\"om pointed out to us that this result could also be
obtained using ideas from disagreement percolation.
\setcounter{equation}{0}
\section{Proof of Theorem {\bar{d}eltarotect{\ref{th:2trees}}}.} \labelel{sec:potts}
While we assume that $q$ is an integer, the case of nonintegral $q$
can be made sense of via
the random cluster representation, and it is worth noting here that
the break between $q=2$ and $q=3$ happens at $q = 2 + \mbox{\rm \small e}psilonsilon$.
See~\cite{Ha} for a discussion of the qualitative differences between
the random cluster model on a tree when $q \leq 2$ as opposed to $q > 2$.
\begin{equation}gin{lem} \labelel{lem:robust}
Assume that all of the hypotheses of Theorem~\ref{th:gen ii} are in force
(in particular,~(\ref{eq:ixix}) and $\thetaextstyle {br} (\Gamma) \cdot {\bf Op}_J < 1$
hold and so there is no RPT for the parameter $J$) and in addition that
$\sup_{y\in {\bf S}} \|K_{J,y}\| < \infty$ and~(\ref{eq:ixix}) holds for
all $f\in{\bf P}P(J)$ (instead of just ${\bf P}P_+(J)$).
Then there is a tree $\Gamma'$ with
$\thetaextstyle {br} (\Gamma') = \thetaextstyle {br} (\Gamma)$
such that $\Gamma'$ has no PT for the parameter $J$.
\mbox{\rm \small e}nd{lem}
\noindent{\bf Proof.} We mimic the proof of Theorem~\ref{th:gen ii}.
Choose $\mbox{\rm \small e}psilonsilon$, $\mbox{\rm \small e}psilonsilon_0$ and
cutsets $\{ C_n \}$ as in the proof of Theorem~\ref{th:gen ii}
where we can assume that the cutsets $\{ C_n \}$ are disjoint.
Choose an integer $m$ sufficiently large so that the $m$-fold iterated
convolution operator ${\cal K}J^m$ satisfies
$||{\cal K}J^m \bar{d}elta_y-1|| \leq \mbox{\rm \small e}psilonsilon_0 {\bf Op}_J$.
For each increasing sequence $\{ n(k) : k = 1 , 2 , \ldots \}$
of integers, define a tree $\Gamma'$ by replacing each edge from an element
of $C_{n(k)}$ to its parent by $m$ edges in series, for all cutsets
in the sequence $\{ C_{n(k)} \}$. It is not too great an abuse of
notation to let $C_n$ denote the cutset of $\Gamma'$ consisting of
the same vertices as before. It is now possible to
establish~(\ref{eq:ind}) for all $v \in D$, where $D$ is the set of
vertices in $\Gamma'$ that are in $C^i$ and in $\Gamma$ (i.e., are not
in a chain of parallel edges that was added).
The only adjustment
in the proof is as follows. Use Lemma~\ref{lem:rec} to represent
$f^{J , +}_{C_n , v}$ in terms of $f^{J,+}_{C_n , w}$ where $w$
are the children of $v$ in $\Gamma$ rather than in $\Gamma'$, i.e., we leap
the whole chain of $m$ edges at once. Then the case $w \in C_n$ that
was handled by the choice of $J'$ is replaced by a case
$w \in \Gamma' \setminus \Gamma$, which is handled by the choice of $m$.
In fact, (\ref{eq:ind}) holds when + is replaced by any boundary condition
as the exact same proof shows.
By choosing $\{ n(k) \}$ sufficiently sparse, we can ensure that
$\thetaextstyle {br} (\Gamma') = \thetaextstyle {br} (\Gamma)$.
Fixing any such choice of $\{ n(k) \}$,
it follows that there is no phase transition by the above together with
Proposition~\ref{prop:SB=}.
$
\Box$
We proceed now with the description of a counterexample.
For $\Gamma_1$, we choose the homogeneous binary tree, where each vertex
has precisely 2 children. Recall from
Section~\ref{sub:potts} that under + boundary conditions, the functions
$f^{J , +}_{C , v}$ all lie in a one-dimensional set. The most
convenient parameterization for the segment is by the log-likelihood ratio
of state ${\hat{0}}$ to the other states.
Thus the probability measure $a \bar{d}eltata_0 + \sum_{i=1}^{q-1}
((1-a)/(q-1)) \bar{d}eltata_i$ is mapped to the value $\log [(q-1) a / (1-a)]$.
Let $g(v)$ denote the log-likelihood ratio at $v$ under some interaction
strength and boundary conditions.
The recursion~(\ref{eq:recurse}) of Lemma~\ref{lem:rec} boils down to
$$g(v) = \sum_{v \rightarrow w} \bar{d}eltahi (g(w)) ; \;\;\;\; \bar{d}eltahi (z) := \log
{ p e^z + 1-p \over {1-p \over q-1} e^z + (1 - {1-p \over q-1})} \, ,$$
where
\begin{equation}gin{equation} \labelel{eq:p}
p := e^J / (e^J + (q-1) e^{-J}) \, .
\mbox{\rm \small e}nd{equation}
Taking a Taylor expansion to the second order gives
$$\bar{d}eltahi (z) = \left ( p - {1-p \over q-1} \right ) z + {1-p \over 2 (q-1)^2}
[p(q-1)^2 - (q-1) + (1-p)] z^2 + O(z^3) .$$
To see that the second derivative is positive at 0
for $q > 2$, first take the $q$-derivative of the $z^2$ coefficient which is
$[q+2p-3](1-p)/(2(q-1)^3)$.
The definition of $p$ and the fact that $J > 0$ imply
that $p > 1/q \geq 1/(2(q-1))$. Since $x+1/(x-1) -3 >0$ on $(2,\infty)$
and $2p> 1/(q-1)$,
it follows that the $z^2$ coefficient has a positive
$q$-derivative for $q \ge 2$, and is therefore positive for all $q > 2$.
(This also implies that for $q\in (2-\bar{d}elta,2)$ for some $\bar{d}elta$,
the function $\bar{d}eltahi$ is concave (see~\cite{PP} for a detailed analysis of
the critical case $q=2$).)
The Taylor expansion gives $\bar{d}eltahi'(0) = p - (1-p)/(q-1)$. Note that
$p_0: = (q+1)/(2q)$ satisfies $p_0 - (1 - p_0) / (q-1) = 1/2$.
The value of $p_0$ is chosen to make $\bar{d}eltahi' (0) = 1/2$; by
convexity of $\bar{d}eltahi$ near zero, there is an interval
$I := (p_0 - \mbox{\rm \small e}psilonsilon , p_0)$ such that for $p \in I$, the equation
$\bar{d}eltahi (z) = z/2$ has a positive solution, call it $z(p)$. Take
$\mbox{\rm \small e}psilonsilon>0$ so small that $p_0 -\mbox{\rm \small e}psilonsilon > 1/q$.
For any $1>p > 1/q$ there is a unique $J > 0$ such that~(\ref{eq:p})
holds. If $p \in I$, then $z(p)$ is a fixed point for the function
$2 \bar{d}eltahi$ and it is easy to see by induction that under + boundary conditions
on the binary tree, one will always have $g(v) \geq z(p)$. Thus
we have shown that $\Gamma_1$ has a phase transition for any
$J$ such that $p \in I$.
To find $\Gamma_2$, we examine the connection between $p_0$ and
$\| {\cal K}J \|$ where for the rest of the proof, the operator norm
refers to the $L^\infty$ norm on the orthogonal complement of the constants.
Observe that
$$p - {1-p \over q-1} = {e^J \over e^J + (q-1) e^{-J}} - {e^{-J} \over
e^J + (q-1) e^{-J}} = \| {\cal K}J \|$$
by the computation in Section~\ref{sub:potts}. Thus $p_0$ is
chosen to make $\| {\cal K}J \| = 1/2$ and for any $p \in I$, $\| {\cal K}J \| < 1/2$.
Fix any $J$ so that $p \in I$, and let $\Gamma$ be any tree with
$$2 = \thetaextstyle {br} (\Gamma_1) <
\thetaextstyle {br} (\Gamma) < \| {\cal K}J \|^{-1}.$$
Let $\Gamma'$ be as in Lemma~\ref{lem:robust} and set $\Gamma_2 = \Gamma'$.
Then there is no phase transition on $\Gamma_2$ for the chosen parameters,
and since we have seen there is a phase transition for $\Gamma_1$,
this completes the proof of Theorem~\ref{th:2trees}. $
\Box$
\noindent
{\bf Acknowledgements.}
We thank Richard Askey for discussions and showing us the proof of
Lemma~\ref{lem:incr}, J\"{o}ran Bergh, Yuval Peres
and Paul Terwilliger for discussions, Anton Wakolbinger
for providing us with reference \cite{E} and the referee for a correction
and some suggestions.
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\mbox{\rm \small e}nd{thebibliography}
\noindent
\begin{equation}gin{tabbing}
enoughs \= fffffffffffffffffffffenoughennnnnnnnnnnnnnn \= \kill
\> Robin Pemantle \> Jeffrey E.~Steif \\
\> Department of Mathematics \> Department of Mathematics \\
\> University of Wisconsin-Madison \> Chalmers University of Technology \\
\> Van Vleck Hall \> S--41296 Gothenburg \\
\> 480 Lincoln Drive \> Sweden \\
\> Madison, WI 53706 \> [email protected] \\
\> [email protected]
\mbox{\rm \small e}nd{tabbing}
\mbox{\rm \small e}nd{document} | math |
Maha Samudram సినిమా రివ్యూ తారాగణం: శర్వానంద్, సిద్ధార్థ్, అదితీరావు, అనూఇమ్మాన్యుయెల్, రావు రమేష్, శరణ్య తదితరులుసినిమాటోగ్రఫీ: రాజ్ తోటసంగీతం: చైతన్ భరద్వాజ్ నిర్మాత: రామబ్రహ్మం సుంకర నిర్మాణ సంస్థ: ఏకే ఎంటర్టైన్మెంట్స్ రచనదర్శకత్వం: అజయ్ భూపతి మల్టీస్టారర్ చిత్రాల పట్ల ప్రేక్షకుల్లో ఆసక్తి ఎక్కువగా ఉంటుంది. అందునా శర్వానంద్, సిద్ధార్థ్ వంటి యువహీరోల కలిస్తే ఆ సినిమాలో ఏదో కొత్తదనం ఉంటుందని ఆశిస్తారు. కెరీర్ ఆరంభం నుంచి ఈ యువహీరోలిద్దరూ కథాంశాల ఎంపికలో వైవిధ్యానికి పెద్దపీట వేస్తుంటారు. ఆ కారణంగానే మహాసముద్రం చిత్రానికి నిర్మాణం నుంచే మంచిహైప్ క్రియేట్ అయింది. ఆర్.ఎక్స్.100 వంటి యూత్ఫుల్ ఎమోషన్ లవ్స్టోరీతో తొలి చిత్రంతోనే ప్రతిభను చాటుకున్నారు యువ దర్శకుడు అజయ్భూపతి. ఆయన ద్వితీయ ప్రయత్నంగా ఈ సినిమాను తెరకెక్కించడంతో ప్రేక్షకులు ఉత్సుకతతో ఎదురుచూశారు. ఈ నేపథ్యంలో ప్రేక్షకులముందుకొచ్చిన మహాసముద్రం ప్రేక్షకుల్ని ఏ మేరకు ఆకట్టుకుందో తెలుసుకోవాలంటే కథలోకి వెళ్లాల్సిందే.. కథ గురించి.. అర్జున్ శర్వానంద్, విజయ్ సిద్ధార్థ్ ఇద్దరు ప్రాణస్నేహితులు. విశాఖ నగరంలో ఎన్నో కలలతో జీవితాన్ని సాగిస్తుంటారు. ఎస్.ఐ.కావాలన్నది విజయ్ లక్ష్యం. అధికారం, డబ్బు ఉంటే జీవితంలో ఏమైనా చేయొచ్చని నమ్ముతుంటాడు. అతని ప్రేయసి మహా అదితిరావు. మరోవైపు సాగరతీరంలో మాదకద్రవ్యాల స్మగ్లింగ్ కార్యకలాపాల్ని నిర్వహిస్తుంటాడు ధనుంజయ్ కేజీఎఫ్ రామ్. నగర నేర సామ్రాజ్యానికి అధిపతిగా చలామణి అవుతుంటాడు. అనుకోని సంఘటన వల్ల ధనుంజయ్ పై హత్యాయత్నం చేస్తాడు విజయ్. ఆ భయంతో నగరాన్ని వదిలి వెళ్లిపోతాడు. ఆ తర్వాత ఏం జరిగింది? వీళ్ల జీవితంలో చెంచు మామ జగపతిబాబు పోషించిన పాత్ర ఏమిటి? తన స్నేహితుడు విజయ్ను కాపాడుకోవడానికి అర్జున్ చేసిన ప్రయత్నాలేమిటి? ఇద్దరి మధ్య చోటుచేసుకున్న మనస్పర్థలు ఎలాంటి పరిణామాలకు దారితీశాయి? ఇద్దరు స్నేహితులు తీసుకున్న నిర్ణయాలు వారి జీవితాల్ని ఎలాంటి మలుపులు తిప్పాయి? ఇలాంటి ఆసక్తికరమైన అంశాలు ఏమిటో తెలుసుకోవాలంటే సినిమా చూడాల్సిందే.. ఎలా ఉందంటే.. ఇద్దరి స్నేహితు జీవితాల నేపథ్యంలో అనేక పొరల్లో సంక్లిష్టంగా అల్లుకున్న కథ ఇది. స్నేహితుల మధ్య ప్రేమ, సంఘర్షణ, అపనమ్మకం, శత్రుత్వం అంశాలతో భావోద్వేగభరితంగా కథను రాసుకున్నారు. మధ్యతరగతి యువకుల జీవితానికి మాఫియా నేపథ్యాన్ని ముడిపెట్టి..అదే సమయంలో ఓ సంఘర్షణాత్మక ప్రేమకథను చెబుతూ.స్నేహంలోని గాఢతను ఆవిష్కరిస్తూ భిన్న ఎమోషన్స్తో కథాగమనాన్ని నడిపించారు. సిద్దార్థ్అదితిరావు, శర్వానంద్అనుఇమ్మాన్యుయెల్ ప్రేమకథలతో మొదలై తొలిభాగం అనేక మలుపులతో కనిపిస్తుంది. చెంచు మామతో ఇద్దరు మిత్రులకు ఉన్న అనుబంధం, ధనుంజయ్ తమ్ముడు గూని బాబ్జీ రావురమేష్ ఎపిసోడ్తో తొలిభాగమంతా కథను, అందులోని పాత్రల్ని పరిచయం చేస్తూ సాగింది. మహా సముద్రం దర్శకుడు అజయ్ భూపతితో ప్రత్యేక ఇంటర్వూ ద్వితీయార్థం అర్జున్ జీవితం తాలూకు సంఘర్షణ ప్రధానంగా సాగింది. విజయ్ ప్రేయసి మహా బాధ్యతలు తీసుకున్న అర్జున్ మాఫియా డాన్గా ఎదగడం, కొత్త డాన్గా అవతరించిన గూని బాబ్జీని సవాలు చేయడం వంటి అంశాలతో సెకండాఫ్ ఊపందుకుంటుంది. అయితే విజయ్ తన ప్రేయసిని ద్వేషిస్తూ వదిలివెళ్లిపోవడానికి సరైన కారణాలు ఏమిటో కన్విన్సింగ్గా చెప్పలేకపోయారు. అడిగినప్పుడల్లా డబ్బులిచ్చి ఎంతో అప్యాయంగా ఉండే ప్రేయసి పట్ల విజయ్ అకారణ ద్వేషమేమిటో అర్థం కాదు. నాలుగేళ్ల తర్వాత తిరిగొచ్చిన విజయ్..అర్జున్ పట్ల పగను పెంచుకోవడం.. అతన్ని అంతం చేయాలనుకోవడం కూడా సబబుగా అనిపించదు. అయితే విజయ్ తిరిగొచ్చిన తర్వాత పతాకఘట్టాలు ఉద్వేగంగా సాగాయి. అర్జున్ అనతికాలంలోనే మాఫియా డాన్గా ఎదగడం..విశాఖను శాసించడం పూర్తి సినిమాటిక్గా అనిపిస్తుంది. అందుకు దారితీసిన పరిస్థితుల్ని బలంగా చూపించలేకపోయారు. ధనుంజయ్, గూని బాబ్జీ వంటి కరడుగట్టిన మాఫియా డాన్లు విజయ్, అర్జున్ వంటి సామాన్య యువకుల చేతికి చిక్కి అంత సులభంగా అంతమైపోవడం లాజిక్కు అందదు. అదే సమయంలో ప్రాణస్నేహితుల మధ్య వచ్చిన అపార్థాలు, మనస్పర్థలకు కూడా పెద్దగా కారణాలు కనిపించవు. గూని బాబ్జీ మీద కోపంతో తన స్నేహితులు అర్జున్ను విజయ్ ద్వేషించడం ఏమాత్రం కన్విన్సింగ్గా అనిపించలేదు. ఎవరేలా చేశారంటే.. అనుక్షణం సంఘర్షణకు లోనయ్యే స్నేహితుడిగా శర్వానంద్ తన పాత్రలో జీవించాడు. ఈ తరహా పాత్రల్లో మెప్పించడం ఆయనకు కొత్తేమి కాదు. సిద్థార్థ్ పాత్ర నెగెటివ్ షేడ్స్తో సాగింది. ఆయన కెరీర్లో ఇదొక కొత్త పాత్రగా చెప్పవొచ్చు. అదితిరావు అభినయం బాగుంది. కళ్లలో ప్రేమను, ఉద్వేగాల్ని పలికించిన తీరు ఆకట్టుకుంటుంది. అనుఇమ్యాన్యుయెల్ పాత్ర కొన్ని సన్నివేశాలకే పరిమితమైంది. చుంచు మామగా జగపతిబాబు, గూని బాబ్జీగా రావు రమేష్ తమదైన శైలిలో పాత్రల్ని రక్తికట్టించారు. మిగతా పాత్రధారులందరూ పరిధులమేరకు నటించారు. సాంకేతికంగా అన్ని అంశాలు బాగా కుదిరాయి. రాజ్తోట సినిమాటోగ్రఫీ విశాఖ సాగర అందాల్ని బాగా చూపించింది. పాటల్లో విజువల్స్ని చక్కగా ప్రజెంట్ చేసింది. సంభాషణలు బాగున్నాయి. భుజాల మీద బరువుని ఎవరైనా మోయగలరు కానీ గుండెలోని బంధాల బరువు మోసినవాడే నిజమైన స్నేహితుడు వంటి డైలాగ్స్ మెప్పిస్తాయి. పాటలు మెలోడీ ప్రధానంగా ఆకట్టుకున్నాయి. బ్యాక్గ్రౌండ్ మ్యూజిక్ సన్నివేశాల్లోని ఫీల్ను ఎలివేట్ చేసింది. నిర్మాణ విలువలు ఉన్నతంగా కనిపించాయి. దర్శకుడు అజయ్భూపతి మానవోద్వేగాల నేపథ్యంలో ఓ సంక్లిష్టమైన కథను చెప్పే ప్రయత్నం చేశాడు. స్నేహం, ప్రేమ లోతుల్ని తనదైన భావాలతో తెరపై ఆవిష్కరించారు. తీర్పు.. అక్కడక్కడా కథాగమనంలో కొన్ని లోపాలున్నా చక్కటి భావోద్వేగాలతో కూడిన కథగా మహాసముద్రం ఆకట్టుకుంటుంది. కథా, స్క్రీన్ప్లే పరంగా మరిన్ని జాగ్రత్తలు తీసుకొని ఉంటే మహాసముద్రం మరింతగా ఆకట్టుకునే సినిమాగా మిలిగిపోయేది. బాక్సాఫీస్ బరిలో ఈ సినిమా ఫలితమేమిటో తెలియాలంటే మాత్రం మరికొద్ది రోజులు వేచిచూడాల్సిందే.. రేటింగ్: 2.755 | telegu |
مگر کھاندر گژھہِ شییٚہِ ریٚتۍ پَتَے سَپدُن تِکیٛازِ أمِس چھُ پنٕنۍ مذہبی وَتہٕ ہاوٕکۍ یی کرنہٕ خٲطرٕ ووٚنمُت | kashmiri |
வேலூர் அரசு மருத்துவமனையில் ஒமைக்ரான் வார்டு தயார் வேலுார்: வேலுார் அரசு மருத்துவமனையில், ஒமைக்ரான் சிறப்பு வார்டு அமைக்கப்பட்டு தயார் நிலையில் உள்ளது.இந்தியாவில் ஒமைக்ரான் தொற்று பரவியதையடுத்து, அதற்கு சிகிச்சை அளிக்க அனைத்து ஏற்பாடுளையும் செய்து தயார் நிலையில் இருக்க சுகாதாரத்துறைக்கு தமிழக அரசு உத்தரவிட்டது.இதையடுத்து, வேலுார் அரசு மருத்துவக் கல்லுாரி மருத்துவமனையில் ஒமைக்ரான் சிறப்பு வார்டு இன்று டிச.,4 அமைக்கப்பட்டது. இங்கு ஆக்சிஜன் வசதியுடன் கூடிய 50 படுக்கைகள், தீவிர சிகிச்சைக்காக நான்கு படுக்கைகள் மற்றும் தனிமைப்பதுத்தும் வசதி, வென்டிலேட்டர் வசதி செய்யப்பட்டுள்ளது. 24 மணி நேரமும் செயல்படும் இந்த வார்டில் சிகிச்சையளிக்க டாக்டர்கள், செவிலியர்கள் தயார் நிலையில் உள்ளனர் என்று சுகாதாரத்துறையினர் தெரிவித்தனர். | tamil |
ಅಂಬಲಪಾಡಿ: ಹಡಿಲು ಭೂಮಿ ಕೃಷಿ ನಾಟಿಗೆ ಸುನೀಲ್ ಕುಮಾರ್ ಚಾಲನೆ ಉಡುಪಿ, ಜೂ.15: ಹಡಿಲು ಭೂಮಿ ಕೃಷಿ ಅಂದೋಲನದಡಿ ಕೇದಾ ರೋತ್ಥಾನ ಟ್ರಸ್ಟ್ ವತಿಯಿಂದ ಅಂಬಲಪಾಡಿ ಗ್ರಾಪಂ ವ್ಯಾಪ್ತಿಯ ಕಿದಿಯೂರು ಸಂಕೇಶ ವಿಠೋಬ ಭಜನಾ ಮಂಡಳಿಯ ಎದುರು ಇಂದು 5 ಎಕರೆ ಹಡಿಲು ಭೂಮಿ ಕೃಷಿಯ ನಾಟಿ ಕಾರ್ಯಕ್ಕೆ ಚಾಲನೆ ನೀಡಲಾಯಿತು. ಮತ್ಸ್ಯೋದ್ಯಮಿ ಹರಿಯಪ್ಪ ಕೋಟ್ಯಾನ್ ಅವರೊಂದಿಗೆ ಶಾಸಕ ಕೆ.ರಘುಪತಿ ಭಟ್ ಗದ್ದೆಗೆ ಹಾಲನ್ನು ಅರ್ಪಿಸುವ ಮೂಲಕ ಯಂತ್ರ ನಾಟಿಗೆ ಚಾಲನೆ ನೀಡಿದರು. ಕಾರ್ಕಳ ಶಾಸಕ ಹಾಗೂ ವಿಧಾನಸಭೆಯ ಮುಖ್ಯ ಸಚೇತಕ ವಿ.ಸುನೀಲ್ ಕುಮಾರ್ ನೇಜಿ ನೀಡುವ ಮೂಲಕ ಕೈ ನಾಟಿಗೆ ಚಾಲನೆ ನೀಡಿದರು. ಈ ಸಂದರ್ಭದಲ್ಲಿ ನಗರಸಭಾ ಸದಸ್ಯ ಹರೀಶ್ ಶೆಟ್ಟಿ, ಉಡುಪಿ ನಗರಾಭಿವೃದ್ಧಿ ಪ್ರಾಧಿಕಾರದ ಸದಸ್ಯ ಪ್ರವೀಣ್ ಶೆಟ್ಟಿ ಕಪ್ಪೆಟ್ಟು, ಅಂಬಲಪಾಡಿ ಮಹಾಶಕ್ತಿ ಕೇಂದ್ರದ ಅಧ್ಯಕ್ಷ ರಾಜೇಂದ್ರ ಪಂದುಬೆಟ್ಟು, ನೇಶನ್ ಫಸ್ಟ್ ಸಂಚಾಲಕ ಸೂರಜ್, ಅಂಬಲಪಾಡಿ ಗ್ರಾಪಂ ಮಾಜಿ ಉಪಾಧ್ಯಕ್ಷ ವೆಂಕಟರಮಣ ಕಿದಿಯೂರು, ಪ್ರಮುಖರಾದ ಹಿರಿಯಣ್ಣ ಕಿದಿಯೂರು, ವೇಣುಗೋಪಾಲ್, ಭಾಸ್ಕರ್ ಎ. ಕೋಟ್ಯಾನ್, ಅಂಬಲಪಾಡಿ ಗ್ರಾಪಂ ಸದಸ್ಯರಾದ ಉಷಾ ಶೆಟ್ಟಿ, ಸುಜಾತ ಸುಧಾಕರ್, ಅಂಬಲಪಾಡಿ ಗ್ರಾಮೋತ್ಥಾನ ಸಮಿತಿಯ ಪ್ರಧಾನ ಸಂಚಾಲಕ ಶಿವಕುಮಾರ್, ಕೇದಾರೋತ್ಥಾನ ಟ್ರಸ್ಟ್ನ ಪ್ರಧಾನ ಕಾರ್ಯದರ್ಶಿ ಮುರಳಿ ಕಡೆಕಾರ್, ಕೋಶಾಧಿಕಾರಿ ರಾಘವೇಂದ್ರ ಕಿಣಿ ಉಪಸ್ಥಿತರಿದ್ದರು | kannad |
இனி ஆன்லைன் சூதாடுவோருக்கு ரூ.5,000 அபராதம், 6 மாதம் சிறை தண்டனை.. தமிழக சட்டப்பேரவையில் மசோதா நிறைவேற்றம்!! சென்னை : தமிழகத்தில் ஆன்லைன் சூதாட்டத்தை தடை செய்வதற்கான மசோதா சட்டப்பேரவையில் நிறைவேறியது. தமிழக சட்டப்பேரவையின் 3ம் நாள் கூட்டம் இன்று காலை 10 மணிக்கு தொடங்கியது. அவையின் தொடக்கத்தில் ஆளுநர் உரைக்கு நன்றி தெரிவிக்கும் தீர்மானம் முன்மொழியப்பட்டது. பின்னர் ஆளுநர் உரை மீதான விவாதம் தொடங்கியது. இதைத் தொடர்ந்து, ஆன்லைன் சூதாட்டத்திற்கு தடை விதிக்கும் சட்ட மசோதாவை துணை முதல்வர் ஓ பன்னீர் செல்வம் ஆன்லைன் சூதாட்டத்தை தடை செய்வதற்கான மசோதா 2020தமிழகத்தில் ஆன்லைன் சூதாட்டத்தால் பணத்தை இழந்து உயிரிழப்பவர்களின் எண்ணிக்கை தொடர்ந்து அதிகரித்து வருகிறது. இதையடுத்து ஆன்லைன் சூதாட்டங்களுக்கு எதிராக மக்கள் குரலெழுப்பியதால், கடந்த ஆண்டு நவம்பர் மாதம் தமிழக அரசு ஆன்லைன் சூதாட்டத்திற்கு தடை விதித்து அவசர சட்டம் கொண்டு வந்தது. அந்த சட்டத்திற்கு மாற்றாக தற்போது இந்த மசோதா தாக்கல் செய்யப்பட்டு நிறைவேற்றப்பட்டுள்ளது. ஆன்லைனில் சூதாடுவோருக்கு ரூ.5 ஆயிரம் அபராதமும், 6 மாதம் சிறை தண்டனையும் விதிக்க இச்சட்டம் வழிவகை செய்யும். மேலும், ஆன்லைன் சூதாட்ட அரங்கம் வைத்திருப்போருக்கு ரூ.10,000 அபராதமும் 2 ஆண்டுகள் சிறை தண்டனையும் விதிக்கப்படும்.இதனைத் தொடர்ந்து உள்ளாட்சி அமைப்புகளில் தனி அலுவலர்களின் பதவிக்காலத்தை நீட்டிப்பதற்கான மசோதாவை உள்ளாட்சித்துறை அமைச்சர் எஸ்.பி.வேலுமணி தாக்கல் செய்தார். இதையடுத்து தனி அலுவலர்களின் பதவிக்காலத்தை ஜூன் வரை நீட்டிக்கும் மசோதாவும் பேரவையில் நிறைவேறியது. இதன் மூலம் தேர்தல் நடக்காத மாநகராட்சி, நகராட்சி, பேரூராட்சி அமைப்புகளில் தனி அலுவலர் பதவிக்காலம் நீட்டிக்கப்பட்டது. | tamil |
Jyotish Shastra: बेहद कष्टकारी होते हैं ये दो योग, जीवन कर देते हैं बर्बाद , एक क्लिक में देखें कहीं आपकी कुंडली में तो नहीं Jyotish Shastra: जन्मकुंडली में शुभ और अशुभ दोनों तरह के योग होते हैं। शुभ योग के कारण जातक का जीवन खुशहाल रहता है और वह जीवनभर तरक्की और उन्नति के मार्ग पर चलता है, तो वहीं जन्मकुंडली में अशुभ योग के जातक जीवन पर्यन्त असहाय और दयनीय जीवन जीता है। परेशानियां उसके जीवन में चोलीदामन का साथ बना लेती हैं। वहीं ऐसे जातक को लाखों उपाय करने के बाद भी चैन नहीं आता है और वह विवश होकर ऐसी ही कष्टकारी परिस्थितियों में जीवन जीने के लिए मजबूर हो जाता है। तो आइए जानते हैं कुंडली में बनने वाले दो बेहद कष्टकारी योग और उनके उपाय के बारे में... ये भी पढ़ें: Mauni Amavasya 2022: सोमवती अमावस्या पर दान पुण्य करने से मिलता है अक्षय पुण्य कुज योग मंगल जब लग्न, चतुर्थ, सप्तम, अष्टम या द्वादश भाव में हो तो कुज योग बनता है। इसे मांगलिक दोष भी कहते हैं। जिस स्त्री या पुरुष की कुंडली में कुज दोष हो उनका वैवाहिक जीवन कष्टप्रद रहता है। इसीलिए विवाह से पूर्व भावी वरवधु की कुंडली मिलाना आवश्यक है। यदि दोनों की कुंडली में मांगलिक दोष है तो ही विवाह किया जाना चाहिए। कुज योग से बचने के उपायमंगलदोष की समाप्ति के लिए पीपल और वटवृक्ष में नियमित जल अर्पित करें। लाल तिकोना मूंगा तांबे में धारण करें। मंगल के जाप करवाएं या मंगलदोष निवारण पूजन करवाएं। विष योग जन्म कुंडली में विष योग का निर्माण शनि और चंद्रमा की युति से होता है। इस योग के चलते व्यक्ति का जीवन नर्क के समान हो जाता है। यह योग जातक के लिए बेहद कष्टकारी माना जाता है। नवग्रहों में शनि को सबसे मंद गति के लिए जाना जाता है और चंद्र अपनी तीव्रता के लिए प्रसिद्ध है, लेकिन शनि अधिक पॉवरफुल होने के कारण चंद्र को दबाता है। इस तरह यदि किसी व्यक्ति की जन्म कुंडली के किसी स्थान में शनि और चंद्र साथ में आ जाए तो विष योग बन जाता है। इसका दुष्प्रभाव तब अधिक होता है जब आपस में इन ग्रहों की दशाअंतर्दशा चल रही हो। विष योग के प्रभाव से व्यक्ति जीवनभर अशक्तता में रहता है। मानसिक रोगों, भ्रम, भय, अनेक प्रकार के रोगों और दुखी दांपत्य जीवन से जूझता रहता है। यह योग कुंडली के जिस भाव में होता है उसके अनुसार अशुभ फल जातक को मिलते हैं। विष योग से बचने के उपाय जिस जातक की कुंडली में या राशि में विष योग बना हो वे शनिवार के दिन पीपल के पेड़ के नीचे नारियल फोड़ें। या हनुमानजी की आराधना से विष योग में बचाव होता है। Disclaimer: इस स्टोरी में दी गई सूचनाएं सामान्य मान्यताओं पर आधारित हैं। Haribhoomi.com इनकी पुष्टि नहीं करता है। इन तथ्यों को अमल में लाने से पहले संबधित विशेषज्ञ से संपर्क करें | hindi |
TS Politics: రెండేళ్లలో తెరాస ప్రభుత్వం అడ్రస్ గల్లంతు: కిషన్రెడ్డి భువనగిరి: తెలంగాణ రాష్ట్రంలో కేసీఆర్ కుటుంబ పాలన సాగుతోందని.. రెండేళ్లలో తెరాస ప్రభుత్వం అడ్రస్ గల్లంతు కావడం ఖాయమని కేంద్ర పర్యాటక శాఖ మంత్రి కిషన్రెడ్డి అన్నారు. జన ఆశీర్వాద యాత్రలో భాగంగా ఆయన మూడో రోజు భువనగిరిలో పర్యటించారు. ఈ సందర్భంగా ఆయన మాట్లాడారు. రాష్ట్రంలో జాతీయవాద భాజపా ప్రభుత్వం ఏర్పడుతుందని తెలిపారు. కాంగ్రెస్కు భవిష్యత్ లేదని.. ఒకరో, ఇద్దరో గెలిచినా తిరిగి తెరాస గూటికి చేరుతారని జోస్యం పలికారు. హుజూరాబాద్లో కేసీఆర్ ఎన్ని కుట్రలు చేసినా.. రూ.కోట్లు ఖర్చు పెట్టినా అంతిమంగా ధర్మమే గెలుస్తుందని కిషన్రెడ్డి ధీమా వ్యక్తం చేశారు. పార్టీ జిల్లా అధ్యక్షుడు పీవీ శ్యామసుందర్రావు, రాష్ట్ర ఉపాధ్యక్షురాలు బండ్రు శోభారాణి, నాయకులు గూడూరు నారాయణరెడ్డి, బర్ల నర్సింగరావు ఆయనతో పాటు ఉన్నారు. తొలుత సాయిబాబా గుడి నుంచి వినాయక్ చౌరస్తా వరకు ర్యాలీ నిర్వహించారు. అనంతరం ప్రగతినగర్లోని చౌక ధరల దుకాణాన్ని కిషన్రెడ్డి సందర్శించారు. అక్కడి నుంచి బీబీనగర్కు బయల్దేరారు. | telegu |
In a division filled with talent it can be a tough task for a rising prospect to distinguish himself from the pack and catch the attention of the boxing public. For a fighter plying his trade in the 140 pound division, that task can be especially difficult as it is currently stacked with young and talented fighters looking to make their mark. Last Friday night at the Northern Quest Casino in Airway Heights, Washington, rising Jr. welterweight prospect Ruslan Provodnikov scored one of his most impressive victories to date and did so in devastating fashion on ESPN2′s Friday Night Fights. In the Main event of the Banner promotions card, Provodnikov knocked out Othello, Washington’s David Torres in the sixth round with a vicious barrage, claiming the WBO intercontinental title and moving himself one step closer to world title contention. | english |
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Plus: Mr. Bean opposes British religious hate-crime bill, religious summit opens in Indonesia, Vatican condemns 'Christianophobia', Christmas dilemma, praying for the home team, and other articles from online sources around the world.
In two separate attacks, gunmen emptied an Armenian and a Chaldean church today before setting off explosives, damaging both churches. Three people were injured according to the Associated Press. No one was killed.
"Smoke poured from the Armenian church and flames could be seen inside the Chaldean church … It was not clear how many people had been in the churches when they were attacked but the number was apparently not large," Reuters reports.
It has been nearly a month since the last attack on churches in Iraq. "At least eight people were killed in two church bombings in the capital on Nov. 8, and a car bomber attacked police guarding the hospital where the wounded had been taken."
Last weekend, Yonadem Kana, the leader of the Assyrian Democratic Movement in Iraq and a member of the Iraqi National Council, told the Associated Press that the Assyrian Democratic Movement would be sending 1,500 people to Baghdad to protect Christians from attacks.
"We do not want to transform our movement into a militia," Kana said. "But if needed, we can arm more than 10,000 people."
"We will not accept that our people's ethnic and religious background be used as a card in the hands of foreign forces to interfere in Iraq and to prolong the occupation," Kana said. | english |
ایونٹ 30 مئی سے 14 جولائی تک انگلینڈ اور ویلز میں کھیلا جائے گا فوٹو فائل دبئیانٹرنیشنل کرکٹ کونسل ائی سی سی نے ورلڈ کپ 2019 کا حتمی شیڈول جاری کردیا جس کے مطابق ایونٹ 30 مئی سے 14 جولائیتک انگلینڈ اور ویلز میں کھیلا جائے گا ورلڈکپ 2019 کا حتمی شیڈول جاری کردیا گیا 10 ٹیمیں لیگ کی بنیاد پر ایونٹ میں شریک تمام حریفوں کے ساتھ برتری کی جنگ لڑیں گی پوائنٹس ٹیبل پر سرفہرست ٹیمیں سیمی فائنل کھیلیں گیجب کہ افتتاحی میچ 23 مئی کو جنوبی افریقا اور انگلینڈ کے مابین اوول میں کھیلا جائے گا پاکستان کو پہلا چیلنج 31 مئی کو کوالیفائر ویسٹ انڈیز کا درپیش ہوگا3 جون کو انگلینڈ7 جون کو سری لنکا12 جون کو سٹریلیا16 جون کو بھارت23 جون کو جنوبی افریقا26 جون کو نیوزی لینڈ 29 جون کو افغانستان اور جولائی کو بنگلادیش سے میچز ہوں گے سیمی فائنلز اور11 جولائی جب کہ فائنل 14 جولائی کو لارڈز کے تاریخی میدان میں کھیلا جائے گا مجموعی طور پر مانچسٹرسب سے زیادہ میچز کی میزبانی کرے گا 80000 20 200000 50 52 4647 26 2018 واضح رہے ورلڈکپ 2019 میں روایتی حریف پاکستان اور بھارت کے میچ کا اعلان پہلے ہی ہوچکا تھا تاہم اب تمام میچز کی فہرست جاری کردی گئی ہے پاک بھارت ٹاکرا 16 جون 2019 کو اولڈ ٹریفرڈ میں ہوگا 16 2019 194 26 2018 پاکستان نے ابھی سے ورلڈکپ میں عمدہ کارکردگی پر نگاہیں مرکوزکر لیں پاکستان ٹیم نے ابھی سے ورلڈکپ میں عمدہ کارکردگی پر نگاہیں مرکوزکر لیںکپتان سرفراز احمد نے کہا کہ میگاایونٹ میں دنیا کی نظریں اپ کی کارکردگی پر ہوتی ہیںکھلاڑیوں کو اپنی اہمیت اور اہلیت ثابت کرنے کا موقع ملتا ہےہیڈ کوچ مکی ارتھر نے کہا کہ کرکٹ کے گھر میں کھیلنا ہمیشہ ہی ایک بڑا خوشگوار تجربہ ہوتا ہے ورلڈکپ میں اچھی کارکردگی سے اس تجربے کو یادگار بنایا جا سکتا ہےپیسر محمد عامر نے کہا کہ ورلڈ کپ میں ملک کی نمائندگی ہر کرکٹرکا خواب ہوتا ہےائندہ سال اپنے کیریئر میں پہلی بار میگا ایونٹ کا حصہ بننے کے حوالے سے پرجوش ہوں کرکٹ ورلڈکپ 2019 ٹکٹوں کے نرخوں کا اعلان بھی کردیا گیا ورلڈکپ 2019کے ٹکٹوں کے نرخوں کا اعلان بھی کردیا گیاقیمتیں 20سے 50پائونڈز تک رکھی گئی ہیں4افراد کی فیملی کیلیے ٹکٹ 52 جبکہ بچوں کیلیے6پائونڈ کا ہوگاائی سی سی کے چیف ڈیو رچرڈسن کا کہنا ہے کہ انگلینڈ کے ہر میدان میں کرکٹرز کو بھرپور سپورٹ ملے گیورلڈکپ کے منیجنگ ڈائریکٹراسٹیو ایلوردی نے کہا کہ شیڈول کے اعلان کے ساتھ ہی جوش خروش بڑھ گیا تارکین وطن کی وجہ سے کئی ٹیموں کو ہوم گرائونڈ جیسا ماحول میسر ائے گاپاکستان اور بھارت سمیت کئی روایتی حریفوں کے مقابلے بھرپور توجہ حاصل کرینگے | urdu |
راولپنڈی14مئی اردو پوائنٹ اخبارتازہ ترین اے پی پی14 مئی2016ءمحکمہ زراعت پنجاب راولپنڈی کے ترجمان کے مطابق بہتر نگہداشت کی بدولت انگور کی کاشت سے 600 من فی ایکڑ تک پیداوار حاصل کی جا سکتی ہے دوسرے باغات کی طرح انگور کے باغ کی پیداواری زندگی 30 تا 35 سال ہے درجہ حرارت انگور کے معیار اور مٹھاس پر براہ راست اثر انداز ہوتا ہے اگر موسم گرما میں درجہ حرارت زیادہ ہو گا تو انگور میں مٹھاس زیادہ ہو گی ترجمان کے مطابق انگور کے پودوں پر اپریل میں پھول نکلنا شروع ہو جاتے ہیں لہذا اس دوران پودوں کی خصوصی دیکھ بھال کریں تاکہ فی ایکڑ بہتر پیداوار حاصل کی جا سکے ترجمان کے مطابق انگور کی بیلوں کو پھول نے کی وجہ سے پانی کی زیادہ ضرورت ہوتی ہے لہذا بپاشی میں وقفہ کم کر دیں انگور کی بیلوں کو نائٹروجن اور پوٹاش کی دوسری قسط پھل بننے کے بعد اپریل میں ڈالیں کھاد ڈالنے کے بعد ہلکی گوڈی کریں اور بھرپور پانی لگائیں انگور کے پودوں پر سیاہ گلا پھپھوندی اور کوڑھ کی بیماریاں حملہ ور ہو سکتی ہیں ان کے تدارک کے لئے کاپر کسی کلورائیڈ جبکہ تھرپس کے تدارک کیلئے امیڈا کلوپرڈ کا سپرے کریں | urdu |
IPL 2020: ಭರ್ಜರಿ ಪ್ರದರ್ಶನ ನೀಡಿ ಮನೆಗೆ ಬಂದ ಸೂರ್ಯಕುಮಾರ್ ಯಾದವ್ಗೆ ಕಾದಿತ್ತು ಬಿಗ್ ಶಾಕ್ 13ನೇ ಆವೃತ್ತಿಯ ಇಂಡಿಯನ್ ಪ್ರೀಮಿಯರ್ ಲೀಗ್ ಆವೃತ್ತಿಗೆ ತೆರೆಬಿದ್ದಾಗಿದೆ. ಫೈನಲ್ ಕಾದಾಟದಲ್ಲಿ ಡೆಲ್ಲಿ ಕ್ಯಾಪಿಟಲ್ಸ್ ವಿರುದ್ಧ ಮುಂಬೈ ಇಂಡಿಯನ್ಸ್ ಭರ್ಜರಿ ಗೆಲುವು ಸಾಧಿಸಿ ಇತಿಹಾಸ ಸೃಷ್ಟಿಸಿತು. ರೋಹಿತ್ ಪಡೆ ಐದನೇ ಬಾರಿ ಕಪ್ ಗೆಲ್ಲಲು ತಂಡದ ಮಧ್ಯಮ ಕ್ರಮಾಂಕ ಆಟಗಾರ ಸೂರ್ಯಕುಮಾರ್ ಯಾದವ್ ಕೊಡುಗೆ ಅಪಾರ. ಟೂರ್ನಿಯ ಆರಂಭದಿಂದ ಬಹಳಷ್ಟು ಸುದ್ದಿಯಲ್ಲಿದ್ದ ಯಾದವ್ ಅಮೋಘ ಪ್ರದರ್ಶನ ನೀಡಿ ತಂಡಕ್ಕೆ ನೆರವಾದರು. ಸದ್ಯ ಟೂರ್ನಿ ಮುಗಿಸಿ ಮನೆಗೆ ತೆರಳಿರುವ ಯಾದವ್ಗೆ ಕುಟುಂಬ ವರ್ಗ ದೊಡ್ಡ ಶಾಕ್ ನೀಡಿತು. ಪ್ರತಿಬಾರಿಯ ಐಪಿಎಲ್ ಸೀಸನ್ನಲ್ಲಿ ರನ್ ಮಳೆಯನ್ನೇ ಸುರಿಸುತ್ತಿದ್ದ ಸೂರ್ಯಕುಮಾರ್ ಈ ಬಾರಿ ಅದೆ ಲಯದಿಂದ ಬ್ಯಾಟ್ ಬೀಸಿದರು. ಟೂರ್ನಿಯಲ್ಲಿ 480 ರನ್ ಕಲೆಹಾಕಿದರು. ಇಷ್ಟಾದರು ಇವರಿಗೆ ಭಾರತ ತಂಡದ ಪರ ಆಡುವ ಭಾಗ್ಯ ಇನ್ನೂ ಒದಗಿಬಂದಿಲ್ಲ. ಈ ವಿಚಾರ ಐಪಿಎಲ್ ಮಧ್ಯಂತರದಲ್ಲಿ ಸಾಕಷ್ಟು ಚರ್ಚೆಕೂಡ ಆಯಿತು. IPL 2020: ಐಪಿಎಲ್ನ ಈ ಟೀಂಗೆ ಭಾರತ ತಂಡವನ್ನೇ ಸೋಲಿಸುವ ಶಕ್ತಿ ಇದೆ ಎಂದ ಆಕಾಶ್ ಚೋಪ್ರಾ ಆಸ್ಟ್ರೇಲಿಯಾ ಸರಣಿಗೆ ಭಾರತ ತಂಡವನ್ನು ಆಯ್ಕೆ ಮಾಡುವಾಗ ಆಯ್ಕೆ ಸಮಿತಿ ಐಪಿಎಲ್ನಲ್ಲಿ ಉತ್ತಮ ಪ್ರದರ್ಶನ ನೀಡುತ್ತಿದ್ದ ಅನೇಕರಿಗೆ ಮಣೆ ಹಾಕಿತು. ಆದರೆ, ಅನೇಕ ವರ್ಷಗಳಿಂದ ಅವಕಾಶಕ್ಕಾಗಿ ಕಾಯುತ್ತಿರುವ ಸೂರ್ಯಕುಮಾರ್ ಹೆಸರು ಮಾತ್ರ ಇರಲಿಲ್ಲ.ಇದರಿಂದ ಕೇವಲ ಅಭಿಮಾನಿಗಳು ಮಾತ್ರವಲ್ಲದೆ ಕೆಲ ಕ್ರಿಕೆಟ್ ಪಂಡಿತರು ಕೂಡ ಆಯ್ಕೆ ಸಮಿತಿ ವಿರುದ್ಧ ತಿರುಗಿಬಿದ್ದರು. ಇದಾದ ಮುಂದಿನ ಪಂದ್ಯದಲ್ಲೇ ಟೀಂ ಇಂಡಿಯಾ ಹಾಗೂ ಆರ್ಸಿಬಿ ನಾಯಕ ವಿರಾಟ್ ಕೊಹ್ಲಿ ಹಾಗೂ ಸೂರ್ಯಕುಮಾರ್ ನಡುವೆ ಸಣ್ಣ ಸಂಘರ್ಷ ನಡೆದ ವಿಚಾರ ಗೊತ್ತೇ ಇದೆ. IPL 2021: 9 ತಂಡಗಳ ಜೊತೆ ಐಪಿಎಲ್ 2021ರಲ್ಲಿ ಇರಲಿದೆ ಮತ್ತೊಂದು ಬಿಗ್ ಸರ್ಪ್ರೈಸ್: ಏನದು?, ಇಲ್ಲಿದೆ ಮಾಹಿತಿ ಆದರೆ, ಇದು ಯಾವುದಕ್ಕೂ ತಲೆಕೆಡಿಸಿಕೊಳ್ಳದ ಯಾದವ್ ಮುಂಬೈ ತಂಡಕ್ಕೆ ತನ್ನಲಾದ ಎಲ್ಲ ಕೊಡುಗೆಗಳನ್ನು ನೀಡಿದರು. ಹೀಗೆ ಮುಂಬೈ ಇಂಡಿಯನ್ಸ್ ಐದನೇ ಬಾರಿ ಟ್ರೋಫಿ ಎತ್ತಿ ಹಿಡಿಯಿತು. ಸದ್ಯ ಟೂರ್ನಿ ಮುಗಿದು ಮನೆಗೆ ಬಂದ ಸೂರ್ಯಕುಮಾರ್ ಯಾದವ್ಗೆ ಕುಟುಂಬದವರೆಲ್ಲ ಒಟ್ಟಾಗಿ ಸರ್ಪ್ರೈಸ್ ನೀಡಿದ್ದಾರೆ.ವಿಡಿಯೋ ಕೃಪೆ: ಕ್ರಿಕ್ವಿಕ್ಮುಂಬೈ ವಿಮಾನ ನಿಲ್ದಾಣದಿಂದ ನೇರವಾಗಿ ತಮ್ಮ ಮನೆಗೆ ಕಾರಿನಲ್ಲಿ ಬಂದು ಇಳಿಯುತ್ತಿದ್ದಂತೆ ಕುಟುಂಬದವರೆಲ್ಲ ಒಂದಾಗಿ ಸೂರ್ಯಕುಮಾರ್ಗೆ ಆರತಿ ಎತ್ತಿ, ತಿಲಕ ಇಟ್ಟು ಅದ್ಧೂರಿಯಾಗಿ ವೆಲ್ಕಮ್ ಮಾಡಿದ್ದಾರೆ. ಸದ್ಯ ಈ ವಿಡಿಯೋ ಸಾಮಾಜಿಕ ತಾಣಗಳಲ್ಲಿ ವೈರಲ್ ಆಗುತ್ತಿದೆ. | kannad |
کراچی اسٹاف رپورٹر انڈر 19 ٹیموں کے چناو کے سلسلے میں ٹرائلز اج سے شروع ہوںگے یہ ٹرائلز ملک کے مختلف شہروں میں منعقد ہوںگے جو 19 ستمبر تک تمام کرکٹ ایسوسی ایشنز کے مرکزی شہروں میں رکھے گئے ہیں یکم ستمبر 2001 یا اس کے بعد پیدا ہونے والے کھلاڑی اوپن ٹرائلز میں شرکت کے اہل ہوں گےان ٹرائلز میں کووڈ 19 کے پروٹوکولز پر سختی سے عملدرامد کیا جائے گا نیشنل ہائی پرفارمنس سینٹر کے کوچز ایل سی سی اے گرائونڈ لاہور اور پنڈی کرکٹ اسٹیڈیم راولپنڈی میں ٹرائلز لیں گے ایبٹ اباد کراچی ملتان اور کوئٹہ میں ٹرائلز کی نگرانی قومی جونیئر سلیکشن کمیٹی کرے گی قومی انڈر 19 ون ڈے ٹورنامنٹ 13 اکتوبر سے اور قومی انڈر19 تھری ڈے ٹورنامنٹ نومبرسے شروع ہوگا | urdu |
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