I was satisfied with the order procedure, customer support and I would recommend SAM Online Stores to others.
When putting a partition wall in your office, room or hall, it is mostly because of one or both of the following reasons: 1) to divide space and 2) for decorative purposes.
For this, you need some options to choose from! We offer three differents heights and 27 (!) different finishing options.
Partition walls can be used as a single wall and in combinations of multiple walls. For instances where your partition wall(s) need to be mobile, they can be effortlessly equipped with sets of fortified wheels.
A reinforced wheel and a setup of multiple walls.
We offer three different sizes: 120x150 cm, 120x180 cm and 120x200 cm. When choosing a size, try to take into account what the partition wall will be used for. For creating private spaces, higher partition walls might be the best option. For simple decorative use, a smaller wall might suit you better.
There are endless ways to use partition walls! They can be used as a decor, to divide spaces, to create an artificial corridor or just as a notice board. For that, you can use as many partition walls as you want. To give you an idea, some possible configurations are shown below.
The only thing you need to know, is how you would like your partition walls placed, such as schematically shown above. We'll make sure you receive the right parts and manual.
Multiple options for using partition walls. 1) a triangular structure, 2) a flexible wall throughout a larger space, 3) a corner setup and 4) a single notice board setup.
Since you've got two sides and the style of frame to choose from, the options are endless! Always a configuration that suits your needs. Make your choice from the overview below.
You can choose between aluminum frames finished with normal aluminum look, or an anthracite finish. Both with corresponding corner pieces and feet.
If desired, it is possible to install your partition wall on mobile feet with durable reinforced wheels. This will allow you to move your partition wall around effortlessly.
High quality felt, as used in our pin board Pro Colour Series.
A magnetic enamel steel dry wipe surface. The highest quality of whiteboards, but then as a division wall!
A non magnetic non dry erasable colour finishing.
We offer natural textures, ranging from various wood types to metal or organic patterns.
There are many options to choose from. In the end however, sketching out your own partition wall(s) is easy! Would you like some assistance? Our expert customer service will guide you through the process.


La Hacienda del Buen Suceso maintains all the splendour from old country houses thanks to its location in the heart of an estate which preserves its colonial style.
We are located in a magical and beautiful setting, surrounded by a never-ending sea of banana plantations. We are just 15 minutes from Las Palmas de Gran Canaria and 45 minutes from the famous beaches with dunes on the south of the island.


text:
Behaim Peak
Behaim Peak (The name as it would appear in a gazetteer)
Behaim Peak (The name as it would appear on a map)
United States Gazetteer Id 122355
Feature type: Peak (2d)
This name originates from United States of America. It is part of the United States Gazetteer and the SCAR Composite Gazetteer of Antarctica.
Behaim Peak (United Kingdom)
A conspicuous pyramid-shaped rock peak (1,150 m) at the S extremity of the mountains separating Meridian Glacier and Doggo Defile, on the W side of Antarctic Peninsula. Photographed from the air by RARE in Nov. 1947, and surveyed from the ground by FIDS in Dec. 1958. Named by UK-APC after Martin Behaim (1459-1506), German cosmographer and navigator who is credited with the first adoption of the astronomer's astrolabe for navigation at sea, in 1480.
View American or international place names within 1.0 degree of this location.

redpajama_set_name: RedPajamaCommonCrawl


This is a faithful transcription of the תחנה פון ליכט בענטשין ("Tkhine for Lighting Candles [for Shabbes]") as it appeared in the Vilna, 1869 edition. I have transcribed it without any changes from The Merit of Our Mothers בזכות אמהות A Bilingual Anthology of Jewish Women's Prayers, compiled by Rabbi Tracy Guren Klirs, Cincinnati: Hebrew Union College Press, 1992. shgiyot mi yavin, ministarot nakeni. If you can scan an image of the page from the 1869 edition this was originally copied from, please share your scan with us. . . .
Shabbat happens, If I let it. . . .


The current price of YAcCoin in US dollars is $0.0005 USD. To compare it's value every 1 YAC coin is worth 0.00000009485380 in BTC.
During the last 24 hours YAcCoin's price has changed 0.00% (or $0.00000000 USD) it reached a low of $0.0005, and high of, $0.0005. A total of 0 YAC coins worth a total of $0 USD was traded in the previous day at crypto exchanges like Kucoin, and Binance.
YAcCoin's market cap is made up of 0 YAC coins valued at $0 USD. That means YAcCoin makes up 0.00% of the entire cryptocurrency market capitalization of $10,446,379.06B!
Due to cryptocurrencies trading 24/7, that value/exchange rate will change constantly. To keep updated on the price, market cap, and trading information on YAcCoin just bookmark the Live YAcCoin Price page.
To embed real-time YAcCoin widget into your website copy the following code.


The first picture is a picture Lovely Cool End Tables 13, the image has been in named with : Lovely Cool End Tables 13, This image was posted on category : Dinning Room, have resolution : 645x430 pixel. This posting entitled Lovely Cool End Tables 13, and many people looking about Lovely Cool End Tables 13 from Search Engine.
Click Thumbnail Bellow to Look Gallery of "Lovely Cool End Tables 13"


Podopro Flatfoot Wedge is best used in high heels, trainers, smart shoes and other types of designer shoes that lack arch support but do not accommodate orthotics.
Designed to be discrete inside tight fitting shoes and provides just enough support to balance the foot and cushion the arch. Its wedge shape supports weakened and fallen arches while correcting and stabilizing your foot's natural shape. Comes in a pair.
A symmetrical shaped, shock absorbing moss rubber with fine leather provides relief from fallen arches.
The resilient Podopro wedge shaped insert backs up weakened longitudinal arches following the foot to regain its natural healthy position. Self adhesive.


Project: K.I.T.T.: KITT, Can You Hear Me Buddy?
The face of the watch is screen accurate and has the added benefit of having the decal behind glass unlike the prop which was just a sticker over the face. This gives it a much more realistic look and offers protection for the decal. Mark even added a little more authenticity to the watch by adding a stainless steel back stamped with the Knight Industries logo.
The leatherette covered watch stand also includes an engraved metalic gold display plaque. Engraved in rich black with text and art saying COMLINK and the Knight Industries logo.
Mark is also very well known for his authentic 'KNIGHT' license plates. It is obvious he gone to great lengths to ensure his plates are screen accurate.
Mark has also created his own 'Knight Industries' plates. These plates are also stamped and show the same level of quality and detail as his 'KNIGHT' plates.


BMO and the DMZ at Ryerson University have announced the winners of the DMZ-BMO Fintech Accelerator Demo Day.
Of the four finalists, Viviplan, a company that automates high-end financial plans, took first place and received $65,000. Fortuna.ai, an artificial intelligence platform that automates business development, came in second with a prize of $35,000.
"We look forward to continuing to work with the winners and exploring how we can couple their technologies within the bank's existing systems and platforms to enhance the customer experience and deliver more industry-leading solutions to market quickly," said Andrew Irvine, head of Canadian business banking and BMO partners.
The DMZ-BMO Fintech Accelerator was created in May with the goal of helping top Canadian FinTech startups expand through four months of incubation and mentorship.
During the incubation, the entrepreneurs were offered a variety of resources including free residency at the DMZ, access to advise from venture capitalists and C-level individuals, learning opportunities at BMO- hosted sessions on macroeconomics and industry trends and insights, and more than 60 hours of mentorship from BMO executives.


Searching the best and the most reputable auto repair shops out there can be tough, especially if you have no clue or hint on where you can find the best. Choosing a reliable auto repair shop can also be confusing since there are so many of them out there. This article should be able to help make the search for the best auto repair shop a lot easier. It is very important that you examine the customer service of the auto repair shop before you choose them. Can the auto repair shop provide you first-rate customer service? If you think that the auto repair shop cannot provide outstanding customer service, then it is best that you look for another shop. It is necessary that you contact the auto repair shop if you want to check whether or not they can provide excellent customer service.
It is advisable that you only choose those auto repair shops that are truly genuine and sincere in helping you get your car or vehicle in tip-top condition again. Apart from contacting the car repair shop, it is also vital that you get to visit their shop. It is necessary that you observe how the employees of the auto repair shops are treating somebody else's car or vehicle. It is very important that the auto repair shop's staff or employees are serious in accomplishing their tasks.
The best and the most reliable auto repair shop out there should be equipped with the latest tools or equipment in order to fix or repair different kinds of cars or vehicles. It is also vital that you avoid those auto repair shops that are not updated with the latest method or technology when it comes to repairing cars and vehicles. Of course, aside from having the latest machine and equipment, it is also very important that their mechanics are skillful and knowledgeable.


text:
The Neighbourhood Planning (General) Regulations 2012
Regulation 19
Open Instrument without Schedules
This is the original version (as it was originally made).
Decision on a plan proposal
This section has no associated Explanatory Memorandum
19. As soon as possible after deciding to make a neighbourhood development plan under section 38A(4) of the 2004 Act or refusing to make a plan under section 38A(6) of the 2004 Act, a local planning authority must—
(a)publish on their website and in such other manner as they consider is likely to bring the decision to the attention of people who live, work or carry on business in the neighbourhood area—
(i)a statement setting out the decision and their reasons for making that decision ("the decision statement");
(ii)details of where and when the decision statement may be inspected; and
(b)send a copy of the decision statement to—
(i)the qualifying body; and
(ii)any person who asked to be notified of the decision.
PrintThe Whole Part
PDF The Whole Part
Web page The Whole Part


Xiong Pei Lu is responsible for the development, assessment and quality delivery of products by Chinese suppliers. With an impressive career dedicated to the China automotive market development, Mr. Xiong has been involved in industry-changing Joint Ventures (Shanghai VW and Shanghai GM), and other important facilities investments and engineering/commercial negotiations.
Prior to joining PAC, Mr. Xiong was President of Shanghai Automotive Industry Corporation (SAIC) in North America, where he had responsibility for providing components to OEMs and Tier 1 suppliers from SAIC Group parts suppliers. At SAIC China, he served in roles such as company General Manager and Plant Executive Director.
He has exceptional knowledge of the China automotive scene, and has provided advice and guidance to emerging suppliers to step on to the world market. Mr. Xiong has been with PAC since 2003.


text:
Q: Is this a issue associated with Ready to Program Java or is it a syntax error? (Object Error) Within this program I am creating an class instance.
I am trying to make a void method to display the person's (objects) attributes outside of the main method.
The errors are:
1.'No field name size was found in People' (5)
2.'No method called DisplayAtt was found in People' (20)
Im wondering if this is an error asociated with my program or the general syntax of RTP.
I am trying to learn OOP.
class People
    {
        public void DisplayAtt ()
        {
            System.out.println (size);
            System.out.println (race);
            System.out.println (personality);
        }

        public static void main (String args[])
        {
            Person thisPerson;
            thisPerson = new Person ();

            thisPerson.size = "Average";
            thisPerson.race = "Caucasian";
            thisPerson.personality = "Stubborn";

            thisPerson.DisplayAtt ();
        }
    }

    /// Object Class ///

    public class Person
    {
        String size;
        String race;
        String personality;

    }

A: Move DisplayAtt to Person not People.
Normally you would override toString() using your IDE to generate the code.

A: The display att needs to be a method in your Person class or needs to accept a person as aparameter.

redpajama_set_name: RedPajamaStackExchange


Hey! My name is Houria and I am a masters degree student at the Faculty of Arts and Human Sciences in Marrakech. At the end of the third semester (the end of January), I had to apply for an internship that will be the base of my graduate research. I quickly found myself holding an administrative position in a company, but after one week, I decided to look for another internship because I simply was not happy there! When I joined the High Atlas Foundation, I easily integrated with the team as well as the activities that demand sharing parts of your days with others.
I read once that the beauty of life does not depend on how happy you are but how happy others can be because of you, and HAF lives by this concept while sustaining prosperity around the country. Among the activities that I run within the foundation are distributing and planting trees in rural primary schools. It is a special feeling when you visit a school and meet the students, talk to them about the environment, encourage them to take care of little things and then plant trees with them. This exact act of spending time with them and bringing new notions to their world makes their day, and this is truly something to live for. At the end of the day, you get a sense of accomplishment and purpose to know you have made a change in someone else's life.
Another act of making others happy is meeting and fulfilling the young people's needs and priorities. HAF has always aims to address water access challenges for rural schools and communities in Morocco. Since its start, HAF and its partners have built 24 clean drinking water systems in Morocco's remote villages, benefiting approximately 5,500 people. These include digging wells, building water towers, and installing solar pumps and gravity flow systems, which deliver safe drinking water to communities.
Sustainability is also about sharing moments with others, and HAF's happiness lies in making its staff, volunteers, and interns experience this joy by giving them a chance to do so. Give yourself that chance and be happy!


text:
Lisa Soronen's blog ›
Supreme Court Decides Indian Hunting Rights Case
Monday, May 20, 2019 at 04:26 PM
What will invariably get everyone's attention about this case is it is the second 5-4 decision where Justice Gorsuch has joined the four more liberal Justices to rule in favor of a tribe. And a ruling in the Court's most interesting tribal case of the term is yet to come. But none of this should distract from the holding of this case.
The Supreme Court answered yes to the question in Herrera v. Wyoming of whether an old treaty allowing Native Americans to hunt on federal land is still valid. According to an amicus brief filed by the Crow Tribe "[a]t least nineteen tribes, in at least a dozen treaties, reserved for themselves the right to hunt on Federal lands away from their respective reservations."
In 1868 the Crow Tribe ceded most of its territory in what is now Montana and Wyoming to the United States in exchange for an agreement the Crow could "hunt on the unoccupied lands of the United State." Clayvin Herrera invoked this treaty to defend against a charge of violating state law by off-season hunting in Bighorn National Forest in Wyoming.
In a 5-4 opinion the Supreme Court held that the treaty's hunting rights survived Wyoming's statehood and that lands in the Bighorn National Forest aren't categorically "occupied" because they are in a national reserve.
Over 100 years ago in Ward v. Race Horse (1896) the Supreme Court ruled that statehood extinguished hunting rights in an identical treaty between the Shoshone-Bannock tribes and the United States. The Court in Race Horse relied in the fact that (1) new states were admitted to the union on "equal footing" with existing states and (2) there was no evidence in the treaty that Congress intended for treaty rights to continue in "perpetuity."
In 1999 in Minnesota v. Mille Lacs Band of Chippewa Indians the Supreme Court explicitly rejected the "equal footing" rationale of Race Horse. The Court in Mille Lacs also criticized the notion that treaty rights fail to survive statehood if they are "temporary and precarious" because all treaty rights can be unilaterally repudiated by Congress. According to the majority of the Supreme Court in Herrera v. Wyoming, "although the decision in Mille Lacs did not explicitly say that it was overruling the alternative ground in Race Horse, it is impossible to harmonize Mille Lacs' analysis with the Court's prior reasoning in Race Horse."
Applying Mille Lacs rather than Race Horse, a majority of the Supreme Court, in an opinion written by Justice Sotomayor, joined by the three more liberal Justices and Justice Gorsuch, concluded Wyoming's admission to the United States didn't abrogate the Crow Tribe's off-reservation treaty hunting rights. "The Wyoming Statehood Act did not abrogate the Crow Tribe's hunting right, nor did the 1868 Treaty expire of its own accord at that time. The treaty itself defines the circumstances in which the right will expire. Statehood is not one of them."
Even though the treaty rights were valid following Wyoming's statehood the treaty does not protect hunting in "occupied" federal lands. The majority of the Court concluded the Bighorn National Forest didn't become categorically "occupied" when the national forest was created. Treaties are construed as "they would naturally be understood by the Indians." According to the Court, "[h]ere it is clear that the Crow Tribe would have understood the word 'unoccupied' to denote an area free of residence or settlement by non-Indians."
Indian tribeNative AmericansSupreme Courtfederal landhunting rightsoff-reservation huntingtreatytreaty abrogationtribe
Policy Area›Government›Federalism
Lisa Soronen's blog
Supreme Court to Decide Off-Reservation Hunting Case
Supreme Court to Decide Tribal Fishing Rights Case
Supreme Court Accepts Significant Oklahoma Indian Reservation Case
Supreme Court Equally Divided on Tribal Fishing Rights Case
On the Supreme Court Docket: Tribal Case of Taxing Travel or Trade


For animals, there is no greater challenge than surviving the vulnerable first years of life. This episode demonstrates that nature's solutions are as varied as those in human society.
How many animals - including zebras, moose and stalk-eyes flies - assess their opponents' fighting prowess before making an attack that risks injury or death.
This edition looks at the various methods employed by species to attract a mate, including whales that sing "songs", hamsters that emit an odour, and manakins that do acrobatic dances.
In the final challenge of the game of life, raising offspring is the ultimate prize. Continuing the line through the next generation, is the next best thing to immortality. But it's far from easy... Some parents must risk their own lives for their offspring.


text:
Q: Can I Install Ubuntu on EEEPC 900 can i Install Ubuntu 12.10 on my EEPC900 ?
The Second SDD is broken , so there are only still a 4GB Harddisk , 1GB RAM

A: Yes! You need laptop with Windows, then you should download and install LiLi USB Creator (it if free program to create bootable USB memory stick), you will need Ubuntu ISO from Canonical, USB memory stick 4GB and that is pretty much it. Install Lili USB Creator, download Ubuntu from Canonical, then insert your USB memory stick and open LiLi USB Creator. You have to find your USB in drop down menu, then you have to choose your ISO from Downloads, make sure to check that USB memory is formatted in FAT32 and press the little lightning in the end. Your USB memory stick will be ready in few minutes.


This set contains 40 images which have the look of real handmade paper and card. That's less than 7p each for quality backgrounds that you can print over and over again! Print them onto quality card or paper for the best results.
This set includes corrugated, mulberry, leatherette, crinkle and waterdrop paper effects.
This is a lovely card for a female friend or relative.This downloadable card kit features 4 A4 sheets.
This fabulous Printable Heaven digital paper pad contains 10 co-ordinating A4 images that you can print over and over onto good quality paper or card, whatever suits your project.This pad feature 10 sheets of natural coloured paper effects. Choose from corrugated, crinkle, leatherette, two dew drop prints, mica, waterdrop, linen, mulberry and glitter.
Pack of approximately 50 brads with a 4mm head size.


text:
Asaphocrita lucis is a moth in the family Blastobasidae that is endemic to Costa Rica.

References

Moths described in 2002
Endemic fauna of Costa Rica
lucis

redpajama_set_name: RedPajamaWikipedia


This annual convention in Atlanta features some of the most creative and eco-friendly costumes around.
March 14, 2013, 4:14 p.m.
Every year, cardboard-clad men and women gather in downtown Atlanta to celebrate the art of cardboard costuming. There are boxy superheroes, DIY dragons and a few last-minute attendees who craft masks from discarded Amazon packaging. This is CardboardCon.
The gathering bills itself as "the world's most affordable science fiction/fantasy convention. "Accidentally founded" in 2010 by Captain Drew of the Cardboard Troopers, the "traveling convention of tens of devoted attendees," spans several Atlanta hotels over five hours.
"Unlike other sci-fi conventions you might be familiar with in the city, we like to keep it small," Captain Drew said.
CardboardCon occasionally even draws celebrities. In 2012, Candice Accola of "The Vampire Diaries" was in attendance.
This year, about 50 cardboard costumers gathered in early March, making appearances at several Atlanta bars and hotels and holding a short parade down Peachtree Street.
Lucy Bartash, who came dressed as a cardboard dragon, was the winner of this year's costume contest and had her name "permanently inscribed" onto The Cardboard Cup, a trophy composed of cardboard, bubble wrap and duct tape.
"I just grabbed some empty boxes from work and threw this together. It took less than hour," Bartash said.
Check out some photos from this year's convention and get inspired to make your own cardboard costume.


text:
FARMAK PHARMACEUTICAL COMPANY OPENS OFFICE IN UAE
Farmak pharmaceutical company, one of the largest exporters of pharmaceuticals, has opened an office in the United Arab Emirates, and plans to further strengthen its expansion in the Middle East and localization in Saudi Arabia and Egypt, its press service said on Tuesday. According to the press release, the company's products have been presented in the Middle East market since 2016.
"While selling drugs through local distributors, the company audited the market potential and analyzed the product niches of the region's pharmaceuticals. This year, in order to consolidate business management in the Middle East, Farmak's management decided to open an office in the UAE," the company said in the press release.
The new headquarters will be headed by Mourad I.Habib, who previously served as CEO of Tabuk Pharmaceuticals and led Sandoz's Middle East operations for over eight years. According to Habib, who is quoted in the press release, the opening of the office in the UAE is only the first strategic step for Farmak; in the future, the company plans to strengthen its expansion in the region and localization in Saudi Arabia and Egypt.
The company said that at present, Farmak's production facilities have successfully passed certification in the UAE government bodies. The company also registered a number of injectable drugs produced by Farmak, which are already being purchased at public and local hospital tenders in the region.
"The Middle East market is not new for us, and we are actively scaling up our presence in this region. We have chosen the United Arab Emirates as the center of activity in the Middle East," Business Development Director of Farmak Viktor Kostiuk said.
At the same time, he recalled that the UAE has a reputation as a state with a very high level of the national healthcare system and strict regulation of activities related to the production and distribution of medicines. "The fact that Farmak products are represented on this market once again confirms the high level of quality of our products," Kostiuk said.
Farmak is the leader of the Ukrainian pharmaceutical market. The company's product portfolio includes more than 220 complex-component modern medicines. Among the main directions are endocrinological, gastroenterological, cardiological, neurological, anti-cold and other drugs.
The UAE office is the sixth international office of the company. In 2020, Farmak increased its export deliveries by 40%. Today, the manufacturer's products are represented in more than 30 countries of the EU, Central and South America, the CIS, the Middle East and Asia.
FARMAK, OFFICE, PHARMACEUTICAL COMPANY, UAE
UKRAINE INTERNATIONAL AIRLINES LAUNCHES FLIGHTS FROM KIEV TO RAS AL-KHAIMAH (UNITED ARAB EMIRATES)
Ukraine International Airlines (UIA) is launching flights from Boryspil International Airport (Kyiv) to Ras al-Khaimah (the United Arab Emirates) from June 25, 2021, the airline's press service said on Monday.
"UIA will become the first Ukrainian airline to operate direct flights to Ras al-Khaimah and one of the main strategic aviation partners for the Emirate, which is currently developing dynamically," the UIA said.
The airline said that it will take five hours to fly from Kyiv to Ras al-Khaimah international airport. Upon arrival, all tourists undergo mandatory PCR testing at the airport. In addition, they can also undergo free PCR testing before returning to Ukraine.
According to UIA, Ras al-Khaimah received safety certifications from the world leader in the inspection and certification services Bureau Veritas, as well as from the World Tourism and Travel Council (WTTC).
"Ukraine is a fast growing and important market for the emirate of Ras al-Khaimah, and our partnership with Ukraine International Airlines is another step in the strategy of increasing tourist flow through introducing direct flights… This is a key step in the restoration of international tourism on our broad strategy of exploring new routes through main, secondary and emerging markets thanks to charter and scheduled flights," CEO at Ras Al Khaimah Tourism Development Authority Raki Phillips was quoted as saying.
In turn, UIA CEO Yevhen Dykhne said that the airline plans to increase the frequency of flights to Ras al-Khaimah, given the expected high demand, especially in summer.
UAE, UIA, UKRAINE INTERNATIONAL AIRLINES, UNITED ARAB EMIRATES
SEVERAL COMPANIES FROM UAE INTERESTED IN CONSTRUCTION OF MARINA AND LARGE PORT IN UKRAINE
Several companies from the UAE are interested in building a marina in Odesa, as well as port infrastructure, Ukrainian President Volodymyr Zelensky said at a press conference on Monday.
"There is a question of ports. They [companies from the UAE] are professionals. They are now in our market. We are talking about a large project – the construction of a large marina in Odesa and a large separate port. And one of the companies we met will be in Ukraine this week, and we will talk specifically about river transport, in which they are professionals and are ready to build river ports," he said.
According to the president, he discussed these issues with representatives of large companies from the UAE during a meeting with business as part of his trip to the UAE.
Zelensky also said that river transportation is the cheapest in Ukraine, while it can be a profitable industry for both business and the budget.
As reported, the UAE plans to increase the turnover of agricultural products with Ukraine tenfold and bring this figure to $2 billion per year.
CONSTRUCTION, MARINA, PORT, UAE
UAE DONATES 100,000 COVID-19 RAPID TESTS, 200,000 PROTECTIVE MASKS TO UKRAINE
Ukraine has received from the government of the United Arab Emirates (UAE) 100,000 kits for rapid testing for COVID-19 IgM/IgG and 200,000 protective masks as part of agreements on medical care, the website of the President of Ukraine said on Wednesday.
Deputy Head of the Office of the President of Ukraine Yulia Sokolovska, at a meeting with the wife of the UAE Ambassador, Mrs. Al-Kaabe, thanked the UAE for its support in overcoming the COVID-19 pandemic in Ukraine and said that the tests and personal protective equipment received will be transferred to the Public Health Center of the Ministry of Health of Ukraine, which will be distributed to them by regions.
The Deputy Head of the Office of the President also congratulated the UAE Embassy in Ukraine on the occasion of the UAE National Day, which is celebrated on December 2.
CORONAVIRUS, COVID-19, MASK, PROTECTIVE MASKS, UAE
UAE EMBASSY DONATES 5,000 COVID-19 TO UKRAINE
The wife of Ambassador of the United Arab Emirates Sheikh Al-Kaabi donated over 5,000 rapid tests for coronavirus (COVID-19) infection to Kyiv.
As deputy head of Kyiv City State Administration Maryna Khonda said, these tests will be transferred to Kyiv orphanages and nursing homes for the elderly.
"Unfortunately, the pandemic did not recede. In the spring, when the phase of strict quarantine was underway, an outbreak of coronavirus was detected in Darnytsia orphanage boarding school for girls. Fortunately, everything went well, but in order to prevent such outbreaks in the future, we need to quickly and promptly identify disease and respond to cases of infection. These rapid tests will be sent to Sviatoshyn and Darnytsia orphanages, as well as to Kyiv geriatric boarding house and Kyiv boarding house of labor veterans. Thus, we will be able to control outbreaks of COVID-19 among people who are in the so-called 'risk zone', and not to allow further spread. I am very grateful to the Embassy of the United Arab Emirates for this assistance," the press service of Kyiv City State Administration said.
It is noted that 724 people live in these four institutions: in orphanages 239 children with disabilities aged from seven to 35 years of various disorders, in geriatric institutions 485 people of retirement age.
COVID-19, EMBASSY, UAE
AIR ARABIA RESUMES FLIGHTS FROM UNITED ARAB EMIRATES TO UKRAINE
Air Arabia has resumed regular flights from the United Arab Emirates (UAE) to the Boryspil International Airport.
"Yesterday we met flight G9 261 from Sharjah and congratulated the crew on the resumption of regular flights," the airport said on its Facebook page on Monday.
According to the Boryspil airport, Air Arabia will operate flights four times a week: on Wednesdays, Fridays, Saturdays and Sundays.
AIR ARABIA, FLIGHT, UAE


text:
Home 2009: 5 Traitors and terrorists
Traitors and terrorists
Hishamuddin Yahaya
Tok Bahaman, Mat Kilau, Tok Gajah and Tok Janggut were dubbed "traitors" by the British and Chin Peng and his followers were dubbed "terrorists", observes Hishamuddin Yahaya.
The controversy surrounding Chin Peng's return to Malaysia is not coming to an end yet. First it was the Court's decision and then the Government's decision that Chin Peng should not be allowed to return to his homeland. But a certain group, it seems, is fighting for his return.
I am one of the victims of the communist's terrorism of the fifties. My father's house and his sister's were razed to ashes by the communist terrorists, simply because my father was a penghulu and deemed by the communists to be on the side of the government. But what about my aunt? Probably being the penghulu's sister was reason enough to burn her house as well. That was the depth of the communists callousness.
But a few years ago, I happened to read Chin Peng's memoir. I cannot but conclude that Chin Peng was a freedom fighter, ranking with Tok Bahaman, Mat Kilau, Tok Gajah of Pahang and Tok Janggut of Kelantan who fought the British colonialists. The difference was Chin Peng chose the wrong path both in political philosophy and its modus operandi to force the British out of the country. It was not acceptable to the Muslim populace as well as the Chinese capitalists in this country.
Tok Bahaman, Mat Kilau, Tok Gajah and Tok Janggut were dubbed "traitors" by the British and Chin Peng and his followers were dubbed "terrorists". But he was a freedom fighter just like Ho Chi Minh, who fought and defeated first, the French, and then the Americans, in Vietnam. The world hailed 'Uncle Ho' as a hero.
A feared 'terrorist'
While Chin Peng, towards the end of the Emergency years decided to settle in Thailand, Musa Ahmad (the Chairman of MCP) and Shamsiah Pakeh decided to settle in Beijing. By British accounts, Shamsiah Pakeh was a terrorist attached to the 10th Regiment in the jungle of Pahang. She was an illusive and influential communist who could disappear within seconds of sighting her. She was shot many times but escaped unscathed. She was rumoured to be invincible. She was a terrorist feared by the armed forces and a reward was put on her head, dead or alive.
I happened to read Shamsiah Pakeh's memoir too. By her account, she was never a terrorist.Throughout her jungle days in Pahang, she was never armed, nor did she harm anybody. Her responsibility was recruiting cadres for the women's wing of the MCP. But her alleged "terrorism" was so much spoken about, that we boys in Temerloh, Pahang, knew her name well, along with other communists like Wan Ali (Kuala Lipis), Manaf Jepun (Temerloh), Abdullah C D and many others.
But despite her alleged "terrorism", why was Shamsiah Pakeh and Musa Ahmad allowed to return to this country? What's the difference between them and Chin Peng in the communist hierarchy? Musa Ahmad was the Chairman of MCP and Chin Peng was the Secretary-General. All of them applied to return on humanitarian grounds: to spend their last days in the country of their birth.
What can Chin Peng do at his age? Furthermore, what can a man of Chin Peng's age do to revive the MCP? And if there is an iota of evidence against him, detain him under the obnoxious ISA. Is not the ISA a potent political weapon of the BN government?.
Yes, a particular group may say the return of Chin Peng may revive the memory of bitter fighting with the communists. What more for those who are still alive and who have been incapacitated by the loss of sight and limb, or the loss of loved ones.
But why single out Chin Peng? Did not the Japanese soldiers who came to invade Malaya in 1942 commit untold atrocities, plundering, raping and killing innocent people including women and children? How many innocent civilians were beheaded, tortured and killed? How many civilians got their tongues cut off and their limbs severed? How many of our parents and their parents had their education interrupted because of the Occupation? And how many of us lost our grandparents at the death railway in Siam?
We have lost our loved ones too during the Emergency years. But think of it, were they not incidents of war, that happen everywhere in the world whenever there is war. Those killed by the communists were mostly members of the Armed Forces who were deemed to protect the British government's interests, the very government they were fighting against. Apart from the existing Armed Forces, the British made a special recruitment of the Special Constable (SC), whose main responsility was to protect the British rubber estates. They were the British government's operatives for all intents and purposes and the communists saw them as tools and collaborators of the imperialists.
Should not Chin Peng be forgiven?
Yes, the communists occasionally destroyed our railway system and water supply which caused a lot of inconvenience and loss of revenue. But all of us know in war, work of sabotage is part of war games. The communists too suffered death through hunger, when the government decided to cut off their food supplies by settling all the isolated villagers into controlled areas now known as "New Villages". But we cannot say that depriving the communists of sustenance was in violation of human rights, because the country was in a state of war. But once the war is over, all should be forgotten and forgiven. Should not Chin Peng be forgiven?
Dato Hishamuddin Bin Haji Yahaya, DIMP, SAP, is a laywer and one time MP for Temerloh.
Chin Peng
Dato Hishamuddin bin Haji Yahaya, a practising lawyer and former MP for Maran, is a long-time contributor to Aliran.


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Choose your movie here!
15 Best Korean Horror Movies
The October style onslaught gets underway proper at the sound of the starting gun with this Shudder authentic. Josh Ruben writes, directs and stars as Fred, a pissed off copywriter who retreats to an isolated cabin to put in writing a novel and meets a successful horror creator named Fanny (Aya Cash) whereas out jogging.
She challenges him to a scary storytelling contest, and the spooky video games begin. Ruben makes his characteristic directorial debut on what's billed as a "metafictional horror comedy" with social underpinnings. It's darkish and twisted and already has a remake in growth by screenwriter Simon Barrett and director Adam Wingard, who have beforehand collaborated on horror movies like You're Next and V/H/S.
It's the story of an outbreak of a lethal infection in downtown Manhattan however it works extra with mood and rigidity than action. Remember when major stars appeared in bizarre-ass horror films that performed all over the nation? That happened in 2002 with this actually unusual telling of the city legend of the mothman, starring Richard Gere and Laura Linney.
Every Pixar Movie Ranked From Worst To Best
Amazon Prime is among the better streaming companies for horror followers (and that's even earlier than you add on the important Shudder service for slightly additional blood and guts). The indie horror writing, directing and appearing team of Justin Benson and Aaron Moorhead, creators of the striking Spring and The Endless, have provide you with perhaps their most bold film but in Synchronic. More sci-fi than horror, the movie nonetheless has loads of unnerving touches because it unspools the story of latest drug that causes its users to vanish — and generally come back useless or mutilated. Anthony Mackie is superb as a paramedic who actually races in opposition to time to stop the spread of the drug and save somebody close to him.
Who could have presumably guessed that Jim from The Office could be behind one of the successful horror movies of the 2010s? Or that it will be on streaming companies only a 12 months after its launch? You've most likely already seen this story of a world in which silence is the one method to survive, nevertheless it's value another look to marvel at its taut filmmaking and a stellar performance from Emily Blunt. We're digging deep for this film, which originally premiered as a part of a DTV series from After Dark Films called eight Films to Die For. This was the most effective of the eight, helmed by a young Jim Mickle, who would go on to direct We Are What We Are and Stake Land.
The streaming service offers many genres of flicks together with comedy, romantic, thrillers etc.
So far, Netflix has added numerous scary films which look absolutely terrifying and we can't wait to look at it.
I myself am a fan of Netflix's horror movie collection and that's why we bring you one of the best horror motion pictures streaming on Netflix right now.
We have rigorously chosen the 30 best horror films on Netflix to look at in 2020.
The movie will now come three years after the original film made $340 million on a $17 million production finances and rave reviews. Antlers was initially expected for spring 2020, but was topic to nearly a yr delay as a result of COVID-19 pandemic.
There's additionally a Netflix prequel collection (which is actually fairly good). But this is still the tentpole of all of them, the 2002 flick that actually defined the style of those vicious ghost motion pictures. Claire Denis' 2018 sci-fi/horror film is among the most WTF films you could watch on any streaming service and incorporates just enough terrifying sequences to qualify it for a listing like this one. Robert Pattinson stars as a passenger aboard what is essentially a prison ship to the edge of the universe. Juliette Binoche, Mia Goth, and Andre Benjamin join him on this unforgettable journey.
Gere performs a reporter who begins investigating the stories of a creature generally known as the Mothman in Point Pleasant, West Virginia, and will get sucked into the supernatural truth of the story. It's onerous to overstate what a juggernaut the Ju-On franchise has turn into over the last two decades. There are over a dozen movies in this franchise and three American versions, including one earlier this year.
Antlers follows Keri Russell as a instructor dwelling in Oregon and her police officer brother performed by Jesse Plemons as they turn into entangled with a state of affairs together with her pupil Lucas who is maintaining a creature in his home. The movie relies on the brief story The Quiet Boy, Guillermo del Toro produced the movie and Scott Cooper (who previously helmed Out of the Furnace, Black Mass and Hostiles) directed the horror movie now set for February 2021. From blaxploitation classics like "Blacula" to the fourth installment of "The Purge" franchise, there are great horror movies by Black creatives that everyone ought to see. Luca Guadagnino directed this 2018 remake of the Dario Argento basic, one of the best horror films ever made. This one may not hold as much as the unique, but it has an intense, gory power of its personal due to Guadagnino's visible presents and fearless performances from Dakota Johnson, Tilda Swinton, Mia Goth, and more.
Horror Anthology Series In Nineteen Fifties Television
With such a strong horror genre, it's a disgrace to not share a few of these unimaginable South Korean horror films with the world. Here are five additional titles assured to give you nightmares for the subsequent few weeks.
Posted in: Horror movie | Tagged: horror, korean, movies
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Manchester by the Sea (2016)
It takes place outside Boston. Of course this movie is going to use the f-bomb like a comma. R-rating. I'm not even looking it up. (Edit: I looked it up out of paranoia and was right. R.)
DIRECTOR: Kenneth Lonergan
People love crying at movies. Man alive, we just need it as a culture. I don't cry unless it's Christmas because I'm broken inside, but there are movies that simply need to exist to make us cry. Manchester by the Sea is about all the crying. If you don't cry like I don't cry, you just feel awful leaving. That cathartic release is that thing I'm craving and I wish I got it. That's not Manchester's fault. It's mine. This movie hit every button that was needed for sweet release and my dead soul just felt really sad without letting go. Some people consider themselves awesome for not crying. I ridicule myself. IF ONLY THIS TOOK PLACE AT CHRISTMAS!
Perhaps the role of film is to capture real experiences. We live a real moment vicariously. We feel what we feel in reality, but without the consequence of sadness. It's why we're happy that Annie finds Daddy Warbucks. We never want to be the orphan, but we do want to experience the reality of the moment. The first unit of my sophomore English class is about the fact that "fiction" doesn't mean "fake." There is truth in fiction. It's just that this specific story hasn't happened like how we experienced it. There is truth and that's what Manchester is. That's Manchester's greatest gift. I've dealt with death and funerals more than I should by this point. Some people have only experienced death from a grandparent or a removed relative. It is something very different when your direct family deals with death. What Lonergan does with Manchester is provide the sheer misery and annoyance that comes with having to deal with the immediate loss of a close loved one. There is a tedium and a stress that comes with working with funeral homes and lawyers. It is the last thing that you want to do, but it also provides the value of distracting your brain just enough to be responsible. I guess the whole process with funeral homes is symbiotic. It forces you to deal with your emotions later until you are ready. There is something about death that puts you into a different mode. Manchester by the Sea is specific because it activates the audience into triage mode. It's depressing, but not in the way a Hallmark movie is. (I'm sorry I keep attacking the fine people at the Hallmark Channel. They have done nothing to me, yet I wage war against them at every turn.)
Lee Chandler, portrayed by Casey Affleck, is a man who constantly takes an emotional beating. I don't know how to survive as Lee Chandler. I would hate even having to walk a mile in his shoes. While Affleck brings his typical intensity once again, I don't think that it is the largeness of his performance that separates Manchester by the Sea. He once again does what he is good at: drawing attention. People are raving about his performance and it is good, but what is more impressive is the understanding of what this character has gone through. Watching a clip of this movie out of context doesn't really provide an understanding of why this role is important. I'm sure that a clip will be shown at the Academy Awards. (He's gonna get the nomination, guys. People won't shut up about him.) People are going to wonder from that clip why he deserves to win. He kind of does, but not because of the scene performances. It is in the nuanced changes. It is in the fact that he lives the character. Lee Chandler can't do something huge. He can't punch walls. He can't cry in the rain. (He can and does punch people though.) This is about conversations and moments that seem like selfishness. His performance exists in relation to the grand picture. I applaud Lonergan, who not only directed the movie but also wrote it, in naming the movie Manchester by the Sea. The town is his enemy. Everything in this town hurts him. The trailer makes him look like a man child who can't accept responsibility, but his change can't be a light switch moment. That would cheapen everything that he goes through. Nicely done.
While I think Casey Affleck is great in pretty much everything (especially fake Dunkin' Donuts commercials), the real attention should go to Lucas Hedges as Patrick. Geez, he gets everything. Sure, Casey Affleck is going to get most of the attention for this movie, but I think that Hedges has such a great parallel performance and storyline that I can't determine which is more compelling. (Okay, it's Affleck, but that's because he has more to work with. I guess that is something that a story about a kid losing his dad is less traumatic than Affleck's story.) But he's allowed moments of levity that Affleck is not really given a right to explore. Hedges walks a really fine tightrope to maintaining tone while making the story accessible. If it wasn't for Hedges, this would just be a sad story about sad people, like The Lower Depths. (I like sad stories, guys!) But this is a sad story about real people who happen to be sad overall. On top of that, he makes his awful lifestyle appealing. There isn't a moment where Hedges feels like a sick puppy being kicked. He is a real person, warts and all. The warts don't make him evil at any point, but make him someone we know and relate to. We want to save him, sure. But more so, we want him to save himself.
This movie is going to wreck you. I don't even recommend it to everyone. There are people who don't need this in their lives. I guess this movie is dangerous in some ways. But there is nothing wrong with being sad. This is a healthy exploration of what death is and what it isn't. It isn't people breaking down and shattering dishes. It is in the stupidity and boringness of it all. It is about death not coming like a whirlwind, but in selfish moments and the absurdity of the whole situation.


text:
namespace v8 {
namespace internal {

ACCESSORS(JSCollection, table, Object, kTableOffset)
ACCESSORS(JSCollectionIterator, table, Object, kTableOffset)
ACCESSORS(JSCollectionIterator, index, Object, kIndexOffset)

ACCESSORS(JSWeakCollection, table, Object, kTableOffset)

CAST_ACCESSOR(JSSet)
CAST_ACCESSOR(JSSetIterator)
CAST_ACCESSOR(JSMap)
CAST_ACCESSOR(JSMapIterator)
CAST_ACCESSOR(JSWeakCollection)
CAST_ACCESSOR(JSWeakMap)
CAST_ACCESSOR(JSWeakSet)

Object* JSMapIterator::CurrentValue() {
  OrderedHashMap* table(OrderedHashMap::cast(this->table()));
  int index = Smi::ToInt(this->index());
  Object* value = table->ValueAt(index);
  DCHECK(!value->IsTheHole());
  return value;
}

}  // namespace internal
}  // namespace v8

#include "src/objects/object-macros-undef.h"

#endif  // V8_OBJECTS_JS_COLLECTION_INL_H_

redpajama_set_name: RedPajamaGithub


Berlin-Liga. Die höchste Berliner Spielklasse spielt um den Berliner Meister. Die beiden letzten Mannschaften steigen in die Bezirksliga ab. Apr. Meisterschaft. Berlin-Liga Männer (Saison /) 12, VC Rotation Mitte I( H) · Berliner Volleyballverein Vorwärts III · (). 13, Berliner. Spiel, Liga, Ergebnis, Team 1, Team 2, Schieri 35 volleyballberlin (@)sopoker.eu VR B | Betr.-Nr. Präsident: René Hecht.
The Polish team delivered us a thrilling four-setter, while. Arnhem, Netherlands, January 31, Yerevan, Armenia, January 31, Trento, Italy, February 1, All sides from Pool B will take to the.
Stuttgart, Germany, January 31, Yet another new German Beach Volleyball duo is introduced after the German ship was shook by the early retirement of Olympic Champion Kira Walkenhorst.
It was the third edition of. Yerevan, Armenia, January 21, Despite the freezing temperatures the event took place at Tsaghkadzor. Erciyes, Turkey, January 13, Bandar Anzali, Iran - October , Yangzhou, China - Final Standings.
BVV Herren I - SV Preußen Berlin 2016-01-17 Chetumal, Mexico - October September October 20, Buenos Aires - final standings. Stuttgart, Germany, January 30, Ljubljana, Slovenia - Final standings. Arnhem, Netherlands, January 31, Erciyes, Turkey, January 13, Annual ELC meeting held in Luxembourg. All sides from Pool B will nächsten wahlen to the. Qinzhou, China - Fc bayern münchen trikot kinder Standings.
Beach and Snow Volleyball. Gibraltar, January 29, Saint Petersburg, Russia, January 29, The edition of the Russian Snow Volleyball championship took place in Zelenogorsk, in the outskirts of Saint Petersburg.
Not to be missed. Next to this, he had a. Continental Cup Senior Youth. Chantal Laboureur picks Sandra Ittlinger. Volleyball legend Khamuttskikh helps grow the game among youngsters in Chelyabinsk.
Snow Volleyball champions crowned in Armenia. Russia sweep gold and silver medals at European Tour stop in Turkey. Annual ELC meeting held in Luxembourg.
Coaches Commission meeting held at home of European Volleyball. VNL stars set the pace with clubs across the globe. May 21 - July 14, December 4 - 9, November 26 - December 2, September October 20, Because I love volleyball!
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I can't believe how quickly this week flew by. So much to do and so little time. We have a wedding to attend this weekend in the beautiful Berkshires and another next weekend in Baltimore. Plus, I have a ton of work to do. I have a few freelance gigs and I'm getting a body of work together for a little Shiny Squirrel show next month. Plus, I'm thinking of doing another trade show and I'd have to make a whole new body of work appropriate for apparel and home decor. I'm just getting settled back into teaching the little ones art all day too. Sleep is such a bother. I wish I didn't have to do it. Do you feel like there's not enough day to do what you want to?
Last weekend Jessica of Shiny Squirrel got a bunch of incredible blogging women (and Sean, half of Sub-Studio, he was the token male) together for a brunch at a hip Williamsburg joint (I kind of sound like an old lady using words like "hip" and "joint", please insert "phat" and "spot" (now I sound like a hip hopper from the 90's)). It was incredibly fun. I wish I had more of an opportunity to talk with the amazing artists/designers/producers/bloggers.
We're going to have to get together again soon. I'm sure at the very least we'll meet up at the Shiny Squirrel party.
I have so much to say about each blogger and her work but I thought for today I'd just introduce you to their blogs to peruse over the weekend. They've been added to my reader and I'm going to add them to my blogroll too. Some are already on there. Hijiri also posted about the meet up on heart fish and featured some of my work (I'm so happy about it! Thanks Hijiri and thanks everyone else for a fun brunch).
Samantha! Thank you for your sweet post! You made my day!! Happy Friday and have a great time at the wedding and good luck with everything – can't wait to see more of your wonderful work soon!
Thank you Hijiri!!!! You are so sweet. See you soon!
Thanks for linking to everyone's blogs – I'm having fun perusing! It was great to meet you, too!
Glad you are looking Anna!! Have a great weekend. See you and Sean soon.
It was sooo nice having everyone there. I had sucha good time and can't wait till the next one, probably in late october. what do you think?
It's a great idea. It was so much fun. You were responsible for bringing such a great group of bloggers together, so thank you! Yay Jessica. Can't wait for the party and the next brunch.
You are so sweet to mention particular aesthetic in your post! It was lovely meeting you and hope to see you in a couple of weeks.
my absolute pleasure Laura…see you so soon!!
i just got back from a few days offline, and i'm loving your updates. once again, it was lovely to meet you in person!!!
It was so lovely meeting you too! I hope you are coming to the next meet up!?


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Section Zero
( 180 followers)
Monday 8:55 PM on Canal+ (FR)
Set in the near future, multi-national corporations are Europe's new leaders. One of the most powerful, Promethee, wishes to further secure their grow... (more)ing dominance by replacing the police force with their own private militias, the Black Squad, led by Henry Munro. Following the shooting of his daughter, his life in shambles and darkest secrets exposed, an idealistic law enforcement officer, Sirius, with nowhere to turn, aligns himself with an old cop Franck Varnove. Sirius takes charge of Franck's clandestine, elite squadron, Section Zéro, to battle these dark, violent militias, promising a return to traditional law enforcement before the world they've known disappears forever.
Season 1 Episode 8, Apr 25, 2016
Sirius Requiem
Between the Living and the Dead
Shadow Soldiers
In the Kingdom of the Dead
The Chimera
Pascal Gregorry, Laurent Malet, Ola Rapace, Françis Renaud, Tchéky Karyo, Michaël Erpelding, Catherine Marchal, Juliette Dol
People who like Section Zero also like
When is Section Zero back?


There are times when we allow fear to run our lives.
Don't get me wrong, there are times when fear is very useful. Fear can save our lives. Fear lets us know when we are about to do something potentially dangerous. But there are also times when fear tries to hold us back when we should move forward. If we give in to it, if we choose to let it run our lives, we can end up looking back and regretting the opportunities wasted.
After I graduated 8th grade, my parents sent me to a christian boarding school. They had a work study program, meaning all students were required to work and the money earned was put toward their school bill. The summer before my freshman year I worked in the greenhouse. I had a coworker whose name I will change to Eden. She had long red hair, glasses, and, I have since discovered, she was my type. She was attracted to me as well, and we started hanging out outside of work.
That's when the teasing started. People teased her for being overweight, and they teased me for spending time with the "fat girl". Looking back, I should have stood up for her and myself. But I didn't. I was afraid of what my peers thought about me. I chose to let that fear make my decisions for me. So I stopped hanging out with her. That choice hurt her so much that she got her parents to take her out of that school.
Why am I writing about this now? Because I work with an attractive woman who reminds me a lot of Eden. More importantly the situation feels very similar. This is the first time since entering a polyamorous relationship that I have wanted to ask someone out. I was afraid to ask her though. I was afraid of rejection. I was afraid of how she and others might react to finding out that I am poly. And so my subconscious dug up this memory and shoved it in my face.
Everyone makes mistakes. Everyone does things they are not proud of. The important thing is that you learn from them and make better decisions the next time that situation comes up. So I asked her out. She didn't freak out. But she did turn me down. And I am ok with that. She needs someone who will be only hers and who she doesn't have to share with anybody else. I respect her relationship needs and I am thankful that she considered my request and gave me a reasonable and well thought out answer. The point is I didn't allow my fear to make my decision for me.
Now when I tell this story to my daughter, I can be proud of the choices I made. When faced with the same decision to follow my heart or give in to fear, I chose to follow my heart. And that is all we can do.
I am also proud of you. As a poly couple we will find lots of rejection and there will be misunderstandings. We have also learned that while some people can handle it intellectually when practiced they can not. I love you!


text:
RADP / Pulse Kenya
Two people succumb to injuries inflicted by police in Mumias, even as police announces ksh500,000 cash reward
Two people succumb to injuries inflicted by the police, as KNHCR launches independent investigation into the alleged police brutality in Mumias.
Kenya National Commission on Human Rights (KNHCR) has launched an independent investigation into the alleged police brutality in Mumias, Kakamega County.
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Two people have already succumbed to injuries inflicted by the police, while hundreds of residents are nursing serious injuries like broken limbs, while a few have even reported sexual assault under the hands of the law enforces.
51 year old Angelina Okoth succumbed to her injuries while undergoing treatment at St Mary Hospital in Mumias, while a day earlier a businessman was killed after his shop was set ablaze by policemen searching for the firearms.
Police are currently involved in a major manhunt operation for a criminal gang who raided Boker police station and stole G3 riffles and several rounds of ammunitions' last weekend.
Also read : GANGSTERS STEALS SEVEN G3 RIFLES AND CLOBBER OFFICER SENSELESS IN A DARING RAID IN MUMIAS, KAKAMEGA POLICE POST
Residents of mumias have decried the high handless of the police who are going round searching every homestead for the stolen ammo.
A host of leaders have strongly condemned the police brutality, Ford Kenya leader and Bungoma senator, moses wetangula has said the alleged police brutality is unwarranted and even wants the whole operation halted
"Police have no right to use force on innocent Kenyans in the name of searching for stolen guns" he said as quoted by the Nation.
This comes on the background of the national police service announcing a cash reward of Ksh500, 000 for any information leading to the recovery of the stolen firearms and arrest of the gang.
Anyone with information can contact the nearest police station near you or get in touch with criminal investigation offices through toll free lines 999 112 911
The office of the inspector general has announced that it has received complaints of police brutality and as a result, the inspector general has ordered for expeditious institutions of investigation on complaints against excess force by the police.


Boyle Heights — Police are asking the public to help find a hit-and-run driver who struck a pedestrian last week in a crosswalk at Lorena and 8th streets.
A surveillance video of the felony hit-and-run shows the pedestrian rolling across the hood of the car and then tumbling to the pavement as the motorist drives away without stopping.
Anyone with information is asked to contact the LAPD Central Traffic Division Detectives at (213) 833-3713 or Detective-II Juan Campos (213) 486-0755 or email him 31480@LAPD.Online. During non-business hours or on weekends, calls should be directed to 1-877-LAPD-24-7 (877-527-3247).


Fruit is a great addition to breakfast or as a snack. Make the most of what's in season. These freshly picked figs were cut in half and baked. I had them with my coconut chia pudding and granola. You could have them on top of porridge or black rice pudding. You could have with yogurt or nuts as a snack. That means the protein and fat in the yogurt or nuts helps slow the sugars down in the fruit.


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En mathématiques, l'anneau des entiers de Q() est l'ensemble des nombres réels de la forme a + b(1+)/2, où a, b sont deux entiers relatifs, muni des opérations usuelles d'addition et de multiplication. C'est le plus petit ensemble de nombres qui contienne à la fois les entiers ordinaires et le nombre d'or φ = (1+)/2, et qui soit stable par addition et multiplication. On le note ici Z[φ].

En théorie algébrique des nombres, on le définit simplement comme l'anneau O des entiers du corps quadratique réel Q(). Cet anneau est euclidien. Il possède donc des propriétés arithmétiques analogues à celles des nombres entiers usuels : il est possible d'y définir une division euclidienne, de calculer le plus grand commun diviseur et le plus petit commun multiple de deux ou plusieurs nombres, d'y démontrer le lemme de Gauss, l'identité de Bézout et une version du théorème fondamental de l'arithmétique, garantissant l'existence de la décomposition de tout nombre en un produit de facteurs premiers. Une différence importante, cependant, est qu'il n'existe dans Z que deux éléments inversibles, 1 et –1, mais qu'il en existe une infinité dans Z[φ].

Cet anneau est souvent utilisé comme un des exemples privilégiés pour illustrer concrètement la théorie plus avancée des entiers dans les corps de nombres. Son arithmétique permet aussi de justifier plusieurs propriétés mathématiques du nombre d'or, et d'étudier certaines équations diophantiennes classiques, comme x + y = z, liée au dernier théorème de Fermat dans le cas de degré égal à 5 ou x – 5y = 1, un cas particulier de l'équation de Pell-Fermat.

Notations
Dans cet article, on utilise des lettres grecques pour désigner des éléments de Z[φ], et l'on réserve les lettres latines pour désigner les entiers relatifs ou les nombres rationnels. La lettre ε est utilisée pour décrire une unité, c'est-à-dire un élément inversible de Z[φ].

Un élément α de Z[φ], par définition, est donc un nombre (réel) qui peut s'écrire α = a + bφ, pour deux entiers relatifs a et b. Cette écriture est unique, et l'on appellera à l'occasion a et b les coordonnées de α.

Structure
Dans cette section sont expliquées les opérations (addition, multiplication…) sur les nombres α = a + bφ, et les structures fournies par ces opérations. La démarche suivie est analogue à celle utilisée dans le cas des entiers de Gauss, qui sont des nombres de la forme a + b, où  est un nombre complexe solution de l'équation x + 1 = 0, une équation quadratique. Ici φ est solution d'une autre équation quadratique, x – x – 1 = 0. Le polynôme X – X – 1 est appelé le polynôme minimal de φ.

Structure d'anneau

De φ = φ + 1, on déduit que :
(par récurrence) toute puissance de φ appartient à Z[φ] — voir plus bas : § Suite de Fibonacci — donc toute fonction polynomiale de φ à coefficients entiers également ;
le sous-ensemble Z[φ] du corps ℝ des nombres réels est donc le sous-anneau engendré par Z ∪ {φ} (ce qui rend légitime de le noter ainsi).

En tant que sous-anneau de ℝ, l'anneau Z[φ] est commutatif, intègre et totalement ordonné (donc de caractéristique nulle).

Une remarque sur Z[]
On aurait pu imaginer (pour mieux imiter les entiers de Gauss, par exemple) d'étudier les nombres, apparemment plus simples, de la forme u + v  , avec u et v des entiers. Ils forment l'ensemble noté Z[], qui est aussi un sous-anneau du corps des nombres réels (le nombre  est solution de l'équation quadratique x – 5 = 0 et les mêmes raisonnements s'appliquent). Ce sous-anneau est inclus dans Z[φ] : en effet,

Cette inclusion de Z[] dans Z[φ] est stricte car d'après la formule ci-dessus, les seuls éléments a + bφ de Z[φ] qui appartiennent au sous-anneau Z[] sont ceux pour lesquels l'entier b est pair.

En fait, si les propriétés algébriques des deux ensembles sont analogues (ce sont des anneaux pour les mêmes opérations), Z[] est trop petit, comme on le verra, pour y faire confortablement de l'arithmétique. Comprendre quels étaient les bons ensembles de nombres à prendre en compte est une des difficultés rencontrées par les mathématiciens du .

Suite de Fibonacci

La « suite » (F) (indexée par ℤ) des entiers de Fibonacci, définie par

vérifie :

Le corps Q()
L'ensemble des réels de la forme a + bφ avec a et b rationnels ou, ce qui revient au même, de la forme u + v   avec u et v rationnels, est — de même que Z[φ] et Z[] étaient des sous-anneaux — une Q-sous-algèbre de ℝ. Puisque  est irrationnel, l'écriture d'un élément de cet ensemble sous la forme u + v   avec u et v rationnels est unique, ou encore : ce nombre n'est nul que si u = v = 0. Autrement dit : (1, ) est une base de ce Q-sous-espace vectoriel, et de même pour (1, φ). (Ceci généralise — donc justifie — l'unicité précédemment admise dans le cas de coordonnées entières.)

Cet ensemble est de plus stable par inverses car si u et v sont rationnels et non tous deux nuls alors u – 5v est un rationnel non nul et 1/(u + v  ) = (u – v  )/(u – 5v). Par conséquent, c'est non seulement un sous-anneau mais un sous-corps de ℝ. On le note Q().

Comme Q() est le plus petit sous-corps de ℝ contenant Q et  (ou Q et φ), il s'identifie au corps des fractions de Z[] et de Z[φ]. On peut se demander comment, inversement, récupérer ces anneaux directement à partir de Q(). C'est la notion d'entier algébrique qui le permet — au moins pour Z[φ], qui va donc apparaître comme plus naturellement attaché à Q().

Comme Q() est un corps quadratique, tous ses éléments sont algébriques de degré 1 ou 2 : si α = u + v   alors (α – u) – 5v = 0. L'élément α est entier si et seulement si les rationnels 2u et  sont des entiers (relatifs). On en déduit (voir « Entier quadratique ») :

L'anneau Z[φ] est donc intégralement clos, si bien que Z[], qui a même corps des fractions mais est strictement plus petit, ne l'est pas. Par conséquent, Z[] n'est pas un anneau à PGCD (et a fortiori pas factoriel), contrairement à Z[φ] qui — voir plus bas — est même euclidien. En fait, Z[] ne vérifie même pas le lemme d'Euclide, c'est-à-dire qu'il possède des éléments irréductibles non premiers. Par exemple, 2 est irréductible dans Z[] (et même dans Z[φ] : cf. § « Détermination des éléments irréductibles de Z[φ] » plus bas). Cependant, dans Z[], 2 n'est pas premier : il divise le produit (1 + )(1 – ) = –2 mais ne divise aucun des deux facteurs. Ce problème disparaît dans Z[φ], qui contient  et (1 – )/2 = 1 – φ. La définition des entiers, qui autorise ici le dénominateur 2, est donc ce qui leur garantit les meilleures propriétés. Plusieurs auteurs se penchèrent sur ces problèmes au cours du , mais c'est Richard Dedekind qui donna une présentation complète de la notion d'entier algébrique, dans les suppléments à son édition des cours de Dirichlet, en 1871.

Le discriminant de Z[φ], égal à 5, est le plus petit discriminant d'un corps quadratique réel.

Deux outils importants

Deux des outils pour l'étude de l'anneau Z[φ] sont constitués de fonctions. Une de ces fonctions imite la conjugaison complexe pour les entiers de Gauss, l'autre fait office de mesure pour la taille d'un élément de Z[φ].

Application conjuguée
La conjugaison σ dans Q() (intervertissant  et son opposé) est un automorphisme (involutif) du corps Q() qui laisse stable Z[φ], en intervertissant φ et son élément conjugué φ' = (1 – )/2 = –1/φ = 1 – φ. Par restriction, on obtient ainsi :

Norme

Une fois encore, la situation est un peu analogue à celle des nombres complexes. Pour ceux-ci, l'application module est très utile : à un nombre, elle associe la racine carrée du produit de lui-même et de son conjugué. Comme, dans le cas qui nous intéresse, le produit correspondant n'est pas toujours positif, on évite en général de prendre la racine carrée et l'on définit plutôt :

C'est donc un rationnel, et même un entier relatif si α appartient à Z[φ]. Par exemple, la norme de  est égale à –5 et la norme de φ est égale à –1.

La norme possède une propriété clé plus générale ( articles détaillés) :

Traduite dans la base (1, ), on retrouve le cas n = 5 de l'identité de Brahmagupta :

Division
Dans Z[φ], une condition nécessaire pour qu'un nombre α divise un nombre γ est que N(α) divise N(γ). Par conséquent, le nombre β tel que αβ = γ n'appartient pas à Z[φ] dans le cas général.

Nombre inversible
Pour qu'un nombre α ait un inverse, il faut donc que sa norme soit égale à 1 ou -1. Ces nombres sont donc tels que :

N(α) = a + ab – b = 1, ou

N(α) = a + ab – b = -1

Ces équations ont des solutions entières lorsque 5a+4 ou 5a-4 sont des carrés. N(α) = ±1 est une condition suffisante pour que α soit inversible, son inverse étant son conjugué (si N(α) = 1) ou l'opposé de son conjugué (si N(α) = -1).

Par exemple :

φ a pour inverse -1+φ = -φ''' ; car N(φ) = -1 et φ(-1+φ) = 1
5-3φ a pour inverse 2+3φ = 5-3φ ; car N(5-3φ) = 1 et (5-3φ)(2+3φ) = 1

Tout produit de nombres inversibles est lui-même inversible ; notamment, toute puissance de φ possède un inverse. L'ensemble des nombres inversibles de Z[φ] constitue un groupe commutatif pour la multiplication, appelé groupe des unités (cf section suivante).

 Division euclidienne

La norme permet de définir une division euclidienne. Cette norme n'est pas toujours positive. Le stathme v, c'est-à-dire la fonction permettant d'évaluer le reste de la division — de même que la valeur absolue dans le cas des entiers relatifs — ne doit prendre que des valeurs positives. Pour cette raison, on le choisit égal à la valeur absolue de la norme. On montre alors que 5 fait partie, comme –1, des 21 valeurs de d pour lesquelles l'anneau des entiers de Q() est euclidien pour v :

Il suffit ( fin du § « Définitions » de l'article sur anneaux euclidiens) de vérifier le critère général suivant : pour tout élément ζ de Q(), il existe au moins un élément θ de Z[φ] tel que

Pour tous réels x, y majorés en valeur absolue par 1/2, |x + xy – y| < 1. Donc si ζ = a + bφ avec a et b rationnels, en choisissant des entiers c et d tels que |a – c| ≤ 1/2 et |b – d| ≤ 1/2 puis en posant θ = c + dφ, on a bien |N(ζ – θ)| < 1.

Ceci montre qu'il existe une division euclidienne dans l'anneau Z[φ]. Elle possède un aspect un peu déroutant, au sens où il n'y a pas d'unicité stricte, comme dans le cas usuel. Le nombre des possibilités est en effet lié au groupe des unités. Cette situation n'est en fait pas très différente de celle des entiers relatifs où la division euclidienne n'est définie qu'au signe près, c'est-à-dire à une unité près.

 Groupe des unités

Les unités d'un anneau commutatif comme Z[φ] sont ses éléments inversibles et forment un groupe (commutatif) pour la multiplication, contenant 1 et –1. L'anneau Z ne possède que ces deux unités. Par contre, un anneau d'entiers d'un corps quadratique réel, comme Z[φ], possède toujours une infinité d'unités, ce qui se vérifie facilement dans le cas particulier envisagé. Les unités ne sont pas traitables avec les outils classiques de l'arithmétique ; les notions fondamentales, la définition de nombre premier ou irréductible, la décomposition en facteurs irréductibles sont données au produit par une unité près, d'où l'utilité de décrire celles-ci. On appelle « associés » deux éléments de l'anneau se déduisant l'un de l'autre par multiplication par une unité.

L'étude générale du groupe des unités d'un corps quadratique montre que :
Le groupe des unités de Z[φ] est composé des éléments de norme égale à ±1.
Les unités de Z[φ] sont les φ et –φ, n ∈ Z.

 Nombre premier ou irréductible
Un nombre de Z[φ] est dit premier ou irréductible si toute décomposition du nombre en deux facteurs de Z[φ] comprend un et un seul élément du groupe des unités.

Nota : si α est inversible d'inverse ᾱ, tout nombre γ peut toujours s'écrire :
γ = αᾱγ = αβ, en posant β = ᾱγ

Un nombre de Z[φ] dont la valeur absolue de la norme est un nombre premier est premier ou irréductible.

Exemples :
√5 est irréductible car N(√5) = -5
2+φ est irréductible car N(2+φ) = 5
19 est réductible car N(19)= 19 et 19 = (4+3φ)(7-3φ)

Un nombre non nul de Z[φ] qui n'est pas une unité peut s'écrire comme un produit de nombres premiers.

Les nombres premiers, ou irréductibles, jouent un rôle essentiel dans l'arithmétique de Z et il en est de même dans Z[φ].

Comme dans Z, tout élément de Z[φ] se décompose en facteurs irréductibles, et ce de manière à peu près unique. Le « à peu près » vient des unités : dans Z, 6 possède plusieurs décompositions en facteurs premiers, 2 × 3, mais aussi –2 × –3 par exemple. De même, dans Z[φ], les facteurs irréductibles ne sont fixés qu'à produit près par une unité.

 Détermination des éléments irréductibles de Z[φ]

Un nombre premier de Z n'est pas toujours irréductible dans Z[φ]. Par exemple : 5 = (), ou encore : 11 = 4 – 5 = (4 + )(4 – ).

La classification des idéaux premiers de l'anneau des entiers de Q() pour d quelconque (cf. article détaillé), appliquée ici à d = 5, indique que :

On peut le redémontrer en remarquant d'abord que (d'après les propriétés générales de la norme sur un anneau d'entiers quadratiques) les irréductibles de Z[φ] s'obtiennent en décomposant dans cet anneau les nombres premiers usuels, et pour un tel entier naturel premier p, il n'y a que deux possibilités :
ou bien p reste irréductible dans Z[φ],
ou bien p = |N(π)| = ±πσ(π) pour un certain élément π de Z[φ], qui est alors irréductible.
Il reste à vérifier que ces deux cas correspondent aux congruences annoncées et que 5 est le seul nombre premier « ramifié dans Q() ».

Si p ≡ ±2 (mod 5) alors (d'après la remarque sur les normes modulo 5) p n'est pas de la forme |N(π)|, donc p reste irréductible dans Z[φ].

Si p ≡ ±1 (mod 5), un cas particulier de la loi de réciprocité quadratique montre que 5 est un carré modulo p, c'est-à-dire qu'il existe un entier x tel que p divise x – 5. Dans Z[φ], p ne peut donc pas être irréductible, sinon, divisant  il diviserait l'un des facteurs, ce qui est impossible car les nombres x/p – /p et x/p + /p ne sont pas dans l'anneau.

Le cas p = 5 a déjà été examiné. C'est le seul p = |πσ(π)| pour lequel π et σ(π) sont associés. En effet, soient π = a + bφ un élément de l'anneau et p ≠ 5 un nombre premier divisant π = (a + b) + (b + 2a)bφ. Alors p divise 4b(a + b) + (b – 2a)(b + 2a)b = 5b donc il divise b et — puisqu'il divise a + b — il divise aussi a donc a donc, finalement, π.

 Petit théorème de Fermat

Le petit théorème de Fermat pour tout corps de nombres s'applique en particulier à tout corps quadratique, donc à ℚ() :

La caractérisation des éléments irréductibles donnée plus haut permet de détailler cet énoncé : sous les mêmes hypothèses mais en excluant le cas où π est associé à ,
si |N(π)| = p premier (de la forme 5n + 1 ou 5n – 1) alorset si α n'est pas non plus multiple du conjugué σ(π), alors cette congruence est même vraie non seulement mod π mais mod p ;
si π = q premier (de la forme 5n + 2 ou 5n – 2) alors modulo q, on a non seulement α ≡ α mais même α ≡ σ(α), autrement dit :

On considère un élément irréductible π de Z[φ], et un élément α non divisible par π, qu'on peut écrire a + bφ, avec a et b entiers, ou encore c/2 + (d/2), avec c et d entiers.

Si |N(π)| = p premier (de la forme 5n + 1 ou 5n – 1), on a vu que 5 est un carré mod p. En appliquant le petit théorème de Fermat sur Z, on en déduit que modulo p (et a fortiori modulo π), 2α ≡ (2α) = (c+d) ≡ c + d5 ≡ c + d = 2α. Puisque 2 et α sont premiers à π, on peut diviser par 2α cette congruence mod π et obtenir la relation voulue.Lorsque α est aussi premier à σ(π), donc à |πσ(π)| = |N(π)| = p, on peut diviser par 2α la précédente congruence mod p.
 Si π = q premier (de la forme 5n + 2 ou 5n – 2) et si q > 2, le raisonnement utilisé plus haut montre que modulo q, 2α ≡ c – d = 2σ(α), ce qui donne le résultat voulu en divisant par 2.
Modulo 2, α ≡ a + bφ ≡ a + b(1 – φ) = σ(α).

 Applications : suite de Fibonacci et nombres de Mersenne
Le petit théorème de Fermat dans Z[φ] permet d'établir ce qu'on appelle la « loi d'apparition des nombres premiers au sein de la suite de Fibonacci » : tout nombre premier divise un des termes de la suite de Fibonacci. Plus précisément :

si p est un nombre premier de la forme 5n + 1 ou 5n – 1 (donc un nombre qui se décompose dans Z[φ]), alors p divise F (et F – 1) ;
si q est un nombre premier de la forme 5n + 2 ou 5n – 2 (donc un nombre qui reste irréductible dans Z[φ]), alors q divise F (et F + 1).

En effet, par le petit théorème de Fermat dans Z[φ], p divise φ – 1 = F + Fφ – 1 et q divise φ + 1 = F + Fφ + 1.

On peut tester le résultat numériquement. Par exemple, F = 5 × 11 (et F – 1 = 3 × 11), F = 2 584 = 152 × 17 (et F + 1 = 1 598 = 94 × 17).

Un autre usage du petit théorème de Fermat dans Z[φ] est de fournir une condition nécessaire et suffisante pour que certains nombres de Mersenne soient premiers. Plus précisément, si p = 4n + 3 est un nombre premier, le nombre de Mersenne M = 2 – 1 est premier si et seulement si r ≡ 0 (mod M), où la suite (r) est définie par récurrence : r = 3 et r = r – 2.

La démonstration repose sur le fait que la suite (r) s'exprime en fonction de φ, r = φ + σ(φ). Le critère de primalité fourni par ce résultat est celui utilisé par Édouard Lucas pour prouver que le nombre de Mersenne 2 – 1 est premier.

 Équation de Pell-Fermat

 Équation
L'objectif est, pour un entier fixé d non divisible par 5, de résoudre en nombres entiers l'équation

ou encore, d'après le § « Norme » ci-dessus :

On cherche donc ( § « Une remarque sur Z[] » ci-dessus) les éléments a + bφ de Z[φ] de norme d avec b pair, ces éléments étant reliés aux solutions de (E) par le changement de variables , v = b/2.

Cette restriction au sous-anneau Z[] n'est pas très gênante car

On s'intéresse donc dans un premier temps à tous les éléments de Z[φ] de norme ±d.

 Cas d = ±1
Résoudre les deux équations (E) provient directement de la connaissance des unités de Z[φ] ; elles sont de la forme ±φ où n est un entier relatif et la norme est (–1). La suite de Fibonacci donne les coordonnées des puissances de φ, mais il faut déterminer dans quels cas le coefficient de φ dans l'écriture de ces unités est pair. Or PGCD(F, 2) = PGCD(F, F) = F donc F est pair si et seulement si n est multiple de 3. Les ensembles S des solutions des équations (E) sont par conséquent :

ou encore, en faisant intervenir les nombres de Lucas L = 2F + F :

 Cas d = ±p où p est un nombre premier
L'analyse des éléments irréductibles de Z[φ] permet de résoudre la question : il existe dans Z[φ] des éléments de norme ±p si et seulement si p est congru à 1 ou à –1 modulo 5.

 Cas général
Le cas général s'en déduit :

En effet, la valeur absolue de la norme d'un élément irréductible correspondant à ce type de facteur est nécessairement un carré.

Sous cette hypothèse, les différents facteurs premiers de d, ou leurs carrés dans le cas de facteurs de la forme 5n + 2 ou 5n – 2, correspondent à des normes d'éléments de Z[φ]. En appliquant la multiplicativité de la norme, on fabrique un élément de Z[φ] de norme ±d et l'on en déduit (en le multipliant au besoin par φ ou φ) un élément α = a + bφ de Z[] de norme d ou –d.

Pour en déduire toutes les solutions des deux équations (E) et (E), on procède alors comme dans le cas d = ±1 ci-dessus (pour lequel α était choisi égal à 1) : les solutions correspondent, parmi les ±φα avec m entier relatif pair pour l'une et impair pour l'autre, aux éléments qui appartiennent aussi au sous-anneau Z[]. Compte tenu du fait que b est pair, cette condition supplémentaire sur m se traduit par : aF est pair c'est-à-dire, si a est impair : m multiple de 3 (par le même argument que dans le cas d = ±1).

 Dernier théorème de Fermat pour l'exposant 5

Pour l'exposant 5, le dernier théorème de Fermat énonce qu'il n'existe pas de triplet (x, y, z) d'entiers non nuls et deux à deux premiers entre eux tel que x + y = z. S'il en existe, l'un des trois entiers est évidemment pair mais aussi, d'après le théorème de Sophie Germain, l'un des trois est divisible par 5. On doit donc distinguer deux cas, selon que le même x, y ou z est divisible par 2 et 5 ou non.

En juillet 1825, Gustav Lejeune Dirichlet, alors à Paris, présenta devant l'Académie des sciences une preuve du théorème, dans le cas où l'un des x, y, z est divisible par 10. Adrien-Marie Legendre, rapporteur du mémoire de Dirichlet à l'Académie, compléta la démonstration quelques mois plus tard. Dirichlet en donna finalement une nouvelle version, en suivant les principes de sa propre preuve, en . C'est dans cette preuve que Dirichlet utilise les propriétés des nombres de Z[φ].

La preuve ( article détaillé) repose sur le lemme clé suivant :

Pour cela, Dirichlet démontre plus généralement :

La démonstration suivante de ces deux lemmes n'est pas exactement la sienne. Nous utiliserons le préambule de l'étude des éléments irréductibles de Z[φ], le fait que Z[] = Z + 2Z[φ], et la connaissance des inversibles de Z[].

Plaçons-nous sous les hypothèses du lemme général (dans le dernier point, on en déduira le « lemme clé »).
u + v est le produit d'un inversible ε de Z[φ] par la puissance cinquième d'un élément de Z[] :Pour chaque facteur premier p dans Z de u – 5v = (u + v)(u – v), choisissons — dans Z[], grâce à une remarque du § « Équation » — un facteur irréductible π de p intervenant dans la décomposition de u + v dans Z[φ]. Si p n'est pas premier dans Z[φ], σ(π) ne peut pas intervenir aussi puisque |πσ(π)| = p ne divise pas u + v. Il existe donc un inversible ε de Z[φ] et des entiers naturels k tels queComme u – 5v est une puissance cinquième, tous les k sont donc multiples de 5 et
ε est même un inversible de Z[] :Dans Z[φ], u + v et α sont congrus mod 2 à 0 ou 1, or u + v ≡ u – v n'est pas divisible par 2 donc α non plus, si bien que u + v et α sont congrus à 1 modulo 2 donc ε et ε aussi.
ε peut être choisi de norme 1 :On utilise un inversible de Z[] de norme –1, par exemple ε' = φ. Si la norme de ε vaut –1, il suffit de remplacer ε par εε' et α par ε'α.
Supposons de plus v divisible par 5. Alors ε peut même être choisi égal à 1 :D'après les points précédents, u + v est de la forme ±φα avec n divisible par 6 et α élément de Z[]. Par conséquent, mod 5 dans Z[φ] (ou même Z[]), u est congru au produit d'un entier w par F + Fφ, si bien que mod 5 dans Z', uF ≡ FwF ≡ F0 = 0 donc F est divisible par 5. Or PGCD(F, 5) = PGCD(F, F) = F. Donc n = 5m pour un certain entier m (encore divisible par 6) et u + v'' = β avec β = ±φα.

Notes et références

Voir aussi

Bibliographie

Liens externes
 Robert Ferréol, Les cas n=3, 4 et 5 du théorème de Fermat

Théorie des anneaux
Entier quadratique
Nombre d'or


text:
Q: Django DateTimeField() and timezone.now() OK, weird time zone issues when I'm running function tests.  Django 1.4, Python 2.7.  Are milliseconds truncated in DateTimeField() on MySQL?  That's the only theory I've got.
model file
from django.db import models
from django.utils import timezone

class Search(models.Model):
    query = models.CharField(max_length=200, null=True)
    query_date = models.DateTimeField(null=True)

test.py
from django.test import TestCase
from django.utils import timezone
from search.models import Search

class SearchModelTest(TestCase):
def test_creating_a_new_search_and_saving_it_to_the_database(self):
    # start by creating a new Poll object with its "question" set
    search = Search()
    search.query = "Test"
    search.query_date = timezone.now()

    # check we can save it to the database
    search.save()

    # now check we can find it in the database again
    all_search_in_database = Search.objects.all()
    self.assertEquals(len(all_search_in_database), 1)
    only_search_in_database = all_search_in_database[0]
    self.assertEquals(only_search_in_database, search)

    # and check that it's saved its two attributes: question and pub_date
    self.assertEquals(only_search_in_database.query, "Test")
    self.assertEquals(only_search_in_database.query_date, search.query_date)

The test fails with this:
self.assertEquals(only_search_in_database.query_date, search.query_date)
AssertionError: datetime.datetime(2013, 1, 16, 21, 12, 35, tzinfo=<UTC>) != datetime.datetime(2013, 1, 16, 21, 12, 35, 234108, tzinfo=<UTC>)

I think what's happening is that the milliseconds are being truncated after saving to the database.  Can that be right?  I'm running MySQL v 5.5.  Is MySQL truncating the date?

A: Django 1.8 now supports milliseconds.

Previously, Django truncated fractional seconds from datetime and time values when using the MySQL backend. Now it lets the database decide whether it should drop that part of the value or not

A: According to the mysql developer site:

A DATETIME or TIMESTAMP value can include a trailing fractional
  seconds part in up to microseconds (6 digits) precision. Although this
  fractional part is recognized, it is discarded from values stored into
  DATETIME or TIMESTAMP columns.

A: Django ORM converts DateTimeField to Timestamp in mysql. You can confirm that by looking at the raw sql doing ./manage.py sqlall <appname>
In mysql timestamp does not store milliseconds.
The TIMESTAMP data type is used for values that contain both date and time parts. TIMESTAMP has a range of '1970-01-01 00:00:01' UTC to '2038-01-19 03:14:07' UTC.

It is a bug in MySql which appears to be fixed in v5.6.4,  The Bug
Noted in 5.6.4 changelog.

MySQL now supports fractional seconds for TIME, DATETIME, and
TIMESTAMP values, with up to microsecond precision.

A: Update: This is really old answer and no longer relevant.
DJango ORM does not yet support microseconds for MySQL. They deliberately truncate the microsecond component. If you are using MySQL 5.6.4 or above, you can apply the following change to DJango code to get this working as expected:
This is a 3 line change. Hope Django developers include it. You can follow the ticket here: https://code.djangoproject.com/ticket/19716

In "db/backends/mysql/base.py"
function "def value_to_db_datetime(self, value)"
Change from:
return six.text_type(value.replace(microseconds=0))

to:
return six.text_type(value)

In "db/backends/mysql/base.py"
function "def value_to_db_time(self, value)"
Change from:
return six.text_type(value.replace(microseconds=0))

to:
return six.text_type(value)

In "db/backends/mysql/creation.py"
In definition of "data_types"
Change from:
'DateTimeField': 'datetime',

to:
'DateTimeField': 'datetime(6)',


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A mobile DJ is the perfect choice of entertainer for most weddings, parties and events at Stretton Methodist Church. Choosing the right disc jockey can help make or break your function - you need to ensure that their experience level, style of music and presentation of equipment matches your expectations. Your DJ can also act as your Master of Ceremonies, and keep the whole event swinging - making the necessary announcements, filling in between bands and other entertainers, and sending guests home or off to bed in high spirits.
The following DJs and discos all cover the Burton upon Trent area and are available for events at Stretton Methodist Church.


When buying a used Ford GT it is important to know a bit about the car model. It took inspiration from the 1960 Ford GT40 and was released in 2004. It was only in production for two years and there were a total of three and a half thousand sales. When it first came out, the demand for the car generally outpaced the supply. It sold for a very premium price as the car was highly anticipated. Customers were making orders even before the car was in production.
The GT is an impressive car which showcases a supercharged mid-mounted V8 engine. It also has a carbon fiber engine cover and a superplastic-formed aluminum body panels, complete with an aluminum chassis. During its time, the technology of the GT was beyond other cars in its class. It tested at 0 - 60 mph in 3.2 seconds during a run conducted by Insideline.


To help you plan your busy weekend, we have partnered with Mommy Poppins, the FREE online resource curating the best things to do for kids and families in NYC. Each week they will provide us with their top weekend picks for events and activities in New York City.
Thanks to an inevitable Halloween sugar rush, your kids are going to have a lot of energy to burn off this weekend. Luckily, there are lots of great things to do, including two FREE Day of the Dead festivals, Diwali celebrations at the Asia Society and the Rubin Museum, and even some better-late-than-never Halloween fun.
Another November Go List pick: Head to the New Victory Theater to see this sumptuous puppet adaptation of the classic fairy tale by Italy's Carlo Colla & Sons Marionette Company. Parents of princess-obsessed preschoolers take note: This 90-minute show is faithful to the original story which is much darker than Disney's version, so it's probably best to heed the age recommendation of 7 and up. $14-$38. If you attend on Saturday, you can also try a puppetry family workshop for an extra $17.
Visit Mommy Poppinsto find more events, activities and things to do with your kids this weekend.


text:
require File.expand_path(File.dirname(__FILE__) + '../../../test_helper')
require 'rbbt/util/tmpfile'
require 'test/unit'
require 'rbbt/knowledge_base'
require 'rbbt/knowledge_base/query'

class TestKnowledgeBaseQuery < Test::Unit::TestCase

  EFFECT =StringIO.new <<-END
#: :sep=" "#:type=:double
#SG TG Effect
MDM2 TP53 inhibition
TP53 NFKB1|GLI1 activation|activation true|true
  END

  EFFECT_OPTIONS = {
    :source => "SG=~Associated Gene Name=>Ensembl Gene ID",
    :target => "TG=~Associated Gene Name=>Ensembl Gene ID",
    :persist => false,
    :identifiers => datafile_test('identifiers'),
    :undirected => true,
    :namespace => "Hsa"
  }

  EFFECT_TSV = TSV.open EFFECT, EFFECT_OPTIONS.dup

  KNOWLEDGE_BASE = KnowledgeBase.new Rbbt.tmp.test.kb_foo2, "Hsa"
  KNOWLEDGE_BASE.format = {"Gene" => "Ensembl Gene ID"}

  KNOWLEDGE_BASE.register :effects, EFFECT_TSV, EFFECT_OPTIONS.dup

  def test_subset_all_persist
    Misc.benchmark(1000) do
      assert_equal 6, KNOWLEDGE_BASE.subset(:effects, :all).length

      assert_equal 4, KNOWLEDGE_BASE.subset(:effects, :all).target_entity.uniq.length
      assert_equal %w(Effect), KNOWLEDGE_BASE.subset(:effects, :all).info.first.keys
    end
  end

  def _test_subset_all_persist_format
    assert KNOWLEDGE_BASE.subset(:effects, :all).target_entity.reject{|e| e =~ /^ENS/}.empty?
  end

end


Place the miso, ginger, garlic, mirin and vinegar in a large bowl and mix to combine. Add the chicken, toss to coat and cover with plastic wrap. Place in the refrigerator to marinate for 30 minutes. Remove from the fridge and set aside for 30 minutes to come to room temperature.
Fill a large saucepan two-thirds full with the oil and place over medium heat until the temperature reaches 180°C (350°F) on a deep-frying thermometer. Place the self-raising flour and cornflour in a large bowl and whisk to combine. Place the marinated chicken in the flour mixture and press to coat.
Cook the chicken, in batches, for 2–3 minutes or until golden and cooked through. Drain on paper towel and keep warm.To make the miso mayonnaise, place the mayonnaise, mustard, miso and vinegar in a small bowl and mix to combine. Sprinkle the chicken with the cayenne pepper and serve with the mayonnaise, mint and pickled ginger. Serves 6.
This recipe is a must make - super tasty. I actually made it into fried chicken burger's and every single person raved on about it!


Awards are presented to member companies that consistently have OSHA-recordable injury and fatality rates at levels lower than industry standard and implement internal company safety practices above and beyond basic compliance.
The Zero-Injury Award recognizes those member companies that have worked a full calendar year without recordable incidents.
ing a slight increase in participation and winners for the year.
including the NECA Safety Professionals Conference.
Applications must be received by February 26, 2016—only one application submission is required for both awards. Finalists will be selected after an evaluation of applications on March 18. NECA will notify award recipients by April 4, and awards and letters will be distributed by June 6.
For more information on NECA's Safety Awards Program, go to www.necanet.org.
Safe and sound productivity in electrical construction is the objective in the electrical business. NECA's Safety Excellence and Zero Injury Awards program is an elite and growing safety recognition program focused on recognizing thriving companies that excel in multiple areas of their safety and health programs.
Energized electrical systems and circuits, even if only temporary, present hazards for electrical workers and others in construction. Safe work practices should always be applied when working on temporary wiring. Electrical contractors are usually responsible for installing the permanent wiring during construction. In addition, construction projects require temporary electrical wiring that must be installed and used by all the trades during the construction of buildings or structures. Temporary installations are often viewed as being less dangerous than permanent electrical installations, but temporary electrical wiring on projects should be treated no differently than permanent electrical wiring with regard to the workmanship, wiring methods, and safe work practices.
of the NEC provides minimum requirements for installing temporary electrical power and lighting. NFPA 70E, Standard for Electrical Safety in the Workplace provides the requirements for electrical workplace safety.
NECA is proud to announce that it has just published the NECA Guide to Temporary Power. This new publication provides essential resources for electrical contactors to help them get it right when it comes to temporary power responsibilities. This new guide is organized in an easy-to-read format and includes links to valuable resources that assist in attaining compliance and safety of temporary power systems. The guide contains essentials such as how to effectively plan the installation, how to prefabricate where practical, and how to implement safe work practices when handling temporary wiring, designs, OSHA compliance, and more. Along with the extensive resources, this product provides access to all Letters of Interpretation from OSHA relative to temporary installations. This new guide is a must for all electrical contractors that have to design, install, maintain, and remove temporary power systems. Get your copy today.
The NECA Guide to Temporary Power is available at www. necanet.org/store.
Temporary wiring is often treated as an afterthought—after all, "it's only temporary." But temporary power is not an anything goes situation. Whether electrical workers are handling temporary or permanent wiring, safe work practices are required.