Founded in 1939 by Joe Albertson in Boise Idaho it is the second largest grocery store in America with over 2200 stores and 250000 employees. As a growing company there is always a need for new personnel. You can check out all the available job opportunities through the Albertsons application link at the end of the page.
Albertsons feels responsible to care for the local community it operates in and the people it serves. To meet its obligation to society the company is involved in many projects and partners with organizations that facilitate food drives, youth development and health and nutrition in schools. Other than this they also believe in conserving the environment and practice sustainable business and are proponents of recycling in daily operations.
In addition to being a socially responsible company Albertsons takes good care of its employees too. The company offers employees an opportunity to grow by encouraging an environment of promoting from within and many of the top management executives started with the company at entry level positions. They offer retirement benefits and vacation pay too amongst many other benefits.
There are many locations and positions you can apply for. You can access the free application form for all of Albertsons careers and also send in a direct application through an online application. You can also download application form and send in a printable application form.
As a leading company with an expanding employee base there are many opportunities for people at various levels with different interests and skills. The main areas in which you can send in applications for work are, retail positions, corporate positions, supply chain positions and pharmacy positions.
There are both part time and full time openings based on individual experience and knowledge for which you can apply online. Some of the positions currently available are Pharmacy Manager, Transportation Driver, Courtesy Clerk, Transportation Dispatcher, Director Training and Technology, Field Services Technician, Plant Supervisor, Office Assistant, Corporate Director Warehouse and Internal Auditor.
How old do you have to be to work at Albertsons?
You have to be at least 16 years old to be eligible for working at and putting in an Albertsons application for the available Albertsons jobs online. Some employment positions may require extended work hours and specific experience and qualification requirements, make sure to research requisites before putting in your application.
Albertsons jobs mean you have an opportunity to grow and excel in what you love doing. There are innumerable opportunities to advance your career as they truly believe in employee development at every level of the workforce. You can see how to apply for Albertsons online by clicking the application link at the end of the page.
Pharmacy Manager – If you are someone with a passion for helping your customers in meeting their medical needs not by just filling in prescriptions but also building rapport with them and providing advice and offering assistance with picking out over the counter products, then this may be your opportunity to do just that. At Albertsons the pharmacy manager is responsible in building lasting relationships with customers. In this job you can earn about $130000 per year.
Office Assistant – As an office assistant your responsibilities would be the processing of company payrolls and communication with management when needed. If you are someone who can work as part of a team and yet be a self starter then this may be the right job for you. In this role which requires you to possess excellent communications skills along with customer service skills you can expect to earn about $26000 annually.
Internal Auditor – This is an experienced job position and requires an understanding of the industry in which the company operates. If you are someone who is well organized with excellent analytical and time management skills then this may be the right position for you. You can expect a salary of about $50000 per year in this role.
Transportation Dispatcher – In this role you would be required to ensure all mail is delivered to the right store and also deal with all paperwork in relation to orders and deliveries. If you have excellent interpersonal and organizational skills then this may be the right job for you. In this role you can expect to earn about $27000 per year.
Preparing yourself before the big day with a set of sample interview questions will surely help you confidently tackle these same questions on the interview day for the Albertsons Jobs you have applied for. Below are a list of a few such questions to help prepare you.
Narrate an instance where you had to appease an irate customer? In the retail services industry there are many jobs where you have to deal directly with the customer and keeping them happy is of utmost importance. Be prepared to answer such a question with reference to past job experiences.
Where do you see yourself in three years? At Albertsons most of the employees are promoted from within and therefore candidates who share the company philosophy of career advancement would surely strike a positive note with the hiring manager. So be prepared to answer a question about your future career progression.
Are you flexible in your work schedule? With many jobs at the retail stores there is a requirement for the availability to work odd hours and weekends. It is of utmost importance that the candidates are able to commit to being able to work these shifts before the final decision to get an individual on board is taken. Therefore before you apply for jobs at Albertsons be sure that you are available to work any shift you are assigned to if you are offered a position.
How did you hear about us? For any organization marketing is a big part of its existence, for jobs it is important for the employer to know which means of advertising are most effective and are best at reaching the highest number of the targeted audience. So be sure to handle something like this on the interview day.
Is there anything you would like to ask us? Through this question the recruiter is trying to understand what is going on in the mind of the prospective employee with regard to the position applied for and the company in general. Be sure to ask questions that reflect your enthusiasm towards the position applied for and the ability to grow with the organization.
If you are applying for an entry level position then be sure to highlight aspects of your past qualifications and character that align with requirements of the job. Be sure to proofread your printable application for Albertsons jobs to check for any errors and omissions.
Dress appropriately for the interview paying special attention not to appear too artificial or made up. Be your natural self with an air of self assurity, no one expects you to wear a three piece suit for an entry level store position but neatness and modesty surely make a difference and go a long way in making a statement about you as a person.
Give yourself sufficient time to find and arrive at the venue of the interview a little before the scheduled time so you can gather your thoughts and have some time to calm your nerves. Make sure you take with you all required paperwork and documents including your resume if needed.
During the interview maintain an upright and welcoming posture, maintain eye contact and speak clearly and confidently. Be sure to have a firm handshake and maintain a pleasant facial expression. Body language speaks volumes about your personality to someone who has only just met you. Try your best and leave the rest to fate.


BuildForce Canada has launched a series of blogs entitled Building a Foundation of Respect designed to help recruit and retain underrepresented groups in the construction industry by creating a respectful and inclusive workplace.
The blog posts explore issues such as communication and behaviour and provide research tools and checklists to help recruit and retain workers with diverse backgrounds. Since last March, there have been 11 instalments, aimed at site staff, supervisors and leaders.
The latest blog post, as of press deadline, discusses diversity and inclusivity in the workplace and provides solutions and tips such as active listening, communicating assertively, not aggressively, overcoming bias and assumptions, focusing on "larger picture" issues rather than individual positions and trying to understand the reasons behind the positions people are taking, to name a few.
The blogs are put together with input from the project steering committee which is comprised of mostly women working in the industry from across the country, Ferreira said.
"One of the obstacles that has been identified is that often women in particular tend to find that the construction workplace can be a barrier," stated Ferreira.
The blogs are part of a larger initiative, he added.
An online tool is currently being refined and is expected to launch this year to address some of the behavioural patterns that have been identified as particularly problematic in recruiting and retaining underrepresented groups within the industry, Ferreira explained. BuildForce is working on the initiative with the Status of Women Canada.
"Our intention is to develop a tool that will allow supervisors to identify behaviour that can potentially be disrespectful that could impact recruitment and also retention within the industry and also suggest corrective measures," said Ferreira, adding it is designed as a learning tool.


Last week, I spent a wonderful afternoon with Jean Steubing Maggrett, whom I've known for something over nine years, and Willard Bond, the father of my friend Gretchen. They met for the first time last week, but both of them lived and painted in the heady creative days of Greenwich Village and the Lower East Side in the late 1940s, 50s, and early 60s, and Gretchen and I got to listen to them share memories.
Jean lived in the Village, in a loft studio on East 9th Street, opposite the building that became the site of the 9th Street Show, which introduced the work of the New York School to the world. Jean, a member of the Art Club, and a student of Hans Hofmann's, suggested the space, and collected the money to rent it, and on opening night a floodlight from her studio lit up an enormous canvas sign Franz Kline had painted to announce the exhibit, which hung from an upper floor above the show.
Willard Bond lived and worked in an old synagogue in the Lower East Side, where he painted large contemporary nudes and created painted ceramic murals, including the one at the entrance of the Eugene O'Neill Theatre. He played the drums too, often with other jazz musicians, and Gretchen shared with us a photo of him playing onstage in the production of a Bertolt Brecht play.
Today, Willard is known for his marine paintings, which you can see at http://www.annapolismarineart.com/WillardBond.html, and which you see in the book on the table in front of them.
A note on how I created this image: although it has some of the qualities of block prints, I actually drew it digitally, in Photoshop (with a mouse, not a stylus).
December already! I'm busy preparing for Black Stallion Winery's Holiday Open House & Art Show on December 10th. I'll be bringing my greeting cards and matted reproductions of my paintings, as well as some original paintings.
I may include a few of the relief print-and-stencil (and block print) paintings I've been working on this last month, depending on how much I can squeeze into my space, too.
Black Stallion Winery is at 4089 Silverado Trail, just north of Napa, and the event will be held from noon until 4 p.m. I'll be in good company, with some of my favorite Napa Valley Open Studios colleagues. You can learn more at http://blackstallionwinery.ewinerysolutions.com/events.


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From the creator of the award winning international hitsThe Adventures of Alvin Sputnik: Deep Sea Explorer and It's Dark Outside comes a new low-fi puppetry spectacular. Get ready for an epic adventure that bends time and melts your heart .
Keeping you at the edge of your seat, Bruce will sweep you away on an epic adventure of love and revenge. He may be just a yellow block of foam with a pair of disembodied hands, but BRUCE is out to prove he's got a heart of pure gold. Bruce is a two-man, one-puppet show that fuses mime and puppetry in a non-stop rollercoaster of action, adventure and low-fi nostalgia.
Please note, we recommend that audiences for Bruce are 15+.


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Чха  — 7-я буква кхмерского алфавита, согласная группы «А», в слоге может быть только инициалью, глухая постальвеолярная аффриката.

Подписные чха в кхмерском и телугу:

Литература
 Грамматика кхмерского языка. Ю.А.Горгониев. М.2009

кхмерский алфавит
пали

redpajama_set_name: RedPajamaWikipedia


At 11:00am, on Sunday, November 27th, the UCSB Men's Soccer team visits Creighton University in the 3rd Round of the NCAA Tournament. The Gauchos defeated the Providence College Friars 3-2 at Harder Stadium last week to advance to the Sweet Sixteen for the first time in two years. Now, the 15 seed UCSB team will travel to the Midwest to face the number 2 team in the nation, Creighton University. These teams have met once before just a season ago when the Blue Jays topped the Gauchos at Harder Stadium 1-0. UCSB will be looking to make history in the cold weather as they are trying to become the first California team to ever win in Omaha, Nebraska.
Brent Pella and Mitchell Clements will have the call from Meredith Field at Harder Stadium. The pregame show starts at 10:45am, and kickoff is scheduled for 11am.


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UK Gas Prices Slump Due to Low Demand and Strong Wind Power Output
September 6, 2019 September 6, 2019 daniel	659MW of electricity production., A Record Year for Wind Power, Subsequent Gas Price Slumps, The Future of Renewables in the UK, UK Gas Prices Slump Due to Low Demand and Strong Wind Power Output, Wind Power, Wind Turbine
Renewables are now powering a third of the UK's electricity demand, with provisional government figures stating that wind power accounted for 17.1% of the country's electricity supply last year. This is a record high, compared to just 14.8% in 2017.
While a step in the right direction towards a renewables-powered economy, gas prices are taking a toll. A recent report by Reuters owed mixed gas prices to weaker wind output forecasts and an oversupplied system. National Grid data showed a 158.6 mcm (million cubic meters) daily gas supply, compared to a demand forecast of 132.5 mcm.
This resulted in the British gas system being oversupplied with 26.1 mcm of gas.
A Record Year for Wind Power
Windpower Monthly reported that in 2018, the grid saw an addition of 700MW (megawatts) of onshore wind capacity, bringing the onshore total to 13.5GW (gigawatts) and the offshore total to 8.2GW, thanks to a 1.2GW addition being brought online.
Falls in nuclear, coal and gas power output were offset by a boost in renewables production, with the total electricity generation for 2018 going down 1.4% to a total of 334TWh. Wind, solar and bioenergy were the primary renewables to owe for this shift.
The Department for Business, Energy and Industrial Strategy stated that renewables collectively accounted for 111.1TWh (33.3%) of energy production in 2018, up from 29.7% in 2017. This was partly due to several offshore expansions and new wind sites being brought online.
For instance, the world's largest operational offshore project, Walney Extension, accounted for 659MW of electricity production.
Subsequent Gas Price Slumps
In the gas industry, the September contract went down to 29.9 pence per therm, falling by 0.59 pence. Traders claimed that the day-ahead rise of 0.45 pence was due to a correction in the previous week's low price levels. Additionally, Tuesday's expected decline in wind power output was purported to raise demand for gas power.
While this may be mixed news for traders, businesses can now benefit from these dropping gas prices. With around 80% of British businesses overpaying for gas, now is a good time to compare prices and find a more affordable supplier. Utility Bidder provides businesses with commercial gas deals and supplier comparisons across the most reliable companies.
The Future of Renewables in the UK
Record-breaking figures can be seen across the board for renewables production, demonstrating its unstoppable momentum. While solar PV load factors dropped in Q4 of 2018, hydro, bioenergy, onshore and offshore wind production skyrocketed.
Deputy chief executive of Renewable UK; Emma Pinchbeck, told Windpower Monthly that flexible power, fair markets, cheap generation and innovation funding are compelling enough reasons to push the government to recognise the position of renewables in the future of the UK's power production.
With renewables becoming an increasingly prominent component of power generation in the UK, it's no surprise that traditional energy producers are taking a hit. Only time will tell how this will affect the economy as a whole. For now, businesses can benefit from cheap gas while it lasts.
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redpajama_set_name: RedPajamaCommonCrawl


At HSE Australia, we pride ourselves on our ability to quickly understand and respond to clients. We do this in a way that goes further than reacting to requests so we can pre-empt needs. Our market intelligence about current and potential clients will be second to none. Proactively we seek opportunities to inform and provide our clients with greater understanding about the solution that is right for them. Call us Today!


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redpajama_set_name: RedPajamaGithub


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Augerums landskommun var en tidigare kommun i Blekinge län.

Administrativ historik
Kommunen inrättades som landskommun i Augerums socken i Östra härad i Blekinge när 1862 års kommunalförordningar trädde i kraft.

År 1888 bröts Tjurkö ut för att bilda egen kommun. I kommunen inrättades 14 februari 1908 Långö municipalsamhälle. År 1934 inkorporerades en del av Augerum inklusive municipalsamhället (som då upplöstes) i Karlskrona stad. Vid den landsomfattande kommunreformen 1952 lades Augerum och Lösens landskommun samman till storkommunen Lyckeby, som sedan 1967 uppgick i Karlskrona stad.

Området tillhör sedan 1971 Karlskrona kommun.

Politik

Mandatfördelning i valen 1938–1946

Referenser

Indelningar i Karlskrona kommun
Tidigare kommuner i Blekinge län
Sveriges kommuner 1863-1951


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State Impact
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eMPF
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close alertFHLB Des Moines will be closed on Monday, January 18 in observance of Martin Luther King Jr. Day. We will return to normal operating hours Tuesday, January 19.
FHLB Des Moines MENU
Home / About / News / $51.5 Million in Affordable Housing Grants to Benefit More Than 2,600 Families and Individuals
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$51.5 Million in Affordable Housing Grants to Benefit More Than 2,600 Families and Individuals
posted on Monday, December 16, 2019 in Community News
A collaborative effort between financial institutions and community housing providers will create affordable housing opportunities for more than 2,600 low-income families and individuals this holiday season. Fifty-two financial institutions helped facilitate $51.5 million in Competitive Affordable Housing Program grants through the Federal Home Loan Bank of Des Moines (FHLB Des Moines or the Bank).
From construction of new affordable housing to the rehabilitation of existing homes and rental properties, the funds will benefit low-income families, seniors, persons with disabilities, homeless and at-risk youths.
"FHLB Des Moines is proud of the work our members do each and every day to build strong communities," said Mike Wilson, President and CEO of FHLB Des Moines. "We are committed to providing funding and affordable housing solutions to help meet their local needs."
The Competitive Affordable Housing Program encourages partnerships between FHLB Des Moines member financial institutions and local housing organizations throughout the Bank's district, consisting of 13 states and three U.S. Pacific territories.
Since the inception of the Affordable Housing Program in 1990, FHLB Des Moines member financial institutions have been awarded over $685 million in grants to help more than 115,000 families and individuals in find safe and affordable housing.
Every year, FHLB Des Moines returns 10 percent of its net income to benefit communities in its district.
For a complete listing of 2019 Competitive Affordable Housing Program recipients, click here. For more information, contact the Bank's Community Investment Department by calling 800.544.3452, ext. 2400.
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The factor which has sustained Apple's competitive position in PC is "Digital Hub" Strategy. Apple obtained major of market share in the early days. However, Apple sometimes struggled with other competitors in the market of PC manufacturer due to decline of average selling price (ASP) and emergence of lower priced models equipped with Wintel.
The Macintosh can be the preferred "hub" to control, integrate, and add value to people who are becoming entrenched in a digital lifestyle, using digital devices such as digital cameras, portable music players. Although several industry insiders were anxious for impact of alternative technology such as digital devices (smartphones, PSIII), Steve Jobs had a clear view to position the Macintosh at the heart of business strategy for Apple. Apple's control of both hardware and software is regarded as unique strength, focusing on home consumers' lifestyle. Apple reinforces in four categories to support strength of Mac as "Digital Hub" for other devices in addition to restructuring inside of company such as hiring Taiwanese contract assemblers for manufacturing.
CPU of Apple had been weakness since Macintosh was introduced into the market in 80's. Although Mac had advantage in terms of ease of use, industrial design, and technical elegance, Apple had suffered its slow speed and lack of compatible causing sales decline. Apple introduced Macintosh line-ups mounting Intel-Microprocessor with faster speed and less power-hungry. It resulted in success to capture the consumers expecting to buy Intel Based PC. Apple also launched PC which can run Windows OS with Windows applications. These movements can offset a longstanding disadvantage of Mac.
""digital Hub" Strategy" OtherPapers.com. 05 2011. 2011. 05 2011 <https://www.otherpapers.com/essay/digital-Hub-Strategy/2599.html>.
""digital Hub" Strategy." OtherPapers.com. OtherPapers.com, 05 2011. Web. 05 2011. <https://www.otherpapers.com/essay/digital-Hub-Strategy/2599.html>.
""digital Hub" Strategy." OtherPapers.com. 05, 2011. Accessed 05, 2011. https://www.otherpapers.com/essay/digital-Hub-Strategy/2599.html.


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Корыткув-Дужи () — деревня в Билгорайском повяте Люблинского воеводства Польши. Входит в состав гмины Билгорай. По данным переписи 2011 года, в деревне проживало 718 человек.

География
Деревня расположена на юго-востоке Польши, в пределах Сандомирской низменности, на правом берегу реки , на расстоянии приблизительно 9 километров к северо-западу от города Билгорай, административного центра повята. Абсолютная высота — 217 метров над уровнем моря. Через населённый пункт проходит региональная автодорога .

История
В период с 1975 по 1998 годы деревня входила в состав Замойского воеводства.

Население
Демографическая структура по состоянию на 31 марта 2011 года:

Примечания

Населённые пункты Билгорайского повета


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DMEPOS Round 2021 2021
Registration Bidding Bid Evaluation Contracting Round 2021
Competitive Bidding Areas
Events Handouts
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CMS Announces Registration and Bid Window Dates for Round 2021 of the DMEPOS Competitive Bidding Program
The Centers for Medicare & Medicaid Services (CMS) has announced the bidding timeline with specific dates for the registration and bid window for Round 2021 of the Durable Medical Equipment, Prosthetics, Orthotics, and Supplies (DMEPOS) Competitive Bidding Program. The bid window was originally scheduled to open in June, but in an effort to provide bidders with additional time to prepare, CMS will now open the bid window on July 16, 2019.
CMS encourages bidders to take advantage of this additional time to prepare by utilizing the comprehensive bidder education materials. An array of important information and tools, including the Request for Bids Instructions, bidding rules, a Lead Item Pricing Calculator, fact sheets, checklists, and Bid Preparation Worksheets, are on the Competitive Bidding Implementation Contractor (CBIC) website. These resources are designed to ensure that DMEPOS suppliers interested in bidding receive the information and assistance they need to submit complete bids by the close of the bid window.
Webcast Series
As part of its bidder education program, CMS has announced an upcoming series of three webcasts to assist bidders, sureties, and other interested stakeholders with the key components of the Round 2021 bidding process.
May 14, 3:00 - 4:00 p.m. EDT - Bid Surety Bond and Lead Item Pricing
May 21, 3:00 - 4:00 p.m. EDT - Preparing and Submitting Financial Documents
May 28, 3:00 - 4:00 p.m. EDT - Registering and Submitting a Bid
You may register for each webcast by clicking on the corresponding webcast title above. You will also find other information, such as resources and audio requirements, on the registration page. You will be able to submit questions during the webcast; however, if you have questions before or after the webcasts, please submit them to cbic.admin@palmettogba.com with "Webcast Question" in the subject line. These webcasts will also be recorded and handouts will be available for those who are unable to attend the live sessions by visiting Education Events on the CBIC website.
As a reminder, the CBIC is the official information source for bidders and bidder education. CMS cautions bidders about potential inaccurate information concerning the DMEPOS Competitive Bidding Program posted on websites other than the CBIC website. Bidders that rely on this information in the preparation or submission of their bids could be at risk of submitting a non-compliant bid.
In addition to viewing the information on the CBIC website, bidders are encouraged to call the CBIC customer service center at 877-577-5331 between 9 a.m. and 5:30 p.m. prevailing Eastern Time, Monday through Friday.
Bid Evaluation
Round 2021
Keep up with the latest information about the DMEPOS Competitive Bidding Program by signing up for our email newsletter.
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You might already have a trash drawer that makes it easy to hide away the bin, but how many times have you dropped something behind the trash can? Reaching anything that fell back there – let alone cleaning that space – can be a challenge.
You might already have a trash drawer that makes it easy to hide away the bin, but how many times have you dropped something behind the trash can? Reaching anything that fell back there – let alone cleaning that space – can be a challenge. Now, Scavolini makes it easier to reach things in the back of the cabinet or clean the space under your trash bins with a system that allows you to swing the trash can all the way out. So much more convenient!


Every March, thousands of Minnesotans throughout the state collaborate to raise food and funds for their local food shelves and Minnesota FoodShare. Join individuals, businesses and corporations, schools, community organizations, and faith communities in helping Minnesota's nearly 300 food shelves support over 3 million annual visits.
Your participation in the March Campaign as a Supporter ensures you receive March Campaign materials and support from Minnesota FoodShare, are connected with your local food shelf, and enjoy a bit of joyful competition.
Please note: You are asked to designate what organization you plan to support (food shelf, Minnesota FoodShare, etc.). If you would like to be matched with a food shelf in your area, please mark the appropriate field. Support for Minnesota FoodShare will ultimately be distributed 100% to all March Campaign participating food shelves.
We'd love to follow & share your March Campaign updates on social media. Let us know how you are connected.
Thank you for joining the 2019 March Campaign.
Questions? Please contact Minnesota FoodShare.


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5 Signs You Developed Stockholm Syndrome In Your Abusive Relationship
Categories Abusive relationship
Different types of people can develop Stockholm syndrome at different times in their lives. Most commonly, children of abusive parents and people who were kidnapped become victims of this weird phenomenon.
When people are in emotionally charged situations for too long, they develop this as a means of survival. At some point, it's easier to feel empathy and love for the abuser than to fight them.
People who were subjected to awful conditions because of their abuser depend on the smallest acts of kindness from them.
You may have developed this syndrome if you were in an abusive relationship before. If you're not sure and you haven't still gone to therapy for it, maybe this could be your final push to seek professional help.
1. Without knowing, you were constantly in survival mode
2. You saw his small acts of kindness as a reward
3. He made you cut off everyone else
4. You claim to love him even though he abused you
5. You thought there was no way out
You can develop Stockholm syndrome if you were constantly in survival mode during your relationship. You were always anxious about what he'd do next so you kept yourself quiet and small at all times.
This also meant that you would do everything he asked of you because the alternative was punishment for misbehaving.
In an abusive relationship, everything the abuser does is to inflict pain on the victim and instill fear in them. For that exact reason, you would always do anything to keep him happy. Sometimes, that wasn't enough.
A victim completely depends on the small act of "kindness" (which are more like acts of human decency) from their abuser.
It's one of the first signs of Stockholm syndrome, where you genuinely thought he was doing you a favor when he decided not to raise his voice or his hand at you.
In a healthy relationship, you wouldn't even have to worry about those things.
But even at the times where he was nice to you, you were anxious. You could never feel completely at ease in his presence. You'd always expect the worst.
You thought that he was doing you a favor. Your abuser will do anything he can to isolate you from the most precious people around you because that's how he can gain complete control over you.
When you don't have anyone else in your life, he has authority over you and the decisions you make. You can't even ask anyone else for advice and they won't try to take you away from him.
However, an abuser will do this in a way that'll seem like he's doing it for your own good. Every single time you'd talk about someone, he'd tell you stories about how they're bad for you.
At one point, you started to believe him and his stories, despite them being blatant fabrications. An abuser develops great lying and manipulation tactics in order to keep his victim compliant.
So when you only have him in your life, you start to cling to him. You start to do anything and everything out of fear that he'll leave you.
How can you truly love an abuser?
Love is something beautiful, something that's reserved for real connections between us and the people who treat us right. Unfortunately, we tend to fall in love with people who don't deserve it.
But it's extremely rare to love an abuser. It appears like a coping mechanism. Just like a child loves his abusive parents. A child doesn't know that those people aren't good for him, he just knows that they provide and so, for some reason, the child asks for the approval of those people.
This also happens when however unsafe the environment is, it's still the safest you have.
That's why even though he's still an awful human being who manipulates you and treats you like trash, you love him. He hurts you physically, emotionally, and mentally, but you still choose him over anyone and everyone else.
It doesn't matter how hard you tried, you simply couldn't bring yourself to love anyone more than you loved him. You couldn't even love yourself enough to leave him.
The biggest sign that you truly did develop Stockholm syndrome is when you start to believe that there's no way out so you need to make the best of it. You start to rationalize why you can't leave him to the point where you start to believe it.
You convince yourself and those around you that it's not as bad as it seems. He did such a great job at brainwashing you, that now you can't see past this problem you found yourself in.
It doesn't matter how many times people try to get you out of the relationship, you always find some way to convince them that everything's okay. You believe that he's the best caretaker and that you deserve all the horrifying things he does to you.
But you need to know that there's always a way out. There's always someone willing to help you through this process. Someone out there will be your support system and it's never too late to leave. You're never trapped.
If you need to stay long enough to gather more evidence to get a restraining order against him, then do so. But you don't have to stay with someone who'd probably treat an animal better than he treats you.
Is He A Narcissist Or Just Confident? 6 Ways To Tell The Difference
When You Cheated On Her, You Made A Choice To Break Her Heart


If you go to a fashion show in Paris there is one woman that you will notice for sure: Diane Pernet. She doesn't adopt every trend around but created her consistent very own "shaded black" look. In this interview Diane Pernet talks to fashion designer Bruno Pieters. Directed by Jason Last.
Bill Barminski is a self taught artist whose work extends across a broad range of mediums including painting, interactive media, music videos, graphic design and music. His work includes solo exhibition of paintings and drawings, unique projects such as E3 booth design for Nokia Interactive, billboard design for Absolut Vodka, designing gas masks based on cartoon characters and directing and co-directing music videos.


There is no such postseason carrot in front of the Angels (22.25), A's (24.5) and Padres (26.25). Of the state's five teams, the Angels (4-3 last week) enjoyed the biggest rise with an average of two spots.
Going out of state, but worth noting, the Cubs, who seemed to have clinched the N.L. Central around the Fourth of July, have been ranked no lower than second in USA Today's poll. The team won its 100th game Monday night with a romp over the Pirates.


text:
Minettia albonito är en tvåvingeart som beskrevs av Charles Howard Curran 1926. Minettia albonito ingår i släktet Minettia och familjen lövflugor.

Artens utbredningsområde är Puerto Rico. Inga underarter finns listade i Catalogue of Life.

Källor

Lövflugor
albonito


text:
These environment variables are defined in the image.

__APP_LANG__
>"python"

__APP_ROOT__
>"/opt/app-root"

__JBOSS_IMAGE_NAME__
>"radanalyticsio/radanalytics-pyspark-py36"

__JBOSS_IMAGE_VERSION__
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__PATH__
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__PYTHONPATH__
>"/opt/spark/python"

__RADANALYTICS_PYSPARK__
>"1.0"

__SPARK_HOME__
>"/opt/spark"

__SPARK_INSTALL__
>"/opt/spark-distro"

### Configuration

The image can be configured by defining these environment variables
when starting a container:

## Labels

__io.cekit.version__
> 2.2.7

__io.k8s.description__
> Platform for building a radanalytics Python 3.6 pyspark app

__io.k8s.display-name__
> radanalytics pyspark-py36

__io.openshift.expose-services__
> 8080:http

__io.openshift.s2i.scripts-url__
> image:///usr/libexec/s2i

__io.openshift.tags__
> builder,radanalytics,pyspark

__name__
> radanalyticsio/radanalytics-pyspark-py36

__org.concrt.version__
> 2.2.7

__version__
> 1.0


text:
\section{Introduction}

It is well known that the study of localization properties in
a disordered material can be translated to the study of correlation
functions in a lattice field theory,
with an internal hyperbolic supersymmetry (SUSY),
\cite{sw,efetov-Adv,efetov-book, wegner}.
In the physics literature one usually assumes the sigma model
approximation, which is believed to
capture the essential features of the energy correlations and
transport properties of the underlying quantum system.

The SUSY field theories  which are equivalent to the Anderson
tight-binding model and random band
matrices are  difficult to analyze with mathematical
rigor in more than one dimension. In this context, Zirnbauer
introduced a  lattice field model which may be thought
of as a simplified version of one of Efetov's nonlinear sigma models
\cite{toymodel,migdal-kad}. In Zirnbauer's  sigma model the
field takes values in a target space  $H^{(2|2)}$ which is a
supermanifold extension of the hyperbolic plane.  The model is
expected to reflect the spectral properties of random band matrices,
such as  localization and diffusion, in any dimension.
In  \cite{toymodel} localization was established in one
dimensional chain by analyzing the transfer matrix.
We refer to  \cite{DSZ} for a historical
introduction and motivations.

More recently  the existence of a `diffusive' phase at low
temperatures ($\beta $ large) has been proved for the $H^{(2|2)}$
model in  three or more dimensions, see \cite{DSZ}. For $\beta $ small,
a localized phase was expected.
However, unlike  conventional  statistical mechanics models,
the $H^{(2|2)}$ model has a  noncompact hyperbolic symmetry
and so high temperature expansions cannot be done in the usual way.
In fact, it is known that the bosonic hyperbolic sigma model in 3D has no
localized phase because its effective action is convex for all $\beta >0$.
On the other hand, numerical simulations \cite{td} indicated that the SUSY
hyperbolic sigma model has a phase transition
for  $\beta < \beta_{c}\simeq 0.038$.

In this paper we show that for any dimension $d>1$ the $H^{(2|2)}$
model exhibits localization
for $\beta^{1/2}\ln \beta^{-1} \leq 1 /(2d-1)$.
Thus the sigma model approximation
captures  the physics of both localization and diffusion.
Moreover, for a one dimensional chain we recover localization
for all values of
$\beta $. Localization is also expected in 2D (see \cite{DSZ} section 1.4
and 4.3),   for all values of $\beta$ by both the  renormalization group
and by a simple saddle analysis.
However, a rigorous proof is still missing for this case.

The techniques employed in this work to prove localization are quite
different from the ones used in \cite{DSZ} to prove extended
states. The two papers can be read independently. The only
common point is the use of supersymmetry to prove some identities.
In the present case supersymmetry is applied only to prove that
the partition function is normalized to 1.
We refer to  Section 4 and Appendix C in \cite{DSZ} for an introduction to
supersymmetric Ward identities.

\subsection{The model}

Let $\Lambda$ be a finite subset in $ \mathbb{Z}^{d}$ and $t_{j}$
a real variable for each site $j\in \Lambda $. We will consider periodic
or Neumann boundary conditions. Accordingly for any two points
$x,y\in \lambda $,  $|x-y|$ will denote the Euclidian distance
on the lattice (Neumann bc) or the periodized lattice (periodic bc).

We introduce the probability measure
\begin{equation}\label{eq:tmeasure}
 d\mu_{\Lambda }^{\varepsilon} (t) =
\ \prod_{j\in \Lambda} \frac{dt_{j}}{\sqrt{2\pi }}
e^{-F_{\Lambda } (\nabla t)}e^{- M^{\varepsilon }_{\Lambda } (t)}
\times
\left[\sqrt {\det D^{\varepsilon }_{\Lambda } (t)}\   \right]
\end{equation}
where $dt_{j}$ is the Lebesgue measure, $F$ is the kinetic part and
$M$ is the mass term:
\begin{align}
F_{\Lambda } (\nabla t)  &= \beta \sum_{(jj')\in \Lambda }
(\cosh(t_j - t_{j'})-1) \cr
M^{\varepsilon }_{\Lambda } (t) &=
\sum_{j\in \Lambda }  \varepsilon_{j} (\cosh t_j -1)\ .
\label{eq:FG}
\end{align}
We denoted by $(jj')$ the nearest neighbor pairs $|j-j'|=1$.
 $D^{\varepsilon }_{\Lambda } (t)$ is a positive definite matrix  defined by
\begin{equation}\label{eq:Mmatrix}
\begin{array}{lll}
(D^{\varepsilon }_{\Lambda })_{ij} & = 0  & |i-j|>1\\
(D^{\varepsilon }_{\Lambda })_{ij}   & = -\beta   & |i-j|=1\\
(D^{\varepsilon }_{\Lambda })_{jj}  & = \beta\left[2d+V_{j}\right]
+ \varepsilon_{j} e^{-t_{j}} & i=j\ ,\\
\end{array}
\end{equation}
\begin{equation}\label{eq:Vdef}
V_{j} =  \sum_{k, (jk)}  \left[e^{t_{k}-t_{j}} -1 \right]
\end{equation}
and $\varepsilon_{j}\geq 0$ are regularizing parameters
that are necessary to make the integral well defined.
We remark that $V_{j}+2d>0$ for all $t$ configuration and all
$j$.
Finally $\beta >0$ is a parameter that can be interpreted
as a measure of the temperature or the disorder.

Note that the definition of the matrix $D$ differs from the
one introduced in \cite{DSZ} eq. (1.1). It is not difficult
to see that when you mix the term $\sum_{k}t_{k}$ and the determinant
in the effective
action (1.2) of \cite{DSZ} the result
is indeed the determinant of the  matrix $D$ above, more precisely
\begin{equation}\label{eq:Adef}
A_{ij} = e^{t_{i}} D_{ij} e^{t_{j}} =
\left\{\begin{array}{ll}
0 &\ |i-j|>1\\
- \beta e^{t_{i}+t_{j}} & \ |i-j|=1\\
\beta \sum_{i', (ii')} e^{t_{i}+t_{i'}} & \ i=j\\
\end{array} \right.
\end{equation}
where $A$ is the matrix  introduced in \cite{DSZ} eq. (1.1).
For technical reasons the above representation is more convenient
when we want to prove diffusion as in \cite{DSZ} while the other
is more practical when we study localization (except in the proof
of Theorem~2 where we will go back to the ``diffusion'' representation
for a while).
\medskip

Now, for any function $f (t)$ we will define its average by
\begin{equation}\label{eq:av}
\langle f (t) \rangle \ = \ \int  d\mu^{\varepsilon }_{\Lambda } (t) \ f (t)\ .
\end{equation}

\paragraph{Normalization  and choice of $\varepsilon_{j}$}
By internal supersymmetry (see \cite{DSZ} Sect. 4 and eq.(5.1)) this
measure is already normalized to 1 so the partition function is
\begin{equation}\label{eq:Z}
Z^{\varepsilon }_{\Lambda } = \int\  d\mu^{\varepsilon }_{\Lambda } (t) \  = 1
\ .
\end{equation}
This identity is true regardless of the boundary conditions
and the values of $\beta $ or $\varepsilon_{j}$ as long as
the integral is well defined. Since we consider $\beta>0$ fixed
we only need $\varepsilon_{j}$ to be non zero at \textit{one lattice point}.
In the following we will consider three cases.
\begin{enumerate}
\item{} Uniform pinning: $\varepsilon_{j}= \varepsilon \leq
\frac{1}{|\Lambda |}$ for all $j\in \Lambda $. The measure is
translation invariant with periodic bc. The correlation
function in this case has a divergent prefactor $1/\varepsilon$ in the
localized regime.

\item{} Two pinnings: $\varepsilon_{x}=\varepsilon_{y}=O (1)$
and $\varepsilon_{j}=0$ for all other points. This is the analog of
inserting two electrical contacts in a metal sample.

\item{} One pinning at $j=0$:  $\varepsilon_{0}=O (1)$ and
$\varepsilon_{j}=0$ for all other points.  This is more suitable for
an interpretation of the model as a random walk in a random environment.
Our results suggest that edge reinforced random walk (see
\cite{MR}) will also localize when the reinforcement is strong.

\end{enumerate}

\paragraph{The observable.} We will study the correlation function
\begin{equation}\label{eq-G}
G_{xy} := D^{-1}_{xy}
\end{equation}
where $x,y$ can be
any two points on the lattice such that both
$\varepsilon_{x}>0 $ and $\varepsilon_{y}>0$. This observable
does not give information on localization properties in the
case of one pinning point. In such case a good observable
to study is
\begin{equation}\label{eq:obs1p}
{\cal O }_{j} = e^{+t_{j}/2}
\end{equation}
where $j$ is any point in the lattice.
This observable is analogous to  $x^{1/4}_{e} $ in the notation
of \cite{MR} where $e$ is an an edge $(j,j')$.

\subsection{Main results}

\begin{theor}\label{th-1}
Let $\varepsilon_{x}>0$, $\varepsilon_{y}>0$
 and $\sum_{j\in \Lambda }\varepsilon_{j}\leq 1$.
Then for all $0<\beta <\beta_{c}$  ($\beta_{c} $  defined
below)   the correlation
function $G_{xy}$ \eqref{eq-G} decays exponentially
with the distance $|x-y|$. More precisely:
\begin{equation}\label{eq:decay1}
\langle G_{xy}\rangle \leq  \
C_{0} \left( \varepsilon_{x}^{-1} + \varepsilon_{y}^{-1}\right) \,
\left[I_{\beta}\, e^{\beta (c_{d}-1)}\, c_{d}  \right]^{|x-y|}\ ,
\end{equation}
where $c_{d}=2d-1$,
$C_{0}$ is a constant and
\begin{equation}\label{xidef}
I_{\beta} = \sqrt{\beta } \int_{-\infty}^{\infty} \frac{dt}{\sqrt{2\pi } }
 e^{-\beta  (\cosh t -1) } \ .
\end{equation}
Finally  $\beta_{c}$ is defined by:
\begin{equation}\label{eq:betac}
I_{\beta_{c}} e^{\beta_{c} (c_{d}-1)} c_{d}  =1 \ .
\end{equation}
Our estimates hold uniformly in the volume.
\end{theor}

\paragraph{Remark 1}
The integral $I_{\beta }$ satisfies $I_{\beta }<1$ $\forall \beta >0$:
\begin{equation}\label{eq:Ib}
I_{\beta } = \sqrt{\tfrac{\beta }{2\pi }}
\int_{-\infty}^{\infty} dt\,
 e^{-\beta  (\cosh t -1) }\ <\
 \sqrt{\tfrac{\beta }{2\pi }}  \int_{-\infty}^{\infty} dt\,
\cosh (t/2)\, e^{-\beta  (\cosh t -1) } \ = \ 1\ .
\end{equation}
More precisely
\begin{equation}\label{eq:Iest}
I_{\beta } \leq \
\left\{\begin{array}{ll}
 (\ln \beta^{-1} )\sqrt{\beta } & \beta <0.15\\
c e^{-\frac{1}{\beta }} & \beta >>1\\
\end{array}
 \right.
\end{equation}
where $c>1$ is a constant.

\paragraph{Remark 2}
The constraints $\varepsilon_{x}>0$ and $\varepsilon_{y}>0$  exclude the case
of one pinning. Moreover $\sum_{j\in \Lambda }\varepsilon_{j}\leq 1$
implies $\varepsilon\leq \frac{1}{|\Lambda |} $ when
$\epsilon_{j}=\varepsilon $ is constant. The case of one pinning
is covered by Theorem~2 below.

\paragraph{Main consequence}
For $d=1$ the critical beta is $\beta_{c}=\infty$ since
\begin{equation}\label{eq:betac1}
I_{\beta } e^{\beta (c_{d}-1) } c_{d} = I_{\beta }<1\quad \forall \beta>0
\ .
\end{equation}
Therefore the correlation function decays exponentially for all
values of $\beta $.
On the other hand for $d>1$ we obtain localization only for small
$\beta $ since $\beta_{c}< (2d-1)^{-2}<1$.

\begin{theor}\label{th-2}
Let $\varepsilon_{0}=O (1)$  and $\varepsilon_{j}=0$ $\forall j\neq 0$.
Then for all $0<\beta <\beta_{c}$  ($\beta_{c} $  defined
below), the field $t_{x}$ wants to be as negative as $-|x|$.
More precisely $\langle {\cal O}_{x}\rangle$  (defined in \eqref{eq:obs1p})
decays exponentially
with the distance $|x-y|$
\begin{equation}\label{eq:decay3}
\langle {\cal O}_{x}\rangle \leq  \  C_{0}
\,\left[I_{\beta}\, e^{\beta (c_{d}-1)}\, c_{d}  \right]^{|x|}  \ ,
\end{equation}
where $c_{d}$ and $I_{\beta }$ are defined in Theorem~1 above
and $C_{0}$ is a constant.  Finally
 $\beta_{c}$ is defined by:
\begin{equation}\label{eq:betacc}
I_{\beta_{c}} e^{\beta_{c} (c_{d}-1)} c_{d} =1\ .
\end{equation}
Our estimates hold uniformly in the volume.
\end{theor}

\paragraph{Main consequence.}
For $d=1$ the critical beta is $\beta_{c}=\infty$ since
\begin{equation}
I_{\beta } e^{\beta (c_{d}-1)}  c_{d} = I_{\beta }<1\quad \forall \beta >0\ .
\end{equation}
Therefore  $\langle {\cal O}_{x}\rangle$  decays exponentially for all
values of $\beta $.
On the other hand for $d>1$ the result holds only for small
$\beta $ since $\beta_{c}< (2d-1)^{-2}<1$.

\paragraph{Acknowledgments.} It is our pleasure to thank
A.~Abdesselam for discussions and
suggestions related to this paper. A special thanks to M.~Zirnbauer
who explained the model to us and shared his many insights.

\section{Proof of Theorem \ref{th-1}}
\setcounter{equation}{0}

We want to estimate
\begin{equation}\label{eq:Gav}
\langle G_{xy}\rangle\ =\ \int d\mu^{\varepsilon }_{\Lambda } (t)   G_{xy}
=\int \prod_{j\in \Lambda} \frac{dt_{j}}{\sqrt{2\pi }}
e^{-F_{\Lambda } (\nabla t)}e^{- M^{\varepsilon }_{\Lambda } (t)}
\times
\sqrt{\det D^{\varepsilon }_{\Lambda } (t)} \  D^{-1}_{xy}\ .
\end{equation}

The proof in done in four steps.

\paragraph{Step 1.} We mix the observable $G_{xy}$ and a piece of the
probability measure namely $\sqrt{ \det D}$. The key identity is
\begin{equation}\label{eq:ident}
\sqrt{\det D^{\varepsilon }_{\Lambda } (t)} \  D^{-1}_{xy}=
\sqrt{ D^{-1}_{xy} }\ \sqrt{ D^{-1}_{xy}\det D^{\varepsilon }_{\Lambda } (t) }
\end{equation}
(remember that $D_{xy}^{-1}>0$).
The first term is bounded by
\begin{equation}\label{eq:Gxyb}
D^{-1}_{xy} \leq
\left( \frac{1}{\varepsilon_{x} e^{-t_{x} }} +
\frac{1}{\varepsilon_{y} e^{-t_{y} }} \right)  \ .
\end{equation}
This  is proved in Lemma \ref{lemma1}.
Inserting this in \eqref{eq:Gav} we have
\begin{equation}\label{eq:1}
\langle G_{xy}\rangle\ \leq \
 \int d\nu^{\varepsilon }_{\Lambda } (t)
\sqrt {[  D^{-1}_{xy}  \det D^{\varepsilon }_{\Lambda } (t)]}
\left( \frac{e^{t_{x}/2}}{\sqrt{\varepsilon_{x} }}
+ \frac{e^{t_{y}/2}}{\sqrt{\varepsilon_{y} } }  \right)
\end{equation}
where
\begin{equation}\label{eq:numeasure}
 d\nu^{\varepsilon }_{\Lambda } (t)  =  \prod_{j\in \Lambda}
 \frac{dt_{j}}{\sqrt{2\pi }}
e^{-F_{\Lambda } (\nabla t)}e^{- M^{\varepsilon }_{\Lambda } (t)} \ .
\end{equation}
Unlike the measure $d\mu^{\varepsilon }_{\Lambda}$ given by
\eqref{eq:tmeasure}, this measure is no longer normalized to 1.

\paragraph{Step 2.} We need to extract some decay in the distance $|x-y|$.
This is hidden in $D^{-1}_{xy}\,{\det} D$. By some combinatorial arguments
(the proof is given in Lemma \ref{lemma2} )
we can write
\begin{equation}\label{eq:2}
[ D^{-1}_{xy}  {\det} D^{\varepsilon }_{\Lambda } (t)]\
=\  \sum_{\gamma_{xy}}
\beta^{|\gamma |}  \
\det D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }   }
\end{equation}
where the sum ranges over  non self intersecting paths $\gamma$ made of nearest
neighbor pairs in $\Lambda $ starting at $x$ and ending at $y$.
Let  $|\gamma|,$ denote the length of $\gamma$ and let
$\Lambda _{\gamma } $ be the corresponding set of lattice points
and set $\Lambda _{\gamma }^{c} =\Lambda\backslash \Lambda _{\gamma }$.
Finally $D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }  }$  is the matrix
one obtains by deleting the rows and columns corresponding
to the lattice points $j\in \Lambda_{\gamma }$. It is
is exactly like the matrix
$D^{\varepsilon }_{\Lambda }$, but defined on the complement of $\gamma $,
$\Lambda _{\gamma }^{c}$ and with modified masses:
\begin{equation}
\begin{array}{lll}
D^{\tilde{\varepsilon }}_{ij} & = 0  & |i-j|>1\\
D^{\tilde{\varepsilon }}_{ij}  & = -\beta   & |i-j|=1\\
D^{\tilde{\varepsilon }}_{ii}  & = \beta\left[ 2d + \tilde{V}_{i}
 \right]
+ \tilde{\varepsilon }_{i} e^{t_{i}} & i=j\ ,\\
\end{array}
\label{eq:Dtilde}\end{equation}
where $i,j\in \Lambda^{c}_{\gamma} $ and
\begin{align}
\tilde{V}_{i} &=  \sum_{k\in\Lambda^{c}_{\gamma} , (ki)}
\left[ e^{t_{k}-t_{i}} -1\right] \\
 \tilde{\varepsilon }_{i}&=  \varepsilon_{i} + \beta
\sum_{k\in \Lambda_{\gamma }, (ki)} e^{t_{k}}\ .\label{eq:Vtilde}
\end{align}
By combining \eqref{eq:1}  and \eqref{eq:2}   we have
\begin{equation}\label{eq:3}
\langle G_{xy}\rangle\ \leq \
 \sum_{\gamma_{xy}} \beta^{|\gamma |/2 }
\int d\nu^{\varepsilon }_{\Lambda } (t)
\left( \frac{e^{t_{x}/2}}{\sqrt{\varepsilon_{x} }}
+ \frac{e^{t_{y}/2}}{\sqrt{\varepsilon_{y} } }  \right)
\sqrt {\det D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }}} \ .
\end{equation}

\paragraph{Step 3.}  The measure $ d\nu^{\varepsilon }_{\Lambda } (t) $
defined in \eqref{eq:numeasure}  can be factored as a measure on
$\Lambda_{\gamma } $
times a measure on the complement set $\Lambda_{\gamma }^{c} $
\begin{equation}
 d\nu^{\varepsilon }_{\Lambda } (t)\ = \
 d\nu^{\varepsilon }_{\Lambda_{\gamma } } (t)
\ d\nu^{\varepsilon }_{\Lambda_{\gamma }^{c} } (t) \
 e^{-F_{\partial\gamma  } (\nabla t)} \ ,
\end{equation}
where
\begin{equation}\label{eq:Fborder}
F_{\partial\gamma  } (\nabla t)\  =\
 \sum_{(j,k), k\in \Lambda_{\gamma }, j\not\in \Lambda_{\gamma }}
\beta\, (\cosh (t_{j}-t_{k})-1)
\end{equation}
describes the interaction between $\Lambda_{\gamma } $ and
$\Lambda_{\gamma }^{c} $. Then the integral in  \eqref{eq:3}
can be written as
\begin{equation}\label{eq:4}
\int d\nu^{\varepsilon }_{\Lambda } (t)
\left( \frac{e^{t_{x}/2}}{\sqrt{\varepsilon_{x} }}
+ \frac{e^{t_{y}/2}}{\sqrt{\varepsilon_{y} } }  \right)
\sqrt {\det D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }}} \ = \
 \int d\nu^{\varepsilon }_{\Lambda_{\gamma } } (t)  \
\left( \frac{e^{t_{x}/2}}{\sqrt{\varepsilon_{x} }}
+ \frac{e^{t_{y}/2}}{\sqrt{\varepsilon_{y} } }  \right)
\  Z^{\gamma }_{\Lambda^{c}_{\gamma }} (t_{\gamma })\ ,\end{equation}
where we defined
\begin{align}\label{eq:Zcond}
Z^{\gamma }_{\Lambda^{c}_{\gamma }}(t_{\gamma }) &=\
\int d\nu^{\varepsilon }_{\Lambda^{c}_{\gamma } } (t)\
\sqrt {\det D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }}}\ \
  e^{-F_{\partial\gamma  } (\nabla t)}\nonumber\\
&= \int \prod_{j\in\Lambda^{c}_{\gamma }}\  \frac{dt_{j}}{\sqrt{2\pi }}
\  e^{-F_{\Lambda^{c}_{\gamma } } (\nabla t)}\
e^{- M^{\varepsilon }_{\Lambda^{c}_{\gamma } } (t)}\
 \sqrt{ {\det} D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }  } }
\ \   e^{-F_{\partial\gamma  } (\nabla t)} \ .
\end{align}
Note that $Z^{\gamma }_{\Lambda^{c}_{\gamma }}(t_{\gamma })$ is
still a function of the $t$ variables along the path
$\{t_{k} \}_{k\in \Lambda_{\gamma } }$ (they are not integrated).
Now $Z^{\gamma }_{\Lambda^{c}_{\gamma }}(t_{\gamma })$
   is almost equal to the partition function
\begin{align}\label{eq:Zcond1}
1= Z^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }} =&
 \int
d\mu^{\tilde{\varepsilon } }_{\Lambda^{c}_{\gamma } }  (t)  =
 \int d\nu^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma } } (t)
\sqrt {\det D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }}} \nonumber \\
=& \int \prod_{j\in\Lambda^{c}_{\gamma }} \frac{dt_{j}}{\sqrt{2\pi }}
\  e^{-F_{\Lambda^{c}_{\gamma } } (\nabla t)}
e^{- M^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma } } (t)} \
 \sqrt{ {\det} D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }  } }\ ,
\end{align}
where
$Z^{\tilde{\varepsilon }}_{\Lambda_{\gamma }^{c}} =1$  by supersymmetry
(see \eqref{eq:Z}).
Comparing  \eqref{eq:Zcond} and \eqref{eq:Zcond1}
we see that there are two main differences:
\begin{enumerate}
\item [-] the mass term $M^{\varepsilon}_{\Lambda^{c}_{\gamma } }$
in  \eqref{eq:Zcond} depends on $\varepsilon $ instead of
$\tilde{\varepsilon }$ and is smaller than what it should be
\[
M^{\varepsilon}_{\Lambda^{c}_{\gamma } }\leq
M^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma } }
\]
since $M^{\tilde{\varepsilon }}$ contains additional mass terms;
\item [-] the exponent in \eqref{eq:Zcond} contains the additional factor
 $-F_{\partial\gamma  } (\nabla t)$ coming from the kinetic interaction
between points on $\Lambda_{\gamma }$ and points on $ \Lambda^{c}_{\gamma }$.
\end{enumerate}
This last term is helping us since it makes the integral
smaller. We will use it to recover the missing mass.
This is done in Lemma \ref{lemma3} below. The key ingredient
is a global translation on the $t$ variables.
The result is
\begin{equation}\label{eq:5}
\langle G_{xy}\rangle\ \leq \  e^{1}\
 \sum_{\gamma_{xy}}    \beta^{|\gamma |/2}
 e^{\beta |\partial\gamma | }
  \int d\nu^{\varepsilon }_{\Lambda_{\gamma } } (t)
  \left( \frac{e^{t_{x}/2}}{\sqrt{\varepsilon_{x} }}
+ \frac{e^{t_{y}/2}}{\sqrt{\varepsilon_{y} } }  \right)\ ,
\end{equation}
where $|\partial\gamma |\leq (2d-2)|\gamma |+2$ is the number of points
inside  $\Lambda_{\gamma }^{c} $ on the
boundary with $\Lambda_{\gamma }  $.

\paragraph{Step 4.} We are left with an integral along the path $\gamma $.
The integral in \eqref{eq:5} is bounded by
\[
 \int d\nu^{\varepsilon }_{\Lambda_{\gamma } } (t)
  \left( \frac{e^{t_{x}/2}}{\sqrt{\varepsilon_{x} }}
+ \frac{e^{t_{y}/2}}{\sqrt{\varepsilon_{y} } }  \right)
\ \leq\ \left(  \frac{I^{x}_{1}}{\sqrt{\varepsilon_{x} }}
 + \frac{I^{y}_{1}}{\sqrt{\varepsilon_{y} }}
 \right)  \ I_{2 }^{|\gamma|}\ ,
\]
where
\begin{align}\label{eq:Iint}
I^{x}_{1} &= \int_{-\infty}^{\infty} \frac{dt}{\sqrt{2\pi } }
e^{t/2} e^{-\varepsilon_{x} (\cosh t -1) } = \frac{1}{\sqrt{\varepsilon_{x} }}
\\
I_{2 } &= \int_{-\infty}^{\infty} \frac{dt}{\sqrt{2\pi } }
 e^{-\beta  (\cosh t -1) } = \frac{1}{\beta^{1/2} } I_{\beta }\
\end{align}
where $I_{\beta }$ was defined in \eqref{eq:Iint}.
In the same way $I_{1}^{y}= 1/\sqrt{\varepsilon_{y} }$.
Inserting all this we have
\begin{align}
\langle G_{xy}\rangle\ &\leq \  e^{1}
\left(\frac{1}{\varepsilon_{x} } + \frac{1}{\varepsilon_{y} } \right)
\sum_{\gamma_{xy}} \  e^{\beta |\partial\gamma | }\
(I_{\beta })^{|\gamma|}\label{eq:fb} \\
&\leq \ 2\ e^{1+2\beta }
\left(\frac{1}{\varepsilon_{x} } + \frac{1}{\varepsilon_{y} }
\right) \sum_{n\geq |x-y|}
\left(
  e^{\beta (2d-2)} \, I_{\beta }
\right)^{n} c_{d}^{n}\cr
& \leq  C_{0} \left(\frac{1}{\varepsilon_{x} } + \frac{1}{\varepsilon_{y} }
\right) \,
\left[\, e^{\beta (2d-2) } I_{\beta }\, c_{d}
\right ]^{|x-y|} \nonumber
\end{align}
where $c_{d}= (2d-1)$,  $C_{0}$ is a constant and the second
inequality holds since the
number of self-avoiding walks made of $n$ steps is bounded by
$2d(2d-1)^{n}<2c_{d}^{n}$ and $|\partial \gamma |\leq (2d-2)|\gamma |+2$.
Finally the sum over $n$ is convergent since
$(e^{\beta(2d-2)}I_{\beta}c_{d})~<~1$.

This concludes the proof of Theorem 1.{\hfill $\Box$}

\subsection{The lemmas}

\begin{lemma}\label{lemma1}
The following inequality holds:
\begin{equation}\label{eq:bound}
D^{-1}_{xy} \leq\   \frac{e^{t_{x}}}{\varepsilon_{x} } +
 \frac{e^{t_{y}}}{\varepsilon_{y} } \ .
\end{equation}
\end{lemma}

\paragraph{Proof}
By Cauchy-Schwartz inequality
\[
D^{-1}_{xy}\ \leq \
\sqrt{D^{-1}_{xx} } \ \sqrt{D^{-1}_{yy} } \leq \ D^{-1}_{xx}  +  D^{-1}_{yy}
\ .
\]
Since $(f,Df)\geq \ \sum_{j} \varepsilon_{j} e^{-t_{j}} f_{j}^{2}$
for any $f_{j}\in \mathbb{R}$ we have
\[
D^{-1}_{xx} \leq \  \frac{1}{\varepsilon_{x}e^{-t_{x}} } \ .
\]
Hence the result.
 {\hfill $\Box$}

\begin{lemma}\label{lemma2}
For any invertible matrix $M$ on $\Lambda $ we have the following
identity:
\begin{equation}\label{eq:id}
[ M^{-1}_{xy}  {\det} M]\
=\  \sum_{\gamma_{xy}= (j_{1},\dotsc j_{m})}
\left[ ( -M_{xj_{1}})  ( -M_{j_{1}j_{2}}) \cdots ( -M_{j_{m}y})  \right]\
{\det}_{\Lambda_{\gamma }^{c} } M
\end{equation}
where  $\gamma $ is any non self intersecting path starting at $x$
and ending at $y$.
\end{lemma}

\paragraph{Proof}
This is a classical formula arising from the fact that every permutation
can be decomposed as a product of cycles. One may derive it using the
representation of a determinant as a sum over a gas of disjoint non
self intersecting closed paths:
\[
\det M = \sum_{L_{1},\dotsc L_{p}} {\cal A} (L_{1})\cdots {\cal A} (L_{p})
\]
where  a loop $L= (j_{1},\dotsc ,j_{m})$  is an ordered set of
$m$ distinct points and
\begin{equation}
{\cal A} (L) =
\left\{\begin{array}{ll}
- \left[(-M_{j_{1}j_{2}}) (-M_{j_{2}j_{3}}) \cdots (-M_{j_{m}j_{1}}) \right]
& \ m>1\\
\quad M_{j_{1}j_{1}} &\  m=1\\
\end{array} \right.
\end{equation}
The sign $(-1)^{m-1}$ is the number of pairs inside the loop that
need to be exchanged in order to recover the trivial permutation.
Now since $[ M^{-1}_{xy}  {\det} M]= \frac{\partial}{\partial M_{yx}}
{\det} M $, the derivation selects only loops that contain the pair $yx$.
The corresponding matrix element disappears and the loop becomes
a path from $x$ to $y$. The sign $-1$ from $-M_{yx}$ cancels the global
$-1$ in front of the product. {\hfill $\Box$}

\begin{lemma}\label{lemma3}
For any configuration of $\{t_{k}|\ k\in \Lambda_{\gamma } \}$,
the conditioned partition function
$Z^{\gamma }_{ \Lambda^{c}_{\gamma }} (t_{\gamma })$ given by \eqref{eq:Zcond}
is bounded by
\begin{equation}\label{eq:Zbound}
 Z^{\gamma }_{ \Lambda^{c}_{\gamma }} (t_{\gamma }) \leq
e^{\beta \sum_{k\in \Lambda_{\gamma }}  d^{\gamma }_{k} (1-e^{t_{k}-t^{*}}) }
e^{\sum_{j\in \Lambda_{\gamma }^{c} } \varepsilon_{j} (1-e^{-t^{*}}) }\leq\
e^{\beta|\partial\gamma | }
e^{\varepsilon |\Lambda^{c}_{\gamma }|}\ ,
\end{equation}
where $t^{*}$ is any real number satisfying
\begin{equation}\label{eq:tbound}
t^{*}\geq 0\ ,\qquad \mbox{and}\qquad t^{*}\geq t_{k}\qquad  \forall k\in
\Lambda_{\gamma } \ ,
\end{equation}
and $ d^{\gamma }_{k}$ is the number of points nearest neighbor
to $k$ that do not belong to $\Lambda_{\gamma }$:
\[
 d^{\gamma }_{k} = \#\{j\not\in \Lambda_{\gamma }\ |\  |j-k|=1\} \ .
\]
\end{lemma}

\paragraph{Proof}
Before doing any bound we perform a global translation inside
the integral:
\begin{equation}
t_{j}\ \rightarrow\ t_{j}+ t^{*}\qquad \forall j\in
\Lambda^{c}_{\gamma }\ .
\end{equation}
Then inside the exponential we have:
\begin{align}
F_{\Lambda^{c}_{\gamma } } (\nabla t)  & \mapsto
F_{\Lambda^{c}_{\gamma } } (\nabla t)\\
M^{\varepsilon }_{\Lambda^{c}_{\gamma } } (t)
 & \mapsto M^{\varepsilon }_{\Lambda^{c}_{\gamma } } (t+t^{*}) \\
F_{\partial\gamma  } (\nabla t)& \mapsto
F_{\partial\gamma  } (\nabla t+t^{*})=\hspace{-0.5cm}
 \sum_{(j,k), k\in \Lambda _{\gamma }, j\in \Lambda^{c}_{\gamma }}
\hspace{-0.5cm}\beta\, (\cosh (t_{j}+t^{*}-t_{k})-1)\ .
\end{align}
In the numerator we have
\[
\left[
 \det D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma }  }
\right] \mapsto
\left[
 \det D^{\tilde{\varepsilon } e^{-t^{*}}}_{\Lambda^{c}_{\gamma }  }
\right]
\]
so the only effect of the translation is to modify the mass
$\tilde{\varepsilon }_{j}$ defined in \eqref{eq:Vtilde} at each lattice point.
After the translation
\begin{align}
&\hspace{-0,2cm}  Z^{\gamma }_{ \Lambda^{c}_{\gamma }}=
\int\left[ \prod_{j\in\Lambda^{c}_{\gamma }} \tfrac{dt_{j}}{\sqrt{2\pi }}
 \right]
\  e^{-F_{\Lambda^{c}_{\gamma } } (\nabla t)}
 \sqrt{
\det D^{\tilde{\varepsilon }e^{-t^{*}}}_{\Lambda^{c}_{\gamma }  } }
e^{- M^{\varepsilon }_{\Lambda^{c}_{\gamma } } (t+t^{*})}
e^{-F_{\partial\gamma  } (\nabla t+t^{*})
}\label{eq:2.28}\\
& = \int \left[ \prod_{j\in\Lambda^{c}_{\gamma }} \tfrac{dt_{j}}{\sqrt{2\pi }}
 \right]
 e^{-F_{\Lambda^{c}_{\gamma } } (\nabla t)}
e^{- M^{\tilde{\varepsilon }e^{-t^{*}} }_{\Lambda^{c}_{\gamma }}
\hspace{-0.2cm} (t)}
  \sqrt{
\det D^{\tilde{\varepsilon }e^{-t^{*}}}_{\Lambda^{c}_{\gamma }  } } \
 e^{M^{\tilde{\varepsilon }e^{-t^{*}} }_{\Lambda^{c}_{\gamma }}
\hspace{-0.2cm} (t)
 - M^{\varepsilon }_{\Lambda^{c}_{\gamma } } (t+t^{*})
-F_{\partial\gamma  } (\nabla t+t^{*})}
\cr
& = \int d\mu^{ \tilde{\varepsilon }e^{-t^{*}} }_{\Lambda_{\gamma }^{c} }
\hspace{-0.2cm} (t)\
\   e^{\sum_{j\in\Lambda^{c}_{\gamma }  } {\cal E}rr_{j} } \
\leq\    Z^{\tilde{\varepsilon }e^{-t^{*}} }_{ \Lambda^{c}_{\gamma }}
\ e^{\sum_{j\in\Lambda^{c}_{\gamma }  }
\sup_{t_{j}} {\cal E}rr_{j}  }
\ = \ \prod_{j\in\Lambda^{c}_{\gamma } }
   e^{ \sup_{t_{j}} {\cal E}rr_{j}  } \ ,
\nonumber\end{align}
where  we used
$ Z^{\tilde{\varepsilon }e^{-t^{*}} }_{ \Lambda^{c}_{\gamma }}=1$
(see \eqref{eq:Z}) and  we defined
\begin{equation}
\sum_{j\in\Lambda^{c}_{\gamma }  } {\cal E}rr_{j} = \left[
\ M^{\tilde{\varepsilon }e^{-t^{*}} }_{\Lambda^{c}_{\gamma } } (t)
- M^{\varepsilon }_{\Lambda^{c}_{\gamma } } (t+t^{*})\
- F_{\partial\gamma  } (\nabla t+t^{*})
 \right]\end{equation}
\begin{equation}
 {\cal E}rr_{j}  =
\tilde{\varepsilon}_{j} e^{-t^{*}} (\cosh t_{j}-1)\  -\
\varepsilon_{j}   (\cosh ( t_{j}+t^{*}) -1)
\ -\   \hspace{-0.4cm} \sum_{k\in \Lambda_{\gamma }, (j,k)}
\hspace{-0.4cm}\beta\  (\cosh (t_{j}+t^{*}-t_{k})-1).
\end{equation}
To conclude we shall prove that the right hand side of \eqref{eq:2.28}
is bounded by the rhs of \eqref{eq:Zbound}:
\[
 \ \prod_{j\in\Lambda^{c}_{\gamma } }   e^{ \sup_{t_{j}} {\cal E}rr_{j}  }
\ \leq \
e^{\beta \sum_{k\in \Lambda_{\gamma }}  d^{\gamma }_{k} (1-e^{t_{k}-t^{*}}) }
e^{\sum_{j\in \Lambda_{\gamma }^{c} } \varepsilon_{j} (1-e^{-t^{*}}) }\ .
\]
We distinguish two cases.

\paragraph{Case 1.}
When $j$ is far from the path $\gamma $ that is $|j-k|>1$ for all
$k\in \Lambda_{\gamma }$ then $\tilde{\varepsilon}_{j}=\varepsilon_{j} $
and we have
\begin{align}
 {\cal E}rr_{j}&= \varepsilon_{j} \left[
e^{-t^{*}} (\cosh t_{j}-1) -  (\cosh ( t_{j}+t^{*}) -1)
 \right]\cr
&
 = \varepsilon_{j} \left[ e^{t_{j}} \sinh (-  t^{*}) + 1 -
e^{-t^{*}}  \right] \ \leq \
\varepsilon_{j} ( 1 -  e^{-t^{*}} ) \ ,
\end{align}
where the last inequality holds for $t^{*}\geq 0$.

\paragraph{Case 2.}
When $j$ is near to the path $\gamma $ that is $|j-k|=1$ for some
$k\in \Lambda_{\gamma }$ then $\tilde{\varepsilon}_{j}=\varepsilon_{j} +
 \sum_{k\in \Lambda_{\gamma }, (j,k)} \beta e^{t_{k}} $ and
we have
\begin{align}
 {\cal E}rr_{j} =&\varepsilon_{j} \left[
e^{-t^{*}} (\cosh t_{j}-1) -  (\cosh ( t_{j}+t^{*}) -1)
 \right]  \\
&\quad + \beta \hspace{-0.5cm}
\sum_{k\in \Lambda_{\gamma }, (j,k)}
\left[  e^{t_{k}-t^{*}}  (\cosh t_{j}-1)   -
 (\cosh (t_{j}+t^{*}-t_{k})-1)
 \right]\cr
&= \varepsilon_{j} \left[ e^{t_{j}} \sinh (-  t^{*}) + 1 -
e^{-t^{*}}  \right] +  \beta
\hspace{-0.5cm}\sum_{k\in \Lambda_{\gamma }, (j,k)}
 \left[ e^{t_{j}} \sinh (t_{k}-  t^{*}) + 1 -  e^{t_{k}-t^{*}}  \right]
\cr
&\leq   \varepsilon_{j} (1 - e^{-t^{*}}) + \beta
\hspace{-0.5cm}\sum_{k\in \Lambda_{\gamma }, (j,k)}
( 1 -  e^{t_{k}-t^{*}})\ ,\nonumber
\end{align}
where the last inequality holds if  $t^{*}\geq 0$ and
$t^{*}\geq t_{k}$ $\forall k\in \Lambda_{\gamma }$.
\medskip

Finally
\begin{align}
\hspace{-1cm}\sum_{j\in\Lambda^{c}_{\gamma }  } {\cal E}rr_{j}
&\leq
 \ \sum_{j\in \Lambda^{c}_{\gamma }}\
[ \  \varepsilon_{j} (1 - e^{-t^{*}}) + \ \beta
\hspace{-0.2cm}\sum_{k\in \Lambda_{\gamma }, (j,k)}
( 1 -  e^{t_{k}-t^{*}}) \  ]\cr
& \leq  \beta \sum_{k\in \Lambda_{\gamma }}
d^{\gamma }_{k} (1-e^{t_{k}-t^{*}})
\ +\  \sum_{j\in \Lambda^{c}_{\gamma } }   \varepsilon_{j} (1-e^{-t^{*}})\ .
\end{align}
This concludes the proof of the lemma. {\hfill $\Box$}

\section{Proof of Theorem 2}
\setcounter{equation}{0}

The proof of Theorem~2 is almost identical to that of
Theorem~1.
This time there is no term $D^{-1}_{xy}$ ensuring we
can extract a path $\gamma $ connecting $x$ to $y$.
On the other hand,
since there is a pinning only at one position the matrix-tree
theorem (see \cite{abdesselam} for a simple proof and many references)
applied to the  ``diffusion'' representation $A$ given in \eqref{eq:Adef}
 of the matrix $D$ gives
\begin{equation}\label{eq:detp}
 {\det} A = \varepsilon_{0} e^{t_{0}}    \sum_{T} \prod_{jj'\in T}\,
(-A_{jj'}) =
\varepsilon_{0} e^{t_{0}} \sum_{T}
\prod_{(jj')\in T}\, \left[\beta e^{t_{j}+t_{j'}} \right]\ ,
\end{equation}
where the sum is over the spanning trees on $\Lambda $ made of
nearest neighbor pairs (since $A_{jj'}=0$ when $|j-j'|>1$).
Therefore each term in the sum contains a path $\gamma $ from $0$ to $x$.
Actually using \eqref{eq:detp} it is easy to see that
\begin{equation}
A^{-1}_{0x}\  {\det} A = \frac{1}{\varepsilon_{0}e^{t_{0}} }\  {\det} A
\end{equation}
for all $x\in \Lambda $, $x\neq 0$. Therefore
$\varepsilon_{0}e^{t_{0}}  A^{-1}_{0x}=1$ and
\begin{equation}
{\det} D = \varepsilon_{0}e^{t_{0}}\  A^{-1}_{0x} \ {\det} D =
 \varepsilon_{0} e^{-t_{x}}\   D^{-1}_{0x} {\det} D =
 \varepsilon_{0} e^{-t_{x}}\ \sum_{\gamma_{0x} } \beta^{|\gamma |}
  {\det}_{\Lambda_{\gamma }^{c} } D\ ,
\end{equation}
where $  A^{-1}_{0x}=e^{-t_{0}} D^{-1}_{0x}e^{-t_{x}}$ and
 in the last term we applied Lemma \ref{lemma2}.
Inserting this result in
\eqref{eq:tmeasure} we have
\begin{align}
&\langle {\cal O}_{x}\rangle \
= \  \int  d\mu^{\varepsilon }_{\Lambda } (t)
\  {\cal O}_{x}\ = \
 \int d\nu^{\varepsilon }_{\Lambda }(t)
\sqrt{\det D^{\varepsilon }_{\Lambda } }\  e^{t_{x}/2} \\
&\  = \sqrt{\varepsilon_{0} }
 \int d\nu^{\varepsilon }_{\Lambda }(t)   e^{t_{x}/2} e^{-t_{x}/2}
\sqrt{  \sum_{\gamma_{0x} } \beta^{|\gamma |}\,
 {\det} D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma } } } \cr
&\ \leq  \ \sqrt{\varepsilon_{0} }  \sum_{\gamma_{0x}} \beta^{|\gamma |/2}
\int d\nu^{\varepsilon }_{\Lambda_{\gamma } } (t)
  \ Z^{\gamma }_{\Lambda^{c}_{\gamma }} (t_{\gamma })\
\leq \  \sqrt{\varepsilon_{0} }  \sum_{\gamma_{0x}} \beta^{|\gamma |/2}
\int d\nu^{\varepsilon }_{\Lambda_{\gamma } } (t)\
e^{\beta |\partial \gamma |}\
\cr
&\ \leq   \sum_{\gamma_{0x}}\
 e^{\beta |\partial \gamma |}\
I_{\varepsilon_{0} } \  I_{\beta }^{|\gamma |}
\ \leq \ C_{0}\   (c_{d} e^{\beta (c_{d}-1)} I_{\beta })^{|x|} \ ,
\nonumber\end{align}
where  $ d\nu^{\varepsilon }_{\Lambda }(t) $ was defined
in \eqref{eq:numeasure},  $Z^{\gamma }_{\Lambda^{c}_{\gamma }} (t_{\gamma })$
in \eqref{eq:Zcond},  $I_{\beta }$ in \eqref{eq:Ib}
and the same definition holds for $I_{\varepsilon  }$.
In the  second line we used  $ {\det}_{\Lambda_{\gamma }^{c} } D =
{\det} D^{\tilde{\varepsilon }}_{\Lambda^{c}_{\gamma } } $  (see
\eqref{eq:Dtilde}). We used  Lemma~3
eq. \eqref{eq:Zbound} to bound
$Z^{\gamma }_{\Lambda^{c}_{\gamma }}(t_{\gamma })$.
Finally  the last inequality holds since $ (c_{d}e^{c_{d}-1} I_{\beta })<1$.
This concludes the proof of  Theorem~2.{\hfill $\Box$}

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


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text:
Export Credit Line for Yapi Kredi in Turkey
Supporting Export to Turkey of Machinery and Equipment Related to Renewable Energy and Climate Change Mitigation
The Japan Bank for International Cooperation (JBIC; Governor: Hiroshi Okuda) signed a general agreement with Yapi ve Kredi Bankasi A.S. (Yapi Kredi), a commercial bank in Turkey, for the purpose of offering an export credit line*1 amounting up to the equivalent of 90 million U.S. dollars (JBIC portion) to finance the sector of renewable energy and climate change mitigation (henceforth, "renewable energy and other related sectors").*2 *3 The credit line is cofinanced with private financial institutions, *4 which brings the overall cofinancing amount to the equivalent of 150 million U.S. dollars. This is the credit line offered by JBIC to Turkey that specializes in supporting the export of machinery and equipment in the field of renewable energy and other related sectors.
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*1 An export credit line is a form of export credit in which JBIC makes a commitment of the maximum amount of credit to be extended to foreign banks or other entities to finance the export of machinery and equipment from Japan.
*2 Although the loan agreement was already concluded on November 14, 2012, the press release was issued today, after the related procedures of relevant parties were completed.
*3 JBIC has separately signed on November 14, 2012, a general agreement with Yapi Kredi for the purpose of offering an export credit line amounting up to the equivalent of 210 million U.S. dollars (JBIC portion) to finance Japanese exports to Turkey and its neighboring countries (including in the Middle East, Central Asia and North Africa). See Press Release on November 19, 2012.
*4 Nippon Export and Investment Insurance (NEXI) will provide Buyer's Credit Insurance for the portion cofinanced by private financial institutions.
*5 Carbon dioxide Capture and Storage (CCS) is a technology that separates and captures carbon dioxide, the main culprit behind global warming, from emissions from fossil fuel power plants and stores it in deep waterbeds or geological formations.
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Moving into a care home can be viewed by the older person as the 'end of the line' after failure to attain a positive outcome following a rehabilitative process. Yet there are many situations where an older person's condition improves following admission to a home, despite no formal rehabilitation. While this suggests that rehabilitation potential can be missed and active rehabilitation should continue beyond the move, it also highlights the importance of supporting residents through the transition from active rehabilitation to long-term care.


Elon Musk speaks in Hong Kong in 2016.
DETROIT — For about four months, Elon Musk behaved, adhering to the terms of a court settlement that required his prolific posts on Twitter to be approved by a lawyer if there were a chance they could mislead investors.
Then came 13 words on Feb. 19 saying that Tesla would produce around 500,000 vehicles this year — a tweet that wasn't blessed by the person in charge of baby-sitting Musk's Twitter account.
While the tweet was posted and corrected after U.S. markets closed, regulators won't care much because stocks are traded nearly around the clock these days, Cox said. Tesla's stock rose by just $1.10, or less than 1%, the next day.
Musk's behavior is an indicator that he'll likely run afoul of the SEC again, regardless of any finding by Judge Nathan, said Erik Gordon, a law and business professor at the University of Michigan. "Musk just will not constrain himself," Gordon said.


text:
Mozambique revolution, no. 29 (1967 June-July)
FRBL.IMO
U^vvwu4a/^ MH Ux
CABO DELGADO PROVINCE
FRELIMO guerrillas have intensified their campaign in the
Cabo Delgado province and between the 1st of April and the
7th of June 28 military operations were carried out. %a  the
course of these, 16 military vehicals were destroyed and
over 350 Portuguese soldiers were killed.
- On the 3rd of April FKELIMO guerrillas ambushed a convoy
of 4 jeeps and 2 lorries, which v/ere escorting a shipment of
food supplies from MONTEPUEZ to MUEDA. 3 vehicals were
destroyed and more than 20 Portuguese soldiers were killed.
- 26th Aprils at 3-15 am. a platoon of FRELIMO forces attacked
the ennemy camp of MUGUIA, 30 kms. from the post of NATULO,
which controlled a strategic hamlet. In this attack 17
Portuguese soldiers were killed and about 20 were wounded.
After the attack, most of the people of that hamlet escaped
and asked for protection from FRELIMO forces.
- 1st of Mays FRELIMO guerrillas in cooperation with the
people blocked the road between CHITOLO and NJUDI with tree
trunks, and placed a mine under the tunks.On the same day, -
at 8.15 am. a group of enemy soldiers, with the mission to
build a bridge over the river MUMU arrived at the sabotaged
zone and started to clear the blockade. The mine exploded
killing 4 soldiers and wounding 1.   The Portuguese asked for
reinforcements from CHITOLO. Some hours later 5 lorries
loaded with soldiers arrived at the spot and cleared the
road. Our guerrillas prepared another ambush on the same
road, waiting for the return of the 5 lorries to CHITOLO.
When thefy returned they fell into the ambush. 2 lorries were
destroyed and 17 more enemy soldiers put out of action.
- On the'7th of June 1967, at 4 pm. a company of FRELIMO
guerrillas attacked the military post of MARERE, near the
coast. The enemy was on parade, for the lowering of the
flag. Our guerrillas advanced as far as the barbed wire and
attacked by surprise with bazooka, greneades and machine gun
fire.One platoon was annihilated and the other soldiers
Title Mozambique revolution, no. 29 (1967 June-July)
Description Contents: Editorial (p. 1); Communique (p. 4); Israeli aggression (p. 6); The United Nations Committee of 24 (p. 8); In memory of Sigauke (p. 10); Factual reports (p. 11); Ambush in a Shamba (p. 12); Vietnam (p. 14); On the death of Chief Luthuli (p. 16).
Creator Mozambique Liberation Front (FRELIMO). Information and Propaganda Department, Dar Es Salaam, U.R. of Tanzania
Full text FRBL.IMO MOZAMBIQUE LIBERATION FRONT U^vvwu4a/^ MH Ux CABO DELGADO PROVINCE FRELIMO guerrillas have intensified their campaign in the Cabo Delgado province and between the 1st of April and the 7th of June 28 military operations were carried out. %a the course of these, 16 military vehicals were destroyed and over 350 Portuguese soldiers were killed. - On the 3rd of April FKELIMO guerrillas ambushed a convoy of 4 jeeps and 2 lorries, which v/ere escorting a shipment of food supplies from MONTEPUEZ to MUEDA. 3 vehicals were destroyed and more than 20 Portuguese soldiers were killed. - 26th Aprils at 3-15 am. a platoon of FRELIMO forces attacked the ennemy camp of MUGUIA, 30 kms. from the post of NATULO, which controlled a strategic hamlet. In this attack 17 Portuguese soldiers were killed and about 20 were wounded. After the attack, most of the people of that hamlet escaped and asked for protection from FRELIMO forces. - 1st of Mays FRELIMO guerrillas in cooperation with the people blocked the road between CHITOLO and NJUDI with tree trunks, and placed a mine under the tunks.On the same day, - at 8.15 am. a group of enemy soldiers, with the mission to build a bridge over the river MUMU arrived at the sabotaged zone and started to clear the blockade. The mine exploded killing 4 soldiers and wounding 1. The Portuguese asked for reinforcements from CHITOLO. Some hours later 5 lorries loaded with soldiers arrived at the spot and cleared the road. Our guerrillas prepared another ambush on the same road, waiting for the return of the 5 lorries to CHITOLO. When thefy returned they fell into the ambush. 2 lorries were destroyed and 17 more enemy soldiers put out of action. - On the'7th of June 1967, at 4 pm. a company of FRELIMO guerrillas attacked the military post of MARERE, near the coast. The enemy was on parade, for the lowering of the flag. Our guerrillas advanced as far as the barbed wire and attacked by surprise with bazooka, greneades and machine gun fire.One platoon was annihilated and the other soldiers -4-


text:
Kristen Thometz | February 12, 2019 11:06 am
A pair of Illinois Institute of Technology researchers developing technology to detect early stage tumors have been named the winners of the university's Nayar Prize, which includes a $500,000 award.
The Agent-Dependent Early Photon Tomography (ADEPT) Cancer Imager was developed by Kenneth Tichauer, associate professor of biomedical engineering, and Jovan Brankov, director of the university's Advanced X-ray Imaging Lab and associate professor of electrical and computer/biomedical engineering.
Last week, IIT announced the duo won the final round of the inaugural Nayar Prize, which was established in 2015 to encourage university faculty, staff and students to develop breakthrough innovations that will produce meaningful results with a societal impact. Including previous rounds of funding, the ADEPT team has received $800,000 in funding through the Nayar Prize competition.
Tichauer and Brankov teamed up in 2015 to develop the technology with the intent of finding smaller tumors in the lymph nodes of breast cancer patients.
"Physicians are often faced with this very important decision of whether or not to give a patient chemotherapy after they have surgically removed the primary cancer or completed the mastectomy," Tichauer said in an IIT video about the technology. "The decision is currently based on whether or not cancer has spread to the lymph nodes."
Currently, the process to detect whether cancer has spread to a patient's lymph nodes involves slicing a sample of the lymph node, dyeing it and then making a diagnosis, which can take up to 24 hours.
"The problem is that they will cut two or three slices and look at only the surface," Tichauer said in a statment. "So they are looking at less than 1 percent of the tissue volume."
The ADEPT Cancer Imager dyes the entire lymph node, rather than a small sample, and uses an advanced laser imaging system that allows pathologists to find tumors that are 10 times smaller than those found using conventional methods, according to researchers.
"In 10 minutes the imager will map the cancer within a lymph node in 3D," Tichauer said. "Then a pathologist can guide the cut of the node and verify if it is cancer."
Researchers estimate that more than 40,000 women will be properly diagnosed annually using the technology, allowing them to begin "critical, lifesaving chemotherapy" when it is more effective, Tichauer said.
While research has been focused on breast cancer, Brankov said the technology can have widespread applications, especially in drug development. Cancers are composed of different types of cells, yet current drugs only target one type of cancer cell, according to Brankov. Using the ADEPT system researchers can determine the composition of the cancer, including a breakdown of the different types of cells within the cancer, and then use that information for targeted drug treatment, he said.
Researchers are planning a clinical trial of the ADEPT system in breast cancer through a partnership with Sanford Research in Sioux Falls, South Dakota, and the University of Chicago Department of Pathology.
"Our vision for the ADEPT system is for it to become an essential tool in every hospital's cancer pathology lab and throughout the drug-development labs of every pharmaceutical company and academic medical center," Tichauer said in a statement. "This will prolong the lives of cancer patients and improve their quality of life by identifying cancer early and by enabling life-saving drugs to be brought to market."
Contact Kristen Thometz: @kristenthometz | kthometz@wttw.com | (773) 509-5452
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text:
FIS Releases New Look for Its Bill Pay Interface
FIS has released a new bill pay interface for Metavante users that provides tools aimed at easing "new user" apprehension and increasing usage.
By Marc Rapport | January 12, 2010 at 07:00 PM | The original version of this story was published on Credit Union Times Magazine
FIS has released a new bill pay interface for Metavante users that provides tools aimed at easing "new user" apprehension and increasing usage. The new interface uses task-oriented, configurable modules that answer consumer questions at the landing page, along with a product tour and setup assistant, the company said. Other features include a "bill rack" that organizes bills based on due dates, expedited payment functions and a balance worksheet that shows current and pending payments to help avoid overdrafts, the company said. The redesign followed extensive research and usability testing, the company said. "Helping banks and credit unions increase bill pay adoption is directly related to the product's ability to solve consumers' bill pay predicaments. Above all, consumers have told FIS they need answers to two vital questions upon logging in: 'What bills do I need to pay?' and 'Will this payment overdraft my account'," said Frank D'Angelo, executive vice president of the FIS Payment Solutions Group. The new interface is being offered initially to users of the Metavante Bill Payment Manager platform with future plans for a company-wide rollout, FIS said. Jacksonville, Fla.-based FIS completed its acquisition of Metavante in October and said it now provides services to more than 14,000 financial institutions and businesses in over 100 countries. –[email protected]


text:
Remembering the Late Star Wars Icon Carrie Fisher
Andrea Fort
I discovered Star Wars around the age of 10, when I noticed a significant difference between myself and other girls my age. While they wanted to play house and had binders covered with flowers, I was quite literally the only girl who not only studied ballet on weekends but carried a superhero pencil case. I spent much of my time trying to fit in until I saw Princess Leia played by Carrie Fisher; beautiful, tough, and handy with a blaster, she instantly became my new role model.
As a nerdy kid, I was teased and bullied, but Leia was a bright light who reminded me that it was okay to be feminine and strong at the same time—she reminded me that it was all right to be one of the boys. Fisher was many things; best known for her role as Princess Leia in Star Wars, she was so much more than the fiery love interest in one of the best-loved science-fiction franchises of all time. Fisher was a writer, performer, and advocate. Most importantly, she took her status as an icon and became a role model. When Fisher passed away on Dec 27, 2016, the Internet mourned—posting tributes to her in a wave of lightsabers and sketches showcasing the iconic hairstyle. For me, she will always be so much more than a princess. In my eyes, Fisher represents the woman I always wanted to be, the woman I strive to be. She was a woman who was unapologetically herself despite the consequences.
Fisher knew the meaning of celebrity at a young age, born in 1956 to the incomparable Debbie Reynolds (who sadly passed away the day after her daughter at the age of 84) and singer Eddie Fisher. After her stage debut alongside her mother in the Broadway revival of Irene at age 15, Carrie Fisher began to focus on performing. In 1977, she made her mark by playing Leia and helping to put Star Wars on the map. This performance made Fisher a household name at the young age of 19, and while she is fondly remembered for her breakout role, she also made so many other contributions that are far too often overlooked. Fisher had an acerbic wit and was not shy about sharing it. Amongst her other performances, she also worked as a script doctor and a writer. She made alterations to a number of well-known movies, like Hook and Sister Act as well as Star Wars. In fact, she was largely instrumental in creating Leia's quippy and no-nonsense voice, but these contributions went unmentioned. She also wrote five novels, three memoirs, and a handful of stage and screenplays. Beyond her professional accomplishments, Fisher's life was a struggle. She was very vocal about her bouts of addiction as well as her struggle with her mental health. When she publicly declared that she was battling bipolar disorder, she instantly became an advocate for anyone who had ever faced a mental health concern. Fisher was a renaissance woman.
As I got older, Fisher took a different role in my life. She spoke openly of her struggles with bipolar disorder and her drug addiction, and her advocacy for mental health and her refusal conform to the expected standards was my battle cry. She appeared on television and in films just as she was—entirely unapologetic and courageous. She mesmerized me. She was the picture of strength and bravery that I so desperately wanted to be. She allowed me to embrace myself and walk into the world with all my quirks and foibles and never be ashamed.
Carrie Fisher's last book The Princess Diarist released Nov 22, 2016
I, like so many others, will never have the opportunity to thank her for the ways in which she has contributed to our lives. In her performances, in her writing, and in how she conducted herself, she was a constant source of inspiration. As I sat down to reflect on the impact that Carrie Fisher had on me, I found it strange to be eulogizing someone I had never met. I was also deeply saddened by my inability to ever give Fisher anything in return for all she has done for me.
Carrie Fisher blazed the way—relentlessly defying convention—and made room for those following her example. She wanted us to be real. She wanted us to be unapologetic. She wanted us to embrace be courageous, even when we were terrified. So let's do that. I am putting out a call to anyone who has ever found inspiration in something Carrie Fisher has done, let's be courageous and unapologetic together. I know that she would be proud.
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