Democratic gubernatorial candidate Lupe Valdez is greeted as she takes the stage in June during the general session at the Texas Democratic Convention in Fort Worth, Texas.
AUSTIN — The gun issued to Democratic gubernatorial candidate Lupe Valdez while she was Dallas County sheriff has been located after it was reported missing earlier this year. A search this week uncovered the Beretta 9 mm pistol in the department's property room, according to a statement from the Dallas County Sheriff's office.
The gun had been turned in on January 2, but wasn't entered into inventory at that time, the release said. A previous audit had failed to locate the firearm.
The Dallas Morning News first reported earlier this month that Valdez's department-issued pistol had gone missing. Critics attacked Valdez's credibility and Republican Gov. Greg Abbott's campaign posted an online video questioning whether she was responsible enough to lead the state.
In a written statement, Valdez said she has been a responsible gun owner for more than 40 years and has always followed protocol when returning issued property.
Valdez was first elected sheriff of Dallas County in 2004. She stepped down in December to run for governor and won the Democratic party primary in a run-off.
This post has been updated with a comment from Valdez.


Product description:Glutathione has two important role: antioxidant and integrate detoxification. Glutathione, easy iodoacetate, mustard gas (a gas), heavy metals such as lead, mercury, arsenic salt complexation, which is the integration of detoxification. Glutathione (particularly liver intracellular GSH) has very important physiological function is to integrate detoxification, with certain drugs, such as paracetamol, toxins (such as free radicals, heavy metals), participate in bioconversion, harmful to the body of toxins into harmless substance, drain out of the body.


text:
Luigi Martella (9 March 1948 – 6 July 2015) was a Roman Catholic bishop.

Ordained to the priesthood in 1977, Martella was named bishop of the Roman Catholic Diocese of Molfetta-Ruvo-Giovinazzo-Terlizza, Italy.

Notes

1948 births
2015 deaths
20th-century Italian Roman Catholic bishops

redpajama_set_name: RedPajamaWikipedia


Joe Jonas and Sophie Turner have really been on their A-game this Halloween season. While we didn't think it could get any better than Joe's Sansa Stark costume, the singer proved us wrong when he and his fiancée dressed up as Morticia and Gomez from The Addams Family. While the Game of Thrones actress looked absolutely spooky in her dramatic makeup and long black wig, Joe really sealed the deal with his pinstripe suit and pencil mustache. He even had a fake hand on his shoulder! Their costumes were really to die for. See even more of their spot-on looks ahead!


Just browsed your Facebook. Really love your style, and not just on the falconry related items. Really unique stuff.
Ever draw anything with red tails?
Thanks for the kind words .
Yea I'm actually planning a few other birds and the redtail is on the top of the list for a treatment.
I've been looking through post for ideas on the nicknames people use for them , as well as going through the manuals I have just hoping to have a spark .
All that said , if anyone has some good nicknames for their favorite birds I'm all ears .
An example would be , rt Allison once referred to his gos has a hand dragon , and i loved that , I've read that coopers hawks are nicked name blue racers . Anyone know any other s?
Nice John I made up a couple of bumper stickers Dirt Hawker Badge of Honor I like how you got the Aplomado in orange.
i had to put the orange in there somewhere, otherwise i dont think it would have completed the look .
these things are great practice to get the skills up .


text:
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The OMIG List of Restricted and Excluded Providers exists as notification that a person is excluded from the Medicaid program and for the purpose of preventing Medicaid payments for care, services, or supplies, furnished, ordered, or prescribed by that person. Use of the list for other purposes is beyond the scope of its intended use.
List of Restricted and Excluded Providers Search
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If a business, then only enter the first two words of the name of the business.
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redpajama_set_name: RedPajamaCommonCrawl


When we were first asked to look after Bella we must admit she was a breed of cat that we were not familiar with. It's always very exciting to come across a new breed of dog or cat that we don't know. This little lady is an absolute delight. Every sitter who has sat for her has been captured!
NextHope you have enjoyed your first sit?


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The list of the top 100 British entrepreneurs is led by Victoria Beckham - Tuugo Blog
Home Blog October 2014
The list of the top 100 British entrepreneurs is led by Victoria Beckham
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Art, Entertainment & Media
Shopping & Speciality Stores
The specialized business magazine "Management Today" has released the list of the hundred most successful entrepreneurs in the UK in 2014, and on the top of the list is the British designer Victoria Beckham.
The wife of the ex-English soccer player David Beckham, and former lead singer of the popular pop group Spice Girls, managed to win over all British businessmen ranking compiled by the magazine.
The turnover of the signing Beckham has gone from € 1.26 million in 2009 to € 38 million in 2014
Victoria Beckham last month opened a new store in London, located in the upscale Mayfair district, the renowned designer has launched a three-story home with over 6000 square meters. The local was designed by architect Farshid Moussavi, a professor at Harvard University whose previous works include the Museum of Contemporary Art Cleveland (Ohio, USA), and where perhaps most curious is how to pay for the products.
As explained Victoria herself, the architect decided that the typical cash registers and their corresponding cashiers would not be good in the design devised. Therefore, customers who stop by the shop Beckham should use a number of iPads to make the payment of purchases they have made.
Thanks to these strategies its brand revenues have grown by 2,900% in five years. The turnover of the firm last Beckhamha generate 1.26 million euros to 38 million euros recorded in 2014, as highlighted by business magazine said.
Victoria Beckham is considered a trendsetting icon in the fashion world.
As noted by Philip Beresford, the British Sunday Times Sunday, it's:
«her well adjusted insight with business is what makes her the top in the ranking of MT 2014 of the 100 British entrepeneurs»
Two other names come out of fashion among the top 10 list of "Management Today" are Mahmud Kamani of Boohoo.com, online shop for male and female clothing, third, and Julian Dukerton, business Supegroup the Own clothing store Japanese inspired Superdry, who ranks fourth.
October 2014, Personal Care, Shopping & Speciality Stores
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text:
class TestModel
  include ::Mongoid::Document

  field :title
  field :reticulated, default: false
  embeds_many :child_models

  def reticulate!(*_args)
    update_attributes!(reticulated: true)
  end
end

redpajama_set_name: RedPajamaGithub


SAS Ceramics – Emma Teaches Art!
Pratt Institute, Saturday Art School Ceramics class for 10-12 year old students.
The show was absolutely amazing. I was so happy to see each student showing of there artwork to their parents. I think the students also had a good time re-arranging the room and writing up the descriptions of each lesson. They took the whole show very seriously and I couldn't be happier with the result!
This past Saturday was our second to last day of ceramics at Pratt Institute's Saturday Art School. After my experience last semester where several pieces of student art work not being fired in time for our final show, I decided that the second to last week we would already be done with glazing and that I would bring in a mix of medias for my students, instead of having people glazing up until the last minute, and risk not having everything ready for our final show. So the week before this one I had each student glaze all of their work, every last piece, no matter what. So most everything was out of the kiln this week and had been through it's second firing. It was a pleasant surprise to see that the studio technicians had prioritized our work. Considering there are also ceramics graduate students sharing the same studio, this was very nice of them.
I came equipped with two glue guns: one for me, one for my 15 year old assistant. I also brought, a bunch of paper scraps, pipe cleaners, acrylic model paint, pom-poms, feathers, and a big bag of multi-colored plastic beads. Each student could pick up to 3 of their finished pieces to decorate. They were encouraged to plan before they brought me things to hot-glue to their work, and also we took a moment to look at a few mixed media artists including Paul Klee's puppets, which I love. I also provided white Elmer's glue in case they wanted to do the gluing themselves.
Here are some more amazing examples of my Pratt Saturday Art School students glazing their amazing objects.
In case you are wondering what our inspiration has been (not story books) we have been looking at some living artists including: Megan Bogonovich, Alyssa Ettinger, and many more. I like to bring living, practicing, local artists into the classroom, because I feel like it gives ceramics more serious context.
Here are some images from last week in Saturday Art School Ceramics. Not only did we have students on the wheel, but we were doing drop molds AND glazing. I am looking forward to getting back to SAS Ceramics this week after our short Spring Break.
Each student had to draw and write a proposal to me before they were aloud to grab handfuls of squishy fresh clay. "You need to have a direction!" I stressed. I also explained that if, while working with the clay, they changed their mind, they could. All I wanted was for them to have a well thought out place to start their experimentation.
I am lucky to have a calm, respectful group of young tweens in my Saturday Art School. They respect me and my advice, but since they are kids they often get overly excited and make a goof here and there. Today we had some clay go through the slab roller with no canvas to protect it, and of course I wasn't really annoyed, but I felt that I had to a stink. I wanted to make it into an example of how important it is that we respect the studio space.They bought it. I stressed that I didn't care who did it just that it never happened again, and I am positive it wont.
So we created bowls using drop molds. It was a great day for experimentation.
Very funny. Ten year olds think they're hilarious. This past Saturday Art School ceramics class we tried out the pottery wheel. Everyone looked excited… little did they know, what frustration and disappointment lay in wait. Fortunately for them, I was experienced in the difficulties and disappointment of the pottery wheel, and not a whole lot else. I have years of experience when it comes to using the wheel, but I have never really enjoyed it enough to pursue it and perfect my technique. I was nervous I wouldn't be able to give a good example. As it turned out, my inability to make it look easy set my students up to feel better about how difficult this technique was. By the end of the class each student had made at least one, and no-one had gotten upset about their one or two or three failed attempts.
This is an example of my ceramic students hard at work. Here you can see students working in pairs at the slab rolling station. Using communication and asking each other "are you ready?" before they begin, we learn that some art takes team work and more than two hands.
We used tools to add and subract from our tiles. When students came in each of them had a pre-rolled tile that was theirs to practice with before they began decorating their final tiles.


In crisp, clean white or cheery blue, the Gridlock collection will clear your path when you have things to do. Made of industrial epoxy-coated wire, these fresh, clean organizers will mesh with any color palette or decorating scheme in your home or office.
PRODUCT DIMENSIONS: 11 x 11.5 x 4.5 in.


Ever since the ground-breaking trial of Roe v. Wade in 1973, abortion has been declared a fundamental right. But in this day and age, virtually every American can agree lawmakers and the government as a whole need strict accountability and oversight when it comes to decision-making. This forces each U.S. citizen to carefully contemplate each legality at hand and democracy allows us to then act upon our opinions, allowing us to voice our beliefs rather than making the superiority of one side the assumption. In today's culture, an incredibly controversial subject that arises time and again evolves around the question – should abortion be a right to choose or a right to life?
Perhaps the biggest argument made by pro-choice advocates is that pregnancy is merely that, a fetus that is not human until it is born. But ponder this: if there is an official declaration of death the moment a person's heart stops, shouldn't life commence when the heart begins beating?
Another coinciding point is that a human isn't human until it is physically apart from it's mother; an independent person. Until then, it exclusively falls under her umbrella of authority. But if one leaves a six-month-old child on the street, will it survive? The very definition of a child automatically and universally includes the presumption it is codependent. Even a four-year-old is more reliant on another than a 24-year-old, as is an Alzheimer's patient than an average healthy person. Thus, with this argument, there is a clear promotion of a culture where life is disposable based on discrimination of age and health.
Defunding Planned Parenthood would definitely contribute to an increase in nationwide healthcare and a healthier government budget. Out of the staggering $1.3 billion in combined annual revenue they accounted for in their 2013 report, $530 million of that was taxpayer money.
Pro-choice advocates argue that those contradicting their beliefs are pro-birth rather than pro-life, but that yearly $530 million could easily go a long way towards healthcare, maternity leave and the overall welfare of both the child and mother.
The company recorded net assets at the end of the last fiscal year totaling more than $1.6 billion. Surely the company can go without government funding, especially considering the half a billion in private donations they already rank in every year would undoubtedly increase. This argument can easily be backed by stifling through each Planned Parenthood financial report. Can't they at least afford their own operating costs instead of forcing non-consenting citizens to pay?
There are also adoption agencies and prospective parents willing to pay for baggy clothing to hide the bump, a temporary out-of-town living situation, medical expenses and anything else needed to keep a pregnancy easy and completely confidential, such as American Adoptions. But although Planned Parenthood states referrals are one of their main services, with the 321,384 annual abortions that were performed in their latest 2017 report, there were only 3,889 adoption referrals. This means that many women have no idea there is a better option. In their latest report, both revenue and surgical procedures grew drastically, yet referrals fell from 8 percent to just .5 percent, along with a 17 percent drop in prenatal care. The company revolves around abortion rather than women's healthcare.
The discrete underlying corruption within Planned Parenthood and the movement itself deserves to be heard. The timeliness and urgency with this topic is no less than predominant because according to the latest Guttmacher Institute statistics, an average of 200 lives were taken by abortion since the beginning of this article.
The opinions in this article solely reflect the views of the writer. It does not represent the views of the editorial board of the Student Voice.
Kirk on June 21st, 2018 3 p.06.
What a helpful article to further the discussion on this important issue! Thank you, Student Voice, for publishing this article and encouraging respectful conversation among your students. I found the author of this article to be respectful, well informed with solid information, courageously outapoken, and seasoned with compassion for both women and babies. Well done.
John and Sonia Wolfe on June 21st, 2018 3 p.06.
Well written article, with good information we all need to know about!
Latham B Lawton on July 3rd, 2018 3 p.07.
It's nice to see a pro life individual openly expressing their beliefs. The fear of being ridiculed forces a lot of people into the dark. Great article!
Francisco Molina on October 10th, 2018 3 p.10.
Great article Kaylee! I agree with you and I applaud the student voice for allowing your opinion to be heard.


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Home Theatre Theatre review: Urinetown cast raises the roof and dances up a storm
Theatre review: Urinetown cast raises the roof and dances up a storm
Studio 58 production is evidence the future of musical theatre in this country is in excellent hands
Christine Pilgrim
Members of the cast of the Studio 58 production of Urinetown. Photo by Emily Cooper.
The cast and crew of Urinetown confirm that Studio 58 is a breeding ground for some of the finest contributors to Canada's performing arts.
Many shine in this musical about how the shortage of water inflicts misery upon the poor, as they're denied free access to the city's public toilets by the bully who owns the franchise. Those who stand out aren't just in the starring roles. A case in point is Vuk Prodanovic who plays Tiny Tom, among other ensemble parts. His compelling performance, atop each note, ahead of each step, steeped in his worm-like, crippled character, exhibits the stuff of which stars are made.
But Prodanovic is not alone by any means.
Ivy Charles attacks the part of down-market urinal chatelaine, Penelope Pennywise, with sassy energy and conviction. Gabriel Covarrubias's uses his huge presence to encapsulate Caldwell B. Cladwell, the ignorant real estate mogul who wields power over the bladder-bursting inhabitants of Urinetown, with the arrogance of a president who act like a king. As with all such ill-doers, he finally gets his comeuppance; in this instance, at the hands of his daughter, played delicately – until she takes charge – by Emma Ross.
Another performance worthy of mention is that of Caleb Dyks as Bobby Strong. He leads the second act with quiet strength, in the same way he leads an uprising against Cladwell. Spoiler Alert: His attempt to save his fellow-strugglers-for-justice, though heroic, tragically fails, through no fault of his own. A monumental fall is so superbly choreographed and executed that it jolts the audience into thinking it's real.
Like most of his counterparts and his character Strong, Dyks comes into his own in the second half, when the musical matures from a bit of a romp into a play with something pithy to say. Many fine performances emerge, from significant roles such as Emily Case's cute but sad Little Sally, to those so small that their names are lost in the mix. For example, a revolutionary, hiding in the sewers from the cops, gives a deadpan pull of his long legs just in time to avoid the flashlight of the cop pursuing him and his buddies. His timing and casual attitude are spot-on.
Caleb Dyks & Ivy Charles in the Studio 58 production of Urinetown. Photo by Emily Cooper.
Yvan Morissette's dramatic set reflects the chasm between those inhabiting the glass skyscrapers uptown and the underground brute structures that support them in downtrodden Urinetown. Here exist the miserable beings whom the one percent living the good life exploit or ignore. Huge faucets grow from the walls of the skyscrapers, like orchids, while the poor beg to be allowed to pass water.
As in most musicals, good eventually overcomes evil. The people rise up and triumph. But Greg Kotis, who wrote the book and many of the lyrics, adds a word of caution to all would-be revolutionaries, not to sit back on their laurels after their successes.
The cast is supported by the brilliant choreography of Julie Tomaino and tight direction of Courtenay Dobbie. Further support comes from a five-piece band that started out a tad untidily on opening night but, once the action got underway, played in tune and as one.
Takeaway life lessons and a sense of hope, as well as an awareness of pitfalls en route to, or even after achieving our goals, make for a fine piece of theatre. Add to that the Broadway-quality of this presentation of Urinetown, particularly in the second half, and it's assured that the future of musical theatre in this country is in excellent hands.
Urinetown with books and lyrics by Greg Kotis & music and lyrics by Mark Hollman. Directed by Courtenay Dobbie. Musical direction by Diane Speirs. Choreography by Julie Tomaino. A Studio 58 production on stage at Langara College's Studio 58 (100 W 49th Ave, Vancouver) until February 16. Visit langara.ca/studio-58 for tickets and information.


By pressing by a finger, a pencil or other similar subject button "м" hours are translated at 1 o'clock forward.
By pressing by a finger, a pencil or other similar subject button "M" hours are translated for 1 minute forward.
For installation of minutes zero unitary press and release a finger, a pencil or other similar subject on button "R". Thus there will be an exact installation of time to zeroing of minutes.
For example, if will press button "R" in an interval between 9:01 and 9:29, hours at installation of minutes on zero will show 9:00. If will press button "R" in an interval between 9:30 and 9:59, hours at installation of minutes on zero will show 10:00.


TeamLease Skills University (TLSU) is a private university established under Gujarat Private Universities (Amendment) Act, 2013 vide Gujarat Act. No. 18 of 2013. TeamLease Skills University (TLSU) is located within the ITI Tarsali campus at Vadodara aad is clearly focused on putting India to work by offering employment oriented programs and developing a career path for non-graduate employees.
The University offers custom made programs catering to the needs of 18-23 year olds drawn from the academic streams of secondary education system. Efforts are also under process for opening higher education/training avenues for the pass-outs/teachers of Industrial Training Institutes (ITIs), Vocational Higher Secondary Schools (VHSSs) and Polytechnics.
The formal and informal sectors of the employed category will be provided skill upgrade options through credential based educational programs and non-credit oriented training programs. Non-formal pedagogy will be deployed for community enrichment programs.
To contribute to workforce productivity, socioeconomic development and social harmony through well rounded and industry relevant educational programs with employment at the heart of academic offerings, technology at the heart of operation and academic mobility as the focus deploying inclusive, distributed and low cost delivery methodology.
To enable all individuals acquire skills and capabilities, prepare them to get appropriate employment and ensure their competitiveness in national and international work environment.
Selection Criteria: 12th Pass from any stream (Arts, Commerce, Science, 2 year ITI Trade after 10th Standard) can apply.


There are actually not one but two different types of leg length discrepancies, congenital and acquired. Congenital means you are born with it. One leg is anatomically shorter in comparison to the other. As a result of developmental stages of aging, the human brain senses the gait pattern and identifies some variance. Your body usually adapts by dipping one shoulder to the « short » side. A difference of under a quarter inch is not blatantly uncommon, require Shoe Lifts to compensate and in most cases doesn't have a profound effect over a lifetime.
Leg length inequality goes mainly undiscovered on a daily basis, yet this problem is simply remedied, and can eliminate numerous instances of low back pain.
Treatment for leg length inequality commonly involves Shoe Lifts. Most are cost-effective, regularly priced at under twenty dollars, in comparison to a custom orthotic of $200 or higher. When the amount of leg length inequality begins to exceed half an inch, a whole sole lift is generally the better choice than a heel lift. This prevents the foot from being unnecessarily stressed in an abnormal position.
Lumbar pain is easily the most common health problem affecting men and women today. Around 80 million people experience back pain at some stage in their life. It is a problem which costs employers millions of dollars every year as a result of lost time and production. New and improved treatment solutions are continually sought after in the hope of reducing the economical impact this condition causes.
Men and women from all corners of the world suffer from foot ache as a result of leg length discrepancy. In these cases Shoe Lifts are usually of worthwhile. The lifts are capable of eliminating any pain and discomfort in the feet. Shoe Lifts are recommended by many qualified orthopaedic physicians.
To be able to support the body in a balanced manner, feet have got a very important task to play. Despite that, it can be the most overlooked zone in the body. Many people have flat-feet meaning there may be unequal force placed on the feet. This causes other areas of the body like knees, ankles and backs to be affected too. Shoe Lifts guarantee that ideal posture and balance are restored.


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Military, NPHCDA partner to improve healthcare delivery to Armed Forces personnel
January 21, 2022 Favour Lashem 0
The Chief of Defence Staff (CDS), Gen. Lucky Irabor, says the Armed Forces of Nigeria (AFN) are committed to sustaining the collaborative healthcare arrangement with […]
Ondo commissioner solicits cooperation to enhance healthcare delivery
December 17, 2021 Favour Lashem 0
The Ondo State Commissioner for Health, Dr Banji Ajaka, has solicited the support of officials of the ministry, departments, agencies and other stakeholders for an […]
79 PHCs get N418m as Zulum launches Borno's Basic Healthcare Fund Zulum is exceptional, says Minister, others
December 8, 2021 Favour Lashem 0
Governor Babagana Umara Zulum on Tuesday launched Borno State's Basic Healthcare Provision Fund, with the disbursement of N418m to 79 Primary Healthcare Centres (PHCs) across […]
World Bank charges Nigeria to tax alcohol, cigarettes to improve primary healthcare
The World Bank Group has called on the Federal Government to impose special taxes on alcohol, cigarettes and sugar-sweetened beverages to improve primary healthcare. "If […]
Healthcare delivery vital to improving economic status of rural dwellers-Rep Chike Okafor
November 27, 2021 Danlami Nmodu 0
The member representing Ehime-Mbano/ Ihitte-Uboma/ Obowo Federal Constituency of Imo State in the House of Representatives, Rep. Chike Okafor has described the provision of health […]
SERAP asks court to stop Buhari from spending N26bn on travels, meals, others
Socio-Economic Rights and Accountability Project (SERAP) has filed a lawsuit asking the Federal High Court in Abuja to "stop President Muhammadu Buhari from spending N26bn in the […]
What Happens in Anambra On Saturday? It Depends
By Azu Ishiekwene Just hours before voters in Anambra State decide the next governor, a party not on the ballot is getting serious attention. The […]
Expert alerts healthcare workers on Arboviral diseases
Prof. Olatunji Kolawole of the Department of Microbiology, University of Ilorin (Unilorin), has alerted healthcare workers on early identification and diagnosis of arboviral infections, which […]
Foundation begins 6 days free medical treatment in Badagry
A non-governmental organisation, Ejalonibu Foundation, on Thursday began a six-day medical eye treatment to people in different communities in Badagry area of Lagos State. Mr […]
Gender equality: NGO tackles barriers against gender inequality
A public health non-governmental organisation, Nigeria Health Watch (NHW), is bringing to the fore, the barrier that gender inequality continues to pose to the realisation […]
People living with HIV/AIDS in Bauchi State seek government's intervention in treatment cost
The Network of People Living with HIV/AIDS in Nigeria, Bauchi State chapter, on Tuesday sought the state government's intervention in the treatment of members to curtail health […]
Osinbajo leads prayers against forces of evil, hate, division, injustice
Vice President Yemi Osinbajo, on Thursday, in Kafanchan, Kaduna State, led other clergymen in praying against forces of evil, hate, division, injustice, insurgency and other […]
Lalu to provide healthcare services, education for PWDs in FCT
By Rosemary Ogbonnaya Executive Secretary, National Commission for Persons with Disabilities, Mr. James David Lalu, has pledged his willingness to support Persons with Disabilities by […]
Corruption: Nigeria loses $2.9 billion yearly from tax incentives to corporations – Rafsanjani
By Chimezie Godfrey The Executive Director, Civil Society Legislative Advocacy Center (CISLAC) and Head of Transparency International TI, Nigeria, Auwal Rafsanjani says Nigeria loses $2.9 […]
Prison Fellowship Nigeria set to support vulnerable children in Nasarawa State
Prison Fellowship Nigeria (PFN), a faith-based NGO, says it is set to support 47 vulnerable and "at-risk'' children in Nasarawa State on education, safety, healthcare, social […]
Senate condemns $200 m loan to buy nets
By Haruna Salami The Senate has roundly condemned the proposal by the Federal Ministry of Health to borrow 200million dollars under the Malaria programme to […]
Committee advises parents to continue to vaccinate children against polio
The Nigeria National Polio Plus Committee (NNPPC) has advised Nigerian parents to continue to get their children immunised against polio despite the fact that the […]
Kogi govt to provide 10,000 vulnerable citizens free quality healthcare—Official
Kogi Government says it will provide no fewer than 10, 000 vulnerable residents of the state, free quality healthcare services under the BelloCare equity fund […]
Incessant restrictions, insecurity hinder healthcare delivery in Nigeria- Red Cross
The International Committee for Red Cross (ICRC) has raised an alarm over increasing impediment to health care delivery due to incessant restrictions and insecurity across […]
Nigerian Army to partner Lagos hospitals for better healthcare delivery
The Ag. Corps Commander Medical (CCM), Nigerian Army (NA), Col. Babatunde Solebo said that collaborating with major healthcare institutions in Lagos State will foster synergy […]
CBN says banks remain stable, resilient despite pandemic
The Central Bank of Nigeria (CBN) says banks in the country have remained stable, robust and resilient in spite of the COVID-19 pandemic. The Director, […]
Micronutrient powder initiative, a new era of preventing malnutrition in Kaduna state – UNICEF
The United Nations Children's Fund (UNICEF) says the introduction of Micronutrient Powder (MNP) complementary home-based food fortification programme in Kaduna State signifies a new era […]
9 out of 10 schools in Nigeria have no hand-washing facility for children – UNICEF
The UN Children's Fund (UNICEF) says nine out of 10 schools in Nigeria have no place for children to wash their hands. This, according to […]
How I Remember #ENDSARS One Year After
By Azu Ishiekwene On October 3, 2020, I watched a video of a policeman attached to the Special Anti-Robbery Squad (SARS) shooting a young man […]
NMA urges investment in health sector to stop medical tourism
The Nigeria Medical Association (NMA), Ondo State Chapter, has urged government at all levels to make quality health service available to the people instead of […]
NYSC to enhance digitalised work environment for staff January 21, 2022
Buhari inaugurates Sabon Gari Market, road projects, in Zaria January 21, 2022
NOA begins sensitisation campaign on Petroleum Industry Act January 21, 2022


When you add a bookmark, you can pick a thumbnail that makes it easier to spot the page you need.
but I could not find out anything more about it.
I would like to be able to highlight Bookmark entries which require Cookies.
PS Please put the Markdown link ABOVE this field instead of below it.
Click on the heart icon while in the page.
Heart, red as on playing card?
I have scoured the Amazon.co.uk web page and the associated toolbars and the Bookmark properties and I can't find a heart icon.
The heart icon in the right of the address bar.
When you're bookmarking a page, you can click through the suggested thumbnails and choose the one that would be the best for highlighting that page on the list. It works the same way for changing the image for an existing bookmark: just click on the heart icon when you're on the bookmarked page.
I haven't got anything like this when I am bookmarking a page. Maybe I need to download something?
Do you not have a heart icon at the right hand end of the address bar?
What happens if you right click on a page and select "Add to bookmarks"?
can you tell your Opera version?
davehawley: On this page I just have a grey star at the right-hand end (and a yellow padlock off the Left-hand end).
When I right click in a page I get a dialog with Bookmark Page... This gives me the Add Bookmark dialog - with nothing about thumbnails. I usually right click on my required folder in the Bookmarks column to get the Add Bookmarks dialog.
Could there be something in Tools/Preferences/Advanced/Tabs. Thumbnails are mentioned but I don't see the relevance?
You're using a Presto version of Opera, which doesn't have the heart icon.
When you reload a Speed Dial in that version, it will retrieve a thumbnail of the website, and I don't think there is any other option that can be done easily.
There is a way of using another image, but it's not straightforward.
Find your profile folder (the path will be listed in Help>About Opera).
In that folder, you will find a folder called "thumbnails".
Using an image viewer, look at the contents of that folder, and identify the image you want to change.
Prepare the image you want to change it to, making sure it's saved as a .png format image.
Copy the name of the image you want to replace, and re-name the new image to be the same.
Then copy that image into the profile folder, overwriting the original.
The Speed Dial should now show the new image.
The images generated by Opera normally seem to be 1024 pixels wide, so you may get a strange result if your new image isn't that width.
Once you've got the image you want, right click on the thumbnail, and from the dialogue that pops up, select that dial to never refresh.
If you don't do that, it will eventually refresh and undo all your work!
Aplogies for this late reply.
I will certainly try out your suggestion.
I researched Presto via Google and by all accounts it seems I am better off with the Presto rendering engine for the work I do, even if I don't have thumbnails on tap.


text:
/ Rasputin, Grigori Yefimovich
Rasputin, Grigori Yefimovich
Rasputin, Grigori Yefimovich răspyo͞o´tĭn, Rus. grĭgô´rē yĭfē´məvĭch rəspo͞o´tyĭn [key], 1869–1916, Russian holy man and courtier, a notorious figure at the court of Czar Nicholas II. He was a semiliterate peasant and debauchee who preached and practiced a doctrine of salvation that mixed religious fervor with sexual indulgence. Because of his personal magnetism and his ability to check the bleeding of the czarevich Alexis, who suffered from hemophilia, Rasputin gained a powerful hold over Czarina Alexandra Feodorovna and, through her, over the czar, and from 1911 Rasputin's appointees began to fill high positions. Rasputin never had a clear political program, but unscrupulous and reactionary officials, financiers, and ecclesiastics profited through his influence. During World War I, when the czar went (1915) to the front, Rasputin's influence predominated. Those who opposed him were often removed from their posts; fortune hunters and incompetents were appointed to replace them. Rasputin's disgraceful behavior, the czarina's attempts to shield him, and a series of scandals involving his appointees helped to undermine the imperial government. Suspecting that Rasputin and the czarina were working for a separate peace with Germany, a group of right-wing patriots, including Prince Felix Yussupov and the czar's cousin, Grand Duke Dmitri, conspired in Dec., 1916, to assassinate Rasputin. A generous dose of poison failed to produce any visible effect, and the terrified conspirators riddled him with bullets and threw his body into the frozen Neva River. Later buried, Rasputin's corpse was exhumed and burned by the mob during the February Revolution of 1917.
See biographies by Prince F. F. Yussupov (1927), R. Fülöp-Miller (tr. 1928), and D. Smith (2016); studies by M. V. Rodzianko (tr. 1927 and 1973) and E. Radzinsky (tr. 2000).


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Middlebury Shape-Note Singing
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text:
George II of Antioch was Patriarch of Antioch in the 7th century. Little is known about him except that he attended the Quinisext Council in 691–692. It is speculated that he died of heat exhaustion caused by a long period of being outdoors. After his death the period of Arab tolerance that had allowed the continued existence of Christianity in regions under their domination ended. George II of Antioch's reign was one well known for peace, due to his love of many religions. The Byzantine Empire, it is thought, worked alongside him to be able to better the Empire altogether.

References
 Ann van Dijk, "Jerusalem, Antioch, Rome, and Constantinople: The Peter Cycle in the Oratory of Pope John VII (705–707)", Dumbarton Oaks Papers, 55 (2001), p. 326

7th-century archbishops
Greek Orthodox Patriarchs of Antioch
7th-century Syrian people


Jenny Grinch and the Spirit of Christmas – Laugh.Cry.Giggle.Smile.
I've got my Christmas music on. I opened three more Christmas cards when the mail arrived. I've read my devotion for the day. And still… it's easy to see my reflection in the mirror as the Grinch. I don't get it. I'm just struggling.
Could it be that I'm trying to juggle too many things right now? Home projects, work, parenting responsibilities, normal home upkeep like laundry & dishes, and then of course, Christmas preparations. I'm definitely not burning the midnight oil trying to get everything done. I was so cooked by the time I got the kids home, fed and in jammies, and spent 30 minutes on and off connecting with my husband while taking on the kid responsibilities – I cashed it in at 7:30pm.
Honestly, I think the root of it is the focus of Christmas this year. My focus since childhood has been on celebrating Jesus's birth with church family and biological/ extended family. That is personal for me. Believer or non-believer, Christmas flat-out MEANS something to most people and it typically isn't all about the gifts.
This year I've been bombarded for 2 months about "what does child A and child B want?" Can I be completely honest here? We live a pretty simple life. We work and are humbly successful. No flashy Joneses here. These children of mine are happy with sticks and rocks. No, truly they are. Child A got in trouble (repeatedly) for a sassy mouth and had his room cleaned out and stored in trash bags. He got to keep his bed, covers & pillow, and puzzles and books. You know what he was thrilled playing with when all the fluff was removed? Cardboard boxes and nuts and bolts from the junk drawer. Child B likes to play with stickers, crayons, and markers. She is creative. She rocks her dolls to sleep and drags them all over the house in the blankets I used when my littles were babies.
Last night as I was talking to my husband, I realized that this is the drain I've been feeling. The focus on this holiday has been put on the material side of life. How much are you spending? Will my 6 year old like this $100 gift? Does my 4 year old want this $100 sparkly item? Yuck. Yuck. Yuck. Make it stop.
My hubs agreed with me that this is NOT how we are going to live. So how do I fix this? Do we outlaw gifts? We agreed that is pretty extreme and not really a mountain we want to climb with our families at this point. (A conversation will be necessary before next year though to prevent the madness experienced this year.) He took the first step by talking to my father-in-law. I also talked to one of my sisters and my mother about my concerns about the focus being too gift-centered.
I am actively looking for local options for our family to volunteer or celebrate OUR reason for the SEASON with others with a giving, humble, and loving heart. We will celebrate with our local church family this coming Sunday and again on Christmas Day. We will read the Christmas story and talk about its meaning. We will write thank-you notes for the gifts we do receive. If our home project is far enough along and I have an oven, we will make Jesus a birthday cake and invite a widowed neighbor over to share it. We MUST refocus on our personal reason for the season of Christmas. It speaks so much louder than words when we put our gratitude, love, kindness, and care for others in action.
I refuse to let this become just another holiday marked with material stuff.
Now that I've wrapped my head around all of that, I think I can punch out a fabulous Christmas letter. My Grinchiness was giving me writer's block and I'm pretty sure it would have been a bitter bite to arrive in the mail.


text:
Теряевка — название нескольких населённых пунктов:
 Теряевка — село в Неверкинском районе Пензенской области.
 Теряевка — деревня в Воловском районе Тульской области.


text:
Virgin America's CMO and CIO come together with 'techmarketing'
The airline's IT and marketing leaders stress the importance of collaboration, empathy and teamwork in building effective modern marketing strategy
Virgin America vice-president of marketing, Luanne Calvert (left) and CIO and VP, Dean Cookson
Collaboration and empathy with IT is vital for CMOs looking to be effective in the new age of customer-driven, digital conversations, according to Virgin America's CMO.
Speaking during the keynote opening of the Oracle Interact conference in San Francisco, Virgin America vice-president of marketing, Luanne Calvert, and her CIO and VP counterpart, Dean Cookson, explained how their teams have come together under the tag 'techmarketing' to better tap into each other's skillsets and improve customer experiences.
The pair used the recent launch of Virgin America's website as an example of the work now being done in partnership, and why marketing today can only be effective if it's driven and supported by technology smarts.
Calvert pointed out digital channels are core to the airline's interactions with consumers, and said marketing's role has changed dramatically as a result.
"Marketing used to be like being a film director, where we controlled the conversation, you could polish things up, it was all one-way, and it was rather more glamorous," she told attendees.
"Today, it's more like being a farmer – it's 24 hours a day, you don't know what people are going to be doing on Twitter overnight, so you have to be aware of it, and there are these seeds we need to plant in conversations. These are going on between our guests, consumers and the brand. We need to put those thought starters out there as well as have a product people want to talk about."
Calvert cited a number of recent campaigns where Virgin America has strived to trigger conversations by tapping into social and digital channels, all in the name of making flying a more enjoyable experience.
One example is the 'My Virgin Experience' social campaign, where consumers were asked to take photos of themselves flying on the airline's planes, which were flashed on a billboard in Times Square, New York. The campaign generated significant social engagement, as well as consumer generated content, Calvert said.
The airline's VX safety video is another example of trying to kickstart a digital conversation, Calvert said, and has had nearly 10 million views since its launch.
Read more IAB shortlists four suppliers for new cross-device digital user metric
"When we launched the video, we treated it like a movie, with a premiere, interviews with the director, our dancers went on The Ellen DeGeneres Show and it was supported by an email campaign with attributed revenue," she said. "We also had a safety video fare sale, which generate half a million dollars in value. The idea that a safety video could generate that kind of content for us was pretty astonishing."
Calvert then moved on to overhauling Virgin America's website, stressing the importance of the technology team in its creation and efforts to change the travel booking process. The pair began work on the new site two years ago and shared revenue management and design.
While Cookson said his priorities were a responsively designed site for all devices and touchpoints, as well as a superior ecommerce experience, Calvert said protecting customer data was a key consideration for her.
To ensure the site met everyone's needs, the two teams built a personal relationship and worked in partnership, a key to minimising animosity, Cookson said.
Read more How Tyreright is cracking the customer lifecycle challenge
"Reaching into each other's sphere of influence and understanding the importance of both sides is a big part of how we work well together," he added.
"Dean knows things that I don't, so getting together to create effective marketing is crucial," Calvert continued. "Having collaboration and working in a startup mode is vital to this."
Cookson stressed the role of today's CIO is about helping the business do things faster, smarter and better not just for marketing, but all lines of business.
"Tech is great – I'm a geek at heart ... but it's important to make sure the technology team helps the rest of the business get its job done," he said. "Our business needs marketing to do more, to be faster and better. The only way marketing can do more with a flat budget is by being able to lean on tech as a force multiplier for getting things done.
Read more Domino's Pizza Mogul puts product creation and marketing in consumers' hands
"If we are able to support each other in getting the job done, then when it comes to going for budget and priorities, we have an understanding of what everyone needs."
Cookson compared the changing relationship between IT and marketing to the struggles IT operational executives have had with developers over recent years and the rise of the 'DevOps' methodology, which emphasises constant collaboration, communication and information sharing.
"DevOps has been an attempt to straddle the line between development and operations. Together, they make something more reliable, that's faster and gets to market easier. 'Techmarketing' is extending this concept into the rest of the business and about getting out of this tug of war between marketing and technology teams," he said.
Nadia Cameron travelled to Oracle Interact as a guest of Oracle.
Read more Oracle: Marketers overwhelmed by complex technology ecosystem
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Forrester: Digital change means embracing contextual marketing
Better CIO/CFO relationships see CMO salaries soar
Tags: digital marketingVirgin AmericaCMO/CIO relationshipOracle Interact
CMO interview: Data-driven marketing at a home loan provider
CMO to CEO: Sportsbet's Barni Evans on the trappings of the top job


text:
// Copyright (c) Microsoft. All rights reserved.
// Licensed under the MIT license. See LICENSE file in the project root for full license information.

using Xunit;

namespace System.IO.Tests
{
    public class FileInfo_Directory : FileSystemTest
    {
        protected virtual string Directory(string path)
        {
            return new FileInfo(path).Directory.FullName;
        }

        [Fact]
        public void ValidCase()
        {
            var directory = Directory(Path.Combine(TestDirectory, "Test", "test2"));
            Assert.Equal(Path.Combine(TestDirectory, "Test"), directory);
        }

        [Fact]
        public void TrailingSlashes()
        {
            var directory = Directory(Path.Combine(TestDirectory, "a") + Path.DirectorySeparatorChar);
            Assert.Equal(Path.Combine(TestDirectory, "a"), directory);
        }

        [Fact]
        public void AltSeparatorCharInPath()
        {
            var directory = Directory(Path.Combine(TestDirectory, "File").Replace(Path.DirectorySeparatorChar, Path.AltDirectorySeparatorChar));
            Assert.Equal(TestDirectory, directory);
        }

        [Fact]
        public virtual void Root_FileInfo_Returns_Null_Directory()
        {
            Assert.Null(new FileInfo(Path.GetPathRoot(TestDirectory)).Directory);
        }

        [Fact]
        public void DotsInPathAreValid()
        {
            var directory = Directory(Path.Combine(TestDirectory, "Test", "..", ".", "Test"));
            Assert.Equal(TestDirectory, directory);
        }

        [Fact]
        [PlatformSpecific(PlatformID.Windows)]
        public void UNCShares()
        {
            var directory = Directory(new string(Path.DirectorySeparatorChar, 2) + Path.Combine("Machine", "Directory", "File"));
            Assert.Equal(new string(Path.DirectorySeparatorChar, 2) + Path.Combine("Machine", "Directory"), directory);
        }
    }

    public class FileInfo_DirectoryName : FileInfo_Directory
    {
        protected override string Directory(string path)
        {
            return new FileInfo(path).DirectoryName;
        }
    }
}


text: Q: Imghdr module in Python 3.9.5 misidentifying .png file When I call imghdr.what(sampleImage.png) it recognizes it as a jpeg for some reason. For example if I use print(imghdr.what(sampleImage.png)) it will output the string "jpeg". I checked the image file and it is displayed as having the expected PNG file format on Mac OSX.

redpajama_set_name: RedPajamaStackExchange


text:
Oil & Acrylic Paintings, Studio & Plein Air
Home | Bio | Gallery | Instruction | Events | Blog | Guestbook | Contact
Roger Jackson
His love of old world architecture is prominent in Roger's paintings, transporting the viewer into history, other times and places. His use of bold colours and sense of perspective enhances the illusion of being there.
He is intrigued by and has great respect for working boats, whether at sea, at anchor or at the dock. "I feel that as an artist, details count and when I paint a boat, it is my responsibility to paint that boat reflecting the accuracy of its lines." For Roger, it is exciting when a seaman shares "I recognize that boat. I used to work on it."
He is not just painting a wall or window, or a boat or a wave on a beach, he is telling a story or inviting the viewers to tell theirs. "I paint because I love the process and the challenge of a blank canvas, and the sometimes unpredictable, yet exciting, outcome."
Roger now lives and paints on Vancouver Island, painting in oil and acrylic, en plein air or in studio, on canvas or wood panels. He conducts workshops and teaches courses. His approach to teaching is that it's not really teaching; it's more guiding and encouraging, building confidence.
His work has been exhibited in Calgary, Vancouver and various shows and venues on Vancouver Island, including but not limited to:
Federation of Canadian Artists, Calgary AB
Federation of Canadian Artists, Granville Island, Granville Island
Federation of Canadian Artists, Victoria Chapter
Cowichan Valley Fine Art Show, Duncan
Visions Artists Studio Tour, Cowichan Valley
Artishow Victoria, Artist-in-Residence Program
TD Paint-in, Art Gallery of Greater Victoria
Arts on the Avenue, Ladysmith
McMillan Art Centre, Parksville
Maple Bay Painters, numerous spring and fall shows
Sooke Fine Art Show
Copyright © 2022, Roger Jackson. All rights reserved. | Administration | Powered by ArtSites.ca


Meike "MK-AR7 Battery Grip (For Sony Alpha A7, A7S, A7R Digital Camera) + Wireless Remote Controller"
The Meike MK-AR7 is now available in Singapore. The cheapest Meike MK-AR7 price in Singapore is S$ 132.29 from Lazada. Meike MK-AR7 price details are updated April 2019.
Andoer TP-630 From S$ 148.21 Features: Strong and durable magnalium alloy tripod, maximum load bearing capacity 20kg. Height can be adjusted from 62cm to 180cm. Three-dimensional photographic head with dual handles and scale, great for panoramic shooting. 8.1cm long quick release plate with 1/4 screw and non-slip rubber, hold your valuable camera stably. With vertical and horizontal level spirit levels and a compass, help to make exact balance. Center column can be reversed for macro photography. Gravity hook maintain strong stability in windy days. Foam leg offer comfortable texture and rubber foot avoid unexpected slip.


As you may know, I lost my darling Sly (Sylvester) almost a year ago. At the time, I swore I wouldn't have any more cats while we lived here. We lost Sly's brother, Kiwi, many years ago, hit by a car on the road. What was more heartbreaking than his loss, was that we didn't find him for several days and he was still alive (though very, very injured).
Roll forward to last November, and we adopted two little boys from our local cat shelter. They were deeply traumatised when we got them but slowly developed into a couple of adorable hooligans.
Every day, I was terrified they wouldn't come home, that they would get hit by a car. Every single day. I was less worried about Max - he seemed to stay pretty close to home - but Nero... Nero had that same Wanderlust that Kiwi had.
Just over a week ago, Nero didn't come home. We hoped he had just got himself shut in a shed or a garage, but deep down, we knew he hadn't. We found his body the next day. The small mercy is that he would have been killed instantly.
I've been trying to console myself with the thoughts that we gave him everything he wanted - food, warmth, shelter, love and the opportunity to explore and roam to his heart's content. I just wish he'd had the sense to roam in the acres and acres of fields at the back of us and not on the main road.
He was a beautiful, beautiful boy and my heart is broken.


The benefits of being an Authorized Economic Operator and the procedures that businesses follow to gain this status were the focus of discussions between experts of the World Bank and some members of AmCham Albania. The World Bank and the Albanian Government are currently in a process of designing new development policies aimed at increasing the country's competitiveness. One of the fundamental pillars of this project is the facilitation of trade procedures and logistics. The World Bank notes that despite the achievements that have been made to improve the regulatory framework of the Authorized Economic Operator, the program is still not functional. World Bank experts Mr. Andrew Filmer and Mr. Periklis Saragiotis met at the AmCham office with businesses who have applied for the Authorized Economic Operator program or are interested in doing so, to ask about their understanding of the program, their needs and their expectations of this program. The meetings concluded with renewed commitment to cooperation for improving the business climate in Albania.


Here are some examples of businesses in the Handbags industry who have chosen a stylish ecommerce website theme, customized for their online store, added products, and got ready to accept payments.
bagbelly™ specializes in micro-bead handbag inserts designed to protect your bag from moisture, preserve it's shape & prolong it's life!
Nour Amira was established to satisfy your desire for couture collections. Shop our hand-crafted genuine leather goods.
Unique jewelry, handbags, scarves and watches. Animal friendly, charitable company with a love for great taste.


MyCRM Blog | The "Customer is King" or should it be "CRM is king" … Why is CRM so important?
In this day and age, it's quite surprising that there is still a low percentage of businesses with a CRM system. Just 35% of businesses in the UK have a fully integrated CRM system and with the endless possibilities with CRM, we wonder why the other 65% haven't jumped on the same bandwagon! Ok ok, CRM isn't classed as "cheap", but it is an investment and the positives to having a CRM implemented definitely out way the negatives.
We came across two articles that sum up pretty well why a CRM system is important for your business.
CRM is "a process of managing interactions with current and potential customers" with the use of "activities, strategies and technologies". CRM enables a company to build relationships easily and allows them to retain their current ones. Some people think that CRM systems are mostly for large businesses, but we know that they can work for smaller businesses and SMEs. The main thing is, is that it should help you to manage and communicate with your current and potential customers.
CRM systems keep all of your customers and their information in one place, helping you to see the bigger picture when it comes to knowing what your customers want and why they purchase what they do. Having this kind of data helps in the long run as it highlights what a potential customer expects from your business and in turn allows your business to fulfil this in future products and marketing - everyone's a winner!
The one thing that MyCRM try to exaggerate a lot about CRM, is that it significantly improves the organisation in your business. How so? Well for one (as already mentioned above), it keeps all of your customers in one place. It also paves the way for automation, for example sending newsletters to all of your customers or sending any quick campaigns for that matter. Organisation is key in any business and should be made a priority. It can even tell you how far your customer is in the sales funnel. We honestly don't know how a business runs without CRM, however we are biased!!


Beer for Boston — Tree House Brewing Co.
Tomorrow at 3 PM-12 AM Jack's Abby Brewing and Three Tides & Marshall Wharf Brewing Company are hosting a fundraising event at The Tavern Framingham to benefit victims of yesterday's tragic events in Boston. Tree House (Deano representing) will be there with a keg of Space & Time, along with a ton of great beer from many other New England breweries. There will be a raffle of dry goods / bottles and 100% of the proceeds from the evening's events will be donated The One Fund Boston, a charitable fund set up by Deval Patrick and Mayor Tom Menino. Please come out to this event if you're in the area!
So much support. We hope to see you there.


text:
\section{Introduction}\label{s1}

Without touching deeply a history of the question (see \cite{Fi04} for an excellent account of this), we notice that the irrationality of the \emph{zeta values} --- values of Riemann's zeta function
\begin{gather*}
\zeta(s)=\sum_{n=1}^\infty\frac1{n^s}
\end{gather*}
at integers $s=2,3,\dots$, is known for even $s$ and also for $s=3$, while there are only partial results in this direction for odd $s\ge5$.
A starting point here has been set in the work \cite{BR01} with further development, particularly focusing on $\zeta(5)$, in~\cite{Ri02} and~\cite{Zu04}.

We fix an odd integer $s\ge7$. Our strategy is constructing two sequences of linear forms~$r_n$ and~$\hat r_n$ living in the $\mathbb Q$-space $\mathbb Q+\mathbb Q\zeta(3)+\mathbb Q\zeta(5)+\dots+\mathbb Q\zeta(s)$, for which we have a control of the common denominators $\lambda_n$ of rational coefficients and an elementary access to their asymptotic behaviour as $n\to\infty$; more importantly, the two coefficients of $\zeta(3)$ in these forms are proportional (with factor $7$), so that $7r_n-\hat r_n$ belongs to the space $\mathbb Q+\mathbb Q\zeta(5)+\dots+\mathbb Q\zeta(s)$. Finally, using $7r_n-\hat r_n>0$ and the asymptotics $\lambda_n(7r_n-\hat r_n)\to0$ as $n\to\infty$ of the linear forms
\begin{gather*}
\lambda_n(7r_n-\hat r_n)\in\mathbb Z+\mathbb Z\zeta(5)+\mathbb Z\zeta(7)+\dots+\mathbb Z\zeta(s)
\end{gather*}
when $s=25$, we conclude that it cannot happen that all the quantities $\zeta(5),\zeta(7),\dots,\allowbreak\zeta(25)$ are rational.

The original idea of using the so-called well-poised hypergeometric series to construct linear forms in zeta values of a given parity is due
to Ball and Rivoal~\cite{BR01}; our new ingredient here is using simultaneously such series and their `twists by half', for an appropriate choice of the parameters. More precisely, our hypergeometric series assume the form
\begin{gather}
r_n=\sum_{\nu=1}^\infty R_n(\nu) \qquad\text{and}\qquad \hat r_n=\sum_{\nu=1}^\infty R_n\big(\nu-\tfrac12\big),
\label{e01}
\end{gather}
where the rational-function summand $R_n(t)$ is defined as follows:
\begin{align}
R(t)=R_n(t)
&=\frac{n!^{s-5}\prod_{j=1}^n(t-j)\cdot\prod_{j=1}^n(t+n+j)\cdot2^{6n}\prod_{j=1}^{3n}\big(t-n-\frac12+j\big)} {\prod_{j=0}^n(t+j)^s}\nonumber\\
&=\frac{2^{6n}n!^{s-5}\prod_{j=0}^{6n}\big(t-n+\frac12j\big)}{\prod_{j=0}^n(t+j)^{s+1}}.\label{e02}
\end{align}

The following Sections~\ref{s2} and~\ref{s3} discuss, respectively, the arithmetic and analysis of the forms~\eqref{e01}. In Section~\ref{s4}
we use this information to conclude with the proof of the claimed result and make some relevant comments.

\section{Arithmetic ingredients}\label{s2}

The notation $d_n$ will be used for the least common multiple of $1,2,\dots,n$. Recall that the prime number theorem is equivalent to the asymptotics
\begin{gather}
\lim_{n\to\infty}d_n^{1/n}=e.\label{e03}
\end{gather}

A rational function $S(t)$ of the form
\begin{gather*}
S(t)=\frac{P(t)}{(t-t_1)^{s_1}(t-t_2)^{s_2}\dotsb(t-t_q)^{s_q}},
\end{gather*}
whose denominator has degree larger than its numerator, possesses a unique partial-fraction decomposition
\begin{gather*}
S(t)=\sum_{j=1}^q\sum_{i=1}^{s_j}\frac{b_{i,j}}{(t-t_j)^i}.
\end{gather*}
The coefficients here can be computed on the basis of explicit formula
\begin{gather*}
b_{i,j}=\frac1{(s_j-i)!} \bigl(S(t)(t-t_j)^{s_j}\bigr)^{(s_j-i)}\Big|_{t=t_j}
\end{gather*}
for all $i$, $j$ in question. This procedure can be illustrated on the following examples, in which all the exponents $s_j$ are equal to~1:
\begin{gather*}
\frac{n!}{\prod_{j=0}^n(t+j)}
=\sum_{k=0}^n\frac{(-1)^k\binom nk}{t+k},
\displaybreak[2]\\
\frac{\prod_{j=1}^n(t-j)}{\prod_{j=0}^n(t+j)}
=\sum_{k=0}^n\frac{(-1)^{n+k}\binom{n+k}n\binom nk}{t+k},
\displaybreak[2]\\
\frac{\prod_{j=1}^n(t+n+j)}{\prod_{j=0}^n(t+j)}
=\sum_{k=0}^n\frac{(-1)^k\binom{2n-k}n\binom nk}{t+k},
\displaybreak[2]\\
\frac{2^{2n}\prod_{j=1}^n(t+\frac12-j)}{\prod_{j=0}^n(t+j)}
=\sum_{k=0}^n\frac{(-1)^{n+k}\binom{2n+2k}{2n}\binom{2n}{n+k}}{t+k},
\displaybreak[2]\\
\frac{2^{2n}\prod_{j=1}^n(t-\frac12+j)}{\prod_{j=0}^n(t+j)}
=\sum_{k=0}^n\frac{\binom{2k}k\binom{2n-2k}{n-k}}{t+k},
\displaybreak[2]\\
\frac{2^{2n}\prod_{j=1}^n(t+n-\frac12+j)}{\prod_{j=0}^n(t+j)}
=\sum_{k=0}^n\frac{(-1)^k\binom{4n-2k}{2n}\binom{2n}k}{t+k}.
\end{gather*}
It also means that the function $R(t)$ in \eqref{e02} can be written as
\begin{gather}
R(t)=\sum_{i=1}^s\sum_{k=0}^n\frac{a_{i,k}}{(t+k)^i}\label{e04}
\end{gather}
with the recipe to compute the coefficients $a_{i,k}$ in its partial-fraction decomposition. At the same time, the function $R(t)$ is a product of `simpler' rational functions given above, with all coefficients of their partial fractions being integral.

\begin{lemma}\label{l1}
Let $k_1,\dots,k_q$ be pairwise distinct numbers from the set $\{0,1,\dots,n\}$ and $s_1,\dots,s_q$ positive integers. Then the coefficients in the expansion
\begin{gather*}
\frac1{\prod_{j=1}^q(t+k_j)^{s_j}} =\sum_{j=1}^q\sum_{i=1}^{s_j}\frac{b_{i,j}}{(t+k_j)^i}
\end{gather*}
satisfy
\begin{gather} d_n^{s-i}b_{i,j}\in\mathbb Z, \qquad\text{where}\quad i=1,\dots,s_j \quad \text{and}\quad j=1,\dots,q, \label{e05}
\end{gather}
where $s=s_1+\dots+s_q$.

In particular,
\begin{gather}
d_n^{s-i}a_{i,k}\in\mathbb Z, \qquad\text{where}\quad i=1,\dots,s \quad \text{and}\quad k=0,1,\dots,n, \label{e06}
\end{gather}
for the coefficients in~\eqref{e04}.
\end{lemma}

\begin{proof} Denote the rational function in question by $S(t)$. The statement is trivially true when $q=1$, therefore we assume that $q\ge2$. In view of the symmetry of the data, it is sufficient to demonstrate the inclusions \eqref{e05} for $j=1$. Differentiating a related product $m$ times, for any $m\ge0$, we obtain
\begin{align*}
\frac1{m!}\bigl(S(t)(t+k_1)^{s_1}\bigr)^{(m)}
&=\frac1{m!}\left(\prod_{j=2}^q(t+k_j)^{-s_j}\right)^{(m)}
=\sum_{\substack{\ell_2,\dots,\ell_q\ge0\\ \ell_2+\dots+\ell_q=m}}\prod_{j=2}^q\frac1{\ell_j!}\bigl((t+k_j)^{-s_j}\bigr)^{(\ell_j)}\\
&=\sum_{\substack{\ell_2,\dots,\ell_q\ge0\\ \ell_2+\dots+\ell_q=m}}\prod_{j=2}^q(-1)^{\ell_j}\binom{s_j+\ell_j-1}{\ell_j}(t+k_j)^{-(s_j+\ell_j)}.
\end{align*}
This implies that
\begin{gather*}
b_{i,1}=\sum_{\substack{\ell_2,\dots,\ell_q\ge0\\ \ell_2+\dots+\ell_q=s_1-i}}
\prod_{j=2}^q(-1)^{\ell_j}\binom{s_j+\ell_j-1}{\ell_j}\frac1{(k_j-k_1)^{s_j+\ell_j}}
\end{gather*}
for $i=1,\dots,s_1$. Using $d_n/(k_j-k_1)\in\mathbb Z$ for $j=2,\dots,q$ and $\sum_{j=2}^q(s_j+\ell_j)=s-i$ for each individual summand, we deduce the desired inclusion in \eqref{e05} for $j=1$, hence for any~$j$.

The second claim in the lemma follows from considering $R(t)$ as a product of the `simpler' rational functions.
\end{proof}

\begin{lemma}\label{l2} For the coefficients $a_{i,k}$ in \eqref{e04}, we have
\begin{gather*}
a_{i,k}=(-1)^{i-1}a_{i,n-k} \qquad\text{for}\quad k=0,1,\dots,n \quad\text{and}\quad i=1,\dots,s,
\end{gather*}
so that
\begin{gather*}
\sum_{k=0}^na_{i,k}=0 \qquad\text{for} \ i \ \text{even}.
\end{gather*}
\end{lemma}

\begin{proof}
Since $s$ is odd, the function \eqref{e02} possesses the following (well-poised) symmetry: $R(-t-n)=-R(t)$. Substitution of the relation into~\eqref{e04} results in
\begin{align*}
-\sum_{i=1}^s\sum_{k=0}^n\frac{a_{i,k}}{(t+k)^i}
&=\sum_{i=1}^s\sum_{k=0}^n\frac{a_{i,k}}{(-t-n+k)^i}=\sum_{i=1}^s(-1)^i\sum_{k=0}^n\frac{a_{i,k}}{(t+n-k)^i}\\
&=\sum_{i=1}^s(-1)^i\sum_{k=0}^n\frac{a_{i,n-k}}{(t+k)^i},
\end{align*}
and the identities in the lemma follow from the uniqueness of decomposition into partial fractions. The second statement follows from
\begin{gather*}
\sum_{k=0}^na_{i,k}=(-1)^{i-1}\sum_{k=0}^na_{i,n-k}=(-1)^{i-1}\sum_{k=0}^na_{i,k}.\tag*{\qed}
\end{gather*}
\renewcommand{\qed}{}
\end{proof}

\begin{lemma}\label{l3} For each $n$,
\begin{gather*}
r_n=\sum_{\substack{i=2\\i\;\text{odd}}}^sa_i\zeta(i)+a_0
\qquad\text{and}\qquad
\hat r_n=\sum_{\substack{i=2\\i\;\text{odd}}}^sa_i\big(2^i-1\big)\zeta(i)+\hat a_0,
\end{gather*}
with the following inclusions available\textup:
\begin{gather*}
d_n^{s-i}a_i\in\mathbb Z \qquad\text{for}\quad i=3,5,\dots,s,
\quad\text{and}\quad d_n^sa_0, d_n^s\hat a_0\in\mathbb Z.
\end{gather*}
\end{lemma}

Notice that
\begin{gather*}
\big(2^i-1\big)\zeta(i) =\sum_{\ell=1}^\infty\frac1{\big(\ell-\frac12\big)^i}
\end{gather*}
for $i\ge2$.

\begin{proof}
Our strategy here is to write the series in \eqref{e01} using the partial-fraction decomposition~\eqref{e04} of $R(t)$. To treat the first sum $r_n$ we additionally introduce an auxiliary parameter $z>0$, which we later specialise to $z=1$:
\begin{align*}
r_n(z) &=\sum_{\nu=1}^\infty R_n(\nu)z^\nu
=\sum_{\nu=1}^\infty\sum_{i=1}^s\sum_{k=0}^n\frac{a_{i,k}z^\nu}{(\nu+k)^i}\\
&=\sum_{i=1}^s\sum_{k=0}^na_{i,k}z^{-k}\sum_{\nu=1}^\infty\frac{z^{\nu+k}}{(\nu+k)^i}
=\sum_{i=1}^s\sum_{k=0}^na_{i,k}z^{-k}\left(\operatorname{Li}_i(z)-\sum_{\ell=1}^k\frac{z^\ell}{\ell^i}\right)\\
&=\sum_{i=1}^s\operatorname{Li}_i(z)\sum_{k=0}^na_{i,k}z^{-k}-\sum_{i=1}^s\sum_{k=0}^n\sum_{\ell=1}^k\frac{a_{i,k}z^{-(k-\ell)}}{\ell^i},
\end{align*}
where
\begin{gather*}
\operatorname{Li}_i(z)=\sum_{\ell=1}^\infty\frac{z^\ell}{\ell^i}
\end{gather*}
for $i=1,\dots,s$ are the polylogarithmic functions. The latter are well defined at $z=1$ for $i\ge2$, where $\operatorname{Li}_i(1)=\zeta(i)$, while $\operatorname{Li}_1(z)=-\log(1-z)$ does not have a limit as $z\to1^-$. By taking the limit as $z\to1^-$ in the above derivation and using $R_n(\nu)=O\big(\nu^{-2}\big)$ as $\nu\to\infty$, we conclude that
\begin{gather*}
\sum_{k=0}^na_{1,k}=\lim_{z\to1^-}\sum_{k=0}^na_{1,k}z^{-k}=0,
\end{gather*}
and
\begin{gather}
r_n=\sum_{i=2}^s\zeta(i)\sum_{k=0}^na_{i,k}-\sum_{i=1}^s\sum_{k=0}^na_{i,k}\sum_{\ell=1}^k\frac1{\ell^i}.\label{e07}
\end{gather}

We proceed similarly for $\hat r_n$, omitting introduction of the auxiliary parameter $z$. Since $R(t)$ in \eqref{e02} vanishes at $t=-\frac12,-\frac32,\dots,-n+\frac12$, we can shift the starting point of summation for $\hat r_n$ to $t=-m-\frac12$, where $m=\big\lfloor\frac{n-1}2\big\rfloor$, so that
\begin{align}
\hat r_n &=\sum_{\nu=-m}^\infty R_n\big(\nu-\tfrac12\big) =\sum_{\nu=-m}^\infty\sum_{i=1}^s\sum_{k=0}^n\frac{a_{i,k}}{\big(\nu+k-\frac12\big)^i}
\nonumber\\
&=\sum_{i=1}^s\sum_{k=0}^na_{i,k}\sum_{\nu=-m}^\infty\frac1{\big(\nu+k-\frac12\big)^i} \displaybreak[2]\nonumber\\
&=\sum_{i=1}^s\sum_{k=0}^ma_{i,k}\sum_{\nu=-m}^\infty\frac1{\big(\nu+k-\frac12\big)^i}
+\sum_{i=1}^s\sum_{k=m+1}^na_{i,k}\sum_{\nu=-m}^\infty\frac1{\big(\nu+k-\frac12\big)^i} \displaybreak[2]\nonumber\\
&=\sum_{i=1}^s\sum_{k=0}^ma_{i,k}\left(\sum_{\ell=k-m}^0\frac1{\big(\ell-\frac12\big)^i}+\sum_{\ell=1}^\infty\frac1{\big(\ell-\frac12\big)^i}\right)
\nonumber\\ &\quad{} +\sum_{i=1}^s\sum_{k=m+1}^na_{i,k}\left(\sum_{\ell=1}^\infty\frac1{\big(\ell-\frac12\big)^i}-\sum_{\ell=1}^{k-m-1} \frac1{\big(\ell-\frac12\big)^i}\right)\displaybreak[2]\nonumber\\
&=\sum_{i=2}^s(2^i-1)\zeta(i)\sum_{k=0}^na_{i,k} +\sum_{i=1}^s\sum_{k=0}^ma_{i,k}\sum_{\ell=0}^{m-k}\frac{(-1)^i}{\big(\ell+\frac12\big)^i}
\nonumber\\ &\quad{} -\sum_{i=1}^s\sum_{k=m+1}^na_{i,k}\sum_{\ell=1}^{k-m-1}\frac1{\big(\ell-\frac12\big)^i}.\label{e08}
\end{align}
Now the statement of the lemma follows from the representations in \eqref{e07} and \eqref{e08}, Lemma~\ref{l2}, the inclusions \eqref{e06} of Lemma~\ref{l1} and
\begin{alignat*}{3}
& d_n^i\sum_{\ell=1}^k\frac1{\ell^i} \in\mathbb Z \qquad&& \text{for}\quad 0\le k\le n \quad \text{and}\quad i\ge1,&
\displaybreak[2]\\
& d_n^i\sum_{\ell=0}^{m-k}\frac{(-1)^i}{(\ell+\frac12)^i} \in\mathbb Z \qquad && \text{for}\quad 0\le k\le m \quad \text{and}\quad i\ge1,\\
& d_{n-1}^i\sum_{\ell=1}^{k-m-1}\frac1{\big(\ell-\frac12\big)^i} \in\mathbb Z \qquad && \text{for}\quad m+1\le k\le n \quad \text{and}\quad i\ge1.
\tag*{\qed}
\end{alignat*}\renewcommand{\qed}{}
\end{proof}

\section{Asymptotic behaviour}\label{s3}

In this section we make frequent use of Stirling's asymptotic formula
\begin{gather*}
n!\sim\sqrt{2\pi n}\left(\frac ne\right)^n \qquad\text{as}\quad n\to\infty,
\end{gather*}
and its corollary
\begin{gather*}
\binom{2n}n\sim\frac{2^{2n}}{\sqrt{\pi n}} \qquad\text{as}\quad n\to\infty
\end{gather*}
for the central binomial coefficients. (One may also use somewhat weaker but `more elementary' lower and upper bounds
\begin{gather*}
\int_1^n\log x\,\d x\le\log(n!)\le\int_2^{n+1}\log x\,\d x
\end{gather*}
for the factorial coming out from estimating integral sums of the logarithm function, with a~nemesis of running into more sophisticated versions for the asymptotics and inequalities below.)

Because the rational function $R_n(t)$ in \eqref{e02} vanishes at $1,2,\dots,n$ and at $\frac12,\frac32,\dots,\allowbreak n-\nobreak\frac12$,
the hypergeometric series \eqref{e01} can be alternatively written as
\begin{gather*}
r_n=\sum_{\nu=n+1}^\infty R_n(\nu)=\sum_{k=0}^\infty c_k \qquad\text{and}\qquad
\hat r_n=\sum_{\nu=n+1}^\infty R_n(\nu-\tfrac12)=\sum_{k=0}^\infty\hat c_k,
\end{gather*}
with the involved summands
\begin{gather}
c_k=R_n(n+1+k)=\frac{2^{6n}n!^{s-5}\prod_{j=0}^{6n}\big(k+1+\frac12j\big)}{\prod_{j=0}^n(n+k+1+j)^{s+1}}
=\frac{n!^{s-5}(6n+2k+2)! (n+k)!^{s+1}}{2 (2k+1)! (2n+k+1)!^{s+1}}\label{e09}
\\ \intertext{and}
\hat c_k=R_n\big(n+\tfrac12+k\big)=\frac{2^{6n}n!^{s-5}\prod_{j=0}^{6n}\big(k+\frac12+\frac12j\big)} {\prod_{j=0}^n\big(n+k+\frac12+j\big)^{s+1}}\nonumber
\end{gather}
strictly \emph{positive}. Observe that
\begin{align}
\frac{c_k}{\hat c_k}
&=\frac{\prod_{j=0}^{6n}(2k+2+j)}{\prod_{j=0}^{6n}(2k+1+j)}
\cdot\left(\prod_{j=0}^n\frac{n+k+\frac12+j}{n+k+1+j}\right)^{s+1}\nonumber\\
&=\frac{6n+2k+2}{2k+1}\cdot\left(2^{-2(n+1)}\frac{\binom{4n+2k+2}{2n+k+1}}{\binom{2n+2k}{n+k}}\right)^{s+1}\nonumber\\
&\sim\frac{6n+2k+2}{2k+1}\left(\frac{n+k}{2n+k+1}\right)^{(s+1)/2} \qquad\text{as}\quad n+k\to\infty. \label{e10}
\end{align}

\begin{lemma}\label{l4} For $s\ge7$ odd,
\begin{gather*}
\lim_{n\to\infty}r_n^{1/n}=\lim_{n\to\infty}\hat r_n^{1/n}=g(x_0)
\qquad\text{and}\qquad \lim_{n\to\infty}\frac{r_n}{\hat r_n}=1
\end{gather*}
where
\begin{gather*}
g(x)=\frac{2^6(x+3)^6(x+1)^{s+1}}{(x+2)^{2(s+1)}}
\end{gather*}
and $x_0$ is the unique positive zero of the polynomial
\begin{gather*}
x(x+2)^{(s+1)/2}-(x+3)(x+1)^{(s+1)/2}.
\end{gather*}
\end{lemma}

\begin{proof}We have
\begin{gather}
\frac{c_{k+1}}{c_k} =\frac{\big(k+3n+\frac32\big)(k+3n+2)}{(k+1)\big(k+\frac32\big)} \left(\frac{k+n+1}{k+2n+2}\right)^{s+1} \sim f\left(\frac kn\right)^2 \qquad\text{as}\quad n+k\to\infty, \label{e11}
\end{gather}
where
\begin{gather*}
f(x)=\frac{x+3}{x}\left(\frac{x+1}{x+2}\right)^{(s+1)/2}.
\end{gather*}
For an ease of notation write $q=(s+1)/2\ge4$. Since
\begin{gather*}
\frac{f'(x)}{f(x)}=\frac1{x+3}-\frac1x+q\left(\frac1{x+1}-\frac1{x+2}\right) =\frac{(q-3)x^2+3(q-3)x-6}{x(x+1)(x+2)(x+3)}
\end{gather*}
and the quadratic polynomial in the latter numerator has a unique positive zero $x_1$, the func\-tion~$f(x)$ monotone decreases from $+\infty$ to $f(x_1)$ when $x$ ranges from~$0$ to~$x_1$ and then monotone increases from $f(x_1)$ to $f(+\infty)=1$ (not attaining the value!) when $x$ ranges from $x_1$ to $+\infty$. In particular, there is exactly one positive solution $x_0$ to $f(x)=1$. Notice that $0<x_0<1$, because $f(1)=4\cdot(2/3)^q<1$.

The information gained and asymptotics in \eqref{e11} imply that $c_{k+1}/c_k>1$ for the indices $k<x_0n-\gamma\sqrt n$ and $c_{k+1}/c_k<1$
for $k>x_0n+\gamma\sqrt n$ for an appropriate choice of $\gamma>0$ dictated by application of Stirling's formula to the factorials defining $c_k$ in~\eqref{e09} (see \cite[Section~3.4]{Br58} as well as the second proof of Lemma~3 in~\cite{BR01}). This means that the asymptotic behaviour of the sum $r_n=\sum_{k=0}^\infty c_k$ is determined by the asymptotics of $c_{k_0}$ and its neighbours $c_k$, where $k_0=k_0(n)\sim x_0n$ and $|k-k_0|\le\gamma\sqrt n$, so that
\begin{align*}
\lim_{n\to\infty}r_n^{1/n}&=\lim_{n\to\infty}c_{k_0(n)}^{1/n}\\
&=\lim_{n\to\infty}\Biggl(\left(\frac ne\right)^{(s-5)n}\left(\frac{6n+2k_0+2}e\right)^{6n+2k_0+2}\left(\frac e{2k_0+1}\right)^{2k_0+1}
\\ &\qquad\quad\times
\left(\frac{n+k_0}e\right)^{(s+1)(n+k_0)}\left(\frac e{2n+k_0+1}\right)^{(s+1)(2n+k_0+1)}\Biggr)^{1/n}\\
&=\frac{(2x_0+6)^{2x_0+6}(x_0+1)^{(s+1)(x_0+1)}}{(2x_0)^{2x_0}(x_0+2)^{(s+1)(x_0+2)}}\\
&=\frac{2^6(x_0+3)^6(x_0+1)^{s+1}}{(x_0+2)^{2(s+1)}}\cdot f(x_0)^{2x_0}=g(x_0).
\end{align*}

It now follows from \eqref{e10} that
\begin{gather}
\frac{\hat c_{k+1}}{\hat c_k} \sim\frac{c_{k+1}}{c_k} \qquad\text{as}\quad n+k\to\infty, \label{e12}
\end{gather}
so that the above analysis applies to the sum $\hat r_n=\sum_{k=0}^\infty\hat c_k$ as well, and its asymptotic behaviour is determined by the asymptotics of $\hat c_{k_0}$ and its neighbours $\hat c_k$, where $k_0=k_0(n)\sim x_0n$ and $|k-k_0|\le\hat\gamma\sqrt n$. From \eqref{e12} we deduce that the limits of $\hat c_{k_0(n)}^{1/n}$ and $c_{k_0(n)}^{1/n}$ as $n\to\infty$ coincide, hence $\hat r_n^{1/n}\to g(x_0)$ as $n\to\infty$. In addition to this, we also get
\begin{gather*}
\lim_{n\to\infty}\frac{r_n}{\hat r_n}=\lim_{n\to\infty}\frac{c_{k_0(n)}}{\hat c_{k_0(n)}}
=\lim_{n\to\infty}\frac{6n+2k_0+2}{2k_0+1}\left(\frac{n+k_0}{2n+k_0+1}\right)^{(s+1)/2}=f(x_0),
\end{gather*}
which leads to the remaining limiting relation.
\end{proof}

\section{Conclusion}\label{s4}

We choose $s=25$ and apply Lemma~\ref{l4} to find out that $7r_n-\hat r_n>0 $ for $n$ sufficiently large, and
\begin{gather*}
\lim_{n\to\infty}(7r_n-\hat r_n)^{1/n}=g(x_0)=\exp(-25.292363\dots),
\end{gather*}
where $x_0=0.00036713\dots$. Assuming that the odd zeta values from $\zeta(5)$ to $\zeta(25)$ are all rational and denoting by $a$ their common denominator, we use Lemma~\ref{l3} and the asymptotics~\eqref{e03} to conclude that the sequence of \emph{positive integers}
\begin{gather*}
ad_n^{25}(7r_n-\hat r_n)
\end{gather*}
tends to $0$ as $n\to\infty$; contradiction. Thus, at least one of the numbers $\zeta(5),\zeta(7),\dots,\allowbreak\zeta(25)$ is irrational.

Those who count the prime number theorem as insufficiently elementary may use weaker versions of \eqref{e03}, for example, $d_n<3^n$ from \cite{Ha72} and the choice $s=33$ instead, to arrive at the same conclusion (for the larger value of $s$, of course).

Finally, we remark that the novelty of eliminating an `unwanted' term of $\zeta(3)$ in linear forms in odd zeta values can be further used with the arithmetic method in \cite{Zu04} to significantly reduce the size of~$s$. Since this does not let $s$ be down to $s=9$, hence leaving the achievement `at least one of the four numbers $\zeta(5)$, $\zeta(7)$, $\zeta(9)$, $\zeta(11)$ is irrational' unchanged, we do not discuss this generalisation in greater details. We point out, however, that there are other applications of the hypergeometric `twist-by-half' idea, some discussed in the joint papers~\cite{KZ18,RZ18}, and that a far-going extension to general `twists' introduced by J.~Sprang in \cite{Sp18} leads to an elementary proof of a version of the Ball--Rivoal theorem from~\cite{BR01} as well as to a significant improvement of the latter~--- see \cite{FSZ18} for details.

\subsection*{Acknowledgements}

I thank St\'ephane Fischler, Tanguy Rivoal, Johannes Sprang and the anonymous referees for their feedback on the manuscript.

\pdfbookmark[1]{References}{ref}

redpajama_set_name: RedPajamaArXiv


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text:
MAGNUS, SIR PHILIP:
By: Joseph Jacobs
English educationist; born in London Oct. 7, 1842; educated at University College in that city, and at the University of London (B.A. 1863; B.Sc. 1864). Destined for the Jewish ministry, he pursued his studies in Berlin (1865-66). On his return to England he became one of the ministers of the Berkeley Street Synagogue, London. At the same time he did much private teaching, and was professor of mechanics at the Catholic University. His "Lessons in Elementary Mechanics" (London, 1874) was for a long time the standard text-book on the subject. In 1880 he was appointed secretary of the City and Guilds of London Institute for the Advancement of Technical Education, and in that capacity became the leading authority on technical education in the United Kingdom. He was a member of a royal commission for this subject (1881-84), visiting in connection therewith the chief educational centers of western Europe. In 1886 he was knighted in recognition of his services to education. In 1888 he published a work on "Industrial Education," as one of a series of text-books on education edited by him. He was principal of the Finsbury Technical College from 1883 to 1885, and a member of the London School Board in 1890 and 1891. In 1900 he became fellow of the senate of London University, and at the present time (1904) is connected in an honorary capacity with many important educational institutions.
Magnus' work at the Guilds Institute caused him to resign his position in the Jewish ministry; but he has retained his interest in many communal institutions, being vice-president of the Anglo-Jewish Association, president of the Deaf and Dumb Home, and a representative on the board of deputies of the Berkeley Street Synagogue, of which he has been also a warden.
Men and Women of the Time, 1894;
Who's Who, 1904.


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Tapas are often defined as bite-sized Spanish hors-d'oeuvres, and many people think of them as appetizers. Tapas are more than just appetizers; they are an integral part of Spanish cuisine and customs. Tapas originated many centuries ago in the southern region of Spain known as Andalucía.
The most popular explanation for the origin of tapas is that they began when innkeepers began placing saucers or pieces of bread atop their customers' wine glasses as a way to prevent flies from swarming in. "Tapas" is the Spanish word for "cover" or "lid". These small portions of food that were used to cover glasses proved to be a good way of attracting customers into bars, which is why tapas have evolved from a simple piece of bread into more intricate culinary works.
Although tapas originated in the south, they are served in every region of Spain. Some bars serve tapas for free when a drink is ordered, for example olives or nuts are commonly free of charge.
Tapas are an important part of Spanish tradition and culture because they bring families and friends together. It is common for Spaniards to gather at bars or bodegas for drinks and conversation, while sharing "raciones", or portions of tapas.
This page was last edited on 13 September 2018, at 18:05.


To make your organising a little easier we have tried to include as many services as we can to make your day perfect. All the services listed below are included in the package price along with a 3 course wedding breakfast with choices that you have picked to create your menu.
Children under 10 are half price and under 2 are free if not eating. All children are served juice for the arrival drink, but nothing for the toast and a smaller portion of the menu chosen for the day.
Chair covers and sash for the number of day package guests supplied by XLB events.
Use of gazebo, summer house, gardens etc. for reception drinks and photos.
Decorative cake base and stands to choose from, with decorative sword/knife for cake cutting.
Wrought Iron Tall candle sticks with church candles for all guest tables along with tea lights & circular mirror table centres.
Toast mastering by duty manager.
Printed seating plan to your requirements.
Personal help and advice on all wedding arrangements.
Glass of Prosecco for all guest to drink with toast.
Hot served menu with 3 starters, 2 main courses and 3 desserts.
Coffee and mints for guests to order on day.
The menu chosen by yourselves printed and displayed on the tables.
Complimentary unique honeymoon suite for first night of honeymoon, with Jersey Farm breakfast in bed.
It's been a long, but very memorable and delightful day. To finish your special day in style you can retire to the comforts of the bridal suite, which is a suite with a lounge as well. With full English breakfast in bed the following morning, served to you in the comfort of your suite. You will leave Jersey Farm ready to enjoy your life together.
Designed by hotel owner Mark the honeymoon suite gets the 'WOW' factor. Quirky Kitsch is the order of the day.
'You will certainly remember the first evening of your honeymoon' – 'the perfect end to a perfect day'. Marble and wooden floors, fibre optical star lights in the ceiling. A round spa bath in the lounge. Plasma screen for dvd viewing complete with surround sound. Large soft bed with Heart shaped leather headboard. Fridge, dimming lights, cool colours and a trendy wet room complete with walk in shower and a little cow pattern as well !