text:
Q: Prove that $\text{ord}_{2^k}5=2^{k-2}$ where $k$ is any integer $\geq3$ Prove that $\text{ord}_{2^k}5=2^{k-2}$ where $k$ is any integer $\geq3$.
I am using the fact that for any odd integer $a$ and $k\geq3$, $a^{2^{k-2}}\equiv1\text{ }(\text{mod }2^k)$.
So, by the definition $\text{ord}_{2^k}5$ is the least positive integer $x$ such that $5^x\equiv1\text{ }(\text{mod }2^k)$. And since 5 is odd, then $5^{2^{k-2}}\equiv1\text{ }(\text{mod }2^k)$ by the fact above.
But I am struggling to show that $2^{k-2}$ is the least integer. Any theorems or facts that I can use?
Thanks for the help!

A: You can prove it by induction on $k$.
More precisely, one proves that for any $k\ge 3$, we can write
\begin{equation}5^{2^{k-2}}=1+n_k\cdot 2^k, \quad n_k\enspace\text{odd.}\tag{1}\end{equation}
Initialisation is trivially satisfied (for $n=3$, it means $5 ^2=1+3\cdot 8$).
Inductive step: suppose for some $k\ge 3$, $\;(1)$ is satisfied. Then
$$5^{2^{k-1}}=\Bigl(5^{2^{\scriptstyle k-2}}\Bigr)^2=\bigl(1+n_k\cdot 2^k\bigr)^2=1+n_k2^{k+1}+n_k^2\mkern1mu2^{2k}=1+n_k(1+n_k2^{k-1})2^{k+1}.$$
This proves the inductive step, as $\;n_k(1+n_k2^{k-1})$ is odd.
Relation $(1)$ proves the order is $2^{k-2}$.
Indeed, if for some $k$ it were less, it would be  $2^{k-i}$, $i\ge3$, so we would have $\;5^{2^{k-3}}=1+n\cdot 2^k$. However this would imply
$$5^{2^{k-2}}=(1+n\cdot 2^k)^2=1+(2n+n^22^k)2^k$$
and the coefficient $2n+n^22^k$ would be even, not odd.

redpajama_set_name: RedPajamaStackExchange


text:
Watch This Space: N404 at Flagship Building in George Town
May 29, 2019Blog
By Anna Wootton
Located on Harbour Drive in George Town, Flagship building is not only a stunning property, whose unique architecture catches the eye, but it also offers move-in-ready Class-B office space such as suite N404, located on the fourth floor of this centrally located building.
At 2,011 square feet, this oceanfront office space offers a layout with an open floorplan and select private offices. A communal kitchen and boardroom round out this space, which also features wraparound balconies (perfect for taking an all-important work break to enjoy the unparalleled ocean views). The airy and light-filled office will motivate any employee and ensure a collaborative work style, while the hardwood floors offer an urban chic design to the space that makes a stunning impression to both employees and visitors.
The clincher for both employees and clients will be the unbeatable water views, a daily reminder that living and working in the Cayman Islands is unlike anywhere else. History buffs will be excited to be based in the nation's capital in close proximity to the Cayman Islands courthouse, Heroes Square, the George Town Public Library and Museum and other significant buildings.
Flagship is home to a mix of retail and office businesses, and there are multiple benefits to choosing Flagship as your business's home, including a dedicated building back-up electricity generator; dusk-till-dawn on-site security; and on-site building maintenance. Assistance is available from the dedicated and experienced property management staff from Dart Real Estate and the building features two interior elevators and a new chiller system. Key fob access is also available.
To schedule a viewing of N404 at Flagship, click here to contact our leasing team.
To learn more about spaces available for lease visit our commercial leasing page.
Anna Wootton is the Digital Marketing & PR Manager for Dart's real estate companies and assets, including Dart Real Estate, Provenance Properties, Camana Bay and The Residences at Seafire. Born in the Cayman Islands, with British heritage and a Canadian passport, Anna is multinational with a Caymankind heart. Anna has a background in journalism and a Bachelor's degree in English Literature from University of British Columbia. She has worked for Dart for the past five years.
Subscribe to our newsletter to get the first look at Class-A and Class-B commercial properties available for lease in the Cayman Islands.

redpajama_set_name: RedPajamaCommonCrawl


Suffered from holiday food poisoning?
FOOD POISONING ABROAD? RUINED YOUR HOLIDAY?
You go on holiday to relax, get away and enjoy your time in a foreign land. However there are dangers that threaten to ruin your holiday, one of the most common being food poisoning. If you or your family have had your holiday ruined by food poisoning then you are legally entitled to claim compensation.
The most common forms of food poisoning are E-Coli and Salmonella; fortunately most cases result in mild forms, those that you can recover from within a few days, however some cases do present more serious symptoms. It is quite common for a group of people to experience food poisoning after dining in the same establishment. Negligence in preparing your food correctly resulting in food poisoning abroad is not acceptable and we can help you to claim compensation for your illness.
Shires Law can help you with your food poisoning abroad claim, we operate on a No Win No Fee basis, you will not be out of pocket whether you win or lose.
Some cases can result in more serious ailments,if you would like more advice on your specific predicament then our consultants can provide an initial assessment of your personal circumstances.
Awards for compensation vary depending upon how serious the case of holiday food poisoning you experienced. During an initial assessment our lawyers, experts in food poisoning abroad cases, will be able to give you a better idea of the kind of compensation you may be liable to receive. As a guide, a case considered mild, mainly comprising of stomach cramps and diarrhoea may be rewarded with approximately £600, whereas a more severe case that caused significant discomfort and possibly hospitalisation may receive in the region of £2,000 to £6,000.
Holiday food poisoning cases can be processed fairly quickly where the restaurant or hotel admits liability, however the process may be lengthened if the establishment chooses to fight the case. It is impossible to give a guarantee of an exact time frame, but rest assured that our lawyers will do everything they can to make sure your food poisoning abroad case is closed in as time efficient a manner as possible.
We can help you with your food poisoning abroad claim; our advisors are on hand to talk to you by calling 0800 285 266 or via our Live Chat facility.
If physiotherapy or rehabilitation is required due to your food poisoning incident, we can provide you with an Immediate Needs Assessment and make sure you receive the required rehabilitation quickly and on a private basis.


text:
Meet me at the Museum: Combining Architecture and Art
From the groundbreaking Solomon R. Guggenheim museum in New York City to the revolutionary Mucem Museum in Marseilles, combining art with architecture makes for an electrifying experience. This spring, Montreal and Quebec City are delighting museum visitors and art fans alike with stunning new pavilions and extraordinary exhibits. MONTREAL To mark Montreal's 375th anniversary, The…
From the groundbreaking Solomon R. Guggenheim museum in New York City to the revolutionary Mucem Museum in Marseilles, combining art with architecture makes for an electrifying experience. This spring, Montreal and Quebec City are delighting museum visitors and art fans alike with stunning new pavilions and extraordinary exhibits.
To mark Montreal's 375th anniversary, The Montreal Museum of Fine Arts has opened The Michal and Renata Hornstein Pavillon for Peace. The glass walls on each of the six floors of architectural excellence allow visitors to experience an amazing view of the city and its famous mountain. Behind the Victorian facade lies a structure that varies in appearance based on changes in daylight. At night, the art galleries' soft light penetrates through the lacework of the building, rendering the warm wood framework and the natural heritage of the complex visible to all.
The Montreal Museum of Fine Arts has opened a portal into the life of Marc Chagall, an artist whose art demonstrates a profound connection to music. Featuring over 300 pieces, this multidisciplinary exhibition is the first in Canada that links music into Chagall's colorful world. Through his easel paintings, murals, book illustrations, collections of lithographs, costumes for the stage, sculptures, ceramics, stained glass and mosaics, visitors get a chronological picture of the artist's culturally diverse life. From his years in in Russia, his Parisian period, his time in New York and in Mexico and his life in the South of France, Chagall's art embodies the splendor of this traversal experience.
The Quebec Museum of National Art is celebrating the opening of its fourth art complex. Shedding light onto contemporary art, the Pierre Lassonde Pavilion defines the border between the city life of Quebec and the historic and painteresque landscape of the Plains of Abraham. Devoted to Quebec art, this new complex provides additional space for the continuously growing design and contemporary collections. This pavilion is as much a work of art as the collections themselves. Built on the edge of the city, this pavilion is a gateway into the beautiful park of the Plains of Abraham. Placed beside an old church, the modern and contemporary architectural design draws attention to the new versus old culture of the city. At the heart of this architectural design is a majestic spiral staircase allowing visitors to view the park through the glass facade.
This year, the Quebec Museum of National Art will be hosting the eighth edition of the Manif D'art – Quebec City Biennial, where numerous international artists and well known Canadians gather to promote innovation and creativity through their artwork. This year's theme is the art of joy and was chosen by Alexia Fabre, director at the Musée D'art Contemporain du Val-De-Marne. This theme explores joy beyond its simple notions, as the richness of its artistic expressions in light of current societal trends.
This spring, take the time to visit these architectural sites and discover the transcending experience projected through the beauty of art.
"Museums are places where Time is transformed into Space" ― Orhan Pamuk
By Mobilia
Throws: A Buying Guide And Practical Tips
Whether it's for snuggling up while watching your favorite show or to spruce up your bed, a throw adds style and comfort to your living space. Here are some recommendations for choosing the one that will bring comfort while adding style to the decor of your home.
2023: A Colour Story
2023 is poised to be the year of colour. Not just any colour, either. We're talking bold colours with a retro vibe, and a palette that inspires pure pleasure and comfort. It's brighter days ahead when these nostalgic tones and cheerful hues come to play.
How To Stay In The Holiday Spirit All Year Long
Many of us await the arrival of the Holidays with great excitement. The candles that illuminate the darkness of the long winter evenings, the smells of cinnamon and nutmeg that invade all the rooms of the house, the board games that make us laugh out loud and the evenings curled up with a book by the fireside…
How To Protect a Wooden Dining Table
Scratches, sun, heat, and spills can damage your dinner table. Here are our tips for protecting it properly.
Stay informed of our latest arrivals, receive trendy tips and exclusive offers!
Mobilia is a Canadian retailer of modern furniture for the home. We strive to inspire and guide consumers in their purchases with our 4 worlds of style
The Style Blog communicates the brand's latest news, design trends, tips as well as the passions and discoveries made by Mobilia team members and its collaborators.
Collaborate on the blog
WordPress Maintenance by SatelliteWP
Mobilia © All Rights Reserved 2022


As a former workhorse pitcher, Rick Sutcliffe can vividly recall his desire to pitch at least 200 innings a season, as Cubs ace Jon Lester and his fellow starters continue to push for.
But 24 years after throwing his final pitch, Sutcliffe sees the benefits of getting six quality innings from a starter and letting the relievers finish games. He specifically recalls Tony La Russa maximizing the back end of a bullpen that included Gene Nelson, Rick Honeycutt and Hall of Fame closer Dennis Eckersley with the Athletics in the late 1980s, and how Joe Torre continued that pattern with John Wetteland and Mariano Rivera closing games with the Yankees a decade later.
"I've seen it evolve to where I totally understand it," said Sutcliffe, who's in Cubs camp as a guest instructor.
Sutcliffe points to Jake Arrieta's first spring with the Cubs in 2014. Although Arrieta was sidelined by a shoulder injury, Sutcliffe contends the Cubs' plan was to hold him back because the team wasn't good, the April weather in Chicago was chilly and Arrieta hadn't thrown 150 innings at the major-league level.
Arrieta was 5-3 with a 3.08 ERA in nine postseason starts with the Cubs, including 2-0 with a 2.38 ERA in the 2016 World Series.
Sutcliffe recalled a discussion with Hall of Fame pitcher Nolan Ryan, known for his heavy inning and strikeout totals.
"I asked Nolan what he thought of six innings and three earned runs qualifying as a quality start," Sutcliffe said.
"We totally agree, but now for a lot of guys, you can't ask more than that," Sutcliffe said.


text:
Lou Sullivan | Wisconsin Historical Society
Lou Sullivan
Writer Advocates for Trans Community
Changemaker | Lou Sullivan | 1951 - 1991
Lou Sullivan pictured in 1974 before attending the GPU's drag ball. Courtesy of the Gay, Lesbian, Bisexual, Transgender Historical Society
Lou Sullivan was a transgender gay man born in Wauwatosa, Wisconsin, in 1951. As one of the first FTM (female-to-male) people to speak publicly about his medical transition, he used his long career as an activist and writer to become one of the foremost national advocates for FTM trans people.
During his youth, Sullivan dreamed of becoming a writer. In early journal entries, he explored his identity on the page long before he told anyone he felt like a man trapped in a woman's body.
In 1970, while working at the University of Wisconsin–Milwaukee, Sullivan attended his first meeting of the Gay People's Union (GPU). Through the GPU, Sullivan learned about community organizing and helped the organization become more inclusive for trans people. Ultimately, he was elected as GPU secretary. Continuing the passion for writing that started in his youth, he wrote articles on transgender issues and theory that were published in GPU News during the 1970s.
After moving to San Francisco in 1975, Sullivan sought medical help to transition but was denied access to medical therapy and procedures because it was assumed that individuals who wanted to transition were heterosexual. Sullivan had to break ground to find help, and he was eventually successful. He wrote that "information for the female-to-male transsexual is practically non-existent." In his 1980 book, "Information for the Female-to-Male Crossdresser and Transsexual," Sullivan gave advice on clothing items, hairstyles, and body language for trans men. In 1990, he wrote the biography of another transgender man, "From Female to Male: The Life of Jack Bee Garland."
Sullivan organized correspondence networks and get-togethers, and he edited an FTM newsletter called The Gateway. He is credited with creating the basis for the largest FTM organization in the United States, simply known as FTM. His work in bringing FTM trans people into the public's view helped influence the medical profession to drop assumptions about gender identity and sexual orientation. Sullivan showed how questioning discriminatory practices in the medical establishment could result in progress.
In 1987, Sullivan was diagnosed with AIDS and had to wage a new battle to educate medical professionals on how trans AIDS patients should be supported. In his journal, Sullivan wrote, "You told me I couldn't live as a gay man, but now I am going to die like one." Lou Sullivan was a changemaker and storyteller who used his voice to advocate for the trans community.


text:
Israeli liberals fear new government will undo gains
Tia Goldenberg, The Associated Press Nov 15, 2022 6:06 AM
FILE - an Israeli Arab youth sits at a view point overlooking the Israeli Arab town of Umm al-Fahm, Tuesday, Feb. 4, 2020. Israel's outgoing coalition was one of its most diverse and with it came a slew of progressive policies on the environment, LGBTQ issues and funding for the country's Arab minority. But the country's most likely incoming coalition is hoping to roll back many of the achievements pushed forward by the outgoing government, sparking concern by Israeli liberals. (AP Photo/Oded Balilty, File)
JERUSALEM (AP) — Israel's outgoing coalition has been the most diverse in the country's history, bringing a slew of progressive policies on the environment, LGBTQ issues and funding for the country's Arab minority.
But now, even before it takes office, Israel's expected new coalition government — overwhelmingly male, religious and right-wing — is promising to roll back many of the achievements of its predecessor, prompting concern from activists and liberals over where their country is headed.
If its promises materialize, a tax on environmentally destructive single-use plastics could be abolished. New protections for gay Israelis could be reversed, and generous budgets for the long underserved Arab sector could be slashed.
The outgoing coalition lasted for just over a year and collapsed over disagreements on the Palestinians — although on that subject, its policies were largely unchanged from previous, hard-line governments.
But after Benjamin Netanyahu's 12-year reign, activists say it brought a positive energy to the Knesset, or parliament, and pressed ahead on issues they say were largely ignored during his lengthy rule. Now, with Netanyahu set to take office again as head of what's expected to be the country's most right-wing government, fears are rising that all that will be undone.
"In the last government ... the public discourse was one of rights and equality and ending discrimination," said Hila Peer, chairwoman at Aguda — The Association for LGBTQ Equality in Israel.
What they are hearing now, Peer said, "is a discourse of fear."
Israel's Nov. 1 elections opened the way for Netanyahu's return, bolstered by a stable majority with ultranationalist and ultra-Orthodox allies, among them extremist lawmaker Itamar Ben-Gvir. Netanyahu is expected to complete negotiations on forming a new coalition in the coming weeks.
To mollify his partners, Netanyahu is expected to accede to many of their priorities, vastly different from those advanced by the outgoing government. Liberals' fears are compounded by the coalition's intention to weaken the Supreme Court — often the last recourse for minority groups.
Netanyahu has batted away the fears, saying they arise whenever he is elected and are disproved quickly. His supporters claim the concerns are a result of a scare campaign by his opponents.
"We will not permit anyone to be harmed, not their fundamental rights or personal freedoms," Miki Zohar, a senior Likud lawmaker and Netanyahu confidante, told The Associated Press.
The coalition that ousted Netanyahu last year was made up of eight ideologically diverse parties, from dovish parties that support Palestinian statehood to nationalist ones that don't, as well as centrist factions and for the first time a small Arab Islamist party.
The coalition agreed to sidestep divisive topics such as Palestinian independence, focusing instead on social issues, including the environment and public transportation. Policies toward the Palestinians showed little change. The military carried out daily raids in the occupied West Bank and a brief operation against militants in the Gaza Strip. Settlement construction in the West Bank raced ahead.
While the outgoing coalition's razor-thin majority prevented major policy changes, activists say the government moved forward in small but meaningful ways.
On the environment, it imposed taxes on single-use plastics, and advanced a climate law. On LGBTQ rights, it rescinded a ban on blood donations by gay men, moved to streamline access to gender reassignment surgery and took a clear stand against "conversion therapy," the scientifically discredited practice of using therapy to "convert" LGBTQ people to heterosexuality or traditional gender expectations.
The government imposed a tax on sugary drinks and approved billions of dollars in funding to the country's Palestinian minority, promising more cash than a previous budget passed several years ago under Netanyahu. It took steps to encourage religious pluralism, passing a reform in the country's Kosher certification process.
Beyond the inclusion of an Arab party, the coalition's Health Minister Nitzan Horowitz is openly gay and about half of the coalition's members and a third of ministers were women.
That image of inclusivity is about to change dramatically.
Only nine out of 64 members of Netanyahu's expected coalition are women. Ultra-Orthodox parties, which make up two out of the coalition's four parties, deny inclusion to women members entirely. The expected coalition includes no Arab members. It is set to have one openly gay member of parliament, but his record shows he doesn't focus on LGBTQ issues.
"Large parts of the nation will feel that they have no connection to or influence in the incoming government," said Assaf Shapira, of the Israel Democracy Institute think tank, noting that a lack of representation has a direct effect on the legislative agenda.
Incoming coalition members have already pinpointed policies they plan to undo.
Members of the far-right Religious Zionism party, some of whom are openly anti-LGBTQ, are expected to challenge certain rights. Incoming lawmaker Avi Maoz has said he wants the legality of Israel's raucous Pride parades to be "examined."
The threat — though the parades are likely to continue — has spooked many Israelis.
The ultra-Orthodox parties oppose the single-use plastic tax. They see it as targeting their constituents whose large families tend to use disposable plastic plates and cutlery to avoid washing large piles of dishes. A tax on sugary drinks is also on the chopping block, worrying doctors' associations that say the tax promotes public health.
Netanyahu, who is secular and hails from a socially liberal background, is likely to stand as a bulwark against some of the more extremist elements of his coalition, according to Shapira.
But he is still expected to give in on many of their demands in exchange for legal reforms that could permanently freeze his corruption trial or make it disappear altogether.
Critics warn the next government's policy priorities — coupled with the very real chance that the Supreme Court will no longer be a beacon for challenging discriminatory laws — is a ticking bomb for Israel's democracy.
"Endemic corruption, human rights violations, curbs on minority rights, erosion of the LGBTQ community's hard-won achievements and a takeover of the state coffers by the ultra-Orthodox minority are all tangible threats," wrote commentator Ben Caspit in Al-Monitor, a regional news site.
"They are no longer gloomy scenarios but projects in the making," he added.
Tia Goldenberg, The Associated Press
More Lifestyle News
Noah Cowan, former co-director of the Toronto International Film Festival, dead at 55


text:
Chess Stack Exchange is a question and answer site for serious players and enthusiasts of chess. It only takes a minute to sign up.
Study endgame first before studying opening? Is it true?
While looking for and comparing suggestions that will help me to improve in chess, I have noticed that some people and some chess book authors suggest that you should study the endgame first.
Some people say that by studying endgame first, you will find out the correct middlegame plan to achieve the endgame that will be on your favor.
Is it effective? Could someone please confirm that he became a stronger player by using that method of studying?
positional-play
edited Feb 5, 2017 at 0:37
Dag Oskar Madsen
Study a few openings but focus on the middle and endgame.
– Jimmy360
Endgames are the most powerful way to learn tactics, properties of the pieces, visualization, and calculation. Anyone who thinks they're boring should thumb through a few pages of Van Perlo's Endgame Tactics. You'll be amazed at the creativity, surprises, and overall amazing capabilities of just a few pieces in the hands of a capable player.
What's more, in the middlegame you have pawns shielding and supporting your pieces, and have enough pieces that most or all are always defended. In the endgame, pawns are diminished or scattered, and you only have a couple of other pieces to work with. You have to go out on a limb and leave your pieces loose once in awhile, and the winner is often better at judging when you can get away with this and when you can't, and does more of it, more successfully.
By the way, this means that you should understand some of the strategies for each type of middlegame you're likely to come across, but don't focus on theory all the time. Look at practical endgames from a database, and analyze them.
Get a few openings (1 for White, 1 each for Black against 1.d4 and 1.e4) that you feel comfortable playing. You don't need a backup rep unless you're playing both standard and blitz time controls (you can play much riskier stuff in blitz), until you hit about 1800-1900 ELO.
jaxterjaxter
I'm only a 1600 so take my advice at face value
I hear a lot of people saying all the time not to waste their time on openings, just focus on tactics and endgame. That advice is nice and everything but if you never make it out of the opening the endgame is worthless. I had a game in a tournament where I fell for Lasker's trap in the Albin-Counter Gambit. If I had spent just 5 minutes studying that line I could have avoided that and survived to use the lessons I have studied in the endgame.
I guess what I am trying to say is that instead of thinking of it as "should I do one or the other" you are going to have to do both. If you want to get good you can't avoid any one area you are going to have to give them all attention. Studying openings leads to a strong positional understanding and leads to understandings in similar openings. For instance understanding the sveshnikov sicilian helps with understanding the themes in the kalashnikov.
Study a lot of tactics because every 2000+ I have heard has said tactics are what you need to know. Hope this helps
enikhelAenikhelA
You learn them at the same time. Endgames and Openings are not subjects that you can learn overnight. It can take a strong Grandmaster years to master the endgame phase.
It's the same way with openings; simple guidelines and principles should be learned at the beginner, but strong players > 2000-2200 should know heavy opening theory.
So when you first start playing chess, openings and endgames will not be the decisive factor in your games. You should learn the opening principles and guidelines: don't move the same piece twice unless there is a tactic, control the central squares, don't block your c-pawn on c2 in d4 d5 openings, and so on. It even helps to know some simple opening lines, e.g. 1 e4 e5 is the King's pawn game. 1. d4 d5 2.c4 is the Queen's Gambit.
Similarly, start with the simple endgames. Checkmate with King and Rook, checkmate with King and Queen. Also you learn simple pawn endgames, King and Pawn versus King. How do you promote a pawn, if you can? How do you stop the pawn and get a draw, if you can?
Then when you get to about 1500, when you don't make a lot of material blunders, it makes sense to increase your opening knowledge. Learn lines to about 10 moves deep in a few openings that you play, especially the main lines.
At 1500 learn the simple King and Rook and Pawn versus King and Rook endgames, like the Lucena and Philidor positions. It also helps to have some familiarity with Knight, Bishop, and Queen endgames. However theoretical endgames and openings still will not decide your games. Strategy and positional skills, as well as your technique (ability to convert a positional advantage into a point) will.
When you get to a high level, say 1900-2200, your games will be impacted more and more by opening knowledge and endgame skill. Then it makes sense to be an opening and endgame expert.
limitslimits
Here's my take on it. Listed according to priority:
a) Simplest end-games (RK vs K, QK vs K, BBK vs K, KP vs K)
b) Opening that you are interested (at-least one as white and at-least two as black). Find out first five moves in the opening and what are the general strategies and plans in that specific opening. Guidelines on where pieces are generally placed in the opening and typical pawn formations.
Why I place this as the second important step is that you will never enter an end game with equal chances, if you don't know the opening even this much.
c) Complicated end-games (KPP vs K, KPR vs KPR etc., the whole load of it)
d) Deep opening prep - if you reached this step that is :)
KeshavKeshav
I agree pretty much with Keshav with some minor additions. When I taught my kids I started out alternating between the basic endings and playing a game with just the pawns where first person to queen wins.
This brings up another very important point. You will get best value with an opponent sitting opposite you when you are doing much of this learning / studying, even if it is the computer. Moving pieces on a board rather than doing it in your head is important.
After basic endings and playing with pawns I'd follow Keshav with the first few moves of several basic openings coupled with some basic opening principles like get out a center pawn, move the knights and bishops towards the center, castle, etc.
Before more complicated endings I would put tactics. Pins, forks, skewers, removing the defender, etc.
Assuming you have already mastered the basics, basic endings, pawn play, basic openings, simple tactics, then I would suggest the biggest bang per buck will come from heavy tactical work. Get some of those tactical puzzle books and just work through a dozen or so problems a day. If you can't see the answer on the page then set the position up on a board and move the pieces if you have to.
Longer term keep those daily tactical puzzles going and add work on more difficult endings like KPvK, KRPvKR, KBNvK. Learn the theory, practice both the attack and the defence with a real board against an opponent.
As your play improves and your standard of opponent improves you will need to work on your opening repertoire to make sure you get out of the opening with a good game and plenty of time left on the clock.
Brian Towers♦Brian Towers
It's very difficult for a beginner to study endgames because they think like, "what good does it do to study endings if I get killed in the opening and middle game." Of course this is logical in its own way and I would suggest tactics, tactics, tactics first. However here's a reason for studying endgames that I feel really helps. You really learn the power of the pieces. For example if you study an interesting R+p vs R+p ending you will learn how great the Rook is at defense or its power to attack and defend simultaneously. You start to admire the power of Bishops and learn their weaknesses. You'll discover the power of a well posted Knight or its weakness in stopping rook pawns. These are all concepts that are easier seen with fewer pieces on the board, i.e. endings. Something to think about as it will rollover into your middle game planning. Suddenly you'll look at games (another must is to play through many games) and understand the positioning of pieces, exchange of pieces, pawn structure etc etc.
Glorfindel♦
JeffJeff
Could someone please confirm that he became a stronger player by using that method of studying?
I can confirm, I was 2000-FIDE, struggling to beat players of the same rating. After a month of serious endgame study, I increased my rating to 2200 fairly quickly. Since then, I am continuously studying endgames.
A lot of players at that level have a gap in their knowledge of endgames, which becomes especially visible when they are low on time. By studying endgames myself I scored a lot of extra points by winning equal or holding lost endgame positions.
So if you're at level 2000 or lower, I would advise to focus on studying endgames at your own time and refresh your knowledge on openings/strategy/something else while playing in tournaments.
Some arguments for studying endgames:
Concrete evaluation. The position is a win/draw/loss with a clear explanation of why. This helps to build a rigorous understanding of the game. Contrast that with the phrase in this opening white is slightly better with a subjective explanation.
Everlasting knowledge. You learn once that the Lucena position is winning and this fact remains true forever. Now contrast this with a belief that the Exchange Caro-Kann gives black an equality until someone finds a new idea how to play for an advantage with white.
Useful in practice when you're low on time. Even if you don't know the opening, you can spend a lot of time and come up with a decent move (not necessarily the best). In the endgame, you will be down to your last seconds. It's very unlikely you will find an accurate move with few seconds remaining by yourself - even the top players do not always find!
mercury0114mercury0114
because a won endgame is ending in a checkmate, and you have to learn how to checkmate first.
Fischer's famous chess teaching book does not even start with an endgame but with mate-in-1 positions. Polgar (the father of the three chess sisters) also uses this method. I think it is superior to endgame training.
Sir CornflakesSir Cornflakes
Endgame study seems boring especially for novice players, but it's necessary for two reasons: you need to know what is winning and how, and more importantly IMHO it helps you internalize the basic tactics of these pieces.
That said, I can tell you certainly when I was 1900 to mid 2100 USCF, the majority of my wins from lower rated players, and the easiest, arose from exploitable opening mistakes. You have to do both. Not just five moves and a general idea of where the pieces go. but familiarize ourselves with the associated lines as much as possible. It is much better to know one or two openings pretty well than to try to learn a bunch halfway.
To answer your question explicitly, yes when I was 15 (rated around 1550) I got a hold of an endgame book and went through all of the positions, every chance I got. At that time and that place there were no strong local players so I had to play in tournaments to improve, ten or fifteen games per year. So there are better ways to train, but left to my own devices I feel like that was the first step in improving.
William HamiltonWilliam Hamilton
I like to think of chess as a journey. You have to know your destination before you can decide how to proceed. Unless you know how to win a simple endgame, you'll have no idea how to set the course of the game. Of course games can end earlier, but usually that's due to some tactical mistake. If you can achieve a small advantage and transition into an endgame with that, you'll know how to convert it into a win. Study the basic piece endings first (K & R vs K; K, B & B vs K, etc.) and then study the K & P vs K endings (learn the "opposition" and "triangulation") as well as K, R and P endings and you'll be in good shape when you reach the endgame. It has made a big difference in my game, for example allowing me to win a tournament game where I had a K, B & N opposed to the lone K as well as recently a K & R vs K & N ending. And when I reach K and P endings, I no longer feel unsure of myself as I once did.
CConeroCConero
Thanks for contributing an answer to Chess Stack Exchange!
Can this exchange-down endgame be explained succinctly?
Good master games for learning how to win from a superior position
Positional principles in chess openings
Opening as a Beginner: Mainlines or Offbeaten path?
How to teach (intermediary) chess to small groups with little time
How to improve on the early endgame?
Tips to improve my chess
What are some of the most instructive positional games covered in Agadmator's YouTube channel?


Consider a long straight solenoid having n turn per unit length. Let I be the current flowing in the solenoid. It is experimentally noted that magnetic field outside the solenoid is very small in comparison with the field inside. The lines of induction inside the solenoid are straight and parallel.
Let pq = l. For path pq, B and dl are along same direction.
For paths qr and sp, B and dl are mutually perpendicular.
For more help in Magnetic Field Inside a Long Solenoid click the button below to submit your homework assignment.


text:
Max Seibald (* 15. März 1968 in Lienz, Osttirol) ist ein österreichischer Bildhauer.

Leben
Aufgewachsen in Heiligenblut am Großglockner (Kärnten) absolvierte er zunächst eine Tischlerlehre, anschließend besuchte er eine private Schule für Bildhauerei in Bad Kleinkirchheim. Von 1989 bis 1992 studierte er Bildhauerei an der Akademie der bildenden Künste Wien bei Joannis Avramidis und Michelangelo Pistoletto, in den Jahren 2004 und 2005 studierte er Visual Arts an der IUAV in Venedig bei Antoni Muntadas.

Max Seibald lebte von 1995 bis 2007 im Veneto (Italien); seine Arbeit führte ihn durch ganz Europa, mit Schwerpunkten in Kroatien und Polen. Aktuell lebt und arbeitet er in Wien und Kärnten.

Sein Werk reicht von der klassischen Skulptur über Design bis hin zur zeitgenössischen Architektur.

Max Seibald ist Mitglied der Vereinigung Künstlerhaus Wien, beim Kunstverein Kärnten und beim Kunstwerk Krastal.

Publikationen
 mit Martin Traxl, Silvie Aigner und Luigi Sera: Max Seibald SHAPES of SPACE, Ritter, Klagenfurt 2014, ISBN 978-3-85415-522-5.
 mit Anna Maria Kramm und Salzburger Pressverein: Max Seibald SHAPES of LIVING, Pustet, Salzburg 2021, ISBN 978-3-7025-0998-9.

Ausstellungen und Symposien (Auswahl)

 2020: Simposio scultura in Vergnacco, Italien
 2020/21: ICE Camp Transfiguration am Kitzsteinhorn, Österreich
 2021: Blick ins Unterholz, Bildraum Bodensee, Österreich
 2021: FORMA VIVA, Bildhauer-Symposion in Portoroz, Slowenien
 2022: In der Tat, Ausstellung in MY SPACE 192, Österreich

Preise und Anerkennungen

 1993: Förderungsstipendium für die Diplomarbeit Bewegte Architektur
 1994: Meisterschulpreis für Bildhauerei
 1995: Kunststipendium für Projektarbeit in Italien
 2005: Projektstipendium für Sparten übergreifende Kunstformen
 2008: Förderungspreis für bildende Kunst, Kärnten
 2019: Nominierung Bauherrnpreis für MY SPACE 192
 2021: BIG SEE Architecture Award für MY SPACE 192

Einzelnachweise

Bildhauer (Österreich)
Österreicher
Geboren 1968
Mann

redpajama_set_name: RedPajamaWikipedia


Can't go travelling this year? Never fear, you can bring those iconic landmarks to your own home with a 3D Metal Landmarks Model Kit.
Fancy a trip to romantic Paris or perhaps you'd like to soak up some history in beautiful Italy? Bring some of the world's most iconic buildings into your own home without the need of long haul flights with a clever 3D Metal Landmarks Model Kit. Coming in six different varieties inspired by worldwide landmarks, you can have hours of fun reconstructing these structure in miniature.
Before you can admire the amazing detail on the White House, the Brandenburg Gate, Big Ben, the Leaning Tower of Pisa, the Empire State Building or the Eiffel Tower, you'll have to construct it. Luckily this 3D Metal Landmarks Metal Kit comes with fantastic instructions to help you piece together the laser cut pieces that fit together precisely without the need of glue.
A great gift for intrepid travellers or those with a large list of destinations they'd like to visit, a 3D model of their favourite landmark can be a good way of reminding someone of good memories or give them inspiration for the future. And if you can't choose between them, why not buy all six intricate buildings?!


Sunday the 7th. We got up and got packed. Then headed to the ramp and headed out to a beautiful sunrise.
. On my second cast I caught a Spanish.
. Shortly thereafter a small bird flying towards the boat does not make it and splashes down in the water by the boat. I fished him out with the landing net.
. Poor little guy looked wore out so I put him on the console to rest.
. We needed to move and I knew the little guy wasn't rested enough so i put him inside the console while we ran. After about an hour I opened the console and he flew out landing on a reel. Then he flew off.
. Pretty good fishing today after about 10:30 with 68 degrees water.
. We headed in at lunch with 3 trout a spanish and a pompano. Was a great trip with a good friend. Can't wait till next year.
Looks like I need to try ecofina, I always fish st marks, keaton, or steinhatchee.
That gar eats good too, just a pain to clean. I've seen them on the flats but never caught one.
Thanks for the update. Went to Keaton Saturday and got a limit of trout even with the motor acting up.


text:
Q: how to save and update the application after changing to asyncstorage render(){
const { navigate } = this.props.navigation;
if (this.state.isRefreshing) {
  return(
    <Spinner/>
  )
}
return(
  <Container style={style.container}>
    <Content>
      <List dataArray={this.state.list} renderRow={(data) =>
        <ListItem>
          <CheckBox onPress={() => this.saveLang(data.code)} checked={data.checked} />
            <Text style={style.black}> {data.title}</Text>
        </ListItem>
      }/>
    </Content>
  </Container>
)}

After saving how to update the state and apply the selected language
saveLang(value){
AsyncStorage.setItem("language", value);
this.setState(
  {
    list: [
    {
      'code': 'ru',
      'title': 'Русский',
      'checked': value == 'ru'
    },
    {
      'code': 'en',
      'title': 'English  ',
      'checked': value == 'en'
    }
  ],
  isRefreshing: true,
  }
);
I18n.locale = value;}

refresh passes, but I do not know how to update the application in the background mode
enter image description here

A: It's hard to say without knowing more about what you want to happen, but AsyncStorage.setItem returns a Promise so if you need to do something after it has completed, just use then:
function saveLang(value) {
  AsyncStorage.setItem("language", value).then(() => {
    // Perform your refresh
  });
}

Or alternatively, use async/await syntax:
async function saveLang(value) {
  await AsyncStorage.setItem("language", value);
  // Perform your refresh
}


Inmarsat has agreed to be taken over by a consortium of private equity firms including Apax and Warburg Pincus in a £2.6 billion deal.
As well as UK group Apax and US-based Warburg Pincus, the consortium includes the Canada Pension Plan Investment Board, and the Ontario Teachers' Pension Plan Board.
The offer represents a 46% premium on when the approach was made.
The satellite firm said on Monday: "The Inmarsat board believes that implementation of Inmarsat's existing strategy would continue to generate significant value for Inmarsat shareholders as an independent company; however, there are risks involved in implementation of what is a long-term, capital intensive strategy.
Shares in Inmarsat were up nearly 9% in afternoon trade at 551p.
The deal comes after US rival EchoStar Corp walked away from discussions to buy Inmarsat last year when it rejected an offer worth £3.2 billion.
However, the takeover announced on Monday will have to be scrutinised by the Government, given its position as a strategic asset.
Helal Miah, investment research analyst at The Share Centre, said: "As one of the few large technology groups left in the UK and one that is of strategic and security importance, the Government has previously mentioned that these businesses could be protected from overseas takeovers.
The buyout of Inmarsat would also see it return to private equity hands, having previously been majority-owned by Apax, along with Permira, before they floated the business in 2005.


text:
<?php

namespace Swoft\Bean\Parser;

use Swoft\Bean\Annotation\Id;
use Swoft\Bean\Collector;

class IdParser extends AbstractParser
{
    /**
     * Id注解解析
     *
     * @param string $className
     * @param Id     $objectAnnotation
     * @param string $propertyName
     * @param string $methodName
     *
     * @return mixed
     */
    public function parser(string $className, $objectAnnotation = null, string $propertyName = "", string $methodName = "", $propertyValue = null)
    {
        // 表映射收集
        Collector::$entities[$className]['table']['id'] = $propertyName;
        return null;
    }
}

redpajama_set_name: RedPajamaGithub


text:
Auto-Graphics contracts with the New Jersey State Library for new statewide interlibrary loan system
Press Release: Auto-Graphics, Inc. [March 1, 2002]
Abstract: New Jersey State Library has negotiated a contract with Auto-Graphics, Inc. for a new Statewide Interlibrary Loan System.
The State Library, under the direction of State Librarian, Norma Blake, and Library Development Bureau Head, Carol Nersinger, has negotiated a contract with Auto-Graphics, Inc. for a new Statewide Interlibrary Loan System.
The new system will utilize Auto-Graphics' latest portal technology, AGent, and its proven ILL program, Impact/ONLINE. AGent will provide cross-domain searching of Z39.50 target databases and an Auto-Graphics union database for libraries without Z39.50 capabilities. The new system will deliver a 100% Web based all inclusive resource location and sharing system for New Jersey's public, academic, and school libraries.
Auto-Graphics, Inc. (OTC: AUGR) is an ASP supplier of library automation software and electronic publishing solutions. Auto-Graphics provides Internet based physical and virtual bibliographic catalog and interlibrary loan systems for libraries. Customers include Alibris, Boeing, Houghton Mifflin, State of Texas, State of Connecticut, State of Oklahoma, and the State of Kansas. The Company's web site is located at http://www.auto-graphics.com.
Auto-Graphics, Inc.
System announcements -- selection
Interlibrary loan automation
http://www.auto-graphics.com/pressreleases/2002/New_Jersey_Mar2002.html


text:
De-Policing America: A Street Cop's View of the Anti-Police State
By Steve Pomper
"De-policing" isn't about police apathy—it's about leftist antipathy toward the police. Cops and society's confusion about police work have collided as progressives try to replace equal justice for all with social justice for some.
De-policing is the phenomenon where cops avoid pro-active patrol, meaning, will a police officer respond when you are having the worst day of your life? Will the cops in your town hesitate to act out of fear of being fired, or worse, going to prison just for doing their jobs?
Anti-police groups have fabricated a myth that cops are wantonly slaughtering innocent minorities. They cite the number of suspects killed by police vs. cops killed by suspects as if it's supposed to be a fair fight. But is there another profession where more people claim to know how to do it better than those trained to do it? Why, despite evidence exonerating officers of wrongdoing, does anti-police fervor too often flare into violence? Defending cops does not mean police abuses don't occur, but with millions of interactions every year, they are rare.
How does Steve Pomper know about all this? He knows because as a retired cop, he's dealt with this subject repeatedly in what has become one of the most protest-ridden cities in America: Seattle. De-Policing America is one street cop's view of the destructive effects of social justice indoctrination and the demonization of law enforcement today.
We rarely hear from those directly affected by bad politics—the cops. It's time for that to change. Learning what cops do, and why, and how their leftist leaders are attempting to brainwash them, is the beginning of understanding.


text:
Spain Boss Vicente Del Bosque Tries To End Talk About Cesc Fabregas\' Lack Of Commitment
By Eduardo Fernandez-Abascal
Cesc Fabregas has missed Spain\'s games against Belarus and Germany. Getty
Spain boss Vicente Del Bosque has tried to put an end to any talk about Cesc Fabregas' lack of commitment to the national team, claiming he believes the Chelsea midfielder was not fit enough to play in his country's last two fixtures.
Fabregas' club manager Jose Mourinho claimed after the victory over Liverpool that the midfielder had played carrying an injury and was unable to turn out for Spain. However, with some reports suggesting he didn't trust what he heard from the Portuguese boss, Del Bosque then urged the Chelsea star to fly to Madrid to undergo a scan by the national team doctors.
Only after that scan, was the midfielder pulled out of the games against Belarus and Germany and sent back to London to continue the recovery with his club.
Since the Spanish Federation released a statement saying it officially "rejects any possibility of a hamstring injury", suggesting he just had a minor discomfort, many people in Spain have since accused him of a lack of commitment to the national team.
Even Spain captain Sergio Ramos questioned Fabregas and also club teammate Diego Costa with Del Bosque later adding that the duo may even lose their places to newcomers in the national set up.
Del Bosque has now, however, tried to play down the gathering disquiet revealing a conversation with Fabregas before his was withdrawn. The national boss also added that Fabregas had proved his commitment to Spain over recent years.
"So much has been said this week that it embarrasses me to discuss the matter. I believe in sporting values, trust and I don't understand this lack of compromise," Del Bosque told AS.
"We all know Fabregas. He has a sporting competitive edge. When he came to take his medical, he said: I've attended 125 international get-together's and only played 94 games.
"This is down to me and Luis selecting him 94 times in the past. These players show up and they want to play, if they can't make it I have to believe what they say."
When questioned why they decided to rest him even though the scan revealed he did not have a hamstring injury, he said: "We decided not to let him stay as he said to me: I have a knock and when I move this leg it's sore.
"It's bad news when we enter a dynamic of a lack of trust. Some of those casting opinions should be on the bench."
Related topics : Jose Mourinho Spain


Choosing the right title company can make all the difference in your real estate settlement transaction. For more than 30 years, United Title & Escrow has provided expert settlement services in Anne Arundel county to make closing on a house or commercial property easy for all parties involved.
Annapolis attorney Matthew S. Evans, III offers residential and commercial settlement services through our affiliated company, United Title & Escrow. This Severna Park based, full service real estate settlement company is locally owned and operated and has been in business over 30 years.
We make all settlements happen smoothly and efficiently for all parties to the transaction and specialize in solving difficult title issues. Your settlement services will be overseen by Matthew Evans, III, Esq. and United Title's experienced staff.


Annelore's German Bakery creates authentic German pastries from scratch and brings them to a market near you! Pastries are made using the finest local ingredients, including Bee Blessed honey, Godwin Farm apples, Britt Farm pears, and Redbud Farms certified organic ginger, tomatoes, and basil, when available. Annelore's doesn't use preservatives, dough enhancers, or additives in any of their signature pastries. Fresh and local!


Watercolor ethnic feathers abstract mandala.
Do you want to give your interiors a new look? Take advantage of a simple and fast solution! An interesting shape, selected color, and intriguing motif – choose a decal to enhance any room, while using it in your kid's room will give you a thrill of excitement starting from the moment you apply it to the wall. Custom-made to specifically match your wall, it will be the perfect element of an individual space.
Durable, matte material is moisture-, tear-, and crease-resistant, so you can easily apply it to walls in any room. Use a contour-cut decal to create a one of a kind wall!
Single sheet maximum width: 37 in (94 cm), cut along the outline with a white (non-transparent) margin of up to 0.2 in (5 mm). If dimensions exceed the maximum sheet width, the print will be made up of several equal size sheets.
No, it's not. Big surfaces are divided into smaller equal fragments (sheets). If you want it to be divided differently, include a note in the order comment or write to us at: contact@pixers.co.nz.
This kind of foil is dedicated for window and glass stickers. The colors are semi-transparent and the color white is fully transparent.


text:
Some research notes about
Whitefield's gold & silver mine.
Researched by David Chase for use in his:"A Whitefield Time-Line"
1881- "Paul King Gold Mine started and (?) on top of a hill on Aldridge (sic) Moody Farm on Townhouse Road . 75' from the Branch Brook where the findings were washed." 12
Sept 4 " Elbridge Moody, who lives in the town of Whitefield, has just discovered gold upon his farm. A short time ago he sent some of the rock which came out of a large ledge on the farm to New York to be analyzed and found it contained $20 worth of gold to a ton. This is sufficient to pay to work it, and Mr. Moody has already refused $4,000 for his farm which didn't cost him a quarter of that sum." 9
A 19th century steam driven mining drill
" Some time ago a ledge was discovered on the farm of Elbridge Moody in Whitefield, which was thought to contain gold, and specimens of the surface rock was sent to Nevada and essayed (sic) . The samples sent gave $7.23 in gold and 98 cents in silver to the ton. Mr. Moody with some of his neighbors through whose farms the ledge runs, propose to work into the ledge and see what they can do with it. " 9
1890-Oct 23 " That Whitefield gold mine seems to be showing up in a pretty encouraging manner. The vein which cropped out some four feet wide, assayed $8 at the surface; ten feet down it showed over $13 per ton, and a few feet further they found the vein was yielding ore rising $15 to the ton. As a result the work is to be pushed and at once. A shaft is now under way and is to be continued along the vein as long as the yield justifies it. The workers among whom are experts in this line, being satisfied that there is a rich deposit there. That the gold is not purely local is shown by the fact that a man digging a well in the neighborhood struck the same deposit near the bottom and another well digger in another direction from (sic) the same condition of things. The yield speaks for itself and in a pretty certain tone too." 9
" The Bath Enterprise has the following information in regards to the Whitefield gild mine in which Bath capitalists are interested: Fifteen years ago Elbridge F. Moody of Whitefield while on a business trip to California became somewhat interested in gold digging there, and visited the gold sections making through inspection of the ore from many valuable mines. Previous to this time he never dreamed that there was gold on his farm. In the course of his investigation he was greatly impressed by the remarkable likeness of much of the quartz to a ledge in the center of a wood lot on his farm, which he had repeatedly noticed cropped out in several points on his farm and appeared to be a section of a big vein. Upon returning to Maine he made a careful examination of this vein, as a result of which the previous impression formed in California was doubly strengthened. As it required considerable capital to operate a gold mine, Mr. Moody, although confident from actual tests made that the vein on his land was rich with gold, has done very little in its development. From time to time assays have been obtained, the first three assaying $7, $9 and $13.65 to the ton of roc. Something over a year ago Andrew S. Merrill, of Woolwich, while in Whitefield on business, visited this farm and upon an examination of the gold vein became satisfied of the presence of gold on the farm, and at once bonded the portion of the land. This fall he went on to the ledge, and drilling a six inch hole into the vein a distance of sixteen feet, sent the drilling to the Bay State Smelting Works, and got an assay of $20.60 gold and $1.20 silver to the ton. This rich prospect, with others more recently obtained, has caused no little excitement in Whitefield and adjoining towns, and even in Randolph and Gardiner. Within a few weeks a gold mining company has been organized, and while the thing is being kept as quiet as possible it is known that this company propose to test the gold region here thoroughly, and if the gold prospects warrant, institute gold mining operations on a big scale. The farm upon which the vein has been discovered is located about two miles from East Pittston and Whitefield dividing line, and about eight miles from Gardiner. It is on the west side of the Sheepscot, and directly on the country road from East Pittston to North Whitefield, King's Mills being a short distance below the gold region." 9
another steam drill
" Charles Shute, who has been in Australia Africa and California for 30 years prospecting for gold on the farm of Andrew (sic) Moody at Whitefield. The farm was bonded last week by Andrew Morrill. The quartz has been assayed in California at $13.21 per ton and more recently in Boston, where its value increased 1%. The vein has a width at the bottom of the hole now dug of fifteen feet, at the top 5 feet, and it extends three quarters of a mile. Mr Shute is of the belief that he has discovered gallium in the vicinity of the gold mine. A company will probably be formed soon to investigate the matter." 9
1891- " The Bath Enterprise understands that on the farm adjoining the one bonded by the syndicate of Bath gentlemen at Whitefield, a mine has been opened and the ore assays from $10 to $12 per ton. As soon as the weather permits, work will begin in earnest at the mine, and Bath gentlemen are hopeful. The entire operations will be in charge of a practical miner. A carload of the ore will be shipped to Denver, Col., early In the spring where it will be smelted." 9
April 2" The parties interested in the Whitefield gold and silver mine have commenced operations. They will dig 100 rod and if it will continue to be profitable as it does at present, they will erect a quartz mill "9
9 Lincoln County News
12 Kings Mills Whitefield Maine 1772-1982 by Henry C Waters
www.mndm.gov.on.ca/MNDM/MINES/ hist_album/oldrefiner_e.asp
www.austehc.unimelb.edu.au/ tia/705.htm


text:
VFF Session 1: (Youth, Adult & KO Parkinsons) Levels 1-6 Feb-March 2021
/ VFF Session 1: (Youth, Adult & KO Parkinsons) Levels 1-6 Feb-March 2021
Welcome Rookies/Beginners!
Please fill out your Boxer Profile ASAP!
*includes 14 day free trial to virtual fighting fit 1.0 program!
Please select an option ADULT MONDAY 11:30am - 12:30pm February 15 - March 22, 2021 - $60.00 CAD ADULT TUESDAY 6:30pm - 7:30pm February 16 - March 23, 2021 - $60.00 CAD KO PARKINSONS WEDNESDAY 10:00am - 11:00am Feb 24 - March 24 - $60.00 CAD ADULT WEDNESDAY 11:30am-12:30pm February 17 - March 24, 2021 - $60.00 CAD ADULT THURSDAY 6:30pm - 7:30pm February 18 - March 25, 2021 - $60.00 CAD KO PARKINSONS FRIDAY 10:00am - 11:00am Feb 19 - March 26 - $60.00 CAD ADULT FRIDAY 11:30am -12:30pm February 19 - March 26, 2021 - $60.00 CAD ADULT SATURDAY 11:00am-12:00pm. February 20 - March 27, 2021 - $60.00 CAD YOUTH SAT. 12:30pm - 1:30pm. Feb20-Mar 27 *THREE(3) BI-WEEKLY CLASSES - $60.00 CAD


However, given the imprecise nature of scrolling inputs like touch panning and mousewheel scrolling, it is difficult for web developers to guarantee a well-controlled scrolling experience, in particular creating the effect of paging through content. For instance, it is easy for a user to land at an awkward scroll position which leaves a page partially on-screen when panning.
To this end, we introduce scroll snap positions which enforce the scroll positions that a scroll container's scrollport may end at after a scrolling operation has completed.
This module extends the scrolling user interface features defined in [CSS21] section 11.1.
This specification follows the CSS property definition conventions from [CSS21]. Value types not defined in this specification are defined in CSS Level 2 Revision 1 [CSS21]. Other CSS modules may expand the definitions of these value types: for example [CSS3VAL], when combined with this module, expands the definition of the <length> value type as used in this specification.
The layout of the scroll container's contents in the example. The snapport is represented by the red rectangle, and the snap area is represented by the yellow rectangle. Since the scroll-snap-align is "center" in the X axis, a snap position is established at each scroll position which aligns the X-center of the snapport (represented by a red dotted line) with the X-center of a snap area (represented by a yellow dotted line).
This module introduces control over scroll snap positions, which are scroll positions that produce particular alignments of content within a scroll container. Using the scroll-snap-type property on the relevant scroll container, the author can request a particular bias for the scrollport to land on a snap position after scrolling operations.
Snap positions are specified as a particular alignment (scroll-snap-align) of an element's scroll snap area (its border bounding box, as modified by scroll-snap-margin) within the scroll container's snapport (its scrollport, as reduced by scroll-padding). This is conceptually equivalent to specifying the alignment of an alignment subject within an alignment container. A scroll position that satisfies the specified alignment is a snap position.
If specified on a scroll container, the scroll container is required to be snapped to a snap position when there are no active scrolling operations. If a reachable snap position exists then the scroll container must snap at the termination of a scroll (if none exist then no snapping occurs).
The scroll-padding property defines the optimal viewing region of the scrollport, the region used as the target region for placing things in view of the user. It allows the author to exclude regions of the scrollport that are obscured by other content (such as fixed-positioned toolbars or sidebars) or simply to put more breathing room between a targetted element and the edges of the scrollport.
The scroll-padding effectively reduces the region of the viewport that is considered "viewable" for scrolling operations: it has no effect on layout, on the scroll origin or initial position, or on whether or not an element is considered actually visible, but it should affect whether an element or the caret is considered scrolled into view, and reduce the amount of scrolling for paging operations (such as using the PgUp and PgDn keys or triggering equivalent operations from the scrollbar) so that within the optimal viewing region of the scrollport the user sees a continuous stream of content.
Values are interpreted as for padding, and specify inward offsets from each edge of the scrollport.
This property is a shorthand property that sets all of the scroll-padding-* longhands in one declaration.
The scroll-snap-margin property defines the scroll snap area that is used for snapping this box to the snapport. The <length> values give outsets (interpreted as for margin or border-image-outset). The scroll snap area is the rectangular bounding box of the transformed border box, plus the specified outsets, axis-aligned in the scroll container's coordinate space.
This property is a shorthand property that sets all of the scroll-snap-margin-* longhands in one declaration.
The scroll-snap-align property specifies the box's snap position as an alignment of its snap area (as the alignment subject) within its snap container's snapport (as the alignment container). The two values specify the snapping alignment in the inline axis and block axis, respectively. If only one value is specified, the second value defaults to the same value.
Since the purpose of scroll snapping is to align content within the viewport for optimal viewing, a scroll container cannot be snapped to a snap area if no part of it is within the snapport. For example, a snap area is top-aligned to the snapport if its top edge is coincident with the snapport's top edge; however, this scroll position is nonetheless not a valid snap position if the entire snap area is outside the snapport (because the required alignment, though satisfied, would not be relevant to the viewer).
Note: If the author had instead set mandatory snap positions on the headings of each section (rather than the sections themselves), the contents of the first and fifth sections would be partially inaccessible to the user, as the heading snap area does not extend to cover the whole section.
The scroll container may pass by a snap position defined by this element during the execution of a scrolling operation.
The scroll container must not pass by a snap position defined by this element during the execution of a scrolling operation.
If a page is navigated to a fragment that defines a target element (one that would be matched by :target, or the target of scrollIntoView()), and that element defines some snap positions, the user agent should snap to one of that element's snap positions. The user agent may do this even when the scroll container has scroll-snap-type: none.
These longhands of scroll-snap-margin specify the top, right, bottom, and left edges of the scroll snap area, respectively.
These longhands of scroll-snap-margin specify the block-start, inline-start, block-end, and inline-end edges of the scroll snap area, respectively.
These shorthands of scroll-snap-margin-block-start + scroll-snap-margin-block-end and scroll-snap-margin-inline-start + scroll-snap-margin-inline-end are longhands of scroll-snap-margin, and specify the block-axis and inline-axis edges of the scroll snap area, respectively.
Many thanks to David Baron, Simon Fraser, Håkon Wium Lie, Edward O'Connor, François Remy, Majid Valpour, and most especially Robert O'Callahan for their proposals and recommendations, which have been incorporated into this document.
Renamed scroll-snap-padding to scroll-padding and extended its uses.
Removed renaming issues because nobody came up with a better alternative to scroll-snap-type: mandatory | proximity or scroll-snap-stop: normal.


text:
Q: If $Q$ is a nuclear operator on a Hilbert space with orthonormal basis $(e_n)$, are we able to conclude that $(\left\|Qe_n\right\|_E)$ is summable? Let

*

*$H$ be an infinite-dimensional separable $\mathbb R$-Hilbert space

*$(e_n)_{n\in\mathbb N}$ be an orthonormal basis of $H$

*$E$ be a $\mathbb R$-Banach space

*$Q$ be a nuclear operator from $H$ to $E$

Are we able to show that $\left(\left\|Qe_n\right\|_E\right)_{n\in\mathbb N}$ is summable?

If $H=E$ and $Q$ is nonnegative and self-adjoint, there is a specific $(e_n)_{n\in\mathbb N}$ such that $Qe_n=\lambda_ne_n$ for all $n\in\mathbb N$ and the nuclear norm of $Q$ is equal to $\sum_{n\in\mathbb N}\lambda_n$. Thus, at least in that case and for that specific orthonormal basis, the claim is true.
But I don't know how we could argue in general. Is the claim wrong?

A: In general, $(\lVert Qe_n\rVert_E)_{n\in\mathbb{N}}$ need not be summable. Let $H = \ell^2(\mathbb{N},\mathbb{R})$, with $(e_n)$ the "standard basis". Let $E = \mathbb{R}$ and $\xi \in H$. Then $Q \colon x \mapsto \langle x,\xi\rangle$ is nuclear, but
$$\sum_{n \in \mathbb{N}} \lvert Qe_n\rvert < +\infty \iff \xi \in \ell^1(\mathbb{N},\mathbb{R}).$$


text:
OnePlus 9 Pro benchmark points to a top-end chipset and disappointing RAM
By James Rogerson
A mixed bag of information
The OnePlus 8T (Image credit: Aakash Jhaveri)
The OnePlus 9 Pro is likely to be one of the most powerful phones of early next year, but a benchmark suggests that while its chipset probably won't disappoint, its RAM might, at least slightly.
A Geekbench (opens in new tab) listing for a device with the name 'LuBan LE2117' has been spotted by GizmoChina (opens in new tab), and the second part of that name is a model number that's previously been linked to the OnePlus 9 Pro.
The listing mentions a Qualcomm Snapdragon 875 chipset, which isn't currently used in any phones but is likely to power a large number of Android flagships next year, and is exactly the chipset we expect for the OnePlus 9 range.
Check out the best OnePlus phones
Read our full OnePlus Nord review
The Samsung Galaxy S21 is also expected in early 2021
(Image credit: Geekbench)
So far so good, but there are some concerns. For one thing, the RAM is only listed as 8GB. That isn't totally surprising given that the OnePlus 8 Pro and OnePlus 8T both come in 8GB configurations, but they also both come in 12GB versions, and while the OnePlus 9 Pro surely will as well, it's arguably about time that became the standard, especially with some phones now offering 16GB.
The other potential issue is the scores achieved by the OnePlus 9 Pro on this benchmark. It has a single-core score of 1,122, which is very good – it beats any current Android device, though still sits below the iPhone 12 range. But its multi-core score of 2,733 is actually lower than a few Android phones, including the OnePlus 8 range.
That said, we wouldn't worry too much about this, as assuming the benchmark is even genuine (which there's always a chance it isn't), it will have been run on non-final hardware. The OnePlus 9 and OnePlus 9 Pro aren't likely to land until around April, so the company has plenty of time to keep tweaking them.
For what it's worth, GizmoChina notes that a Weibo user by the name of '@肥威' dug deeper into the benchmark, revealing that the chipset has four cores clocked at 1.80Ghz, three at 2.42GHz, and a prime core clocked at 2.84Ghz.
That speedy prime core is probably responsible for the high single-core result, so we just hope the other cores hold up by the time the phone is finished.
Get the best of TechRadar in your inbox every day: sign up for our newsletter
Via PocketNow (opens in new tab)
Today's best OnePlus 8 Pro and OnePlus 8T deals
James Rogerson
James is a freelance phones, tablets and wearables writer and sub-editor at TechRadar. He has a love for everything 'smart', from watches to lights, and can often be found arguing with AI assistants or drowning in the latest apps. James also contributes to 3G.co.uk, 4G.co.uk and 5G.co.uk and has written for T3, Digital Camera World, Clarity Media and others, with work on the web, in print and on TV.


The slab of Pont d'Arc. Most of the signs written on it are still exactly recognizable.
It is without doubt that it was a human to carve those signs on the stone – they cannot be accidental scratches, or heaven forbid, impressions of seashells. There should be one person in front of our eyes who is sitting down to some comfortable place and starts thinking. The arcs and the firmly drawn lines all suggest that their designer was experienced indeed in activities of the kind. The scribe did not put down a coherent text but was simply experimenting with the characters.
I only took into consideration the signs that are clearly identifiable.
signs meant the same back then.
The painting and the text written on the bison were made around 20.000 BC, and found in the cave of Pech Merle in today's Southern France.
This is a Portuguese, 12-14.000-yearold character.
even the strong emphasis on the thumb is there.
sign here. And its meaning: "su" = hand.
Two Cyprian syllabic signs from 4.000 years earlier.
A collection of signs from various places.
All of these signs had been writing signs, of course.
These series of remarkable concurrence of different times and places (I could present a number of other instances too) can only be explained in one way: in the ancient "comb" sign people had always "visioned" the human hand.
We could 13 signs encounter, which are 30.000 or more years old. Those signs were present in the old but still used "alphabet" of the Carpathian Basin 6-8000BC, the Old-Egyptian Demotic, Aramaic, old Hebrew, all Greek variations and finally in the early Latin alphabet. Etruscan and Latin used only 18 letters, not much more, as the early ancestors. Sumerians used those signs making ligatures to write their syllables, but the early Sumerian signs looked just like them.
See more finds and further explanations in the book "Signs – Letters - Alphabets" by Csaba Varga.
Signs collected from different artifacts of the last 35.000 years.
Signs of the old-Egyptian demotic alphabet.
The "ancient Hungarian" attributive in the enumeration left is confusing.
As this alphabet is fashioned to fit the Hungarian language, just like the Ancient Greek alphabet fits the Greek-, the Aramaic alphabet the Aramaic-, and the Latin alphabet the Latin language, it is reasonable that instead of the many kinds of old definitions, I call the alphabet fashioned for the Hungarian language the "Hungarian alphabet." The more so because the modern Latin alphabet used in Hungary today, is quite a latecomer in Hungarian history.
With this name-simplification I also want to stress that in this book the political maps and the present day-centered approach were given no role.
From the signs of the enumerated four alphabets at the left I mainly Consider those that appear at least in two alphabets. With a couple of exceptions.
newly found signs with the above.


text:
Q: Rspec Test Always Passes Regardless Of Input I'm trying to test the below method in my connect-four game. When a player tries to place a piece in a full column, :puts and error message to the screen.
The problem I'm running into is that the test passes regardless of whether I input a board with a full column or an empty column. I'm also seeing this error message: WARNING: An expectation of `:puts` was set on `nil`. Which I interpret to mean that the board or @player value is not being properly passed into the final expect() assignment.
Where am I going wrong with this test? Thank you!
Method being tested:
def valid_vertical_move
  until @game_board.board[5][@player - 1] == '.'
    puts 'Please place piece in valid spot'
    player_selection
  end
end

This is one of the many tests I've tried:
describe Game do

  describe '#valid_vertical_move' do
    subject(:valid_move) { described_class.new(new_board) }
    let(:new_board) {double('new_board', :board => [['x', 'x', 'x', 'x', '.', '.', '.'],
      ['y', '.', '.', '.', '.', '.', '.'], ['y', '.', '.', '.', '.', '.', '.'],
      ['y', '.', '.', '.', '.', '.', '.'], ['x', '.', '.', '.', '.', '.', '.'],
      ['x', '.', '.', '.', '.', '.', '.']])}

    context 'when the column is full' do

      before do
        allow(valid_move).to receive(:player_selection)
      end

      it 'an error message is :puts' do
         error_message = 'Please place piece in valid spot'
         test = valid_move.valid_vertical_move
         expect(test).to receive(:puts).with(error_message)

      end
    end
  end
end

Game Class:
class Game

  attr_reader :player

  def initialize(game_board = Board.new)
    @game_board = game_board
    @player_turn = 1
    @player = 0
  end

  def player_selection
    loop do
      puts "Choose a column, Player #{@player_turn}:"
      @user_input = gets.chomp

      if @user_input.match?(/\b[1-7]\b/)
        return @player = @user_input.to_i
      else
        puts 'Error: Add number between 1-7'
      end
    end
  end

  def valid_vertical_move
    until @game_board.board[5][@player - 1] == '.'
      puts 'Please place piece in valid spot'
      player_selection
    end
  end
end

Board class:
class Board
  attr_reader :board

  def initialize(board = Array.new(6) { Array.new(['.', '.', '.', '.', '.', '.', '.']) })
    @board = board
  end

  def display_board(board = @board)
    puts "| #{board[5][0]} | #{board[5][1]} | #{board[5][2]} | #{board[5][3]} | #{board[5][4]} | #{board[5][5]} | #{board[5][6]} |"
    puts "| #{board[4][0]} | #{board[4][1]} | #{board[4][2]} | #{board[4][3]} | #{board[4][4]} | #{board[4][5]} | #{board[4][6]} |"
    puts "| #{board[3][0]} | #{board[3][1]} | #{board[3][2]} | #{board[3][3]} | #{board[3][4]} | #{board[3][5]} | #{board[3][6]} |"
    puts "| #{board[2][0]} | #{board[2][1]} | #{board[2][2]} | #{board[2][3]} | #{board[2][4]} | #{board[2][5]} | #{board[2][6]} |"
    puts "| #{board[1][0]} | #{board[1][1]} | #{board[1][2]} | #{board[1][3]} | #{board[1][4]} | #{board[1][5]} | #{board[1][6]} |"
    puts "| #{board[0][0]} | #{board[0][1]} | #{board[0][2]} | #{board[0][3]} | #{board[0][4]} | #{board[0][5]} | #{board[0][6]} |"
    puts "  1 | 2 | 3 | 4 | 5 | 6 | 7  "
  end
end

A: Basically ur expecting a nil test = valid_move.valid_vertical_move to receive a method call which is not what you seem to want to do here. You would want to raise or log some error here and then test for Rails.logger to receive some call or something.


Who actually enjoys long-haul flights? One seabird seems to – the ancient murrelet. It travels almost 8000 kilometres across the north Pacific, then does the whole slog again in reverse, for no obvious benefit.
Most migrating birds travel long distances from north to south, or vice versa, to spend the harsher winter in warmer climates, often crossing the equator. Some travel from east to west, to areas where they can get more food.
But the ancient murrelet is unique, criss-crossing the Pacific to move between areas of similar climate. Some of them breed in western Canada and then winter in seas between Japan, China and Korea, before heading back to Canada – the only bird known to cross the full width of the North Pacific.
The ancient murrelet is, Gaston says, a rather obscure and not well studied seabird. A member of the auk family, which also includes puffins and guillemots, it mainly breeds in the Haida Gwaii archipelago off the coast of British Columbia.
Gaston and his colleagues used geolocator tags to study the migration of ancient murrelets in 2013 and 2014. They managed to recover data from three of the geolocators and found that the birds had slowly crossed the North Pacific from July to November, travelling from Haida Gwaii to Japan.
Then in February, they set off back to Haida Gwaii, rapidly covering almost the whole distance within a month – the longest migration of any bird in the auk family. This is also twice as far as the longest cross-Atlantic migrations undertaken by Brünnich's guillemot, which cover 70 degrees of latitude compared with murellets' 105 degrees, Gaston's team says.
This means they travelled some 270 kilometres per day, probably flying 4 to 5 hours a day.
Gaston is not sure why their outward journey was slower, though he speculates it could be down to moulting hampering flight.
There is no obvious reason for the birds to leave North American waters, which support many other seabirds over winter, for the equally temperate Japan.
Genetic evidence suggests that the ancient murrelet originated from Asia and has only recently colonised North America, says Gaston. So the ancient murrelet could now be retracing the route by which the species colonised America from Asia. "There doesn't seem to be any other suitable explanation," Gaston says.
Other birds are known to follow their ancient migration routes, such as the wheatear, which travels from Alaska and Siberia to Africa, says zoologist Michael Brooke from the University of Cambridge.


text:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<title>Core Plot (iOS): Source/CPTExceptions.h Source File</title>

<link href="tabs.css" rel="stylesheet" type="text/css"/>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="navtree.css" rel="stylesheet" type="text/css"/>

Core Plot (iOS)

Cocoa plotting framework for Mac OS X and iOS

Main Page

Related Pages

Modules

Classes

Files

File List

File Members

Source/CPTExceptions.h

Go to the documentation of this file.

00001 #import <Foundation/Foundation.h>
00002
00004
00007 extern NSString * const CPTException;
00008 extern NSString * const CPTDataException;
00009 extern NSString * const CPTNumericDataException;

CPTExceptions.h

Generated on Sun Sep 25 2011 15:44:21 for Core Plot (iOS) by

     1.7.5


The 12 Day Detox starts tomorrow!
Don't forget to join our facebook group: Brisbane Livewell Clinic 12 Day Detox to support each other along the way. Our dedicated team of health professionals will also be online to answer any questions you have.


Last week, Clutch and Chrome took a closer look at this new touring motorcycle that weighed in with some muscle. From the design to its 113 cubic inch (1854cc) V-twin fuel-injected engine as well as a host of technologies, Yamaha is making a serious play at being one of the major choices in the touring segment.
The Japanese motorcycle manufacturer felt the infotainment aspect of its new model was important enough to look to technology expert Harman for the development of something new.
The result was something that apparently deserved its own video!


Circular coppered bronze medal with loop for ribbon suspension; the face with a horizontal sword with an oak branch imposed and inscribed 'ISÄNMAA' (Fatherland) above and dated '1941-1945' below; the reverse with the arms of Finland; diameter 16.57mm (0.65mm); on original ribbon cut short and with glue residue to the reverse.
The Medal was instituted on 24 May 1957, some 12 years after the end of the war, and awarded to all participants.
The Continuation War was so named to encourage the view that it was a continuation of the Winter War of 1939-1940 in which Soviet forces invaded Finland. The Continuation War, however, was an attempt by Finland to regain territory lost at the end of the Winter War and to occupy Russian territory, taking advantage of the German invasion of Russia, as a defensive buffer against future incursions. The defeat of German forces meant that Finland had to come to an accommodation with the Soviet Union and the war, in effect, achieved nothing.