How Did the Pigskin Get Its Shape?
So according to that story, the football that bounces erratically all over a field and can fly through air in a perfect spiral is not, in fact, the product of high design. At least not initially. Rather, it's the result of a leaky sphere and some lazy inflaters. Initially, football was a very different game – or perhaps I should say games. There were kicking games and running games, but as those two games began to merge together, as rules began to standardize, the ball began to slightly stretch out in order to accommodate more types of use. The unique shape of the ball was somewhat formalized in the early 20th century and that form was exploited to great success when the forward pass was introduced to football in 1906.
As the game continued to change, the ball evolved to accommodate new rules and new plays. Most notably, in the 1930s, it became longer and slimmer as the forward pass became a more dominant–and more encouraged–part of the game. Another change came in 1956 when the white balls traditionally used in night games were replaced with a standard daytime football circled by two white stripes. Though advancements in stadium lighting have made night balls unnecessary, NCAA games still use the white-striped ball.
In 1941, the official football used by the NFL was nicknamed "The Duke," after the Wellington Mara, whose father named him after the Duke of Wellington. That name played a key role in establishing the relationship between the NFL and Wilson Sporting Goods, the company that has for more than 70 years produced the offical football of the NFL. "The Duke" was in play until 1969 when professional football reorganized. In 2006, National Football League owners decided to return the name of the official game ball to "The Duke" in honor of Wellington Mara's passing the previous year.
Today, in order to be used in a National Football League game, a football must meet the following requirements: It shall consist of a urethane bladder inflated to 12.5 to 13.5 pounds and enclosed in a pebble grained, tan leather outer shell designed to provide a good grip – even in the rain. The ball must be 11-11.25 inches long, have a long circumference between 28- 28.5 inches, a short circumference between 21-21.25 inches; and it must weigh 14 to 15 ounces. The variation in the measurements is due to the fact that all NFL footballs are made by hand. Since 1955 every NFL football has been made at Wilson's 130-person factory in Ada, Ohio, which produces up to 4,000 footballs a day.
These NFL footballs are born on the backs of Midwestern cows from Iowa, Kansas, and Nebraska, which are brought to a tannery in Ada and treated with a top secret football-weather-optimizing tanning recipe. Each football is composed of four separate pieces (see above image), with a single cowhide producing ten balls. The construction of the bladder is also a secret process, with each synthetic bladder produced by one man. From pigskin to cowhide, organic bladder to synthetic rubber, the ball has changed and the game itself has evolved into a completely different animal.


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Pfizer-BioNTech Covid-19 vaccine data hit by cyberattack; probe on
PTI, Dec 10, 2020, 11:59 AM IST
Credit: iStock Photo
New Delhi: Two pharmaceutical companies in line for first conditional approval for their Covid-19 vaccine by the EU's medicine regulator said Wednesday their documents were "unlawfully accessed" during a cyberattack on a European Medicines Agency server.
Pfizer and BioNTech said documents relating to its vaccine candidate had been accessed but that "no systems have been breached in connection with this incident."
"We are unaware of any personal data being accessed," Pfizer said in a statement, while BioNTech added, "we are unaware that any study participants have been identified through the data being accessed."
"The EMA has assured us that the cyberattack will have no impact on the timeline for its review," they added.
EU's medicines regulator earlier Wednesday said it had been the victim of a cyberattack, just weeks before it is due to decide on special approval for two coronavirus vaccines.
The Amsterdam-based EMA said the incident was being investigated but did not specify when it took place or whether its work on Covid-19 was targeted.
"EMA has been the subject of a cyberattack. The agency has swiftly launched a full investigation, in close cooperation with law enforcement and other relevant entities," the EMA said in a brief statement.
An EMA spokeswoman later told AFP "the EMA is fully functional and all work continues".
The Dutch national police high-tech crime team was involved in the probe into the cyberattack, but police gave no more information, the Dutch news agency ANP reported.
The EMA's role as the drugs regulator for the 27-nation EU means it has access to data on the safety and quality of medicines from clinical trials and lab tests from companies that apply for authorization.
The agency has said it will give a decision on conditional approval for Pfizer-BioNTech's Covid-19 vaccine at a meeting that will be held by December 29 at the latest, while a ruling on Moderna's version should follow by January 12.
It is also carrying out reviews of vaccines developed by Oxford University-AstraZeneca and Johnson & Johnson.
News of the cyberattack came the day before the EMA's chief Emer Cooke was due to brief the European Parliament about the process for approving coronavirus vaccines.
The EMA — which moved to Amsterdam from London after Britain left the European Union in January 2019 — is also due to hold a special online public meeting to discuss Covid-19.
There have been a series of warnings about hacking related to the coronavirus pandemic.
In July Britain accused Russian-based, Kremlin-linked hackers of targeting labs conducting coronavirus vaccine research.
Cybercriminals have tried to attack several pharmaceutical companies developing vaccines including Johnson & Johnson, Novavax, AstraZeneca and South Korean laboratories, according to the Wall Street Journal.
Spanish laboratories have reportedly been attacked by Chinese cybercriminals, the El Pais newspaper reported in September.
Microsoft urged a crackdown in November on cyberattacks perpetrated by states and "malign actors" after a spate of hacks disrupted healthcare organizations fighting the virus.
IBM said last week that it too had uncovered a string of attacks, again potentially carried out by state actors, against companies involved in the effort to distribute the vaccine.
The European Commission's Directorate-General for Taxation and Customs Union was one target of the attacks, as well as European and Asian companies involved in the supply chain, IBM said.
It is also not the first time a Netherlands-based international body has been targeted by hackers.
Dutch authorities expelled four alleged Russian intelligence agents in 2018 after an alleged bid to hack the Organisation for the Prohibition of Chemical Weapons in The Hague, using equipment in the back of a car parked in a neighbouring hotel.
What is 'Co-WIN' digital platform govt has made for COVID-19 vaccine delivery?
After Cong boycott K'taka Assembly, speaker invites leaders to negotiate

redpajama_set_name: RedPajamaCommonCrawl


It is important to note that the values you pass in the command line have PRECEDENCE over the values you configure in your code by calling the appropriate Log.setXXX methods, *unless* you are calling them from inside a configuration class as we will see below.
Just remember about precedence. The class configuration has precedence over -D option which in turn has precedence over Log.setXXXXX methods. To be clear, if you pass a configuration class with Log.setFile(false) and you perform a call somewhere in your program to Log.setFile(true), this last call will be ignored. You can turn on -DlogShowBypassedConfig=true to see in your logs if any of your config calls are being ignored somewhere in your code.


The pleasant waves from the Yellow Sea, colourful sails and golden sands form Qingdao´s beautiful beach line and gives the city its profile of a City of Sailing. With its face to the sea and mountains in its back Qingdao offers a beautiful scenery in all directions. Add a comfortable climate, green parks, amazing festivals, clear sea water and delicious sea food and you have one of the most attractive cities in the Far East.
The city is a cultural combination of east and west. Through the unique architecture in some parts of Qingdao. Qingdao was a German possession 1898 to 1914, and still features astounding examples of Bavarian style architecture, particularly the railway station, the twin-spire Catholic Church and the former German Governor´s residence. And the best beer of China is brewed here, the Germans started the production already in the 19th century.


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We feature all types of Shtenders, Aronei Kodesh, Mechitzos, and more.
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We had a little discussion in the physics class. We were talking about resistance, and she said that when a wire is heated up, the resistance also increases; but I think that the resistance decreases because when something is heated up the electrons also gain energy, enabling them to move with lower resistance. So what is correct approach and solution to this problem?
Either one can be true depending on the material. In metals, the electrons don't need any additional energy to move, so the main effect of temperature is to cause the atoms to vibrate more, which interferes with the motion of the electrons, increasing the resistance.
On the other hand, in a semiconductor, the electrons do need to gain some non-zero amount of energy before they can start moving at all. In this case, raising the temperature does decrease the resistance for the reason you state.
Near room temperature, the resistivity of metals typically increases as temperature is increased, while the resistivity of semiconductors typically decreases as temperature is increased. The resistivity of insulators and electrolytes may increase or decrease depending on the system.
You can read more about these effects on wikipedia here and here.
The problem with assuming that "hotter" free electrons in a metal convey more current is that their motion is random in direction and so they do not contribute to the electric current as there is no net drift of charge.
Their average velocity due to their thermal motion is zero.
The application of an electric field accelerates the free electrons and so they gain kinetic energy and now the free electrons have a net velocity along the conductor, hence this motion constitutes a movement of charges in a particular direction - an electric current.
However the free electrons collide with the lattice ions and transfer energy to the lattice ions which now have a greater kinetic energy - the temperature goes up as there has been ohmic heating.
So the free electrons have an average velocity along the wire called the drift velocity.
The drift velocity is order of magnitude 1 mm/s whereas the speed of the free electrons due to their thermal motion is order of magnitude 100 km/s.
With more kinetic energy the lattice ions vibrate more and thus there is a greater probability of the drifting free electrons colliding with them - the resistance has increased.
For a metal as the temperature increases its resistance increases because of the lattice ions vibrating more at higher temperatures.
Note that in supra-conductors the temperature is usually very low, so low temperature and apparent mobility restriction are not incompatible with low resistivity.
In fact more thermal agitation also means more vibrations so to sketch it in very simple words, these are counteracting the electric force that forces the electrons to behave and be in a certain state, but they don't want to.
To come back to the question about resistvity of wires, the phenomenon of increasing of resistivity when heating has long been used as a natural current regulator. The intensity increase, so by Joule effect the wire is heating up, so resistivity increases, so intensity decrease and so on. For instance lightbulbs have been used in such a way, as very cheap but efficient current regulators, because the filament reaches hight temperatures and the effect is notable.
How do electrons actually move in a circuit?
How does the specific resistance / conductivity changes, when melting metals?
Is this the reason why a circuit with no components (except wire) would discharge the battery faster?
How accurate is the following description (quoted) of what happens when a liquid is heated in a closed vessel?
Why does internal resistance increase as current decreases?
What is the resistance of an ohmic sphere with surface potential $\phi_0\cos\theta$?


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☰ Football Stars open new sports pitch
You are here: Home » School Life » Latest News » Football Stars open new sports pitch
Football Stars open new sports pitch
Posted on: 05 Nov 2014 by Weston Green School
Sky Sports Commentators Martin Tyler and Tony Gale have officially opened the new sports pitch at Weston Green School, with the help of former professional footballer and current Manager of Hayes & Yeading United, Phil Babb.
To mark the occasion, children aged from 3-11, from Kindergarten to Year 6 also enjoyed training sessions on the new all-weather sports pitch, with Hampton and Richmond FC players and coaches.
The afternoon culminated in an official opening, with the ribbon cut by special guest Martin Tyler.
Parents and other invited guests at the opening also enjoyed tea and cake to celebrate the occasion.
Mr Mike Harrison, Headteacher, said "It is a great thrill and privilege to welcome former professionals to the school as they inspire the children to know that getting to the top is possible. The expertise of these high-class players here today and the new astro will help the children develop their skills and have a most memorable day which I hope inspires them for many months to come. We are committed to delivering the best and today certainly has done that."
Mr Alan Dowson, Specialist Games Teacher and Manager of Hampton and Richmond Football Club, said "It has been fantastic to see our pupils at Weston Green enjoying the new pitch and having the opportunity to learn new skills from the Hampton and Richmond FC coaches. We are all very excited about using these great new facilities, to extend our on-site Sports provision at the school. Thank you to Martin, Tony and Phil and to the Club coaches and players, who made today such a success."
School Developments (4)
Bellevue Education (5)
Parents' Association (3)
Key Stage 1 (89)


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The EU embargo on Russian…
MINING.com is a web-based global mining publication focusing on news and commentary about mining and mineral exploration. The site is a one-stop-shop for mining industry…
German Coal Consumption Continues To Crash
By MINING.com - Nov 04, 2019, 2:30 PM CST
Lignite and bituminous coal produced 50 percent less energy than renewables in Germany during the first three quarters of 2019, a new report by the Centre for Solar Energy and Hydrogen Research Baden-Württemberg (ZSW) and the German Association of Energy and Water Management (BDEW) reveals.
According to the document, coal generated 125 billion kWh, down from the 171.1 billion kWh produced during the same period last year. Solar, wind and other renewable sources, on the other hand, generated around 183 billion kWh of electricity between Q1 and Q3, 2019, which covered 42.9 percent of gross electricity consumption in the country and represented a 5 percent increase over the same period last year.
"Notably, renewables' share climbed as high as 52 percent during an unusually windy March," the report reads. "If wind and solar energy yields in the fourth quarter are in line with the last few years' averages, renewables' share could amount to a good 42 percent in 2019."
In 2018, renewables and coal accounted for close to the same share in energy production, with Germany still sitting as the top eighth consumer of the black fuel.
But Chancellor Angela Merkel is on a quest to phase out coal, having set the goal of withdrawing from coal-fired power production by 2038. Based on the results of a government-commissioned report, she also proposed the idea of producing 65 percent of Germany's electricity through renewable sources by 2030 so that CO2 emissions could be lowered by 61 percent over 1990 levels.
According to BDEW, which represents 1,800 firms in power, gas, water and heat provision, even though renewables consumption continues to grow, achieving the 65 percent target would require an increase in wind and solar generation capacity to between 215 billion and 237 billion kWh.
Related: Is Wireless Electricity Within Our Reach?
In order to do so, BDEW and ZSW say more flexible rules are necessary when it comes to the expansion of wind farms and photovoltaic farms.
The organizations have been pushing for the capacity of offshore wind turbines to be raised to 17 GW each by 2030 from 15 GW, and for more rapid adoption of solar panels so that the installed capacity reaches 98 GW by 2030.
When it comes to wind turbines, the restrictions are stringent because there are fears of adverse effects on tourism and on the maritime environment of the German North and Baltic Seas.
"We are sliding into a real recession for a lack of land and increasingly prohibitive distance regulations. If politicians don't ease off the brakes on the expansion of wind farms, we are going to fall well short of the 65 percent target," Stefan Kapferer, Chairman of BDEW's General Executive Management Board, said in a media statement.
Despite Kapferer's worries, onshore wind power remained the leading source of renewable energy in the Q1-Q3 2019 period, with nearly 72 billion kWh, while offshore wind contributed nearly 17 billion kWh and posted the steepest growth at 31 percent.
Photovoltaics came in second place with around 41 billion kWh, followed by biomass with 33 billion kWh, and hydropower with 16 billion kWh.
By Mining.com
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Would Leaving Canada Solve Alberta's Oil Crisis?


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GFA World Challenges Every Person to Help Save Just One Impoverished Person
by Tork Media LLC October 16, 2019, 8:26 am in Breaking News 169 Views
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Campaign coincides with International Day for the Eradication of Poverty, Oct. 17;
focuses on millions living on less than $2 per day
STONEY CREEK, ON — Faith-based mission agency GFA World (Formerly: Gospel for Asia, www.gfa.ca) has revealed its top tips for those who want to help end global poverty, marking International Day for the Eradication of Poverty on October 17.
Extreme poverty – earning $1.90 or less per day – impacts 736 million people around the world, double the population of the U.S. and Canada combined. The United Nations established Oct.17 each year as International Day for the Eradication of Poverty as a campaign to end abject poverty.
"Poverty is the tip of a Titanic-like iceberg," said GFA founder Dr. K.P. Yohannan who has spent his life helping the poor in Asia. Poverty's hidden impacts include almost three billion people without a toilet, and one billion people without safe drinking water.
No 'Silver Bullet'
"There's no single 'silver bullet' to end poverty completely, but every person is able to help one person, or one family climb out of extreme poverty," said Yohannan, citing five simple steps everyone can take to join the fight to eradicate cycles of poverty.
GFA's "top five" global poverty-fighting tips are:
Give up $5 lattes for a month and donate the savings to a respected charity that helps and empowers the poor
Learn more about the issues – economic, political, cultural and others – that feed poverty and inequality
'Adopt' a specific country, learn about your chosen country, and speak up for that nation on social media, highlighting poverty-related issues
Pray for world leaders to have wisdom on how to change systems that perpetuate poverty and inequality
Consider making one change in your life – perhaps a less expensive phone plan – that could free up money to donate to poverty-fighting causes
"Small actions like these may seem insignificant in the face of global poverty, but they are not small to God," said Yohannan, whose faith-based organization was launched in 1979 with a gift of $10 and now serves millions of impoverished people in 14 nations. (Revolution in World Missions, pg. 68)
Americans Transform Lives
Every year, thousands of GFA donors worldwide give life-transforming gifts to empower the poor. So far, almost two million families from different faith backgrounds have received practical gifts – such as goats or sewing machines – to help generate income or improve their quality of life.
Bhrithi, a young widow with two boys, was evicted from the roadside where she sold vegetables. Through the GFA Gift Catalogue, a donor provided a pull cart – turning Bhrithi into a "mobile market" and boosting her income overnight. Because she knew the gift came from Christians, she started going to church to learn about God.
"Our passion is to see these precious people come to know they have incredible value in God's eyes, and that he loves them deeply," said Yohannan. "The problem of global poverty is huge, but if we each do our part, we can change the world."
Celebrating its 40th anniversary in 2019, GFA World, www.gfa.ca is a leading faith-based mission agency, bringing vital assistance and spiritual hope to millions, especially to those who have yet to hear the "good news" of Jesus Christ. In GFA's latest yearly report, this included more than 70,000 sponsored children, free medical camps conducted in more than 1,200 villages and remote communities, over 4,700 clean water wells drilled, over 11,400 water filters installed, income-generating Christmas gifts for more than 240,000 needy families, and spiritual teaching available in 110 languages in 14 nations through radio ministry. For all the latest news, visit our Press Room at https://press.gfa.org/news.
PHOTO CUTLINE: SAVE JUST ONE: Everyone can help save just one person from extreme poverty, says faith-based mission agency GFA World, www.gfa.ca, marking International Day for the Eradication of Poverty on October 17.
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Дімітріс Сгурос (, 30 серпня 1969, Афіни) — грецький піаніст-віртуоз, поліглот — вільно володіє шістьма мовами.

Біографія
Почав грати на фортепіано у віці шести років, дав свій перший концерт у віці семи років. У 12 років він вде закінчив консерваторію в Афінах із дипломами піаніста та викладача гри на фортепіано, отримавши першу премію і золоту медаль.

1982 року у віці неповних 13 років він виконував Фортепіанний концерт № 3 Рахманінова в Карнегі-Холі в Нью-Йорку із Національним симфонічним оркестром під керуванням Мстислава Ростроповича. Його виконання було представлене як один з найбільш вражаючих музичних дебютів століття.

Сгурос продовжив навчання в Королівській Академії в Лондоні, а пізніше в університеті Меріленда, Коледж-Парк у Сполучених Штатах. Закінчив обидва заклади з найвищими оцінками. Крім свого незвичайного музичного таланту, Дімітріс Сгурос вільно володіє шістьма мовами і з відзнакою закінчив математичний факультет університету Афін.

Гастролі Дімітріса Сгуроса вже відбулись по всьому світу, включаючи Австралію, Австрію, Болгарію, Китай, Францію, Німеччину, Ізраїль, Італію, Японію, Корею, Росію, Румунію, Південну Африку, Іспанію і Туреччину. Він грав для королівських родин Великої Британії, Монако та Швеції, також грав під управлінням таких імен, як Герберт фон Караян, Леонард Бернстайн, Еміль Табаков, Курт Мазур, Євген Свєтланов. З березня 1988 року відбулись три «Фестивалі Сгуроса» в Гамбурзі, Любляні і Сінгапурі.

25 березня 2009 року Дімітріс Сгурос в День незалежності Греції взяв участь в концерті класичної музики у Національній філармонії України.

Відгуки
 Після спільного виступу у Карнегі-холі Мстислав Ростропович назвав Сгуроса «…диво природи, музичне явище, послане Богом».
 Святослав Ріхтер сказав: «Здається, що геній музики схожий на птаха, який літає у пошуках розуму, в якому він міг оселитись. Цей птах зупинився на світлій голові молодого грека — гнізда Дімітріса Сгуроса».
 Артур Рубінштейн поділився за два місяці до смерті: «Я дякую Богові за те, що залишає мене вживих, аби я міг чути гру Сгуроса. Він найкращий піаніст з тих, кого я коли-небудь чув, включаючи мене самого».

Примітки

Джерела
 Офіційна сторінка
 Біографія Дімітріса Сгуроса
 Τάκης Καλογερόπουλος, Λεξικό της Ελληνικής μουσικής, εκδόσεις Γιαλλελή, 2001 — Musipedia
 Детальна біографія нка сайті www.filonas.gr

Грецькі піаністи
Народились 30 серпня
Народились 1969
Поліглоти
Випускники Афінського університету

redpajama_set_name: RedPajamaWikipedia


This is the third part of the solution for Papa Bob's Mega Challenge. In this part of the solution, we'll be setting up the Data Transfer Object to pass an order created in the Presentation layer all the way to the Persistence layer.
Now that we have an orderDTO created within this layer, we need to modify the method calls within the other layers to expect an input parameter of DTO.OrderDTO. This allows for the Presentation layer's orderDTO to be passed through the different layers.
Notice that the method's return type is changed to Order (Entity-type order), which gives the CreateOrder() method the object it needs to store in the database.
Then, save and run your project, click on the Order button, and return to the database to to ensure that the order was saved properly.
This concludes this part of the solution to Papa Bob's Mega Challenge. We've created much of the core functionality needed for the layers to interact and pass information back and forth. In the next part, we'll create the Default page with its controls and styling.


I'm sitting on the bed with my knees up, supporting the laptop. Lucy, as is her custom, has crawled under my legs, but this time her little head was poking out ever so adorably from under the gap in the covers. Doing the "admire".


text:
Q: why the set of all functions in $L_{2}([a,b])$ which are positive almost everywhere on $[a.b]$ is convex (an example in Israel Gohberg) Why the set of all functions in $L_{2}([a,b])$ which are positive almost everywhere on $[a.b]$ is convex ? could anyone explain this for me please?

A: Simply because $tf(x)+(1-t)g(x)>t\cdot 0+(1-t)\cdot 0=0$ for a.e. $x$.

A: Let $C$ be convex and let $L_C = \{ f \in L_2[a,b] | f(t) \in C \text{ ae.} \}$,
then it is straightforward to see that $L_C$ is convex from the definition.
The set $C=[0,\infty)$ is convex.

redpajama_set_name: RedPajamaStackExchange


Guess what, we're not rational.
Fear of flying is a widespread problem which can get in the way of our desire to enjoy a relaxing holiday or build new business connections. Whilst the numbers show that we're far more likely to come to harm in a car accident than a plane crash, this rational reminder makes virtually no difference for someone who experiences fear of flying.
As with most of our problems, fear of flying is driven by our unconscious mind rather than our rational brain. All our unconscious mind wants to do is to keep us safe from harm, whatever the cost. So if you find yourself panicking or overcome with fear during a flight, your unconscious is trying to keep you on alert for danger or even put you off flying altogether.
When clients come to see me about their fear of flying, they are often very frustrated with themselves because they know it's not rational. But beating yourself up over your fear of flying may only make the problem worse. It's important to remember that we all struggle with irrational fears and beliefs and whilst the problem is holding you back, the intention behind the behaviour is positive. Your fear just wants to keep you safe.
When is it better? When is it worse?
Is it different before the flight, take off, turbulence or landing? What's different about those times?
What are you thinking about the experience? Do you have a video that's playing in your mind about what will happen? How does it appear to you?
What are the feelings or sensations you're experiencing when you're feeling your fear?
In treating your fear of flying I would help you clear any negative memories or beliefs you might hold about flying. Sometimes people have a strong negative memory in relation to flying and for others the fear is about what flying means to them e.g. loss of control. I would then draw on a range of powerful techniques to guide your unconscious to move towards what your ideal flight would look like. This would include some valuable self-hypnosis techniques for you to practice and use during a flight to reduce any fearful symptoms.
In the lead up to the flight, write down how the flight would be different if you didn't have your fear of flying. Write this down in a journal with as much detail as possible including waiting for the flight, take-off and landing. Write down what would be different if you experience turbulence. Describe it in positive terms e.g. "I would be laughing and joking with my friend" or "I would enjoy being absorbed by my book" rather than "I wouldn't be doing X".
Starting as far ahead of your flight as possible, revisit the positive story you've written about your flight and re-read it every night. Close your eyes and take your time to visualise the story, rehearsing those key moments that let you know the flight is going well. By the time you get to the flight your mind will be looking for those details that you described. This will reinforce the positive feelings you've associated with those aspects of the flight.
It will boost your confidence if you know you have a 'go-to' strategy if you suddenly experience a wave of panic or fear. Just having this up your sleeve will make it less likely that you will experience a blip. There are many techniques you could adopt, but breathing techniques tend to be the most powerful as they slow your heart-rate down which leads to both your body and mind feeling calmer and quieter.
Try breathing in for 3 seconds in through your nose and out for 5 seconds through your mouth for a minute and see how you feel differently as a result.
There are lots of valuable self-help tips in this article specifically aimed at helping you through turbulence.
If you would like help with your fear of flying, feel free to contact me today for a free, initial consultation. I see hypnotherapy clients face-to-face in Manchester City Centre or online via Skype.


text:
FDA Approves Booster Shot for 12-15 Year Olds
Samantha Elkins, News Editor
As students return to school from winter break, the Omicron variant has contributed significantly to a surge in recent COVID-19 cases. On Monday, the U.S. Food and Drug Administration officially approved the Pfizer-BioNTech COVID-19 booster shot for 12-15-year-olds. The FDA also released new information, approving a shorter waiting period for one to be eligible to receive the booster. The waiting period changed from six months to five months after one's last dose.
The new year began with a boom in Omicron cases due to its high transmissibility rate. However, Omicron is less severe than other variants. Growing evidence confirms that the variant infects the throat, not the lungs as compared to Delta and previous variants, contributing to its contagiousness. Health officials continue to echo that although Omicron is less life-threatening, severity is also measured through contagiousness. On Monday, the U.S. officially hit one million COVID-19 cases — further stressing the importance of getting vaccinated and tested, as well as continuing to wear masks.
After the FDA reviewed a study conducted in Israel, they stated their confidence in lowering booster eligibility to the 12-15-year-old age group. The study stated that "no new safety concerns" from the vaccine threaten this age group. In addition, findings confirmed no new cases of myocarditis or pericarditis, the inflammation of the heart or surrounding tissue, reported in those who received the booster.
Moreover, child hospitalization rates have jumped recently, with reports showing that by the end of the week on Dec. 28, 378 children were admitted to the hospital with COVID-19. As hospitalization rates continue to increase, health care workers become more exposed to the highly transmissible variant and as a result, have a higher chance of infection. Currently, 20% of the healthcare force is in a quarantine period right now, shrinking access to on-site health care services.
Health officials urge all those eligible to get vaccinated and boosted. In order to find out where one can receive the booster shot or a vaccine nearby, click here. For more information on COVID-19 and immunizations, click here.
Samantha Elkins is a junior and News Editor. This is her second year on staff and she looks forward to experiencing newspaper class in-person this year...
Four Hostages Held in Texas Synagogue
Florida Lawmakers Propose Bill Outlawing Abortion After 15 Weeks
Prince Andrew Loses Military Titles Amid Sexual Abuse Lawsuit
Supreme Court Blocks Biden's Vaccine Mandate for Large Businesses
U.S. Top Schools Allegedly Partake In Illegal Conspiracy To Limit Student Financial Aid
Bob Saget Found Dead In Orlando Hotel at Age 65
Miami-Dade Schools Superintendent Alberto Carvalho Accepts Potential Position in Los Angeles
Three Dead and Eight Injured in Michigan High School Shooting


The term 'stress' is widely abused and frequently misunderstood in the workplace. More often than not, it gets used by employers and managers as an easy excuse for ignoring bad management practices or wider environmental or cultural failings. Yet mental ill health at work, in all its shapes and forms, is nevertheless an all-too-real problem that costs the economy, as well as individuals, dear.
According to the government's new mental health at work strategy, New Horizons, which was unveiled in December, at any one time just over a fifth of working-age women and 17% of working-age men are affected by stress and anxiety.
One in six adults will suffer from a mental health problem at some point in their lives. Mental ill health, it argued, is also the most common reason for claiming health-related benefits and costs the economy between £30bn and £40bn through lost production, sick pay and NHS treatment.
The new document comprises a UK-wide national mental health and employment strategy, a cross-governmental delivery plan, and commitments to action that span 11 government departments (see box below).
Employers need to recognise that while, as with physical conditions or disabilities, workers may require adaptations to workplaces or extra support, sometimes the obstacles to work are less tangible.
Government needs to build more effective links between the Department for Work and Pensions (DWP) and health and social services.
Health and social services need to improve extent to which they address employment needs of people with mental health conditions – for instance, by including vocational issues within assessments and consultations and treatment and support plans.
DWP, health and social services need to improve day-to-day support provided to people with mental health conditions and their potential employers – for example, in providing better information.
DWP should examine how better to resource services to provide more flexible and integrated assistance – for example, through reform of Access to Work.
To ease the transition from benefits to work, DWP should make available time-limited internships in parallel with job search for those with mental health issues who need to familiarise themselves with the world of work and build up time in the workplace.
Health and social services should routinely monitor employment outcomes for people they serve, with the DWP regularly monitoring service provision and outcomes for people they serve with a mental health condition.
Alongside the strategy document, the government also published a Department for Work and Pensions-commissioned review of employment support for people with mental health conditions, entitled Realising Ambitions (see box below).
The piloting of the NHS Plus-run workplace health helpline for small to medium-sized enterprises.
Ministers to examine how Access to Work programme could be widened to help more people with mental health conditions get and stay in work.
A New Horizons Ministerial Advisory Group to be set up to examine inequalities and mental health, chaired by the minister of state for care services (Phil Hope).
All advisers within Jobcentre Plus and other welfare-to-work providers to receive skills-based training around mental health issues.
That the government should set up a "single hub" for support and advice on best practice, do more to support national anti-stigma campaigns, and encourage the commissioning of mental health "first aid" or related training for employers, following examples in Scotland and Wales.
That the government should promote better sharing of good employment practice in relation to mental health among employers and ensure the principles and example of good occupational health practice in recruiting and retaining people with mental health conditions are widely disseminated, "so that recruiting managers without access to occupational health can use it as a self-help resource".
That the government should require public sector employers to review their OH arrangements in relation to the recruitment of people with mental health conditions to eradicate unjustified discrimination, and outlaw "inappropriate" use of pre-employment health checks, with checks only being done after and independently of an evaluation of the person's capacity to perform the job, to ascertain any adjustments they might require and to check they meet the essential health requirements of that job.
Both documents are a central part of the government's response to national director for health and work Dame Carol Black's vision for the future of workplace health, with the government's over-arching aim being to have, by 2025, radically narrowed the gap between the employment rate of people in contact with secondary mental health services and those of people with disabilities generally.
The strategy therefore needs to be seen as another piece of the puzzle ministers have been putting together to tackle workplace ill health in the wake of the Black recommendations, including the launch of a new fit note, a Fit for Work service, the reform of incapacity benefits, and a dedicated workplace health helpline for small and medium-sized enterprises (SMEs). In fact, the unveiling of the NHS Plus-run helpline was bundled into the launch of the strategy, such is the way ministers see all the different elements meshing together to create a larger whole.
The strategy also needs to be seen in the context of guidance from the National Institute for Health and Clinical Excellence (NICE) published in November, promoting mental health and wellbeing in the workplace.
As NICE made clear, tackling mental ill health at work effectively is often simply about careful, sensible, common-sense management and intervention, including the promotion of a culture of participation, equality and fairness based on open communication and inclusion, creating better awareness and understanding of mental wellbeing, plus reducing the potential for discrimination and stigma.
NICE also urged employers to put in place better systems for assessing and monitoring mental wellbeing, including employee attitude surveys, information on absence rates, staff turnover, and investment in training and development. Finally, it called for more flexible working (if practicable) for line managers to be given more freedom to promote the mental wellbeing of employees through supportive leadership style and management practices.
The strategy document builds on these recommendations, suggesting a range of responses including the dissemination of good occupational health (OH) practice in recruiting and retaining people with mental health conditions, that public sector employers review their OH arrangements in relation to the recruitment of people with mental health conditions, and that the "inappropriate" use of pre-employment health checks is outlawed.
Mental ill health is one of the major reasons why people are not able to be at work, agrees Black, which is why making this strategy work is so important. "Mental ill health makes a huge contribution to people not being there. But it is not just about what we do to help when people have already got into difficulty, but what we should be doing to help maintain people and keep them well," she explains.
It is the attitudes and effectiveness of line managers in managing people and mental ill health that will make the real difference, adds Eugene Farrell, business manager at Axa Icas.
"Line managers are very much the key because they are on the front line, and they need to be trained to identify conditions and issues and act on them in a sensible way," he says. "You are not going to get very far if you do not train your line managers.
It all comes down to line manager capability, agrees Ben Willmott, adviser at the Chartered Institute of Personnel and Development (CIPD). "Managers can be part of the problem or part of the solution when it comes to tackling mental health in the workplace. And it is not just about managing stress but about encouraging people to become better people managers," he says.
There is also growing recognition that often it is not the workplace per se that may be the stressor, but family life or financial concerns – but a badly managed workplace can in such circumstances be an exacerbator or tipping point.
The test now for the government is whether it can pull together to deliver the important promises made in the strategy, particularly in a climate of very tight public finances, Steve Shrubb, director of the Mental Health Network, said in the wake of the launch.
Work still needs to be done to get employers, GPs and even other health professionals to recognise that mental ill health needn't be a barrier to returning to work, argues Sandra Neylon, director of OH and vocational rehabilitation provider Neylon Occupational Health.
In practical terms, OH can play a central role in showing managers and HR departments how to speak to employees and show them what questions to ask and how to ask them, she recommends.
A version of this article first appeared in the February issue of Occupational Health magazine. Click here for more information.


text:
Доктор Самуел Леон Бриндис има више значења:

 Доктор Самуел Леон Бриндис (Мапастепек), насеље у савезној држави Чијапас у Мексику
 Доктор Самуел Леон Бриндис (Паленке), насеље у савезној држави Чијапас у Мексику
 Доктор Самуел Леон Бриндис (Соколтенанго), насеље у савезној држави Чијапас у Мексику


Our holistic treatments will nourish you mind, body, and spirit. Step into our tranquil, luxurious space and experience a level of relaxation beyond your wildest dreams.
Ease muscle tension and improve circulation in the areas that affect you most through a light to medium pressure. As your body releases tension and toxins, you will quickly find yourself in a serene, altered state of mind. Uniquely uplifting.
You will feel your tension slipping away as you indulge in our signature full body massage to improve circulation and calm tense nerves.
Using a firm hand, the RAIN therapist melts the neck and back as deep tissue work is continued down the body. This massage incorporates a variety of techniques to increase intensity and target underlying muscle groups where tension may hide. Also ideal for improving circulation. Our experts will relieve muscle tension, leaving you with a feeling of relaxation and well-being.
The Japanese Mint Massage offers Instant relief of muscle tightness, sinus congestions, headaches and rheumatic pain.
Slip into our comfy massage bed and relax as your therapist works to melt your stress away. Treat yourself to a full body relaxation massage.
Melt away stress and tension with our new Hawaiin Pohaku Stone Massage.


This service is used to schedule academic and non-academic use of space. It runs through a web-based user interface as well as an application that runs on Windows.
The ability for a user to successfully log in and perform actions, such as viewing or making room reservations within EMS at https://ems.uoregon.edu.


Are you planning a trip to Saco River this summer? There are plenty of water safety tips that you should keep in mind before heading out to ensure a safe and fun time out on the river with your entire family.
Never go for a swim alone on the river. There are plenty of things that could go wrong during an innocent casual swim such as slippery surfaces causing you to lose your balance, muscle pull, uneven surfaces or even submerged objects that could knock you over. Although rare, these instances could potentially occur, so it's always best to have a swim buddy come along while taking a dip.
Consider this: 25% of adult drowning accidents have involved some degree of alcohol. Additionally, 44% of all drowning incidents in the United States have occurred in rivers. Rivers can be very dangerous places for those who fail to take the right precautions. Alcohol is likely to impair your judgment and lead to riskier behaviors.
This is really a no-brainer. Not all the river canoeing and paddling will go smoothly. The boat could capsize forcing you to swim back. If you are a poor swimmer or don't know how to swim at all, you could easily drown. It's always best for both adults and children to wear a lifejacket.
If you are going out camping by the riverside, it's a great idea to equip yourself with some lifesaving skills in case of emergency. Being able to administer critical first aid as you wait for medical help to arrive after river accidents is essential. You never know when you may need to be relied upon to save lives. Knowing some basic first aid skills, such as how to dress wounds properly or CPR could potentially help save a life in the future.
Don't immerse yourself in situations that might put you in danger. It is important to know your limits as far as your activities on the river are concerned. A long day out in the sun is draining, it's important to know when your body is telling you to kick back and relax.
The most important thing to remember while on the river this summer is to have some FUN and make everlasting memories with your family! We're hoping that these tips will not only help you stay safe throughout your visit to Saco River Camping Area, they will also be shared throughout the community to help keep others safe as well.
Ready for some fun? Click here to book your next stay at Saco River Camping Area.


text:
namespace client {

// Views framework implementation of a top-level window in the browser process.
// The methods of this class must be called on the main thread unless otherwise
// indicated.
class RootWindowViews : public RootWindow,
                        public ClientHandler::Delegate,
                        public ViewsWindow::Delegate {
 public:
  // Constructor may be called on any thread.
  RootWindowViews();
  ~RootWindowViews();

  // RootWindow methods:
  void Init(RootWindow::Delegate* delegate,
            bool with_controls,
            bool with_osr,
            const CefRect& rect,
            const CefBrowserSettings& settings,
            const std::string& url) OVERRIDE;
  void InitAsPopup(RootWindow::Delegate* delegate,
                   bool with_controls,
                   bool with_osr,
                   const CefPopupFeatures& popupFeatures,
                   CefWindowInfo& windowInfo,
                   CefRefPtr<CefClient>& client,
                   CefBrowserSettings& settings) OVERRIDE;
  void Show(ShowMode mode) OVERRIDE;
  void Hide() OVERRIDE;
  void SetBounds(int x, int y, size_t width, size_t height) OVERRIDE;
  void Close(bool force) OVERRIDE;
  void SetDeviceScaleFactor(float device_scale_factor) OVERRIDE;
  float GetDeviceScaleFactor() const OVERRIDE;
  CefRefPtr<CefBrowser> GetBrowser() const OVERRIDE;
  ClientWindowHandle GetWindowHandle() const OVERRIDE;

  // ViewsWindow::Delegate methods:
  bool WithControls() OVERRIDE;
  CefRect GetWindowBounds() OVERRIDE;
  void OnViewsWindowCreated(CefRefPtr<ViewsWindow> window) OVERRIDE;
  void OnViewsWindowDestroyed(CefRefPtr<ViewsWindow> window) OVERRIDE;
  ViewsWindow::Delegate* GetDelegateForPopup(
      CefRefPtr<CefClient> client) OVERRIDE;
  virtual void OnTest(int test_id) OVERRIDE;
  virtual void OnExit() OVERRIDE;

 protected:
  // ClientHandler::Delegate methods:
  void OnBrowserCreated(CefRefPtr<CefBrowser> browser) OVERRIDE;
  void OnBrowserClosing(CefRefPtr<CefBrowser> browser) OVERRIDE;
  void OnBrowserClosed(CefRefPtr<CefBrowser> browser) OVERRIDE;
  void OnSetAddress(const std::string& url) OVERRIDE;
  void OnSetTitle(const std::string& title) OVERRIDE;
  void OnSetFavicon(CefRefPtr<CefImage> image) OVERRIDE;
  void OnSetFullscreen(bool fullscreen) OVERRIDE;
  void OnSetLoadingState(bool isLoading,
                         bool canGoBack,
                         bool canGoForward) OVERRIDE;
  void OnSetDraggableRegions(
      const std::vector<CefDraggableRegion>& regions) OVERRIDE;

 private:
  void CreateClientHandler(const std::string& url);

  void InitOnMainThread(const CefBrowserSettings& settings,
                        const std::string& startup_url);
  void CreateViewsWindow(const CefBrowserSettings& settings,
                         const std::string& startup_url,
                         CefRefPtr<CefRequestContext> request_context);

  void NotifyViewsWindowDestroyed();
  void NotifyDestroyedIfDone();

  // After initialization all members are only accessed on the main thread
  // unless otherwise indicated.
  // Members set during initialization.
  RootWindow::Delegate* delegate_;
  bool with_controls_;
  bool is_popup_;
  CefRect initial_bounds_;
  CefRefPtr<ClientHandler> client_handler_;

  bool initialized_;
  bool window_destroyed_;
  bool browser_destroyed_;

  CefRefPtr<CefBrowser> browser_;

  // Only accessed on the browser process UI thread.
  CefRefPtr<ViewsWindow> window_;

  DISALLOW_COPY_AND_ASSIGN(RootWindowViews);
};

}  // namespace client

#endif  // CEF_TESTS_CEFCLIENT_BROWSER_ROOT_WINDOW_VIEWS_H_

redpajama_set_name: RedPajamaGithub


text:
Standing Up To Powerful Interests
Statement Commending New Military Consumer Enforcement Act
Gives CFPB More Tools To Protect Those Who Serve
"These senators have the right idea-- strengthen the CFPB's ability to protect those who serve. Why do others want to weaken the CFPB?"
Statement by Mike Litt, U.S. PIRG Consumer Advocate On How the Military Consumer Enforcement Act further empowers the Consumer Financial Protection Bureau (CFPB) to protect servicemembers and veterans
Washington, DC – "Today, U.S. PIRG applauds U.S. Senators Jack Reed (RI), Sherrod Brown (OH) and other Senators (list below) for introducing the Military Consumer Enforcement Act. The bill enhances the CFPB's ability to protect servicemembers and veterans from abuses in the financial marketplace by giving it jurisdiction over enforcing key parts of the Servicemembers Civil Relief Act (SCRA).
The CFPB and its Office of Servicemember Affairs have already demonstrated a strong commitment to protecting those who serve. For example, it has taken at least 12 major legal actions against financial firms targeting young servicemembers, older veterans and their families, securing approximately $130 million in relief for them. It has also successfully investigated banks to ensure compliance with the Military Lending Act.
And it has handled over 72,000 complaints from the military community. A U.S. PIRG Education Fund report released earlier this month found that debt collection abuses were the leading source (32%) of servicemember complaints to the CFPB. (2-page report summary).
But the SCRA offers important additional protections that have been, at best, unevenly enforced by other regulators. The SCRA includes provisions that prohibit the eviction of military members and their dependents from rental or mortgaged property, and the law caps interest at 6% on debts incurred prior to an individual entering active duty military service.
Given its proven track record for protecting our military community, giving the CFPB the jurisdiction over key parts of the SCRA means that the law will actually be enforced. These Senators have the right idea - we should be strengthening the CFPB's ability to protect those who serve. Why do others want to weaken the watchdog?
While we commend the Senators for this effort, we also warn the entire Senate that it must reject threats to the CFPB. Threats include the House-passed Financial Choice Act, HR 10, and proposals from other Senators to weaken the CFPB. The better-named Wrong Choice Act would leave the CFPB an unrecognizable husk and also roll back most of the Dodd-Frank Act's other protections against another collapse of our financial system and economy.
Dismantling the CFPB would place servicemembers, veterans and their families in "financial harm's way," thereby threatening unit preparedness since financial problems are a leading cause of revocation of security clearances.
Our troops, their families and our veterans and all the rest of us deserve a strong watchdog protecting their interests. That watchdog is the CFPB."
Other original co-sponsors of the Military Consumer Enforcement Act include Sens. Jon Tester (Mont.), Richard Blumenthal (Conn.), Tim Kaine (Va.), Tammy Duckworth (Ill.), Elizabeth Warren (Mass.), Tammy Baldwin (Wis.), Al Franken (Minn.), Amy Klobuchar (Minn.), Chris Van Hollen (Md.) and Catherine Cortez-Masto (Nev.).
U.S. PIRG is the federation of state Public Interest Research Groups. PIRGs are non-profit, non-partisan public interest advocacy organizations that stand up to powerful interests whenever they threaten our health and safety, our financial security, or our right to fully participate in our democratic society. On the web at www.uspirg.org.
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Modernize the Vote
Zero Out Toxics
Make It Toxic-Free
Ban Roundup
Ban Bee-Killing Pesticides
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Defend Net Neutrality
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Defend The Consumer Bureau
21st Century Transportation
Transform Transportation
Electric Buses, Healthy Kids
Stop Highway Boondoggles
Make Higher Education Affordable
High Value Health Care
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text:
\section{Definition and notation} \label{def}
Let the power series $E_{\alpha,\beta}(z) := \sum\limits_{n\ge 0} \frac{z^n}{\Gamma(\alpha n + \beta)}\ %
\ (\alpha, \beta\in {\mathbb C};\ \Re(\alpha) > 0)$ define the classical two-parametric Mittag-Leffler (M-L for short) function (see e.g, \cite[\color{cyan}1953]{Agar53,HumAgr53}, \cite[\color{cyan}1905]{Wiman05}). In the case when $\alpha$ and $\beta$ are real positive, the series converges for all values of $z\in {\mathbb C}$, so $E_{\alpha,\beta}(z)$ is an entire functions of $z\in {\mathbb C}$~\cite[\color{cyan}Lect.~1]{Levin96} of order $\rho = 1/\Re(\alpha)$ and type $\sigma = 1$ (see~\cite[\color{cyan}\S1.1]{Lavault17}). From here on, this latter two-parametric M-L function of $z\in {\mathbb C}$ is denoted for simplicity by $E_\alpha(z; \beta)$, as defined in~\cite{Djrba60,Djrba66}.

The two-parametric M-L function of $z\in {\mathbb C}$ extends to the generalized M-L type function $E_{\alpha,\beta}(x,y;\mu)$ of two variables $x, y\in {\mathbb C}$. The latter is an entire function defined by the double power series~\cite[\color{cyan}Eq.~12]{OgorYasha10}
\begin{equation} \label{def_ml}
E_{\alpha,\beta}(x,y;\mu) := \sum\limits_{n,m\ge 0} \frac{x^n y^m}{\Gamma(n\alpha + m\beta + \mu)}\ \qquad (\alpha,\, \beta,\, \mu\in {\mathbb C},\ \Re(\alpha),\, \Re(\beta) > 0),
\end{equation}
where the arbitrary parameter $\mu$ takes in general a complex value.

Following~\cite{Djrba60,Djrba66} (see also e.g. \cite{GoKiMaRo14,HaMaSa11,Temme96}, \cite[\color{cyan}\S1.2 \& App.~A, C \& D]{Lavault17}, and references therein), the Hankel's integral contour is denoted by $\gamma(\epsilon;\theta) := \bigl\{0 < \theta\le \pi,\ \epsilon > 0\bigr\}$ oriented by non-decreasing $\arg \zeta$. It consists in the following parts:
\begin{enumerate}
\item the two rays $S_{\theta} =  \bigl\{\arg \zeta = \theta,\ |\zeta|\ge \epsilon\bigr\}$ and $S_{-\theta} = %
\bigl\{\arg \zeta = -\theta,\ |\zeta|\ge \epsilon\bigr\}$;
\item the circular arc $C_\theta(0;\epsilon) =  \bigl\{|\zeta| = \epsilon,\ -\theta\le \arg \zeta\le \theta\bigr\}$.
\end{enumerate}
If $0 < \theta < \pi$, then the Hankel contour $\gamma(\epsilon;\theta)$ divides the complex $\zeta$-plane into two unbounded regions, namely $\Omega^{(-)}(\epsilon;\theta)$ to the left of $\gamma(\epsilon ;\theta)$ by orientation and $\Omega^{(+)}(\epsilon;\theta)$ to the right of it. If $\theta = \pi$, then the contour consists of the circle $|\zeta| = \epsilon$ and the twice passable ray $-\infty < \zeta\le -\epsilon$.

\section{Integral representations} \label{rep}
This section provides a few lemmas, which show various integral representations of the generalized M-L type function~\eqref{def_ml} corresponding to different domains of variation  of its arguments.

\begin{lem} \label{lem1}
Let $0 < \alpha, \beta < 2$, $\alpha\beta < 2$. Let $\mu$ be any complex number and let $\theta$ meet the condition
\begin{equation} \label{cond1}
\pi \alpha\beta/2 < \theta\le \min\bigl(\pi, \pi\alpha \beta\bigr).
\end{equation}

If $x\in \Omega^{(-)}(\epsilon_\alpha;\theta_\alpha)$\ and $y\in \Omega^{(-)}(\epsilon_\beta;\theta_\beta)$, where $\epsilon_\alpha := \epsilon^{1/\beta}$, $\epsilon_\beta := \epsilon^{1/\alpha}$, $\theta_\alpha := \theta/\beta$\ and $\theta_\beta := \theta/\alpha$, then the integral representation based on Hankel's contour integral holds
\begin{equation} \label{mlrep1}
E_{\alpha,\beta}(x,y;\mu) = \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha\beta} \int\limits_{\gamma(\epsilon;\theta)} %
\frac{\mathrm{e}^{\zeta^{1/(\alpha \beta)}} \zeta^{\frac{\alpha + \beta - \mu}{\alpha \beta} - 1}} %
{(\zeta^{1/\alpha} - y)(\zeta^{1/\beta} - x)}\, \mathrm{d} \zeta.
\end{equation}
\end{lem}
\begin{proof}
First, let $|x| < \epsilon_\alpha$. Taking into account the fact that $\epsilon_\alpha = \epsilon^{1/\beta} = %
\left(\epsilon_\beta^\alpha\right)^{1/\beta} = \epsilon_\beta^{\alpha/\beta}$ yields
\[\sup_{\zeta\in \gamma(\epsilon_\beta;\theta_\beta)} \bigl|x\zeta^{-\alpha/\beta}\bigr| < 1.\]

By the statement of the definition in~\eqref{def_ml}, the expansion of $E_{\alpha,\beta}(x,y;\mu)$ may be rewritten as follows in terms of the corresponding two-parametric M-L function $E_\beta(y; \alpha n + m)$ of one variable,
\begin{flalign} \label{oneparml}
E_{\alpha,\beta}(x,y;\mu) &= \sum\limits_{n=0}^\infty \sum\limits_{m=0}^\infty \frac{x^n y^m} %
{\Gamma(\alpha n + \beta m + \mu)} \nonumber\\
&= \sum\limits_{n=0}^\infty x^n \sum\limits_{m=0}^\infty \frac{y^m}{\Gamma(\beta m + (\alpha n + \mu))} %
= \sum\limits_{n=0}^\infty x^n E_\beta(y; \alpha n + m).
\end{flalign}
Under the assumptions of Lemma~\ref{lem1}, it is possible to use the known integral representation of $E_\beta(y; \alpha n + m)$ (see e.g. \cite[\color{cyan}Eq.~(2.2)]{Djrba66}). Taking the above $\epsilon_\beta$ and $\theta_\beta$ as the parameters defining the Hankel contour, which is admissible according to inequalities~\eqref{cond1} provided that $\theta_\beta = \theta/\alpha$, gives for $y\in \Omega^{(-)}(\epsilon_\beta;\theta_\beta)$,
\begin{flalign} \label{intrep1}
E_{\alpha,\beta}(x,y;\mu) &= \sum\limits_{n=0}^\infty x^n E_\beta(y; \alpha n + m) %
= \sum\limits_{n=0}^\infty x^n\, \frac{1}{2\pi\mathrm{i}} \frac{1}{\beta} \int\limits_{\gamma(\epsilon_\beta;\theta_\beta)}
\frac{\mathrm{e}^{\zeta^{1/\beta}} \zeta^{\frac{1 - \alpha n - \mu}{\beta}}} {\zeta-y}\, \mathrm{d} \zeta\nonumber\\
&= \frac{1}{2\pi\mathrm{i}} \frac{1}{\beta} \int\limits_{\gamma(\epsilon_\beta;\theta_\beta)} %
\frac{\mathrm{e}^{\zeta^{1/\beta}} \zeta^{\frac{1-\mu}{\beta}}} {\zeta-y}\, \left(\sum\limits_{n=0}^\infty %
\left(x\zeta^{\alpha/\beta}\right)^{n}\right)\, \mathrm{d} \zeta \nonumber\\
&= \frac{1}{2\pi\mathrm{i}} \frac{1}{\beta} \int\limits_{\gamma(\epsilon_\beta;\theta_\beta)} %
\frac{\mathrm{e}^{\zeta^{1/\beta}} \zeta^{\frac{1 + \alpha - \mu}{\beta}}} %
{(\zeta - y)(\zeta^{\alpha/\beta} - x)}\, \mathrm{d} \zeta.
\end{flalign}
Now, rewriting the above integral representation~\eqref{intrep1} along the suitable integral contour
$\gamma(\epsilon;\theta)$, we get Eq.~\eqref{mlrep1},
\begin{flalign*}
E_{\alpha,\beta}(x,y;\mu) &= \frac{1}{2\pi\mathrm{i}} \frac{1}{\beta} \int\limits_{\gamma(\epsilon;\theta)} %
\frac{ \mathrm{e}^{\left(\xi^{1/\alpha}\right)^{1/\beta}} \left(\xi^{1/\alpha}\right)^{\frac{1 + \alpha - \mu}{\beta} } } %
{(\xi^{1/\alpha} - y)(\xi^{1/\beta} - x)}\, \frac{1}{\alpha}\, %
\xi^{\frac{1 - \alpha}{\alpha}}\, \mathrm{d} \xi\nonumber\\
&= \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha\beta} \int\limits_{\gamma(\epsilon;\theta)} %
\frac{\mathrm{e}^{\xi^{1/(\alpha \beta)}} \xi^{\frac{\alpha + \beta - \mu}{\alpha \beta} - 1}} %
{(\xi^{1/\alpha} - y)(\xi^{1/\beta} - x)}\, \mathrm{d} \xi.
\end{flalign*}
The above resulting integral is absolutely convergent and it is an analytic function of $x$ and $y$ for
$x\in \Omega^{(-)}(\epsilon_\alpha;\theta_\alpha)$, $y\in \Omega^{(-)}(\epsilon_\beta;\theta_\beta)$.

The open disk $D = \{|x| < \epsilon_\alpha\}$ is contained into the complex region $\Omega^{(-)}(\epsilon_\alpha;\theta_\alpha)$ for all values of $\theta_\alpha$ in the open interval $\bigl]\pi\alpha/2, \min(\pi,\pi \alpha)\bigr[$. Therefore, from the principle of analytic continuation Eq.~\eqref{mlrep1} is valid everywhere within the complex region $\Omega^{(-)}(\epsilon_\alpha;\theta_\alpha)$ and the lemma follows.
\end{proof}

\begin{lem} \label{lem2}
Let $0 < \alpha, \beta < 2$, $\alpha\beta < 2$ Let $\mu$ be any complex number and let $\theta$ verify inequalities~\eqref{cond1}: $\pi \alpha\beta/2 < \theta\le \min\bigl(\pi, \pi \alpha\beta\bigr)$.

If $x\in \Omega^{(-)}(\epsilon_\alpha;\theta_\alpha)$\ and $y\in \Omega^{(+)}(\epsilon_\beta;\theta_\beta)$, where $\epsilon_\alpha := \epsilon^{1/\beta}$, $\epsilon_\beta := \epsilon^{1/\alpha}$, $\theta_\alpha := \theta/\beta$\ and $\theta_\beta := \theta/\alpha$, then the integral representation holds
\begin{equation} \label{mlrep2}
E_{\alpha,\beta}(x,y;\mu) = \frac{1}{\beta}\, \frac{ \mathrm{e}^{y^{1/\beta}} %
y^{\frac{1 + \alpha - \mu}{\beta}} } {y^{\alpha/\beta} - x} + \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha\beta} %
\int\limits_{\gamma(\epsilon;\theta)} \frac{ \mathrm{e}^{\zeta^{1/(\alpha \beta)} } \zeta^{\frac{\alpha + \beta - \mu} %
{\alpha \beta} - 1} } {(\zeta^{1/\alpha} - y)(\zeta^{1/\beta} - x)}\, \mathrm{d} \zeta.
\end{equation}
\end{lem}
\begin{proof}
By assumption, the point $y$ is located to the right of the Hankel contour $\gamma(\epsilon;\theta)$, that is $y\in \Omega^{(+)}(\epsilon_\beta;\theta_\beta)$. Then, for any $\epsilon_{\beta_1} > y$, $y\in \Omega^{(-)}(\epsilon_{\beta_1};\theta_\beta)$\ and $x\in \Omega^{(-)}(\epsilon_{\alpha_1};\theta_\alpha)$. Thus, by~\eqref{intrep1} we get the integral representation
\begin{equation} \label{intrep2}
E_{\alpha,\beta}(x,y;\mu) = \frac{1}{2\pi\mathrm{i}} \frac{1}{\beta} \int\limits_{\gamma(\epsilon_{\beta_1} ; %
\theta_\beta)} \frac{ \mathrm{e}^{\zeta^{1/\beta} } \zeta^{\frac{\alpha + \beta - \mu}{\beta}} } %
{(\zeta - y)(\zeta^{\alpha/\beta} - x)}\, \mathrm{d} \zeta.
\end{equation}
On the other hand, if $\epsilon_\beta < y < \epsilon_{\beta_1}$, $|\arg y| < \theta_\beta$ and then, by Cauchy theorem,
\begin{equation} \label{intrep3}
E_{\alpha,\beta}(x,y;\mu) = \frac{1}{2\pi\mathrm{i}} \frac{1}{\beta} \int\limits_{\gamma(\epsilon_{\beta_1} ; %
\theta_\beta) - \gamma(\epsilon_\beta;\theta_\beta)} \frac{ \mathrm{e}^{\zeta^{1/\beta}} %
\zeta^{\frac{1 + \alpha - \mu}{\beta}} } {(\zeta^{1/\alpha} - y)(\zeta^{1/\beta} - x)}\, \mathrm{d} \zeta %
= \frac{1}{\beta}\, \frac{ \mathrm{e}^{y^{1/\beta}} y^{\frac{1 + \alpha - \mu}{\beta}} }{y^{\alpha/\beta} - x}.
\end{equation}
From Eqs.~\eqref{intrep2} and~\eqref{intrep3} we obtain the representation~\eqref{mlrep2}, and Lemma~\ref{lem2} follows.
\end{proof}

\begin{rem} \label{rem1}
For $x\in \Omega^{(+)}(\epsilon_\alpha;\theta_\alpha)$ and $y\in \Omega^{(-)}(\epsilon_\beta;\theta_\beta)$\ $E_{\alpha,\beta}(x,y;\mu)$, the integral representation is shown in a similar manner to be
\begin{equation} \label{mlrep3}
E_{\alpha,\beta}(x,y;\mu) = \frac{1}{\alpha}\, \frac{ \mathrm{e}^{x^{1/\alpha}} %
x^{\frac{1 + \beta - \mu}{\alpha}} } {x^{\beta/\alpha} - y} + \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha\beta} %
\int\limits_{\gamma(\epsilon;\theta)} \frac{ \mathrm{e}^{\zeta^{1/(\alpha \beta)} } \zeta^{\frac{\alpha + \beta - \mu} %
{\alpha \beta} - 1} } {(\zeta^{1/\alpha} - y)(\zeta^{1/\beta} - x)}\, \mathrm{d} \zeta.
\end{equation}
\end{rem}

\begin{lem} \label{lem3}
Let $0 < \alpha, \beta < 2$, $\alpha\beta < 2$. Let $\mu$ be any complex number and let $\theta$ verify inequalities~\eqref{cond1}.
If $x\in \Omega^{(+)}(\epsilon_\alpha;\theta_\alpha)$\ and $y\in \Omega^{(+)}(\epsilon_\beta;\theta_\beta)$, where $\epsilon_\alpha := \epsilon^{1/\beta}$, $\epsilon_\beta := \epsilon^{1/\alpha}$, $\theta_\alpha := \theta/\beta$\ and $\theta_\beta := \theta/\alpha$, then the integral representation holds
\begin{flalign} \label{mlrep4}
E_{\alpha,\beta}(x,y;\mu) = \frac{1}{\alpha}\, \frac{ \mathrm{e}^{x^{1/\alpha}} %
x^{\frac{1 + \beta - \mu}{\alpha}} }{x^{\beta/\alpha} - y} &+ \frac{1}{\beta}\, \frac{\mathrm{e}^{y^{1/\beta}} %
y^{\frac{1 + \alpha - \mu}{\beta}} } {y^{\alpha/\beta} - x}\nonumber\\
& + \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha\beta} \int\limits_{\gamma(\epsilon;\theta)} %
\frac{ \mathrm{e}^{\zeta^{1/(\alpha \beta)} } \zeta^{\frac{\alpha + \beta - \mu}{\alpha \beta} - 1} } %
{(\zeta^{1/\alpha} - y)(\zeta^{1/\beta} - x)}\, \mathrm{d} \zeta.
\end{flalign}
\end{lem}
\begin{proof}
By assumption, each of the points $x$ and $y$ lies on the right-hand side of the Hankel contours $\gamma(\epsilon_\alpha;\theta_\alpha)$ and $\gamma(\epsilon_\beta;\theta_\beta)$, respectively; that is in the two regions of the complex plane defined by $x\in \Omega^{(+)}(\epsilon_\alpha;\theta_\alpha)$ and $y\in \Omega^{(+)}(\epsilon_\beta;\theta_\beta)$ (resp.).
The parameters $\epsilon_\alpha$ and $\epsilon_\beta$ correspond to $\epsilon$. Now choose $\epsilon_1$ ($\epsilon_1 > \epsilon$) such that one of the coordinates is to the right of the contour and the other coordinate to its left (which is always possible provided that $x^\beta\neq y^\alpha$).

By definition, let $x\in \Omega^{(-)}(\epsilon_{\alpha_1};\theta_\alpha)$\ and $y\in \Omega^{(+)}(\epsilon_{\beta_1};\theta_\beta)$ (i.e., $x > y$). Then, by Eq.~\eqref{mlrep2} in Lemma~\ref{lem2}, we have the integral representation
\begin{equation} \label{intrep4}
E_{\alpha,\beta}(x,y;\mu) = \frac{1}{\beta}\, \frac{\mathrm{e}^{y^{1/\beta}} %
y^{\frac{1 + \alpha - \mu}{\beta}}} {y^{\alpha/\beta} - x} + \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha \beta}
\int\limits_{\gamma(\epsilon_1;\theta_)} \frac{ \mathrm{e}^{\zeta^{1/(\alpha\beta)}} %
\zeta^{\frac{1 + \alpha + \beta - \mu}{\alpha \beta} - 1} }{(\zeta^{1/\alpha} - y)(\zeta^{1/\beta} - x)}\, \mathrm{d} \zeta.
\end{equation}
\end{proof}
The above integral in~\eqref{intrep4} may be rewritten in the form
\[
\frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha} \int\limits_{\gamma(\epsilon_1;\theta)} \frac{ \mathrm{e}^{\zeta^{1/\alpha} } %
\zeta^{\frac{\alpha + \beta - \mu}{\alpha}} } {(\zeta - y)(\zeta^{\beta/\alpha} - y)}\, \mathrm{d} \zeta.\]
Now, when $\epsilon_\alpha < x < \epsilon_{\alpha_1}$, $|\arg x| < \theta_\alpha$ and then, by Cauchy theorem,
\begin{equation} \label{intrep5}
E_{\alpha,\beta}(x,y;\mu) = \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha} \int\limits_{\gamma(\epsilon_{\alpha_1} ; %
\theta_\alpha) - \gamma(\epsilon_\alpha;\theta_\alpha)} \frac{ \mathrm{e}^{\zeta^{1/\alpha}} %
\zeta^{\frac{1 + \beta - \mu}{\alpha}} } {(\zeta^{\beta/\alpha} - y)(\zeta - x)}\, \mathrm{d} \zeta = \frac{1}{\alpha}\, %
\frac{ \mathrm{e}^{x^{1/\alpha}} x^{\frac{1 + \beta - \mu}{\alpha}} } {x^{\beta/\alpha} - y}.
\end{equation}
Finally, from Eqs.~\eqref{intrep4} and~\eqref{intrep5} the representation~\eqref{mlrep4} holds true, and the lemma follows.

\begin{lem} \label{lem4}
If $\Re(\mu) > 0$, then the integral representations~\eqref{mlrep1}, \eqref{mlrep2}, \eqref{mlrep3} and \eqref{mlrep4} remain valid for $\alpha = 2$\ or $\beta = 2$.
\end{lem}
\begin{proof}
Passing  to the limit in the integral representations~\eqref{mlrep1}, \eqref{mlrep2}, \eqref{mlrep3} and \eqref{mlrep4} with respect to the corresponding parameters yields the lemma.
\end{proof}

\section{Asymptotic behaviours} \label{as}
The asymptotic properties of the function $E_{\alpha,\beta}(x,y;\mu)$ for large values of $|x|$ and $|y|$ are of particular interest.

\begin{thm} \label{asthm}
Let $0 < \alpha, \beta < 2$, $\alpha\beta < 2$. Let $\mu$ be any complex number and let $\tau_1$ be any real number satisfying inequalities~\eqref{cond1}
\[
\pi \alpha\beta/2 < \tau_1\le \min\bigl(\pi, \pi \alpha\beta\bigr).\]
Then, for all integer $p\ge 1$, whenever $|x|\to \infty$ and $|y|\to \infty$, the following asymptotic formulas for the function $E_{\alpha,\beta}(x,y;\mu)$ hold from its respective integral representations.
\begin{itemize}
\item[{\rm 1)}]\ If $|\arg x|\le \tau_1/\beta$\ and $|\arg y|\le \tau_1/\beta$, then
\begin{flalign} \label{as1}
E_{\alpha,\beta}(x,y;\mu) = \frac{1}{\alpha} &\, \frac{ \mathrm{e}^{x^{1/\alpha}} %
x^{\frac{1 + \beta - \mu}{\alpha}} }{x^{\beta/\alpha} - y} + \frac{1}{\beta}\, \frac{\mathrm{e}^{y^{1/\beta}} %
y^{\frac{1 + \alpha - \mu}{\beta}} } {y^{\alpha/\beta} - x}\nonumber\\
&+ \sum\limits_{n=1}^{p_\beta} \sum\limits_{m=1}^{p_\alpha} \frac{x^{-n} y^{-m}}{\Gamma(\mu - n\alpha - \medskip\beta)} %
+ o\left(|xy|^{-1} |x|^{-p_\beta}\right) + o\left(|xy|^{-1} |y|^{-p_\alpha}\right);
\end{flalign}

\item[{\rm 2)}]\ If $|\arg x|\le \tau_1/\beta$\ and $\tau_1/\alpha < |\arg y|\le \pi$, then
\begin{flalign} \label{as2}
E_{\alpha,\beta}(x,y;\mu) &= \frac{1}{\alpha}\, \frac{ \mathrm{e}^{x^{1/\alpha}} %
x^{\frac{1 + \beta - \mu}{\alpha}} }{x^{\beta/\alpha} - y}\nonumber\\
+& \sum\limits_{n=1}^{p_\beta} \sum\limits_{m=1}^{p_\alpha} \frac{x^{-n} y^{-m}}{\Gamma(\mu - n\alpha - \medskip\beta)} %
+ o\left(|xy|^{-1} |x|^{-p_\beta}\right) + o\left(|xy|^{-1} |y|^{-p_\alpha}\right);
\end{flalign}

\item[{\rm 3)}]\ If $\tau_1/\beta < |\arg x|\le \pi$\ and $|\arg y|\le \tau_1/\alpha$, then
\begin{flalign} \label{as3}
E_{\alpha,\beta}(x,y;\mu) &= \frac{1}{\beta}\, \frac{ \mathrm{e}^{y^{1/\beta}} %
y^{\frac{1 + \alpha - \mu}{\beta}} }{y^{\alpha/\beta} - x}\nonumber\\
+& \sum\limits_{n=1}^{p_\beta} \sum\limits_{m=1}^{p_\alpha} \frac{x^{-n} y^{-m}}{\Gamma(\mu - n\alpha - \medskip\beta)} %
+ o\left(|xy|^{-1} |x|^{-p_\beta}\right) + o\left(|xy|^{-1} |y|^{-p_\alpha}\right);
\end{flalign}

\item[{\rm 4)}]\ If $\tau_1/\beta < |\arg x|\le \pi$\ and $\tau_1/\alpha <|\arg y|\le \pi$, then
\begin{flalign} \label{as4}
E_{\alpha,\beta}(x,y;\mu) =& \sum\limits_{n=1}^{p_\beta} \sum\limits_{m=1}^{p_\alpha} \frac{x^{-n} y^{-m}} %
{\Gamma(\mu - n\alpha - \medskip\beta)}\nonumber\\
&+ o\left(|xy|^{-1} |x|^{-p_\beta}\right) + o\left(|xy|^{-1} |y|^{-p_\alpha}\right).
\end{flalign}
\end{itemize}
\end{thm}
\begin{proof}
The proof below focuses on the first case since, in the three other cases, the proofs are easily completed along the same lines as the one in case 1), that is the proof of asymptotic formula~\eqref{as1}.

So, under the constraints in case 1) (i.e., $|\arg x|\le \tau_1/\beta$\ and $|\arg y|\le \tau_1/\alpha$), pick a real number $\tau_2$ satisfying the inequalities~\eqref{cond2}
\begin{equation} \label{cond2}
\pi \alpha\beta/2 < \tau_1 < \tau_2\le \min\bigl(\pi, \pi \alpha\beta\bigr).
\end{equation}
It is easy to show the expansion
\begin{equation} \label{exp}
\frac{1}{(\zeta^{1/\beta} - x)(\zeta^{1/\alpha} - y)} = \sum\limits_{n=1}^{p_\beta} \sum\limits_{m=1}^{p_\alpha} %
\frac{ \zeta^{\frac{n - 1}{\alpha} + \frac{m - 1}{\beta}} }{x^n y^m} + %
\frac{ x^{p_\beta} \zeta^{ \frac{p_\alpha}{\alpha} } + y^{p_\alpha} \zeta^{ \frac{p_\beta}{\beta} } %
- \zeta^{ \frac{p_\alpha}{\alpha} + \frac{p_\beta}{\beta}} }{x^{p_\beta} y^{p_\alpha} %
(\zeta^{1/\beta} - x)(\zeta^{1/\alpha} - y) }\,.
\end{equation}
Here we use the formula~\eqref{mlrep4} from Lemma~\ref{lem3}. Set $\epsilon = 1$ in~\eqref{exp}, then to the right of the contour $\gamma(1;\tau_2)$ (that is, within the complex region $\Omega^{(+)}(1;\tau_2)$), in view of expansion~\eqref{exp} and by Eq.~\eqref{mlrep4} the integral representation of $E_{\alpha,\beta}(x,y ;\mu)$ can be expressed in the form

\begin{flalign} \label{mlrep5}
E_{\alpha,\beta}(x,y;\mu) &= \frac{1}{\alpha}\, \frac{ \mathrm{e}^{x^{1/\alpha}} %
x^{\frac{1 + \beta - \mu}{\alpha}} }{x^{\beta/\alpha} - y} + \frac{1}{\beta}\, \frac{\mathrm{e}^{y^{1/\beta}} %
y^{\frac{1 + \alpha - \mu}{\beta}} } {y^{\alpha/\beta} - x}\nonumber\\
&+ \sum\limits_{n=1}^{p_\beta} \sum\limits_{m=1}^{p_\alpha} \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha\beta}\, %
\left(\int\limits_{\gamma(1;\tau_2)} \mathrm{e}^{\zeta^{1/(\alpha \beta)}} \zeta^{ \frac{\alpha + \beta - \mu}{\alpha \beta} %
- 1 + \frac{n - 1}{\beta} + \frac{m - 1}{\alpha} }\, \mathrm{d} \zeta)\right)\, x^{-n} y^{-m}\nonumber\\
&+ \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha \beta} \int\limits_{\gamma(1;\tau_2)} \mathrm{e}^{ \zeta^{1/(\alpha \beta)} } %
\zeta^{ \frac{\alpha + \beta - \mu}{\alpha \beta} - 1 }\; \frac{ x^{p_\beta} \zeta^{\frac{p_\alpha}{\alpha}} %
+ y^{p_\alpha} \zeta^{\frac{p_\beta}{\beta}} - \zeta^{\frac{p_\alpha}{\alpha} + \frac{p_\beta}{\beta}} } %
{x^{p_\beta} y^{p_\alpha} (\zeta^{1/\beta} - x )(\zeta^{1/\alpha} - y) }\, \mathrm{d} \zeta.
\end{flalign}
By Hankel's formula, the integral representation of the reciprocal gamma function~(see e.g. \cite[\color{cyan}Eq.~C3]{Lavault17}, \cite[\color{cyan}Chap.~3, \S3.2.6]{Temme96}, etc.) writes
\begin{flalign*}
& \kern3cm \frac{1}{\Gamma(s)} = \int\limits_{\gamma(\epsilon;\tau)} \mathrm{e}^u u^{-s}\, \mathrm{d} u,\\
\intertext{%
and, as a consequence, the summand of the second term in~\eqref{mlrep5} satisfies the identity
}
\frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha\beta}\, & \int\limits_{\gamma(1;\tau_2)} \mathrm{e}^{\zeta^{1/(\alpha \beta)}} %
\zeta^{ \frac{\alpha + \beta - \mu}{\alpha \beta} - 1 + \frac{n - 1}{\beta} + \frac{m - 1}{\alpha} }\, %
\mathrm{d} \zeta = \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha\beta}\, \int\limits_{\gamma(1;\tau_2)} \mathrm{e}^{\zeta^{1/(\alpha \beta)}} %
\zeta^{ \frac{1- \mu}{\alpha \beta} - 1 + \frac{n}{\beta} + \frac{m}{\alpha} }\, \mathrm{d} \zeta\nonumber\\
&= \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha\beta}\, \int\limits_{\gamma(1;\tau_2)} \mathrm{e}^{\zeta^{1/(\alpha \beta)}} %
\zeta^{ -\frac{1}{\alpha \beta}\bigl(\mu - \alpha n - \beta m\bigr) + \frac{1}{\alpha \beta} - 1 }\, \mathrm{d} \zeta %
= \frac{1}{\Gamma(\mu - \alpha n - \beta m)}\,.
\end{flalign*}
Therefore, under the constraints resulting from inequalities~\eqref{cond2}, Eq.~\eqref{mlrep5} can be transformed into
\begin{flalign} \label{mlrep6}
E_{\alpha,\beta}(x,y;\mu) &= \frac{1}{\alpha}\, \frac{ \mathrm{e}^{x^{1/\alpha}} %
x^{\frac{1 + \beta - \mu}{\alpha}} }{x^{\beta/\alpha} - y} + \frac{1}{\beta}\, \frac{\mathrm{e}^{y^{1/\beta}} %
y^{\frac{1 + \alpha - \mu}{\beta}} } {y^{\alpha/\beta} - x} + \sum\limits_{n=1}^{p_\beta} %
\sum\limits_{m=1}^{p_\alpha} \frac{x^{-n} y^{-m}}{\Gamma(\mu - \alpha n - \beta m)}\nonumber\\
&+ \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha \beta} \int\limits_{\gamma(1;\tau_2)} \mathrm{e}^{ \zeta^{1/(\alpha \beta)} } %
\zeta^{ \frac{1 + \alpha + \beta - \mu}{\alpha \beta} - 1 }\; \frac{ x^{p_\beta} \zeta^{p_\alpha/\alpha} %
+ y^{p_\alpha} \zeta^{p_\beta/\beta} - \zeta^{ p_\alpha/\alpha + p_\beta/\beta } } %
{x^{p_\beta} y^{p_\alpha} (\zeta^{1/\beta} - x)(\zeta^{1/\alpha} - y) }\, \mathrm{d} \zeta.
\end{flalign}
Next, simplifying the last term in Eq.~\eqref{mlrep6} yields
\begin{flalign} \label{simpmlrep6}
\frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha \beta}\, \int\limits_{\gamma(1;\tau_2)} \mathrm{e}^{ \zeta^{1/(\alpha \beta)} } %
& \zeta^{ \frac{1 + \alpha + \beta - \mu}{\alpha \beta} - 1 }\; \frac{ x^{p_\beta} \zeta^{p_\alpha/\alpha} %
+ y^{p_\alpha} \zeta^{p_\beta/\beta} - \zeta^{p_\alpha/\alpha + p_\beta/\beta} } %
{x^{p_\beta} y^{p_\alpha} (\zeta^{1/\beta} - x)(\zeta^{1/\alpha} - y) }\, \mathrm{d} \zeta\nonumber\\
=& \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha \beta}\, \int\limits_{\gamma(1;\tau_2)}\, %
\frac{ \mathrm{e}^{ \zeta^{1/(\alpha \beta)} } \zeta^{ \frac{ 1 + \alpha + \beta - \mu}{\alpha \beta} - 1 %
+ p_\alpha/\alpha } } {y^{p_\alpha} (\zeta^{1/\beta} - x)(\zeta^{1/\alpha} - y)}\, \mathrm{d} \zeta\nonumber\\
+& \frac{1}{2\pi\mathrm{i}}  \frac{1}{\alpha \beta} \int\limits_{\gamma(1;\tau_2)} %
\frac{ \mathrm{e}^{ \zeta^{1/(\alpha \beta)} } \zeta^{ \frac{ 1 + \alpha + \beta - \mu}{\alpha \beta} - 1 %
+ p_\beta/\beta } } {x^{p_beta} (\zeta^{1/\beta} - x)(\zeta^{1/\alpha} - y)}\, \mathrm{d} \zeta\nonumber\\
-& \frac{1}{2\pi\mathrm{i}} \frac{1}{\alpha \beta}\, \int\limits_{\gamma(1;\tau_2)}\, %
\frac{ \mathrm{e}^{ \zeta^{1/(\alpha \beta)} } \zeta^{ \frac{ 1 + \alpha + \beta - \mu}{\alpha \beta} - 1 + %
p_\alpha/\alpha + p_\beta/\beta } } {x^{p_\beta} y^{p_\alpha}(\zeta^{1/\beta} - x)(\zeta^{1/\alpha} - y)}\, %
\mathrm{d} \zeta = I_1 + I_2 + I_3.
\end{flalign}
Assuming $|\arg x|\le \tau_1/\beta$\ and $|\arg y|\le \tau_1/\alpha$, each integral $I_1$, $I_2$ and $I_3$ in~\eqref{simpmlrep6} can be evaluated for large values of $|x|$\ and $|y|$, and provided that
$|\arg x|\le \tau_1/\beta$ and $|x|$ is large enough, it can be checked that
\[
\min_{\zeta\in \gamma(1;\tau_2)} \left|\zeta^{1/\beta} - x\right| = |x| \sin(\tau_2/\beta - \tau_1/\beta) %
= |x| \sin\left(\tfrac{\tau_2 - \tau_1}{\beta}\right).\]
Similarly, when $|\arg y|\le \tau_1/\beta$ and $|y|$ is large enough,
\[
\min_{\zeta\in \gamma(1;\tau_2)} \left|\zeta^{1/\beta} - y\right| = |y| \sin(\tau_2/\alpha - \tau_1/\alpha) %
= |y| \sin\left(\tfrac{\tau_2 - \tau_1}{\alpha}\right).\]

Hence, for large $|x|$\ and $|y|$ with $|\arg x|\le \tau_1/\beta$\ and $|\arg y|\le \tau_1/\alpha$, we obtain an estimate of the integral $I_1$
\begin{equation} \label{estimateI1}
|I_1|\le \frac{ |x|^{-1} |y|^{-p_\alpha -1} }{ 2\pi \alpha \beta %
\sin\left(\frac{\tau_2 - \tau_1}{\alpha}\right) \sin\left(\frac{\tau_2 - \tau_1}{\beta}\right) }\, %
\int\limits_{\gamma(1;\tau_2)} \left|\mathrm{e}^{ \zeta^{\frac{1}{\alpha \beta}} }\right| %
\left|\zeta^{ \frac{ 1 + \alpha + \beta - \mu}{\alpha \beta} - 1 + \frac{p_\alpha}{\alpha} }\right|\, |\mathrm{d} \zeta|.
\end{equation}
Besides, since the rays defined by $S_{\tau_2} = \bigl\{\arg \zeta = \pm \tau_2,\ |\zeta|\le 1\bigr\}$ belong to the contour $\gamma(1;\tau_2)$, the integral in inequality~\eqref{estimateI1} is convergent. Wherefrom we get the equality
\[
\left|\mathrm{e}^{ \zeta^{1/(\alpha \beta)} }\right| = \exp\left(|\zeta|^{\frac{1}{\alpha \beta}} %
\cos \tfrac{\tau_2}{\alpha \beta} \right).\]
Now, according to inequalities~\eqref{cond2}, we have $\cos \frac{\tau_2}{\alpha \beta} < 0$. Thus,
\[
I_1 = o\left(|xy|^{-1} |y|^{-p_\alpha}\right)\ \qquad \text{and} \qquad I_2 = o\left(|xy|^{-1} |x|^{-p_\beta}\right).\]

Furthermore, referring to the last term in Eq.~\eqref{simpmlrep6} yields the following estimate of $I_3$,
\begin{equation} \label{estimateI3}
|I_3|\le \frac{ |x|^{-p_\beta - 1} |y|^{-p_\alpha -1} }{ 2\pi \alpha\beta %
\sin\left(\frac{\tau_2 - \tau_1}{\alpha}\right) \sin\left(\tfrac{\tau_2 - \tau_1}{\beta}\right) }\, %
\int\limits_{\gamma(1;\tau_2)} \left|\mathrm{e}^{ \zeta^{1/(\alpha \beta)} }\right| \left|\zeta^{ \frac{1 + \alpha + \beta - \mu} %
{\alpha \beta} - 1 + p_\alpha/\alpha + p_\beta/\beta }\right|\, |\mathrm{d} \zeta|,
\end{equation}
which gives $I_3 = o\left(|xy|^{-1} |x|^{-p_\beta} |y|^{-p_\alpha}\right)$.

Hence, this leads finally to the overall asymptotic formula
\[
I_1 + I_2 + I_3 = o\left(|xy|^{-1} |x|^{-p_\beta}\right) + o\left(|xy|^{-1} |y|^{-p_\alpha}\right)\]
and the proof of Eq.~\eqref{as1} (in case 1 of Theorem~\ref{as}) follows.

Similarly, the proofs of Eqs.~\eqref{as2} (case 2), Eqs.~\eqref{as3} (case 3) and Eqs.~\eqref{as4} (case 4) run along the same lines as the above proof of Eq.~\eqref{as1} (case 1), and the proof of Theorem~\ref{as} is completed.
\end{proof}

\newpage
\addcontentsline{toc}{section}{References}
\section*{References}

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redpajama_set_name: RedPajamaArXiv


text:
Q: What are the implications of having a model belong to both a child and its parent in Rails 4? I have the following relational setup in a Rails 4.2 application.  If I wanted Tail to belong_to Kite so I could reference a relationship between the general Kite class and its associated tails - is this a Rails anti-pattern?  At this point in the code I would need to add a kite_id to tail.  (It currently has both a beach_kite_id and a snow_kite_id).  Is there any way to make use of the aforementioned *_kite_id's without having to add a kite_id to tail?
class Kite

end

class BeachKite < Kite
  has_many :tails
end

class SnowKite < Kite
  has_many :tails
end

class Tail
  belongs_to :snow_kite
  belongs_to :beach_kite
end

A: STI (Single Table Inheritance) and polymorphic associations allow you to simplify the associations like so:
class Kite < ActiveRecord::Base
  has_many :tails, as: :kite
end

class BeachKite < Kite
end

class SnowKite < Kite
end

class Tail < ActiveRecord::Base
  belongs_to :kite, polymorphic: true
end

The tails table stores both kite_id and kite_type as it is polymorphic.
Try it:
snow_kite = SnowKite.create(tails: [Tail.create])
Tail.last.kite => snow_kite

beach_kite = BeachKite.create(tails: [Tail.create])
Tail.last.kite => beach_kite


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text:
January, 20, 2020, 8:55:22
Album/EP Reviews
HomeThe Wonder Years
NEWS: The Wonder Years detail acoustic EP, 'Burst & Decay (Volume II)'!
December 15, 2019 Zach Redrup 0
In 2017, The Wonder Years released their first acoustic EP, 'Burst & Decay', and following its success they're now getting ready to share its follow-up. Read More
NEWS: Don Broco to headline Slam Dunk Festival 2020!
September 25, 2019 Zach Redrup 0
Giving us something to look forward to for next year now that summer has been and gone for 2019, Slam Dunk Festival have just made their first line-up announcement for 2020. Read More
PHOTOS: Download Festival 2019
June 25, 2019 Zach Redrup 0
Check out our full gallery of Download Festival at Donington Park in Donington on June 14th-16th 2019. Read More
NEWS: Simple Creatures, The Wonder Years, and more join Download Festival 2019!
February 25, 2019 Zach Redrup 0
A further batch of bands have just been confirmed to join this year's Download Festival line-up, including the first UK performance from newly formed pop-rock supergroup, Simple Creatures. Read More
LIVE REVIEW: Mayday Parade @ Troxy, London (23/02/2019)
February 25, 2019 Lottie Cook 0
Two of pop-punk's finest, The Wonder Years and Mayday Parade, have teamed up for a co-headline tour, and if that doesn't promise an emotional time then what does? Oddly enough, it doesn't seem to have attracted a particularly large audience, and the crowd in the Troxy is noticeably sparse. However, what they lack in numbers, they seem eager to make up for in enthusiasm. Read More
TOP 10 ALBUMS OF 2018!
We here at DEAD PRESS! have pulled our minds and opinions together to carry out the excruciatingly difficult yet always enjoyable debate on what is the year's cream of the crop, and the ten records below are what we truly believe are the top ten albums of 2018. Read More
NEWS: Mayday Parade & The Wonder Years confirm co-headline UK tour for February 2019!
September 12, 2018 Matt Watts 0
Pop-punk fans rejoice! Both Mayday Parade and The Wonder Years have announced that they will be embarking on a co-headline tour of the UK together in February. Read More
NEWS: The Wonder Years share video for 'Raining In Kyoto'!
June 3, 2018 Dylan Tuck 0
Lansdale, Pennsylvania based rockers The Wonder Years are currently on the road supporting their recently released sixth album, 'Sister Cities', and now they've debuted a video for a new single from the record. Read More
LIVE REVIEW: The Wonder Years @ SWX, Bristol (17/04/2018)
April 25, 2018 Zach Redrup 0
The Wonder Years are a band that have been through a steady progression over their whole career. Earlier this month, they released their most astounding and accomplished body of work to date in 'Sister Cities', and are reaping the rewards for it. It's a far cry for the band that had a beginning playing sweaty club shows and belting out pop-punk anthems, though some fans long for those years back. Read More
NEWS: The Wonder Years stream new album 'Sister Cities' in full via The Independent!
April 5, 2018 Lottie Cook 0
If you can't wait to get your hands on 'Sister Cities', the forthcoming sixth studio album from Pennsylvania based sextet The Wonder Years, then fear not – you're in luck. Dan "Soupy" Campbell and co. have surprised their fans by streaming the entire record online ahead of its official release date. Read More
EP REVIEW: Veridian – NoVella
NEWS: Sullii debuts new single, 'Moonlight'!
NEWS: We Came As Romans release video for 'From The First Note'!
NEWS: Avenged Sevenfold share unreleased track, 'Set Me Free'!
NEWS: Green Day unveil video for new song, 'Oh Yeah!'!
NEWS: My Chemical Romance confirm return UK show in June 2020!
January 20, 2020 Tess Hofer 0
NEWS: Suicide Silence deliver video for new song, 'Two Steps'!
January 19, 2020 Zach Redrup 0
NEWS: Giver release new song, 'Every Age Has Its Dragons (Like An Empire)'!
NEWS: The 1975 release new single, 'Me & You Together Song'!
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The natural terrain lent itself to the development of two very distinct nine holes. Each of the 18 holes of championship golf is an absolute treat to play. The breathtaking vistas and pristine natural beauty of our golf course will leave you with memories for a lifetime.
Give yourself the edge you want every time you play at Rifle Creek with a bucket of range balls and a quick warm-up on our practice facilities. Driving range, practice green, and the short-game area are available to all our guests. Make your next round the best it can be with some well-spent time on the practice range. We'll see you on the course!
The spacious clubhouse at Rifle Creek Golf Course offers all the essentials as well as great golf gifts for any occasion. The friendly staff will be happy to assist you with all your questions about club selection and course conditions. Swing by before or after your round.
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Elevation: 5348 feet above sea level.


Filmmaker Darren Aronofsky, whose credits include The Wrestler and Requiem for a Dream, has teamed up with Generation Z activists from all over the country in an effort to get young people to the polls on November 6.
The activists who participated include Brinkley Smithers, Chelsea Turner, Delaney Reynolds, Jackson Hinkle, David Hogg, Delaney Tarr, Edna Chavez, Gavin Grimm, Justice Jamal Jones, Chella Man, Lisbeth Chavarria, Sandra Cornejo, Lulu Cerone, Ohitika Lewis, and Xiuhtezcatl Martinez and are involved in movements for indigenous rights, gun control, rights for the disabled, immigrant rights, climate justice and transgender equality, among others.
Watch the PSA above and, wherever you stand, remember to vote!