American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

sr


London, December 30: American researchers claim to have solved a cryptic formula that renowned mathematician Srinivasa Ramanujan believed came to him in dreams while on his deathbed, the Daily Mail reported on Saturday.

The formula was contained in a letter he wrote to his mentor, the English mathematician G.H. Hardy, from his deathbed in 1920 outlining several new mathematical functions that had never been heard of before, together with a theory about how they worked. It had baffled mathematicians for more than 90 years, but new findings — presented at a conference at the University of Florida last month — reportedly show that Ramanujan's “hunch” about his formula was right — that it could explain the behaviour of black holes.

“We've solved the problems from his last mysterious letters,” said the well-known American mathematician Ken Ono of Emory University.

“For people who work in this area of math, the problem has been open for 90 years … Ramanujan's legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died.”

He said the so-called “deathbed puzzle” which, according to Ramanujan, was revealed to him by the goddess Namagiri, may unlock secrets about black holes. “We proved that Ramanujan was right. We found the formula explaining one of the visions that he believed came from his goddess. No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,” said Professor Ono.

The Mail said that Ramanujan's letter described several new functions that behaved differently from known theta functions, or modular forms, and yet closely mimicked them.

“Functions are equations that can be drawn as graphs on an axis, like a sine wave, and produce an output when computed for any chosen input or value. Ramanujan conjectured that his mock modular forms corresponded to the ordinary modular forms earlier identified by Carl Jacobi, and that both would wind up with similar outputs for roots of 1,” it said. Nobody at the time understood what the Indian mathematical genius was talking about.

“It wasn't until 2002, through the work of Sander Zwegers, that we had a description of the functions that Ramanujan was writing about in 1920,” Prof. Ono said.

His team, which used modern mathematical tools to solve the puzzle, was “stunned” to find the function could be used even today.

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News Network
January 28,2020

Jan 28: China said on Tuesday that 106 people had died from a new coronavirus that is spreading across the country, up from the previous toll of 81.

The number of total confirmed cases in China rose to 4,515 as of Jan. 27, the National Health Commission said in a statement, up from 2,835 reported a day earlier.

The United States warned against travel to China on Monday and Canada issued a more narrow travel warning as the death toll from the spreading coronavirus passed 100, with tens of millions stranded during the biggest holiday of the year and global markets rattled.

Global stocks fell, oil prices hit three-month lows, and China's yuan dipped to its weakest level in 2020 as investors fretted about damage to the world's second-biggest economy from travel bans and the Lunar New Year holiday, which China extended in a bid to keep people at home.

The health commission of China's Hubei province said on Tuesday that 100 people had died from the virus as of Jan. 27, according to an online statement, up from the previous toll of 76, with the number of confirmed cases in the province rose to 2,714.

Other fatalities have been reported elsewhere in China, including the first in Beijing, bringing the deal toll to 106 so far, according to the People's Daily. The state newspaper put the total number of confirmed cases in China at 4,193, though some experts suspect a much higher number.

On Monday, US President Donald Trump offered China whatever help it needed, while the State Department said Americans should "reconsider" visiting all of China due to the virus.

Canada, which has two confirmed cases of the virus and is investigating 19 more potential cases, warned its citizens to avoid travel to China's Hubei province, at the heart of the outbreak.

Authorities in Hubei province are taking increasing flak from the public over their initial response to the virus. Chinese Premier Li Keqiang visited the city of Wuhan, epicentre of the outbreak, to encourage medical workers and promise reinforcements.

Visiting Wuhan in blue protective suit and mask, Li praised medics, said 2,500 more workers would join them in the next two days, and visited the site of a new hospital to be built in days.

The most senior leader to visit Wuhan since the outbreak, Li was shown on state TV leading medical workers in chants of "Wuhan jiayou!" - an exhortation to keep their strength up.

China's ambassador to the United Nations, following a meeting with UN Secretary-General António Guterres on Monday, said "the Chinese government attaches paramount importance to prevention and control of the epidemic, and President Xi Jinping has given important instructions. ...

"China has been working with the international community in the spirit of openness, transparency and scientific coordination," he said.

Guterres said in a statement, "The UN appreciates China's effort, has full confidence in China's ability of controlling the outbreak, and stands ready to provide any support and assistance."

MOUNTING ANGER

On China's heavily censored social media, officials have faced mounting anger over the virus, which is thought to have originated from a market where wildlife was sold illegally.

Some criticised the governor of Hubei province, of which Wuhan is the capital, after he corrected himself twice during a news conference over the number of face masks being produced.

"If he can mess up the data multiple times, no wonder the disease has spread so severely," said one user of the Weibo social media platform.

In rare public self-criticism, Wuhan Mayor Zhou Xianwang said the city's management of the crisis was "not good enough" and indicated he was willing to resign.

The central Chinese city of 11 million people is in virtual lockdown and much of Hubei, home to nearly 60 million people, is under travel curbs.

Elsewhere in China, people from the region faced questioning about their movements. "Hubei people are getting discriminated against," a Wuhan resident complained on Weibo.

Cases linked to people who travelled from Wuhan have been confirmed in a dozen countries, from Japan to the United States, where authorities said they had 110 people under investigation in 26 states. Sri Lanka was the latest to confirm a case.

INVESTORS WORRIED

Investors are worried about the impact. The consensus is that in the short term, economic output will be hit as authorities limit travel and extend the week-long New Year holiday — when millions traditionally travel by rail, road and plane - by three days to limit spread of the virus.

Asian and European shares tumbled, with Japan's Nikkei average sliding 2%, its biggest one-day fall in five months. Demand spiked for safe-haven assets such as the Japanese yen and Treasury notes. European stocks fell more than 2%.

The US S&P 500 closed down nearly 1.6%.

"China is the biggest driver of global growth so this couldn't have started in a worse place," said Alec Young, FTSE Russell's managing director of global markets research.

During the 2002-2003 outbreak of Severe Acute Respiratory Syndrome (SARS), which originated in China and killed nearly 800 people globally, air passenger demand in Asia plunged 45%. The travel industry is more reliant on Chinese travellers now.

Chinese-ruled Hong Kong, which has had eight cases, banned entry to people who had visited Hubei recently.

Some European tour operators cancelled trips to China, while governments around the world worked on repatriating nationals.

Officially known as 2019-nCoV, the newly identified coronavirus can cause pneumonia, but it is still too early to know just how dangerous it is and how easily it spreads.

"What we know about this virus it that transmission occurs through human contact but we are speaking of close contact, i.e. less than a meter," said Jerome Salomon, a senior official with France's health ministry.

"Crossing someone (infected) in the street poses no threat," he said. "The risk is low when you spend a little time near that person and becomes higher when you spend a lot of time near that person."

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News Network
May 21,2020

Washington, May 21: US President Donald Trump China is on a "massive disinformation" campaign and is desperately trying to deflect the "pain and carnage" that it spread throughout the world, US President Donald Trump has said, upping the ante on Beijing over its handling of the coronavirus outbreak.

Trump, who has expressed disappointment over China's handling of the COVID-19 pandemic, claimed that it was the "incompetence" of Beijing that led to the mass killing across the globe. 

"China is on a massive disinformation campaign because they are desperate to have Sleepy Joe Biden win the presidential race so they can continue to rip-off the United States, as they have done for decades, until I came along!" Trump said in a tweet on Wednesday.

"Spokesman speaks stupidly on behalf of China, trying desperately to deflect the pain and carnage that their country spread throughout the world. Its disinformation and propaganda attack on the United States and Europe is a disgrace… It all comes from the top. They could have easily stopped the plague, but they didn't," he said in a series of tweets.

Trump blamed China for spreading the coronavirus globally and accused it of being incompetent.
"Some wacko in China just released a statement blaming everybody other than China for the Virus which has now killed hundreds of thousands of people. Please explain to this dope that it was the 'incompetence of China', and nothing else, that did this mass Worldwide killing!" Trump said.

China has denied covering up the extent of its coronavirus outbreak and accused the US of attempting to divert public attention by insinuating that the virus originated from a virology laboratory in Wuhan.

"China was the first country to report the COVID-19 to the World Health Organisation (WHO), (and) that doesn't mean the virus originated from Wuhan... There has never been any concealment, and we'll never allow any concealment," Chinese Foreign Ministry spokesman Zhao Lijian said last month.

"A discerning person will understand at a glance that the purpose is to create confusion, divert public attention, and shirk their responsibility," he said.

The novel coronavirus which first originated in Wuhan in December last year has claimed 328,120 lives and infected nearly 5 million people globally. The Us is the worst affected country with 93,439 deaths and over 1.5 million infections, according to Johns Hopkins University data.

Meanwhile, the US Senate passed a bill boosting oversight of companies based in China and other nations that could lead to their removal from American stock exchanges.

The Holding Foreign Companies Accountable Act, proposes to increase oversight of Chinese and other foreign companies listed on American exchanges and delist and ban over-the-counter trading for firms that are out of compliance with US regulators for a period of three years.

In a related development, a group of top Republican Senators led by Marco Rubio sent a letter to Secretary of the Treasury Steven Mnuchin following disturbing reports that China's state-owned and-directed enterprises were looking to exploit the economic crisis by buying US and foreign companies.

As companies backed by the Chinese Communist Party (CCP) approach banks to identify the purchase of companies in the US and in Europe affected by the pandemic, the senators urged Mnuchin to protect against the China's and the CCP's predatory economic behaviour during the COVID-19 crisis.

"We write to express our concerns related to the People's Republic of China's (PRC) efforts to exploit the economic crisis wrought by the COVID-19 pandemic to gain control of distressed companies or shirking its international responsibilities amidst a worldwide crisis.

"In both Chinese Communist Party (CCP) and PRC policy documents, Beijing has made no secret of its intentions to dominate strategic industrial and emerging technology sectors as well as influence standards at the expense of liberal, rules-based governance," wrote the senators.

As the crisis reverberates across the globe, the PRC's predatory lending practices — including the use of non-disclosure agreements for bilateral loans — not only damage the fiscal situation of recipient countries but also undermine the international community's ability to respond effectively to the crisis, they said.

"Without US and international pressure for accountability and transparency, those countries that are in debt to the PRC will not have the political cover or protection to open their financial books. Such countries will face the risk of default or a currency crisis, leaving the International Monetary Fund (IMF), World Bank, and Western countries to clean up the PRC's mess," the senators said.

During a campaign round table Katrina Pierson, Senior Advisor to the Trump 2020 Campaign, said that only the US President will defeat the coronavirus, hold China accountable for their negligence, and defend the American people from socialism. 

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News Network
May 6,2020

May 6: In a first, a Pakistani Hindu youth has become the first person from the minority community to join the Pakistan Air Force.

Rahul Dev has been recruited as a General Duty Pilot Officer, the Pakistan Air Force (PAF) said in a tweet.

Dev hails from Tharparkar district of Sindh province.

Sharing the picture of the young man, the PAF recently tweeted, "Good news during #COVID19 tense situation. Thar rocked again...Congratulations #RahulDev who hails from very remote village of Tharparkar has been selected as GD Pilot in #PAF."

Though Dev's exact age is not known, those inducted in PAF at his level are often around 20.

The official Radio Pakistan on Wednesday said it is "for the first time in Pakistan's history" that a Hindu youth has been recruited as a general duty pilot officer in PAF.

The Express Tribune in a report published on Wednesday said the induction showed that the PAF was breaking barriers.

Last year, Kainat Junaid became the first woman from Khyber-Pakthunkhwa province to have been selected for fighter pilot training.

Junaid not only secured the top position in PAF's test for General Duty Pilot, but also became Pakistan’s first female fighter pilot to serve the country alongside her father.

Her father Ahmed Junaid is a Squadron Leader in the PAF.

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