American mathematicians solve Ramanujan's “deathbed” puzzle

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

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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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April 9,2020

Washington, Apr 9: At least 11 Indians have died of COVID-19 in the United States with another 16 testing positive for the infection which has claimed more than 14,000 lives and afflicted more than four lakh people in the US.

All Indian citizens who have succumbed to the deadly infection in the US are male, with ten of them from New York and New Jersey area. Four of the victims are said to be taxi drivers in New York City.

New York City has emerged as the US epicentre for COVID-19 spurt, accounting for more than 6,000 deaths and over 1,38,000 cases of infections. New Jersey accounts for 1,500 fatalities and nearly 48,000 infections.

One Indian national reportedly died in Florida because of coronavirus. Authorities are also ascertaining the nationality of some other Indian origin people in the States of California and Texas.

All 16 Indians, including four females, who have tested positive for coronavirus are in self-quarantine. Coming from diverse background, eight of them are from New York, three from New Jersey and rest from other states like Texas and California. They hail from Indian states like Uttarakhand, Maharashtra, Karnataka and Uttar Pradesh.

Indian Embassy and consulates across the United States are working closely with local authorities and Indian-American organizations to provide necessary assistance to Indian nationals and students affected with COVID-19.

Because of the strict travel restrictions and regulations to prevent the spread of the deadly virus, local city officials have been performing the last rites of the deceased and in many cases are not allowing even their immediate family members to attend their cremations, officials said.

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News Network
January 10,2020

Washington, Jan 10: It is “highly likely” that Iran shot down the civilian Ukrainian jetliner that crashed near Tehran late Tuesday, killing all 176 people on board, U.S., Canadian and British officials declared Thursday.

They said the fiery missile strike could well have been a mistake amid rocket launches and high tension throughout the region.

The crash came just a few hours after Iran launched a ballistic attack against Iraqi military bases housing U.S. troops in its violent confrontation with Washington over the U.S. drone strike that killed an Iranian Revolutionary Guard general. The airliner could have been mistaken for a threat, said four U.S. officials, speaking on condition of anonymity to discuss sensitive intelligence.

Canadian prime minister Justin Trudeau, whose country lost at least 63 citizens in the downing, said in Toronto: “We have intelligence from multiple sources including our allies and our own intelligence. The evidence indicates that the plane was shot down by an Iranian surface-to-air missile.”

Likewise, U.K. prime Minister Boris Johnson and Australian prime minister Scott Morrison offered similar statements. Morrison also said it appeared to be a mistake. “All of the intelligence as presented to us today does not suggest an intentional act,” he said.

The assessment that 176 people were killed as collateral damage in the Iranian-U.S. conflict cast a new pall over what had at first appeared to be a relatively calm aftermath following the U.S. military operation that killed Iranian Gen. Qassem Soleimani.

At the White House, U.S. president Donald Trump suggested he believed Iran was responsible for the shootdown and dismissed Iran's initial claim that it was a mechanical issue with the plane.

“Somebody could have made a mistake on the other side.” Trump said, noting the plane was flying in a “pretty rough neighborhood."

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News Network
June 2,2020

Jun 2: A new female billionaire has emerged from one of Asia's most-expensive breakups.

Du Weimin, the chairman of Shenzhen Kangtai Biological Products Co., transferred 161.3 million shares of the vaccine maker to his ex-wife, Yuan Liping, according to a May 29 filing, immediately catapulting her into the ranks of the world's richest.

The stock was worth $3.2 billion as of Monday's close.

Yuan, 49 this year, owns the shares directly, but signed an agreement delegating the voting rights to her ex-husband, the filing shows. The Canadian citizen, who resides in Shenzhen, served as a director of Kangtai between May 2011 and August 2018. She's now the vice general manager of subsidiary Beijing Minhai Biotechnology Co. Yuan holds a bachelor's degree in economics from Beijing's University of International Business and Economics.

Kangtai shares have more than doubled in the past year and have continued their ascent since February, when the company announced a plan to develop a vaccine to fight the coronavirus. They slipped for a second day Tuesday following news of the divorce terms, losing 3.1% as of 9:43 a.m. in Hong Kong and bringing the company's market value to $12.9 billion.

Du's net worth has now dropped to about $3.1 billion from $6.5 billion before the split, excluding his pledged shares.

The 56-year-old was born into a farming family in China's Jiangxi province. After studying chemistry in college, he began working in a clinic in 1987 and became a sales manager for a biotech company in 1995, according to the prospectus of Kangtai's 2017 initial public offering. In 2009, Kangtai acquired Minhai, the company Du founded in 2004, and he became the chairman of the combined entity.

China's rapidly growing economy has been an engine for the country's richest, and Du is not the only tycoon who's had to pay a steep price for a divorce. In 2012, Wu Yajun, at one point the nation's richest woman, transferred a stake worth about $2.3 billion to her ex-husband, Cai Kui, who co-founded developer Longfor Group Holdings Ltd. In 2016, tech billionaire Zhou Yahui gave $1.1 billion of shares in his online gaming company, Beijing Kunlun Tech Co., to ex-wife Li Qiong after a civil court settlement.

Sometimes, a goodbye can be time-consuming too. South Korean tycoon Chey Tae-won's wife filed a lawsuit in December asking for a 42.3% stake in SK Holdings Co. valued at $1.2 billion. That would make her the second-largest shareholder of the company should she win the case, which is still ongoing.

The most expensive divorce in history is that of Jeff and MacKenzie Bezos. The Amazon.com Inc. founder gave 4% of the online retailer to Mackenzie, who now has a $48 billion fortune and is the world's fourth-richest woman.

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