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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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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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 10,2020

Jun 10: Indian-origin California Senator Kamala Harris has joined former vice president and 2020 Democratic presidential nominee Joe Biden to raise USD 3.5 million for the upcoming November elections.

Tuesday's fundraiser is the second-largest single event haul so far for the Biden campaign, which raised USD 4 million at one event earlier this month.

Harris' presence during the virtual mega fund raiser assumes significance as the Democratic Party leaders consider her to be one of the front-runners to be the nominee for vice president. The 55-year-old lawyer-politician was once considered to be a strong opponent of Biden in the 2020 Democratic primaries.

Introducing Harris to the 1,400 supporters present at the event, Biden underlined the history-breaking nature of her past electoral wins.

"For much of her career, she was the only person in the room who looked like she did," he said.

At the start of the campaign last year, Harris was very critical of Biden. She later endorsed him, months after she decided to withdraw herself from the race to the White House.

During the fundraiser, Harris was effusive in her praise for Biden.

Referring to Biden's meeting with George Floyd's family, she said, "He (Biden)is someone who whether one on one or speaking to the nation always has a sense of how people are experiencing this world, and what their needs are...This moment in the history of our country really represents an extraordinary exercise in contrast."

"On the other hand, we have a Donald Trump who had the gall to dispatch the US military to clear the streets so that he could prance down and then, like a prop, hold up the bible for a photo op," Harris said.

The death of African-American Floyd during police confinement in Minneapolis on May 25 has resulted in widespread protests not only in the US but across the world.

"There are so many contrasts between Joe Biden and Donald Trump that really point to the choice that we as Americans have today," Harris said.

California Lt Governor Eleni Kounalakis also joined the fund raiser.

In his remarks, Biden, 77, said the US is reeling in anguish and anger over the brutal killing of Floyd or the systemic racism that still infects every part of the society. "Harris knows better than anybody," he said.

"At the same time, we're facing the worst economic disaster since the Great Depression. American history is not a fairy tale with a guaranteed ending, a happy ending. This is a battle for the soul of the country.

"It's been a constant tug of war between the American ideal that we all are created equal -- and the harsh reality that racism has long torn us apart...I'm going to ask every American to look where we are now and to think, is this who we are? Is this who we want to be?" Biden asked.

Participating in the questions and answers session, Harris said America has still not fully embraced, acknowledged or addressed its history of racism and its current history of racism.

"One can think of this moment as an inflection moment, and it will require bold action and it will require immediate action...This stresses the importance and the immediacy and the urgency of electing Joe Biden," she said.

Replying to a question, Biden said, "Did you see today where the President of the United States while George Floyd was being buried, was condemning the older man who was knocked down with his head bleeding and everyone walking by. Did you see that? I mean, my lord. What have we become if we abide by this? So much we can do and must do."

Harris said the election is going to be rough and tumble.

"There are very powerful forces that thrive off of the hate and division that Donald Trump has been sowing. This is not going to be easy. And we have about just a few months to get this thing done," she said.

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