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
July 1,2020

Tehran, Jul 1 As many as 19 people have been killed in an explosion and fire at a medical facility in Tehran.

A total of 19 people, including 15 men and 4 women, were killed in the explosion, the emergency services confirmed, RT reported citing KhabarOnline website.

According to a regional official, a gas leak caused the incident. Sputnik quoted a deputy head of Tehran police as saying to YJC news outlet that oxygen tanks exploded in the semi-basement of the clinic.

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News Network
May 6,2020

Washington, May 6: At a time when the coronavirus pandemic has squeezed them, multi-national companies in America are laying off workers while paying cash dividends to their shareholders. Thus making the workers bear the brunt of the sacrifices while the shareholders continue to collect.

The Washington Post said in one of its reports that five big American companies have paid a combined USD 700 million to shareholders while cutting jobs, closing plants and leaving thousands of their workers filing for unemployment benefits.

Since the pandemic was declared an emergency, Caterpillar has suspended operations at two plants and a foundry, Levi Strauss has closed stores, and toolmaker Stanley Black & Decker has been planning layoffs and furloughs.

Steelcase, an office furniture manufacturer, and World Wrestling Entertainment have also shed employees.

Executives of those companies told the Post that the layoffs support the long-term health of their companies, and often the executives are giving up a piece of their salaries. Furloughed workers can apply for unemployment benefits.

But distributing millions of dollars to shareholders while leaving many workers without a paycheck is unfair, critics argue, and belies the repeated statements from executives about their concern for employees' welfare during the coronavirus crisis.

Caterpillar, for example, announced a USD 500 million distribution to shareholders April 8, about two weeks after indicating that operations at some plants would stop. The company however declined to divulge how many workers are affected.

"We are taking a variety of actions globally, but we aren't going to discuss the number of impacted people," spokeswoman of the company, Kate Kenny, said in a reply to an email by the Post.

This spate of dividends is also likely to revive long-standing debates about economic rewards.

"There are no hard-and-fast rules about this," said Amy Borrus, deputy director of the Council of Institutional Investors, a group that argues for shareholder rights and represents pension funds and other long-term investors.

Many large US companies choose to issue a regular, quarterly dividend to shareholders, often increasing it, and they boast about these payments because they help keep the share price higher than it might otherwise be. Those companies might be reluctant to announce that they are cutting or suspending their dividend during a crisis, Borrus was further quoted as saying.

But "companies have to be mindful of the optics of paying dividends if they're laying off thousands of workers," she added.

On March 26, Caterpillar had announced that because of the pandemic, it was "temporarily suspending operations at certain facilities." Two plants, in East Peoria, Ill., and Lafayette, Ind., were coming to a halt, as well as a foundry in Mapleton, Ill., according to news reports.

"We are taking a variety of actions at our global facilities to reduce production due to weaker customer demand, potential supply constraints and the spread of the covid-19 pandemic and related government actions," Kenny said via email.

"These actions include temporary facility shutdowns, indefinite or temporary layoffs," she added.

Similarly, Levi Strauss announced April 7 that the company would stop paying store workers, and about 4,000 are now on furlough. On the same day, the company announced that it was returning USD 32 million to shareholders.

"As this human and economic tragedy unfolds globally over the coming months, we are taking swift and decisive action that will ensure we remain a winner in our industry," Chip Bergh, president and chief executive of the company, also told the Post.

Stanley Black & Decker announced on April 2 that it was planning furloughs and layoffs because of the pandemic. Two weeks later, it issued a dividend to shareholders of about USD 106 million.

The notion that a company's primary purpose is to serve shareholders gained prominence in the 1980s but has come under attack in recent years, even from business executives, the newspaper reported.

Corporate decisions to suspend dividends and buybacks are complex, however, and it is difficult to know whether these suspensions of dividend and buyback programs were motivated by a desire to conserve cash in anticipation of bad times, and how much they are prompted by a sense of obligation to employees.

Over recent decades, the mandate to "maximize shareholder value" has become orthodoxy, for many, and it is often unclear what motivates companies to pare dividends or buybacks for shareholders, said William Lazonick, an emeritus economics professor at the University of Massachusetts at Lowell, who has been one of the leading critics of companies that distribute cash to shareholders through stock buybacks and dividends rather than reinvesting the profits into employees, innovation and production.

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News Network
July 11,2020

Geneva, Jul 11: The World Health Organization said Friday that it is still possible to bring coronavirus outbreaks under control, even though case numbers have more than doubled in the past six weeks.

WHO chief Tedros Adhanom Ghebreyesus said the examples of Italy, Spain, South Korea and India's biggest slum showed that however bad a outbreak was, the virus could still be reined in through aggressive action.

"In the last six weeks cases have more than doubled," Tedros told a virtual press conference in Geneva.

However, "there are many examples from around the world that have shown that even if the outbreak is very intense, it can still be brought back under control," said Tedros.

"And some of these examples are Italy, Spain and South Korea, and even in Dharavi -- a densely packed area in the megacity of Mumbai -- a strong focus on community engagement and the basics of testing, tracing, isolating and treating all those that are sick is key to breaking the chains of transmission and suppressing the virus."

The novel coronavirus has killed at least 555,000 people worldwide since the outbreak emerged in China last December, according to a tally from official sources compiled by AFP on Friday.

Nearly 12.3 million cases have been registered in 196 countries and territories.

"Across all walks of life, we are all being tested to the limit," Tedros said, "from countries where there is exponential growth, to places that are loosening restrictions and now starting to see cases rise.

"Only aggressive action combined with national unity and global solidarity can turn this pandemic around."

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