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 13,2020

Jun 13: Requiring the wearing of masks to prevent the spread of the novel coronavirus in areas at the epicenter of the global pandemic may have prevented tens of thousands of infections, a new study suggests.

Mask-wearing is even more important for preventing the virus' spread and the sometimes deadly COVID-19 illness it causes than social distancing and stay-at-home orders, researchers said, in the study published in PNAS: The Proceedings of the National Academy of Sciences of the USA.

Infection trends shifted dramatically when mask-wearing rules were implemented on April 6 in northern Italy and April 17 in New York City - at the time among the hardest hit areas of the world by the health crisis - the study found.

"This protective measure alone significantly reduced the number of infections, that is, by over 78,000 in Italy from April 6 to May 9 and over 66,000 in New York City from April 17 to May 9," researchers calculated.

When mask-wearing went into effect in New York, the daily new infection rate fell by about 3% per day, researchers said. In the rest of the country, daily new infections continued to increase.

Direct contact precautions - social distancing, quarantine and isolation, and hand sanitizing - were all in place before mask-wearing rules went into effect in Italy and New York City. But they only help minimize virus transmission by direct contact, while face covering helps prevent airborne transmission, the researchers say.

"The unique function of face covering to block atomization and inhalation of virus-bearing aerosols accounts for the significantly reduced infections," they said. That would indicate "that airborne transmission of COVID-19 represents the dominant route for infection."

The U.S. Center for Disease Control and Prevention on Friday urged organizers of large gatherings that involve "shouting, chanting or singing to strongly encourage the use of cloth face coverings to lower the risk of spreading the coronavirus."

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News Network
May 20,2020

Washington, May 20: Once dubbed as historic by him, US President Donald Trump on Tuesday said he now feels ‘differently’ about the trade deal he signed with China earlier this year.

He said this while once again venting out his frustration with the Beijing leadership, accusing it of letting coronavirus spread.

Till Tuesday, over 92,000 Americans have died and 1.5 million tested positive for coronavirus that has globally killed around 320,000 people.

The US and China had signed a deal in January to end their 22-month-long trade war during which the two countries slapped tit-for-tat tariff hikes on products worth nearly half a trillion USD.

Under it, Beijing agreed to increase its purchase of US goods by USD 200 billion in 2020-2021.

“I feel differently now about that deal than I did three months ago,” Trump told reporters during a Cabinet meeting at the White House.

“We will see what all happens, but it's been a very disappointing situation. A very disappointing thing happened with China because the plague flowed in and that wasn't supposed to happen and it could have been stopped," he said.

Trump said he was very excited when the trade deal with China was signed.

“But once the virus came in, once the plague, as I called it, came in, I said how did they let that happen? And how come it didn't go into other sections of China? Why did they block it from leaving Wuhan? But they didn't block it from going to the rest of the world, including the United States. Why is that? Beijing doesn't have it. Other places don't have it,” he said.

Trump did not respond to questions on retaliation against China.

Meanwhile, top American senators continued to press the administration that rules of engagement with China needs to change post-coronavirus.

“As we know, they unleashed this virus on America and the world with their classic communist cover-up, deception, continued propaganda campaign, costing now over 90,000 American lives, 35 million Americans losing their jobs so far,” Senator Martha McSally said during a Congressional hearing.

“We don’t know who patient zero is, they destroyed samples, they silenced doctors, they kicked out journalists, they impacted international travel to seed this and their reckless behaviour continues to be the root of all this,” she said.

As a result of coronavirus, the American economy has been thrown into recession; more than 36 million people have lost their job – the worst ever after last century’s great depression.

Many of the US states have now started opening up, after taking necessary precautions.

By conservative estimates, it will take several quarters for the economy to be back on track.

Trump in the last a few weeks has exuded confidence that the economy will be back on track next year.

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News Network
June 25,2020

London, Jun 25: British Prime Minister Boris Johnson has called on India and China to engage in dialogue to sort out their border issues as he described the escalation in eastern Ladakh as "a very serious and worrying situation" which the UK is closely monitoring.

The first official statement of Mr Johnson came during his weekly Prime Minister's Questions (PMQs) in the House of Commons on Wednesday.

Responding to Conservative Party MP Flick Drummond on the implications for British interests of a dispute between a "Commonwealth member and the world's largest democracy on the one side, and a state that challenges our notion of democracy on the other," he described the escalation in eastern Ladakh as "a very serious and worrying situation", which the UK is "monitoring closely".

"Perhaps the best thing I can say... is that we are encouraging both parties to engage in dialogue on the issues on the border and sort it out between them," the Prime Minister said.

In a statement in New Delhi on Wednesday, the Ministry of External Affairs (MEA) said India and China have agreed that expeditious implementation of the previously agreed understanding on disengagement of troops from standoff points in eastern Ladakh would help ensure peace and tranquillity in the border areas.

During the diplomatic talks between India and China, the situation in the region was discussed in detail and the Indian side conveyed its concerns over the violent face-off in Galwan Valley on June 15. Twenty Indian Army personnel were killed in the clash. There were reports of several casualties for the Chinese army too, but China hasn't declared any official number yet.

The talks were held in the midst of escalating tension between the two countries following the violent clashes in Galwan Valley on June 15.

The Indian and Chinese armies are engaged in the standoff in Pangong Tso, Galwan Valley, Demchok and Daulat Beg Oldie in eastern Ladakh. A sizable number of Chinese Army personnel even transgressed into the Indian side of the Line of Actual Control in several areas including Pangong Tso.

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