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 1,2020

New Delhi, Jun 1: Actor Kendrick Sampson, who stars in HBO series Insecure, was struck by rubber bullets as Los Angeles police officers tried to disperse a crowd protesting George Floyd”s death in Minneapolis.

Floyd, a black man, died last Monday in Minneapolis, Minnesota after a white police officer pressed his knee on his neck for more than eight minutes. The officer was arrested on Friday and charged with third-degree murder.

The actor went live via Instagram on Saturday to show his view of events, but he could be also be seen on a CNN broadcast simultaneously, with viewers watching him get hit by a police baton on TV.

Sampson posted several videos on his page of a large demonstration at Pan Pacific Park near the city”s Fairfax District, where violent clashes took place throughout the day outside the Grove shopping center.

In one video, LAPD officers can be seen firing rubber bullets to try and regain control at the park.

“They shot me four times already. I already got hurt and I got hit with a baton,” Sampson said in the video on Instagram.

Another clip showed him moving away from the police, as he appeared to be hit by an officer”s baton.

“Y”all ain”t see no police f*****g up white folks when they took guns to the statehouse,” he said, referring to an incident in Michigan over coronavirus restrictions, not in California. “Y”all didn”t see police attacking white folks, beating em up with batons, shooting them with rubber bullets when they brought guns to f*****g state houses. We came up here with no weapons, with masks.… And we”re the ones who are not peaceful,” Sampson alleged.

Protests turned violent over Floyd”s death and other police killings of black people spread Saturday in dozens of US cities, with police cars set ablaze, reports of injuries mounting on all sides, shops and showrooms vandalised amid the lockdown.

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News Network
June 13,2020

Shanghai, Jun 13: Authorities in Beijing have temporarily shut a major wholesale agricultural market following a rise in locally transmitted novel coronavirus infections in China's capital city over the past two days.

The closure of the Xinfadi wholesale market at 3 a.m. local time on Saturday (1900 GMT on Friday), came after two men working at a meat research centre who had recently visited the market were reported on Friday as having been infected by the novel coronavirus. It was not immediately clear how the men had been infected.

Concern is growing of a second wave of the new virus, even in many countries that seemed to have curbed its spread. It was first reported at a seafood market in Wuhan, the capital of central China's Hubei province, in December.

Beijing authorities had earlier halted beef and mutton trading at the Xinfadi market, alongside closures at other wholesale markets around the city.

Reflecting concerns over the risk of further spread of the virus, major supermarkets in Beijing removed salmon from their shelves overnight after the virus causing COVID-19 was discovered on chopping boards used for imported salmon at the market, the state-owned Beijing Youth Daily reported.

Beijing authorities said more than 10,000 people at the market will take nucleic acid tests to detect coronavirus infections. The city government also said it had dropped plans to reopen schools on Monday for students in grades one through three because of the new cases.

Health authorities visited the home of a Reuters reporter in Beijing's Dongcheng district on Saturday to ask whether she had visited the Xinfadi market, which is 15 km (9 miles) away. They said the visit was part of patrols Dongcheng was conducting.

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China reported 11 new COVID-19 cases and seven asymptomatic cases for Friday, the national health authority said on Saturday. And all six locally transmitted cases were confirmed in Beijing.

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News Network
April 13,2020

Manila, Apr 13: The Asian Development Bank (ADB) on Monday tripled the size of its response to novel coronavirus disease (COVID-19) pandemic to 20 billion dollars and approved measures to streamline its operations for quicker and more flexible delivery of assistance.

The package expands ADB's 6.5 billion dollars initial response announced on March 18, adding 13.5 billion dollars in resources to help ADB's developing member countries counter the severe macroeconomic and health impacts caused by COVID-19.

The 20 billion dollar package includes about 2.5 billion dollars in concessional and grant resources.

"This pandemic threatens to severely set back economic, social, and development gains in Asia and the Pacific, reverse progress on poverty reduction and throw economies into recession," said ADB President Masatsugu Asakawa.

"Our expanded and comprehensive package of assistance, made possible with the strong support of our board, will be delivered more quickly, flexibly and forcefully to the governments and the private sector in our developing member countries to help them address the urgent challenges in tackling the pandemic and economic downturn," he said in a statement.

ADB's most recent assessment released on April 3 estimates the global impact of the pandemic at between 2.3 and 4.8 per cent of gross domestic product. Regional growth is forecast to decline from 5.2 per cent last year to 2.2 per cent in 2020.

The new package includes the establishment of a COVID-19 pandemic response option under ADB's countercyclical support facility.

Up to 13 billion dollars will be provided through this new option to help governments of developing member countries implement effective countercyclical expenditure programs to mitigate impacts of the COVID-19 pandemic, with a particular focus on the poor and the vulnerable.

Grant resources will continue to be deployed quickly for providing medical and personal protective equipment and supplies from expanded procurement sources.

Some 2 billion dollars from the 20 billion dollar package will be made available for the private sector. Loans and guarantees will be provided to financial institutions to rejuvenate trade and supply chains.

Enhanced microfinance loan and guarantee support and a facility to help liquidity-starved small and medium-sized enterprises, including those run by female entrepreneurs, will be implemented alongside direct financing of companies responding to or impacted by COVID-19.

The response package includes a number of adjustments to policies and business processes that will allow ADB to respond more rapidly and flexibly to the crisis. These include measures to streamline internal business processes, widen the eligibility and scope of various support facilities and make the terms and conditions of lending more tailored.

All support under the expanded package will be provided in close collaboration with international organisations, including the International Monetary Fund, World Bank Group, World Health Organisation, UNICEF, other UN agencies and the broader global community.

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