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 2,2020

Washington, Jul 2: Former US Ambassador to the UN, Nikki Haley, on Wednesday (local time) hailed India's action to ban 59 apps linked to Chinese firms including Tik Tok and said New Delhi is continuing to show it will not back down from China's aggression.

"Good to see India banning 59 popular apps owned by Chinese firms, including TikTok, which counts India as one of its largest markets. India is continuing to show it won't back down from China's aggression," Haley tweeted.

The Indian government on Monday announced that it had decided to block 59 apps in view of the information available that "they are engaged in activities which are prejudicial to sovereignty and integrity of India, defence of India, the security of the state and public order".

Information Technology Minister, Ravi Shankar Prasad said that the government has banned the apps for the safety, security, defense, sovereignty, and integrity of India.

Haley'='s remarks come after US Secretary of State Mike Pompeo welcomed India''s ban on the Chinese apps and stressed that the move would "boost India''s integrity and national security".

"We welcome India''s ban on certain mobile apps. India''s clean app approach will boost India's sovereignty and boost integrity and national security," Pompeo said.

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News Network
May 12,2020

May 12: Several Indians in the US, either on the H-1B work visa or Green Card having children who are American citizens by birth, are being prevented from travelling to India aboard the special repatriation flights being run by Air India amidst the coronavirus-linked global travel restrictions.

According to the regulations issued by the Indian government last month and updated last week, visas of foreign nationals and OCI cards, that provide visa-free travel privileges to the people of Indian-origin, have been suspended as part of the new international travel restrictions.

For some of the Indian citizens like the Pandey couple in New Jersey (name and place changed at request), it's a double whammy. Having lost their H-1B job, they have to go back to India within the stipulated 60 days as required by law. The couple has two kids aged one and six years who are American citizens.

In the wee hours of Monday, they had to return from Newark airport as Air India refused to give their kids a ticket to fly to India along with them, despite them having a valid Indian visa. The young mother and father are Indian citizens.

They said that the officials from Air India and (Indian) Consulate (in New York) were very cooperative.

Also Read: COVID-19: Top senators urge Trump to temporarily suspend all new guest worker visas, including H-1B

But they could not do anything as their hands were tied by the latest regulation issued by the Indian government, a shocked Ratna Pandey told PTI.

"I would like to urge the Indian government to reconsider their decision on the humanitarian basis," said the Indian national who has lost her job but could not leave the US within the stipulated 60 days to avoid any future visa complications.

She now plans to make an appeal to the US Citizenship and Immigration Services (USCIS) to extend their stay.

Last month, H-1B visa holders, mostly Indians, launched a White House petition urging US President Donald Trump to extend their permissible stay from 60 to 180 days after job loss. However, there has been no decision from the White House so far.

While there is no official statistics of how many Indian H-1B visa holders have lost their jobs, it is believed to be substantial.

The US, due to the coronavirus pandemic, is experiencing an unprecedented unemployment rate and more than 33 million Americans have lost their jobs in the last two months. Given this massive job loss, Indians, who have lost their jobs, are unlikely to get one and thus many would have no other option but to travel back home.

In the case of single mother Mamta (name changed), the situation is graver as her son is just three-month old. Only she was given the ticket and the infant was not allowed to fly along with her because he carried an American passport.

"I would like to request the Indian government to let us fly back home. I don't want to stay in the US any longer," she told PTI hours after being prevented from boarding her hometown Ahmedabad-bound flight from Newark on Sunday.

"I am alone here. I don't have a relative here. It's a difficult situation," she said.

"Vande Bharat Mission is a humanitarian mission. But this is certainly inhuman," said Rakesh Gupta (name changed) from Washington DC.

An H-1B professional, Gupta has lost his job and needs to return to India within the stipulated 60 days. He and his wife, Geeta (name changed) being Indian citizens, received the confirmation of their seats in the flight but have been told that their two-and-a-half-year-old daughter cannot travel with them as she carried an OCI card.

"I don't believe this," he said.

Unlike the Pandey couple and Mamta, who had made the payment of USD 1,361 per ticket for their flight back home, Rakesh has not made the payment. Air India has said that the money would be refunded.

All the three Indian citizens requested the Indian government to help them travel back home by making necessary changes in the current regulations.

As per a recent government notification, all existing Indian visa holders, and visa-free travel facility, granted to OCI card holders who are not in India, have been suspended till restrictions on international air travel remains.

New York-based community leader Prem Bhandari said that the May 5 travel advisory has created multiple painful issues for the OCI card holders in the US and also to Indian citizens who are either on Green Card or H-1B visas and want to travel back home, but cannot leave their kids who are Americans by birth.

"We would like to express our disappointment with the discrimination between OCIs and citizens in respect of entering India at this critical stage when many OCIs have lawfully built their homes, families and businesses in India," Bhandari said in a letter to Union Home Secretary Ajay Kumar Bhalla on Monday.

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Agencies
January 20,2020

For the first time in the 15 years of the Global Risks Report, the climate change and environment risk has occupied all the top five slots.

According to the 15th edition of the World Economic Forum's (WEF) Global Risks Report, the top five risks in terms of likelihood are extreme weather, climate action failure, natural disasters, biodiversity loss and human-made environmental disasters. They all fall in the one category of climate change and related environmental disasters.

WEF President Borge Brende said the world was feeling long-mounting and interconnected risks.

The report also points to how citizens are protesting across the world as discontent rises with failed systems that are creating inequality. The citizens' discontent had hardened with systems that had failed to promote advancement, it said.

"Disapproval of how governments are addressing profound economic and social issues has sparked protests throughout the world, potentially weakening the ability of governments to take decisive action should a downturn occur. Without economic and social stability, countries could lack the financial resources, fiscal margin, political capital or social support needed to confront key global risks," it said.

Listing the grim scenario, Borge said the global economy was faced with "synchronised slowdown", the past five years had been the warmest on record and cyber attacks were expected to increase this year.

The report warns that while the myriad risks were rising, time was running out on how to prevent them.

Borge said the growing palpability of shared economic, environmental and societal risks indicated that the horizon had shortened for preventing "or even mitigating" some of the direst consequences of global risks.

"It's sobering that in the face of this development, when the challenges before us demand immediate collective action, fractures within the global community appear to only be widening," he said.

The report points to grave concern about the consequences of continued environmental degradation, including the record pace of species decline.

Pointing to an unsettled geopolitical environment, the report said today's risk landscape was one in which new centres of power and influence were forming and old alliance structures and global institutions were being tested.

"While these changes can create openings for new partnership structures in the immediate term, they are putting stress on systems of coordination and challenging norms around shared responsibility. Unless stakeholders adapt multilateral mechanisms for this turbulent period, the risks that were once on the horizon will continue to arrive," it said.

Calling it a "an unsettled world", the WEF report notes that powerful economic, demographic and technological forces were shaping a new balance of power. "The result is an unsettled geopolitical landscape in which states are increasingly viewing opportunities and challenges through unilateral lenses," it said.

"What were once givens regarding alliance structures and multilateral systems no longer hold as states question the value of long-standing frameworks, adopt more nationalist postures in pursuit of individual agendas and weigh the potential geopolitical consequences of economic decoupling. Beyond the risk of conflict, if stakeholders concentrate on immediate geo-strategic advantage and fail to re-imagine or adapt mechanisms for coordination during this unsettled period, opportunities for action on key priorities may slip away," the WEF said.

In a chapter on risks to economic stability and social cohesion, it said a challenging economic climate might persist this year and members of the multi-stakeholder community saw "economic confrontations" and "domestic political polarisation" as the top risks in 2020.

The report also warned of downward pressure on the global economy from macroeconomic fragilities and financial inequality. These pressures continued to intensify in 2019, increasing the risk of economic stagnation.

Low trade barriers, fiscal prudence and strong global investment, once seen as fundamentals for economic growth, are fraying as leaders advance nationalist policies. The margins for monetary and fiscal stimuli are also narrower than before the 2008-2009 financial crisis, creating uncertainty about how well countercyclical policies will work.

The strategic partners for the WEF report included Marsh & McLennan and Zurich Insurance Group. The academic advisers were National University of Singapore, Oxford Martin School, University of Oxford and Wharton Risk Management and Decision Processes Center, University of Pennsylvania.

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