American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

sr


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
February 1,2020

Washington, Feb 1: The Indian economy experienced some abrupt slowdown in 2019 due to turbulence in non-banking financial institutions and major reform measures such as GST and demonetisation, but it is not in a recession, IMF Managing Director Kristalina Georgieva has said.

"The Indian economy indeed has experienced an abrupt slowdown in 2019. We had to revise our growth projections, downwards to four percent for last year. We are expecting 5.8 per cent (growth rate) in 2020 and then an upward trajectory to 6.5 percent in 2021," Georgieva told a group of foreign journalists here on Friday.

"It appears that the main reason for this slowdown was the non-banking financial institutions experiencing a turbulence," she said on the eve of Union Finance Minister Nirmala Sitharaman presenting the annual budget in Parliament on Saturday.

She said India had undertaken some important reforms that over the longer term would be beneficial for the country, but they do have some short-term impact.

"For example, coming with the unified tax system, and the demonetisation that took place. These are steps that over time are beneficial, but of course they might, might be somewhat disruptive over short term," Georgieva said in response to a question.

The International Monetary Fund (IMF) Managing Director said that there is not a lot of fiscal space in India. “But we also recognise that the policies of the government on that side, on the fiscal side have been prudent. We will see how the reading of the budget, the submission of the budget goes, tomorrow,” she said.

In the medium-term, she said, the IMF remains optimistic about India. “This is why we see that upswing potential for the growth in the country,” she said.

Georgieva said that the current economic slowdown cannot be described as a recession. "No.... You're far from that. But it is a significant slowdown, not the recession," she said.

The IMF managing Director noted that the consumption in India also slowed down and that contributed to the overall slowdown in the economy. The IMF would be keen to see what India does to get relatively sound macroeconomic fundamentals to pay off in terms of better growth trajectory, she said ahead of the budget.

One thing that is important for India is that budgetary revenue have been below target. "The country knows that. The finance minister knows it. They need to increase budgetary revenue collection so they can improve their fiscal position. I said it's tight on the spending side, but I also want to stress that there is room to improve collection on the revenue side," she said.

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News Network
June 26,2020

Washington, Jun 26: The US is reviewing its global deployment of forces to ensure it is postured appropriately to counter the People's Liberation Army, given the increasing threat posed by China to Asian countries like India, Malaysia, Indonesia, and the Philippines, Secretary of State Mike Pompeo said on Thursday.

Mr Pompeo made those remarks in response to a question during the virtual Brussels Forum 2020 of the German Marshall Fund.

"We're going to make sure we're postured appropriately to counter the PLA. We think that the challenge of our times, and we're going to make sure we have resources in place to do that," Mr Pompeo said.
 
The force posture review is being done at the direction of President Donald Trump, as part of which the US is reducing the number of its troops in Germany from about 52,000 to 25,000, he said.

Mike Pompeo said that the force posture would be dictated by the ground realities.

"In certain places there will be fewer American resources. There'll be other places - I just talked about the threat from the Chinese Communist Party, so now threats to India, threats to Vietnam, threats to Malaysia, Indonesia, South China Sea challenges, the Philippines," he said.

"To the extent that that changed, the difference in what the US decided to do impacts adversely a threat some place, it may be that other nations need to step up and take responsibility for their own defense in ways that they hadn't done previously. So, we want to do this in full consultation with all of our partners all around the world, and certainly our friends in Europe," Mr Pompeo said.

President Trump is being criticised for reducing troops from Germany. His critics say that this will increase the threat from Russia to Europe.

Mike Pompeo, however, did not agree with that argument.

It has been a long time since there has been a strategic review of our force posture all across the world. The US undertook that starting about 2.5 years ago, whether that was our forces in Africa, our forces in Asia, the force we have in the Middle East and in Europe, he said.

"We began to say these are often decisions that were made in a different time. Should we reallocate those a different way? Should we have a different composition of those forces? Everyone always wants to talk about ground troops. I get it. I was a young tank officer. You described that. There's nothing I like as much as a good M1 tank.

"But it's often the case that the capacity to deter Russia or other adversaries isn''t determined any longer by just having a bunch of folks garrisoned someplace. So, we really went to back fundamentally relook, what is the nature of the conflict, what''s the nature of the threat, and how should we allocate our resources, whether that''s our resources in the intelligence community, our resources from the Air Force or the Marines and Army," Mr Pompeo said.

Last week, Mike Pompeo criticised the Chinese Army for "escalating" the border tension with India and militarising the strategic South China Sea. He also described the ruling Communist Party of China (CPC) as a "rogue actor".

"Our broad set of allocation of security apparatus, our ability to counter cyber threats, how do we allocate them? What''s the best way to do this? And the decision that you see the president made with respect to Germany is an outcome from a collective set of decisions about how we''re going to posture our resources around the world," said the top American diplomat on Thursday.

Changes in force posture is being taken in consultations with allies and friends, Mr Pompeo said.

"President Trump has spoken to this. (Defense) Secretary (Mark) Esper will be in London today and in Brussels tomorrow. We''ll talk about our plan and how we''re thinking about delivering it," he said.

"But you should understand this, and I hope our European partners will understand this as well. When you see what we ultimately conclude, how we ultimately deliver on the statements of the president made, that they''re aimed squarely at what we believe to be democracies'' fundamental interest and certainly America's most fundamental interest," Mr Pompeo said.

Earlier this month, Mike Pompeo had said that China's actions, be it on the India border, or in Hong Kong or in the South China Sea, were part of the behaviour of the ruling Communist Party in Beijing in the recent past.

China has been fast expanding military and economic influence in the Indo-Pacific region, triggering concern in various countries of the region and beyond.

China is engaged in hotly contested territorial disputes in both the South China Sea and the East China Sea. Beijing has built up and militarised many of the islands and reefs it controls in the region. Both areas are stated to be rich in minerals, oil and other natural resources and are vital to global trade.

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News Network
July 6,2020

Beijing, Jul 6: A city in northern China on Sunday sounded an alert after a suspected case of bubonic plague was reported, according to official media here.

Bayannur, Inner Mongolia Autonomous Region, announced a level III warning of plague prevention and control, state-run People’s Daily Online reported.

The suspected bubonic plague case was reported on Saturday by a hospital in Bayannur. The local health authority announced that the warning period will continue until the end of 2020.

"At present, there is a risk of a human plague epidemic spreading in this city. The public should improve its self-protection awareness and ability, and report abnormal health conditions promptly,” the local health authority said.

On July 1, state-run Xinhua news agency said that two suspected cases of bubonic plague reported in Khovd province in western Mongolia have been confirmed by lab test results.

The confirmed cases are a 27-year-old resident and his 17-year-old brother, who are being treated at two separate hospitals in their province, it quoted a health official as saying.

The brothers ate marmot meat, the health official said, warning people not to eat marmot meat.

A total of 146 people who had contact with them have been isolated and treated at local hospitals, according to Narangerel.

Bubonic plague is a bacterial disease that is spread by fleas living on wild rodents such as marmots. It can kill an adult in less than 24 hours if not treated in time, according to the World Health Organization (WHO).

A couple died of bubonic plague in the western Mongolian province of Bayan-Ulgii last year after eating raw marmot meat.

The news of bubonic plague came after Chinese researchers issued an early warning over another potential pandemic caused by an influenza virus in pigs.

Scientists from China Agricultural University, the Chinese Centre for Disease Control and Prevention and other institutes detected a pig influenza virus bearing genotype 4 (G4), which is contagious among pigs and has the possibility of jumping to humans, as the G4 virus is able to bind with human cells, state-run Global Times reported last week.

The researchers are concerned that it could mutate further so that it can spread easily from person to person, and trigger a global outbreak, BBC reported.

"Controlling the prevailing G4 EA H1N1 viruses in pigs and close monitoring in human populations, especially workers in the swine industry, should be urgently implemented," Chinese researchers warned in the paper.

The new diseases were reported even as China grappled with the second attack of Covid-19 in Beijing after controlling it in Wuhan where it was first reported in December last year.

On Saturday, Beijing reported a single-digit Covid-19, local authorities said Sunday.

The number of newly confirmed Covid-19 cases reached a peak in Beijing on June 13 and 14 and then started declining in general, Xinhua quoted local officials as saying.

From June 11 to July 4, the city reported 334 confirmed locally transmitted cases, 47 per cent of whom are workers of the Xinfadi wholesale food market, the official said.

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