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 18,2020

Washington, Jun 18: US Defence officials are concerned over China's use of COVID-19 situation to gain stakes in strategically important companies of United States as the impact of novel coronavirus has left several companies in dire need of capital.

Amid the pandemic, it getting hard for the defence department to keep an eye on national security and help protect smaller companies down the chain, CNN reported.

"We are paying close attention to any indicators that China is leveraging Covid-19 to take advantage of a situation where defence companies need capital more than ever," a defence official told CNN.

In April, Ellen Lord, undersecretary of defence for acquisition and sustainment said it is paying close attention to 'adversaries' against the 'economic warfare' with the United States.

"We have to be very, very careful about the focused efforts some of our adversaries have to really undergo sort of economic warfare with us, which has been going on for some time," Ellen Lord, undersecretary of defence for acquisition and sustainment was quoted as saying by CNN.

US Committee on Foreign Investment protects its interest against hostile countries gaining ownership in strategically important companies. But the pandemic is changing the definition of national security concerns to include drugs, protective gear and medical supplies.

"These are now national security needs and we probably should have been thinking about it a long time ago in terms of biowarfare that we should have a trusted industrial base or a set of trusted allies -- the UK, or NATO allies or Japan or Korea -- who are trusted in that regard," Bill Greenwalt, a former Pentagon official.

Give the threat posed by foreign acquisition, Pentagon has been offering tools to help small US businesses defend themselves against adversarial investment and conducting background checks with other government agencies to ensure transparency.

US President Donald Trump's trade adviser Peter Navarro recently told CNN if Trump wins reelection, Washington DC will likely take offshore supply chains as national security priorities.

"If we fail to do that in the face of this crisis, we will have failed this country and all future generations of Americans," Navarro said.

The US State Department has also warned US allies to "avoid economic overreliance on China" and "guard their critical infrastructure" from China's influence.

Chad P Bown, a senior fellow at the Peterson Institute for International Economics, pointed to recent China's economic coercion of Australia on the political matter saying, "this is how China operates and everybody knows it."

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News Network
July 14,2020

Washington, Jul 14: The United States has the biggest Covid-19 testing programme in the world, better than big countries like Russia, China, India and Brazil, President Donald Trump said on Monday, asserting that America has "just about the lowest mortality rate" due to the disease in the world.

"We have one of the lowest mortality rates anywhere," Trump said at a White House roundtable. More than 34 lakh Americans have tested positive for Covid-19 so far and over 1,37,000 have died due to the disease, both of which are the largest numbers among all the countries.

The huge number of positive cases, the president said, is due to the massive testing efforts undertaken by his administration, more extensive than any other country.

"We test more than anybody by far. And when you test, you create cases. So we have created cases. I can tell you that some countries, they test when somebody walks into a hospital sick or walks into maybe a doctor's office, but usually a hospital. That is the testing they do, so they do not have cases, whereas we have all these cases. So, it is a double-edged sword," he said.

At the same time, the United States has the lowest mortality rate or just about the lowest mortality rate due to the disease in the world, Trump added. "We are doing a great job. We are doing very well with vaccines and we are doing very, very well with therapeutics. I think we are going to have some very good information coming out soon," he said in response to a question.

"But we have the best and certainly, by far, the biggest testing programme anywhere in the world. If you tested China or Russia or any of the larger countries, if you just tested India, as an example, the way we test, you would see numbers that would be very surprising. Brazil too. You know, Brazil is going through a big problem, but they do not do testing like we do," Trump said.

"So we do the testing and by doing the testing, we have tremendous numbers of cases. As an example, we have done 45 million tests. If we did half that number, you would have half the cases probably -- around that number. If we did another half of that, you would have half the numbers. Everyone would be saying, 'Oh, we are doing so well on cases'," he added.

Responding to a question, Trump said what China did to the world should not be forgotten.

"I think what China has done to the world with what took place -- the China plague -- you can call it the China virus, you can call it whatever you want to call it. It has about 20 different names. What they did to the world should not be forgotten," he said.

The trade deal with China that was signed early this year remains intact, the president said. "It is intact, they (China) are buying. Whether they buy or not, that is up to them. They are buying," he said.

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Agencies
May 4,2020

Washington, May 4: Anxious for an economic recovery, President Donald Trump fielded Americans' questions about decisions by some states to allow nonessential businesses to reopen while other states are on virtual lockdown due to the coronavirus.

After more than a month of being cooped up at the White House, Trump returned from a weekend at the Camp David presidential retreat in Maryland and participated in a “virtual” town hall, hosted Sunday night by Fox News Channel, from inside the Lincoln Memorial.

He pushed for an economic reopening, one his advisers believe will be essential for his reelection chances this November.

“We have to get it back open safely but as quickly as possible," Trump said.

The president acknowledged fear on both sides of the issue, some Americans worried about getting sick while others are concerned about losing jobs.

Though the administration's handling of the pandemic, particularly its ability to conduct widespread testing, has come under fierce scrutiny, the president defended the response and said the nation was ready to begin reopening.

“I'll tell you one thing. We did the right thing and I really believe we saved a million and a half lives,” the president said.

But he also broke with the assessment of his senior adviser and son-in-law, Jared Kushner, saying it was “too soon to say" if the federal government was overseeing a “success story."

Trump's impatience also flashed. While noting that states would go at their own pace in returning to normal, with ones harder hit by the coronavirus going slower, he said that “some states frankly I think aren't going fast enough" and singled out Virginia, which has a Democratic governor and legislature.

And he urged the nation's schools and universities to return to classes this fall.

But many public health experts believe that cannot be done safely until a vaccine is developed.

Trump declared Sunday that he believed one could be available by year's end although his own pandemic task force has predicated it could be another 18 months.

Federal guidelines that encouraged people to stay at home and practice social distancing expired late last week.

Debate continued over moves by governors to start reopening state economies that tanked after shopping malls, salons and other nonessential businesses were ordered closed in attempt to slow a virus that has killed more than 66,000 Americans, according to a tally of reported deaths by Johns Hopkins University.

The U.S. economy has suffered, shrinking at a 4.8 per cent annual rate from January through March, the government estimated last week. It was the sharpest quarterly drop since the 2008 financial crisis.

Roughly 30.3 million people have filed for unemployment aid in the six weeks since the outbreak forced employers to shut down and slash their workforces. It was the worst string of layoffs on record.

Larry Kudlow, Trump's top economic adviser, on Sunday predicted a “spectacular 2021” — with “the right set of policies” — on top of a rebound from July through December of this year.

He said on CNN's "State of the Union" that the administration would "pause” to review the effectiveness of trillions in economic relief spending before making any decision on whether additional aid is needed.

House Speaker Nancy Pelosi, D-Calif., said Thursday that state and local governments are seeking up to USD 1 trillion for coronavirus costs, The Senate planned to reopen Monday, despite the Washington area's continued status as a virus hot spot and with the region still under stay-at-home orders.

The House remains shuttered. The pandemic is forcing big changes at the tradition-bound Supreme Court: The justices will hear arguments, beginning Monday, by telephone for the first time since Alexander Graham Bell patented his invention in 1876.

Congressional Republicans are resisting calls by Democrats for emergency spending for states and local governments whose revenue streams all but dried up in recent weeks.

The GOP is counting on the country's reopening and the rebound promised by Trump as their best hope to forestall another big round of virus aid.

The leaders of California and Michigan are among governors under public pressure over lockdowns still in effect while states such as Florida, Georgia and Ohio are reopening.

Michigan Governor Gretchen Whitmer, a Democrat, said Sunday that the armed protesters who demonstrated inside her state's Capitol “depicted some of the worst racism” and “awful parts” of US history by showing up with Confederate flags, nooses and swastikas.

Trump had tweeted “LIBERATE” and named Michigan and other states in mid-April. In a new tweet Friday, he urged Whitmer to “make a deal” with the protesters. “These are very good people, but they are angry.

They want their lives back again, safely!” Trump said.

Despite the opposition of Michigan's Republican-controlled Legislature, Whitmer has extended a state of emergency declaration and directed most businesses statewide to remain closed.

Some people participating in other public protests across the US have not kept their distance from one another and have rallied without masks, not heeding public health recommendations.

Deborah Birx, coordinator of the White House coronavirus task force, called that behavior “devastatingly worrisome.”

She said people will feel guilty for the rest of their lives if they end up infected and unwittingly spread the virus to vulnerable family members.

“We need to protect each other at the same time we're voice our discontent,” she told CNN's “State of the Union.”

An overwhelming majority of Americans support stay-at-home orders and other efforts to slow the virus' spread, according to a recent survey from The Associated Press-NORC Center for Public Affairs Research.

Asked about states that are reopening before they meet benchmarks laid out in federal guidelines she helped write, Birx said the guidelines “are a pretty firm policy of what we think is important from a public health standpoint.”

She added that she and others have made it clear that people must continue practising social distancing, “scrupulous” hand washing and other measures to protect themselves and others.

Fox News Channel said it asked viewers to submit questions about reopening the country on the network's Twitter, Facebook and Instagram accounts for a chance to appear on the rare broadcast from the Lincoln Memorial. Trump spoke from the memorial's steps last July Fourth.

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