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
April 18,2020

Washington, Apr 18: The United States on Friday passed 700,000 confirmed coronavirus cases, according to a tally maintained by Johns Hopkins University.

With the highest number of cases and deaths of any country in the world, the US had recorded 700,282 cases of COVID-19 and 36,773 deaths as of 8:30 pm (0030 GMT Friday), according to the Baltimore-based university.

That marked an increase of 3,856 deaths in the past 24 hours, but that figure likely includes "probable" virus-linked deaths, which had not previously been counted.

This week, New York City said it would add 3,778 "probable" virus deaths to its official count.

The US Centers for Disease Control and Prevention gave a toll Friday night of 33,049 dead, including 4,226 probable virus-linked deaths.

The United States has seen the highest death toll in the world in the coronavirus pandemic, ahead of Italy (22,745 deaths) although its population is just a fifth of that of the US.

Spain has recorded 19,478 deaths, followed by France with 18,681.

Trump announces $19 billion relief for farmers amid COVID-19 epidemic

President Donald Trump on Friday announced a $19 billion financial rescue package to help the agriculture industry weather the staggering economic downturn sparked by measures to defeat the coronavirus.

Trump told a press conference the government "will be implementing a $19 billion relief program for our great farmers and ranchers as they cope with the fallout of the global pandemic."

The program will include direct payments to farmers, ranchers and producers who Trump said have experienced "unprecedented losses during this pandemic."

Agriculture Secretary Sonny Perdue said US farmers have been hit hard by a sharp shift in demand, as schools and restaurants close and more Americans eat at home.

That has disrupted the food supply chain, forcing farmers in many places to destroy dairy output and plow under crops that no longer have buyers.

"Having to dump milk and plow under vegetables ready to market is not only financially distressing, but it's heartbreaking as well to those who produce them," Perdue said.

Perdue said some $3 billion of the money would go to buying produce and milk from such farmers, and redistribute it to community food banks.

Millions of Americans have recently turned to food pantries for meals and groceries after losing their jobs.

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News Network
April 15,2020

Seoul, Apr 15: Wearing masks and gloves, South Korean voters cast their ballots on Wednesday to elect 300 parliamentary lawmakers amid the coronavirus outbreak.

Voting kicked off at 6 am (local time) and was to run until 6 pm (local time) at 14,330 polling stations across the country, according to the National Election Commission (NEC). The number of eligible voters is 44 million, according to Yonhap news agency.

The once-in-four-years legislative election is widely seen as a referendum on President Moon Jae-in, whose five-year term will end in mid-2022, as well as a test of the country's fight against COVID-19 under the leadership of Moon, The Strait Times reported.

South Korea has received international praise for its massive testing capability and other innovative measures, such as drive-through testing and high-tech contact tracing.

Experts, therefore, expect the ruling Democratic Party (DP) to extend its lead in Parliament, given that the government's handling of the virus outbreak is viewed positively both at home and abroad, as per The Strait Times.

At least 10,564 people in the country have been infected by coronavirus, which has claimed 222 lives. About 2,800 patients are undergoing treatment.

The number of new cases has fallen from a high of 813 on February 29 to below 50 for six days in a row as an intensive social distancing campaign that started on March 21 remained in place.

Several surveys cited by the newspaper also showed that voters consider the pandemic as the biggest factor in their decision. A recent poll showed that 72.6 per cent of respondents rated the government's response to the outbreak as positive.

The NEC has said that public safety at polling stations will be a priority to prevent any possible spread of the virus.

All 14,330 polling stations and 251 counting stations will be disinfected on polling day, the NEC was quoted.

Voters will undergo temperature screening and those registering temperatures of 37.5 degrees Celsius or higher or display respiratory symptoms will have to exercise their franchise at a separate booth.

Tuesday was the last of 13 days of campaigning, which saw most candidates reducing their ground activities and face-to-face encounters with voters. Instead, the candidates boosted their online presence with videos and social media engagements in a bid to win votes, according to The Strait Times.

In addition, the government has also decided to temporarily lift quarantine rules to permit self-isolators to vote in the elections. Some 50,000 people in self-isolation who have no symptoms and expressed a willingness to vote will be allowed to cast ballots after the regular voting ends in the evening.

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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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