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
April 8,2020

Washington, Apr 8: President Donald Trump has threatened to put a "very powerful" hold on US' funding to the World Health Organization, accusing the UN agency of being "very China centric" and criticising it for having "missed the call" in its response to the coronavirus pandemic.

Trump slammed the global health agency for its early guidance aimed at countering the international spread of the coronavirus.

"We're going to put a hold on money spent to the WHO. We're going to put a very powerful hold on it and we're going to see. It's a great thing if it works. But when they call every shot wrong, that's no good," Trump told reporters at his daily White House news conference on Tuesday.

The Geneva-headquartered World Health Organization (WHO), receives vast amounts of money from the United States.

"We pay for a majority or the biggest portion of their money. They actually criticized and disagreed with my travel ban at the time I did it. They were wrong. They've been wrong about a lot of things. They had a lot of information early and they didn't want to - they're very - they seem to be very China centric," Trump said.

The president said his administration was going to look into the US funding to the WHO.

"We give a majority of the money that they get, and it's much more than the USD 58 million. USD 58 million is a small portion of what they've got over the years. Sometimes they get much more than that. Sometimes it's for programs that they're doing, and-it's much bigger numbers. If the programmes are good, that's great as far as we're concerned," he said.

"But we want to look into it, WHO, because they called it wrong. They (WHO) called it wrong. They missed the call. They could've called it months earlier. They would have known and they should have known and they probably did know. So, we'll be looking into that very carefully, and we're going to put a hold on money spent to the WHO," Trump said.

Meanwhile, Senator Jim Risch, chairman of Senate Foreign Relations Committee, called for an independent investigation into the WHO's handling of the COVID-19 response.

"The WHO has failed not only the American people, it has failed the world with its flagrant mishandling of the response to COVID-19," said Risch.

WHO Director general Tedros Adhanom Ghebreyesus' apparent unwillingness to hold the Chinese Communist Party to even the minimum standard of global health and transparency hindered the world's ability to blunt the spread of this pandemic, he said.

"It is completely unacceptable that the world's global health organization has become a political puppet of the Chinese government," he alleged, adding that "an independent investigation into the WHO's handling of the COVID-19 response is imperative."

The United States is the largest contributor to the WHO.

"Our valuable tax payer dollars should go towards investments to prevent the spread of disease, not to aid and abet cover-ups that cost lives and isolate portions of the world's population on political grounds, as has been the case with Taiwan," Senator Risch said.

A bipartisan group of nearly two dozen lawmakers announced Tuesday to introduce a resolution to defund the WHO until Ghebreyesus resigns and an international commission investigates the organisation's role in covering up the Chinese Communist Party's failed COVID-19 response.

"The WHO helped the Chinese Communist Party hide the threat of COVID-19 from the world and now more than 10,000 Americans are dead, a number that is expected to rise dramatically in the coming weeks," Congressman Guy Reschenthaler alleged.

"The United States is the largest contributor to WHO. It is not right that Americans' hard-earned tax dollars are being used to propagate China's lies and hide information that could have saved lives. This bill will hold the WHO accountable for their negligence and deceit," he asserted.

The United States' intelligence community has reported that the Chinese government hid the threat of COVID-19 and, as a result, made it difficult for the rest of the world to respond early, appropriately and aggressively, said Congressman Fred Keller.

"For reasons beyond understanding, the WHO acted as a silent partner in this effort instead of protecting the lives of millions across the world, including hundreds of thousands of American citizens. Our hard-earned tax dollars should not go to a global organization more concerned with not offending the Chinese government than providing accurate information and protecting innocent lives," Keller said.

Senator Marco Rubio accused the Chinese Communist Party of using WHO "to mislead the world."

"The organisation's leadership is either complicit or dangerously incompetent. I will work with the Trump Administration to ensure that WHO is independent and has not been compromised by the CCP before we continue our current funding, he added.

According to Johns Hopkins University, there are over 1.43 million confirmed coronavirus cases across the world and over 82,000 people have died due to the disease. The US has nearly 400,000 infections, the highest in the world.

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News Network
June 10,2020

Jun 10: Indian-origin California Senator Kamala Harris has joined former vice president and 2020 Democratic presidential nominee Joe Biden to raise USD 3.5 million for the upcoming November elections.

Tuesday's fundraiser is the second-largest single event haul so far for the Biden campaign, which raised USD 4 million at one event earlier this month.

Harris' presence during the virtual mega fund raiser assumes significance as the Democratic Party leaders consider her to be one of the front-runners to be the nominee for vice president. The 55-year-old lawyer-politician was once considered to be a strong opponent of Biden in the 2020 Democratic primaries.

Introducing Harris to the 1,400 supporters present at the event, Biden underlined the history-breaking nature of her past electoral wins.

"For much of her career, she was the only person in the room who looked like she did," he said.

At the start of the campaign last year, Harris was very critical of Biden. She later endorsed him, months after she decided to withdraw herself from the race to the White House.

During the fundraiser, Harris was effusive in her praise for Biden.

Referring to Biden's meeting with George Floyd's family, she said, "He (Biden)is someone who whether one on one or speaking to the nation always has a sense of how people are experiencing this world, and what their needs are...This moment in the history of our country really represents an extraordinary exercise in contrast."

"On the other hand, we have a Donald Trump who had the gall to dispatch the US military to clear the streets so that he could prance down and then, like a prop, hold up the bible for a photo op," Harris said.

The death of African-American Floyd during police confinement in Minneapolis on May 25 has resulted in widespread protests not only in the US but across the world.

"There are so many contrasts between Joe Biden and Donald Trump that really point to the choice that we as Americans have today," Harris said.

California Lt Governor Eleni Kounalakis also joined the fund raiser.

In his remarks, Biden, 77, said the US is reeling in anguish and anger over the brutal killing of Floyd or the systemic racism that still infects every part of the society. "Harris knows better than anybody," he said.

"At the same time, we're facing the worst economic disaster since the Great Depression. American history is not a fairy tale with a guaranteed ending, a happy ending. This is a battle for the soul of the country.

"It's been a constant tug of war between the American ideal that we all are created equal -- and the harsh reality that racism has long torn us apart...I'm going to ask every American to look where we are now and to think, is this who we are? Is this who we want to be?" Biden asked.

Participating in the questions and answers session, Harris said America has still not fully embraced, acknowledged or addressed its history of racism and its current history of racism.

"One can think of this moment as an inflection moment, and it will require bold action and it will require immediate action...This stresses the importance and the immediacy and the urgency of electing Joe Biden," she said.

Replying to a question, Biden said, "Did you see today where the President of the United States while George Floyd was being buried, was condemning the older man who was knocked down with his head bleeding and everyone walking by. Did you see that? I mean, my lord. What have we become if we abide by this? So much we can do and must do."

Harris said the election is going to be rough and tumble.

"There are very powerful forces that thrive off of the hate and division that Donald Trump has been sowing. This is not going to be easy. And we have about just a few months to get this thing done," she said.

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News Network
February 17,2020

Feb 17: Chinese authorities on Monday reported a slight upturn in new virus cases and 105 more deaths for a total of 1,770 since the outbreak began two months ago.

The 2,048 new cases followed three days of declines but was up by just 39 cases from the previous day’s figure. Another 10,844 people have recovered from COVID-19, a disease caused by the new coronavirus, and have been discharged from hospitals, according to Monday’s figures.

The update followed the publication late Saturday in China’s official media of a recent speech by President Xi Jinping in which he indicated for the first time that he had led the response to the outbreak from early in the crisis. While the reports were an apparent attempt to demonstrate the Communist Party leadership acted decisively from the start, it also opened Xi up to criticism over why the public was not alerted sooner.

In his speech, Xi said he gave instructions on fighting the virus on Jan. 7 and ordered the shutdown of the most-affected cities that began on Jan. 23.

The disclosure of his speech indicates top leaders knew about the outbreak’s potential severity at least two weeks before such dangers were made known to the public. It was not until late January that officials said the virus can spread between humans and public alarm began to rise.

New cases in other countries are raising growing concerns about containment of the virus.

Taiwan on Sunday reported its first death from COVID-19, the fifth fatality outside of mainland China. Taiwan’s Central News Agency, citing health minister Chen Shih-chung, said the man who died was in his 60s and had not traveled overseas recently and had no known contact with virus patients.

Japanese Prime Minister Shinzo Abe convened an experts meeting to discuss containment measures in his country, where more than a dozen cases have emerged in the past few days without any obvious link to China.

“The situation surrounding this virus is changing by the minute,” Abe said.

Japanese Health Minister Katsunobu Kato said the country is “entering into a phase that is different from before,” requiring new steps to stop the spread of the virus.

Japan now has 413 confirmed cases, including 355 from a quarantined cruise ship, and one death from the virus. Its total is the highest number of cases among about two dozen countries outside of China where the illness has spread.

Hundreds of Americans from the cruise ship took charter flights home, as Japan announced another 70 infections had been confirmed on the Diamond Princess. Canada, Hong Kong and Italy were planning similar flights.

The 300 or so Americans flying on U.S.-government chartered aircraft back to the U.S. will face another 14-day quarantine at Travis Air Force Base in California and Lackland Air Force Base in Texas. The U.S. Embassy said the departure was offered because people on the ship were at a high risk of exposure to the virus. People with symptoms were banned from the flights.

About 255 Canadians and 330 Hong Kong residents are on board the ship or undergoing treatment in Japanese hospitals. There are also 35 Italians, of which 25 are crew members, including the captain.

In China’s Hubei province, where the outbreak began in December, all vehicle traffic will be banned in another containment measure. It expands a vehicle ban in the provincial capital, Wuhan, where public transportation, trains and planes have been halted for weeks.

Exceptions were being made for vehicles involved in epidemic prevention and transporting daily necessities.

Hubei has built new hospitals with thousands of patient beds and China has sent thousands of military medical personnel to staff the new facilities and help the overburdened health care system.

Last Thursday, Hubei changed how it recognized COVID-19 cases, accepting a doctor’s diagnosis rather than waiting for confirmed laboratory test results, in order to treat patients faster. The tally spiked by more than 15,000 cases under the new method.

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