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 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
March 21,2020

Beijing, Mar 21: China reported no domestically transmitted coronavirus cases for the third consecutive day even as seven more fatalities have been confirmed, taking the death toll in the country to 3255.

No new domestically transmitted cases of COVID-19 were reported on the Chinese mainland for the third day in a row on Friday, China's National Health Commission (NHC) said on Saturday.

The overall confirmed cases on the mainland had reached 81,008 by the end of Friday, which included 3,255 who died, 6,013 patients still undergoing treatment, 71,740 patients who had been discharged after recovery, the NHC said.

The NHC said 41 new confirmed COVID-19 cases were reported on the Chinese mainland on Friday from the people arriving from abroad, taking the total number of imported cases to 269.

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News Network
April 21,2020

New York, Apr 21: Oil prices plunged below zero on Monday as demand for energy collapses amid the coronavirus pandemic and traders don't want to get stuck owning crude with nowhere to store it.

Stocks were also slipping on Wall Street in afternoon trading, with the S&P 500 down 0.9%, but the market's most dramatic action was by far in oil, where benchmark U.S. crude for May delivery plummeted to negative $3.70 per barrel, as of 2:15 pm. Eastern time.

Much of the drop into negative territory was chalked up to technical reasons — the May delivery contract is close to expiring so it was seeing less trading volume, which can exacerbate swings. But prices for deliveries even further into the future, which were seeing larger trading volumes, also plunged.

Demand for oil has collapsed so much due to the coronavirus pandemic that facilities for storing crude are nearly full.

Tanks could hit their limits within three weeks, according to Chris Midgley, head of analytics at S&P Global Platts.

Benchmark U.S. crude oil for June delivery, which shows a more ”normal” price, fell 14.8% to $21.32 per barrel, as factories and automobiles around the world remain idled. Big oil producers have announced cutbacks in production in hopes of better balancing supplies with demand, but many analysts say it's not enough.

“Basically, bears are out for blood,” analyst Naeem Aslam of Avatrade said in a report. “The steep fall in the price is because of the lack of sufficient demand and lack of storage place given the fact that the production cut has failed to address the supply glut.”

Halliburton swung between gains and sharp losses, even though it reported stronger results for the first three months of 2020 than analysts expected. The oilfield engineering company said that the pandemic has created so much turmoil in the industry that it “cannot reasonably estimate” how long the hit will last. It expects a further decline in revenue and profitability for the rest of 2020, particularly in North America.

Brent crude, the international standard, was down $1.78 to $26.30 per barrel. .

In the stock market, the mild drops ate into some of the big gains made since late March, driven lately by investors looking ahead to parts of the economy possibly reopening as infections level off in hard-hit areas.

Pessimists have called the rally overdone, pointing to the severe economic pain sweeping the world and continued uncertainty about how long it will last.

The Dow Jones Industrial Average was down 364 points, or 1.5%, to 23,887. The Nasdaq was down 0.1%..

More gains from companies that are winners in the new stay-at-home economy helped limit the market's losses Amazon rose 1.4%, and Netflix jumped 3.8% as people shut in at home buy staples and look to fill their time. Clorox likewise rose toward a new record and was up 1% as households and businesses that remain open look to stay clean.

In Tokyo the Nikkei 225 fell 1.1% after Japan reported that its exports fell nearly 12% in March from a year earlier as the pandemic hammered demand in its two biggest markets, the U.S. and China.

The Hang Seng index in Hong Kong lost 0.2%, and South Korea's Kospi fell 0.8%.

European markets were modestly higher The German DAX was up 0.5%, the French CAC 40 was up 0.7% and the FTSE 100 in London gained 0.7%.

In a sign of continued caution in the market, Treasury yields remained extremely low. The yield on the 10-year Treasury slipped to 0.64% from 0.65% late Friday. It started the year near 1.90%. Bond yields drop when their prices rise, and investors tend to buy Treasurys when they're worried about the economy.

Stocks have been on a generally upward swing recently, and the S&P 500 just closed out its first back-to-back weekly gain since the market began selling off in February. Promises of massive aid for the economy and markets by the Federal Reserve and U.S. government ignited the rally, which sent the S&P 500 up as much as 28.5% since a low on March 23.

More recently, countries around the world have tentatively eased up on business-shutdown restrictions put in place to slow the spread of the virus.

But health experts warn the pandemic is far from over and new flareups could ignite if governments rush to allow ”normal” life to return prematurely.

The S&P 500 remains about 15% below its record high in February as millions more U.S. workers file for unemployment every week amid the shutdowns.

Many analysts also warn that a significant part of the recent recovery in stocks is due to the expectation among some investors that the economy will rebound sharply once economic quarantines are lifted. They're essentially predicting that a line chart of the economy will ultimately resemble the letter “V,” with a wild ride down but then a quick pivot to a vigorous recovery.

That may be to optimistic. “We caution that a U-shaped recovery is also quite likely,” where the economy bottoms out and stays at that low level for a while before recovering, strategists at Barclays warned in a recent report.

Without strong testing programs for COVID-19, businesses likely won't feel comfortable bringing back their full workforces for a while.

”With risk assets now overbought, the chance for a correction has increased,” Morgan Stanley strategists wrote in a report.

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