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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Agencies
January 4,2020

Stockholm, Jan 4: “I’m not the kind of person who celebrates birthdays,” Greta Thunberg said as she turned 17 on Friday, marking the occasion in inimitable style - with a seven-hour hour protest outside the Swedish parliament.

The climate activist braved winter conditions in her native Stockholm to continue the weekly Friday School Strike for the Climate campaign that helped catapult her to international fame.

“I stand here striking from 8am until 3pm as usual ... then I’ll go home,” Thunberg, Time magazine’s Person of the Year for 2019, told Reuters.

“I won’t have a birthday cake but we’ll have a dinner.”

It’s been a busy 12 months for Thunberg, who crisscrossed the globe by car, train and boat - but not plane - to demand action on climate change.

“It has been a strange and busy year, but also a great one because I have found something I want to do with my life and what I am doing is having an impact,” she said.

When she was 15, Thunberg began skipping school on Fridays to demonstrate outside the Swedish parliament to push her government to curb carbon emissions. Her campaign gave rise to a grassroots movement that has gone global, inspiring millions of people to take action.

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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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Agencies
June 8,2020

China is aggressively pursuing a diverse range of tactics -- from cyber-attacks to recruiting insiders for economic espionage, Indian security agencies have warned. The specific alert circulated among key stakeholders suggests that Chinese operatives are not only planning to steal classified cutting-edge defense technology but also eyeing to recruit best academicians and researchers around the globe, especially from the US.

Sources said they have noticed that China has authorized an "aggressive program of stealing US science and technology information by recruiting Americans in the technology sector with access to trade secrets".

In the technology sector of the US, many Indians scientists are working at the forefront. "This is a serious matter for Indian government and security establishments," said a top source further adding that Chinese always pursue economic espionage because it suits their low cost manufacturing sector on the basis of stolen research and costly design developed by top companies across the globe.

"An alert was also issued in early January about Chinese cyber intrusion attempts at several companies where Indian researchers are working. The espionage attempt was to target UAV technology and certain top-end military equipment designs. After stealing the techniques and design, China starts producing these equipment domestically and sells at a cheaper rate, inflicting irreparable damage to the original equipment manufacturers," the sources in the security establishment observed.

Recently, the US accused China for targeting academia by sending researchers to American labs and using talent recruitment programme to steal scientific analysis. The US has also found that young recruits of the People's Liberation Army posing as students are entering into various universities across the globe to get research papers and recruit academia.

Earlier this year, the US charged a former Boston University student of visa fraud for failing to disclose the status as a lieutenant in the China's People's Liberation Army.

The US intelligence agencies have found that their "universities have become a soft target in the global espionage war with China".

In January this year, the US Department of Justice charged a leading academician at the Harvard University for hiding his alleged role in a Chinese government programme.

In July last year, the Federal Bureau of Investigation (FBI) Director Christopher Wray had revealed that the FBI is probing nearly 1,000 cases of economic espionage and attempted intellectual property theft, nearly all of them leading back to China.

Accordingly, Indian Missions have been informed about the threats being posed by Chinese spies and attempts to recruit Indian scientists and technologists working in the US and other parts of the world.

Sources further stated that security establishments in India have informed the scientist fraternity to be on alert amid threat posed by Chinese spies.

The Chinese had earlier recruited a personnel, Dongfan Chung, working at Boeing for economic espionage. Chung had stolen secret technology to benefit Chinese government and during the raid at his house more than 2.5 lakh classified pages related to Boeing were recovered.

"There has been intense debate on the international platforms regarding Chinese-sponsored theft of intellectual property. American agencies have gone on record to say that China was targeting trade secrets. In the backdrop of pandemic and global health crisis, Indian establishments in defence and technology sectors have been told to be extra cautious as China is planning to become the most advanced economy while the other countries are crippled by the highly contagious virus," the sources further added.

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