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
March 2,2020

Paris, Mar 2: A global agency says the spreading new virus could make the world economy shrink this quarter, for the first time since the international financial crisis more than a decade ago.

The Organization for Economic Cooperation and Development says Monday in a special report on the impact of the virus that the world economy is still expected to grow overall this year and rebound next year.

But it lowered its forecasts for global growth in 2020 by half a percentage point, to 2.4 per cent, and said the figure could go as low as 1.5 per cent if the virus lasts long and spreads widely.

The last time world GDP shrank on a quarter-on-quarter basis was at the end of 2008, during the depths of the financial crisis. On a full-year basis, it last shrank in 2009.

The OECD said China's reduced production is hitting Asia particularly hard but also companies around the world that depend on its goods.

It urged governments to act fast to prevent contagion and restore consumer confidence.

The Paris-based OECD, which advises developed economies on policy, said the impact of this virus is much higher than past outbreaks because "the global economy has become substantially more interconnected, and China plays a far greater role in global output, trade, tourism and commodity markets."

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News Network
June 12,2020

Washington, Jun 12: US President Donald Trump is considering suspending a number of employment visas including the H-1B, most sought-after among Indian IT professionals, in view of the massive unemployment in America due to the coronavirus pandemic, according to a media report.

The proposed suspension could extend into the government’s new fiscal year beginning October 1, when many new visas are issued, The Wall Street Journal reported on Thursday, quoting unnamed administration officials.

“That could bar any new H-1B holder outside the country from coming to work until the suspension is lifted, though visa holders already in the country are unlikely to be affected,” the daily reported.

H-1B is the most coveted foreign work visas for technology professionals from India.

Such a decision by the Trump administration is likely to have an adverse impact on thousands of Indian IT professionals. Already a large number of Indians on the H-1B visas have lost their jobs and are headed back home during the coronavirus pandemic.

The White House, however, said that no final decision has been made and the administration is considering various proposals.

“The administration is currently evaluating a wide range of options, formulated by career experts, to protect American workers and job seekers especially disadvantaged and underserved citizens — but no decisions of any kind have been made,” White House spokesman Hogan Gidley said in a statement.

In addition to the H-1B visas, the suspension could apply to the H-2B visa for short-term seasonal workers, the J-1 visa for short-term workers including camp counselors and au pairs and the L-1 visa for internal company transfers, the financial daily reported.

Meanwhile, the US Chambers of Commerce CEO Thomas Donohue on Thursday wrote a letter to Trump, expressing concern over his reported move on temporary work visas.

“As the economy rebounds, American businesses will need assurances that they can meet all their workforce needs. To that end, it is crucial that they have access to talent both domestically and from around the world,” Donohue wrote in a letter to Trump.

According to The Hill newspaper, Donohue said that American businesses need L-1 visa holders, who have a work visa valid for a relatively short amount of time, for necessary expertise.

He noted the importance of H-1B visa holders, who have a work visa valid for multiple years, for various industries, including technology, accounting and manufacturers, the newspaper said.

“Policies that would, for example, impose wide-ranging bans on the entry of nonimmigrant workers or impose burdensome new regulatory requirements on businesses that employ foreign nationals would undermine that access to talent and in the process, undercut our economy’s ability to grow and create jobs,” Donohue added.

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News Network
March 29,2020

Washington, Mar 29: The number of known coronavirus US cases soared well past 115,000, with more than 1,900 dead, as President Donald Trump said on Saturday he was considering imposing a quarantine on the hard hit New York region.

American healthcare workers in the trenches of the pandemic are appealing for more protective gear and equipment to treat a surge in patients that is already pushing hospitals to their limits in virus hot spots such as New York City, New Orleans and Detroit.

Trump told reporters he could order a quarantine on three states, New York, New Jersey and Connecticut, which between them have recorded at least 64,000 infections and 895 deaths.

He also appeared to soften his previous comments calling for the US economy to be swiftly reopened. Asked whether he thought the United States would restart by Easter Sunday, April 12, Trump replied, "We'll see, what happens."

New York Governor Andrew Cuomo said he had no details on any possible quarantine order for his state, telling a briefing: "I don't even know what that means. I don't know how that would be legally enforceable, and from a medical point of view I don't know what you would be accomplishing."

He said New York was postponing its presidential primary election to June 23, from April 28.

As the crisis deepened, nurses at Jacobi Medical Center in New York's borough of the Bronx protested outside the hospital on Saturday, saying supervisors asked them to reuse personal protective equipment, including masks. Some held signs with slogans including "Protect our lives so we can save yours."

"The masks are supposed to be one-time use," one nurse said, according to videos posted online. "Now, all of a sudden the CDC (Centers for Disease Control and Prevention) is saying that it's fine for us to reuse them. These choices are being made not based on science. They're being made based on need."

One resident at New York Presbyterian Hospital said they were issued with just one mask.

"This is your mask forever. You can bring it home with you. Here's how you can clean your mask," said the resident, who asked not to be named because he was not authorized to speak to the media. "It's not the people who are making these decisions that go into the patients' rooms."

Doctors are also especially concerned about a shortage of ventilators, machines that help patients breathe and are widely needed for those suffering from COVID-19, the pneumonia-like respiratory ailment caused by the highly contagious novel coronavirus.

Hospitals have also sounded the alarm about scarcities of drugs, oxygen tanks and trained staff.

By Saturday afternoon, the US number of cases stood at 115,842 with at least 1,929 deaths, according to a Reuters tally. The United States has had the most recorded cases of any country since its count of infections eclipsed those of China and Italy on Thursday.

BLACK MARKET
As shortages of key medical supplies abounded, desperate physicians and nurses were forced to take matters into their own hands.

New York-area doctors say they have had to recycle some protective gear, or even resort to bootleg suppliers.

Dr. Alexander Salerno of Salerno Medical Associates in northern New Jersey described going through a "broker" to pay $17,000 for masks and other protective equipment that should have cost about $2,500, and picking them up at an abandoned warehouse.

"You don't get any names. You get just phone numbers to text," Salerno said. "And so you agree to a term. You wire the money to a bank account. They give you a time and an address to come to."

Nurses at Mount Sinai Hospital in New York said they were locking away or hiding N95 respirator masks, surgical masks and other supplies that are prone to pilfering if left unattended.

"Masks disappear," nurse Diana Torres said. "We hide it all in drawers in front of the nurses' station."

One nurse at Westchester Medical Center, in the suburbs of the city, said colleagues have begun absconding with scarce supplies without asking, prompting better-stocked teams to lock masks, gloves and gowns in drawers and closets.

An emergency room doctor in Michigan, an emerging epicenter of the pandemic, said he was wearing one paper face mask for an entire shift due to a shortage and that hospitals in the Detroit area would soon run out of ventilators.

"We have hospital systems here in the Detroit area in Michigan who are getting to the end of their supply of ventilators and have to start telling families that they can't save their loved ones because they don't have enough equipment," the physician, Dr. Rob Davidson, said in a video posted on Twitter.

Sophia Thomas, a nurse practitioner at DePaul Community Health Center in New Orleans, where Mardi Gras celebrations late last month fueled an outbreak in Louisiana's largest city, said the numbers of coronavirus patients "have been staggering."

In the nation's second-largest city, Los Angeles Mayor Eric Garcetti said spiking cases were putting Southern California on track to match New York City's infection figures in the next week.

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