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
June 3,2020

Islamabad, Jun 3: Pakistan has reported a record 4,132 fresh cases of the coronavirus in the last 24 hours, taking the total number of infections to 80,463, the health ministry said on Wednesday.

The Ministry of National Health and Services said the new infections were detected after conducting a maximum of 17,370 tests in a day.

Of the total cases, Sindh has so far detected 31,086 patients of the coronavirus, Punjab 29,489, Khyber-Pakhtunkhwa 10,897, Balochistan 4,747, Islamabad 3,188, Gilgit-Baltistan 779 and Pakistan-occupied Kashmir reported 289 patients of the viral disease.

"In total 67 patients died in the last 24 hours, taking the tally of deaths to 1,688. Another 28,923 people have fully recovered from the disease," the ministry said in a statement.

The authorities have so far carried out 595,344 tests in the country.

Officials said that Pakistan has more than 100 labs that can conduct over 30,000 tests per day and the number of daily tests will be gradually increased to the maximum level.

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News Network
March 19,2020

Rome, Mar 19: Italy on Wednesday reported 475 new deaths from the novel coronavirus, the highest one-day official toll of any nation since the first case was detected in China late last year.

The total number of deaths in Italy has reached 2,978, more than half of all the cases recorded outside China, while the number of infections stood at 35,713.

The previous record high of 368 deaths was also recorded in Italy, on Sunday. The nation of 60 million has now recorded 34.2 percent of all the deaths officially attributed to COVID-19 across the world.

With the death rate still climbing despite the Mediterranean country entering a second week under an effective lockdown, officials urged Italians to have faith and to stay strong.

"They main thing is, do not give up," Italian National Institute of Health chief Silvio Brusaferro said in a nationally televised press conference.

"It will take a few days before we see the benefits" of containment measures, said Brusaferro. "We must maintain these measures to see their effect, and above all to protect the most vulnerable."

Imposed nationally on March 12, the shutdown of most Italian businesses and a ban on public gatherings are due to expire on March 25.

But school closures and other measures, such as a ban fan attendance at sporting events, are due to run on until April 3.

A top government minister hinted Wednesday that the school closure would be extended well into next month, if not longer.

The rates within Italy itself remained stable, with two-thirds of the deaths -- 1,959 in all -- reported in the northern Lombardy region around Milan, the Italian financial and fashion capital.

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Agencies
February 4,2020

The death toll in China's coronavirus rose sharply to 425 with 64 deaths on Monday alone while 3,235 new confirmed cases were reported, taking the number of those infected with the deadly disease to 20,438, Chinese health authorities said on Tuesday.

The 64 people who died on Monday were all from the Hubei province, the epicentre of the virus, China's National Health Commission said.

Also, 3,235 new confirmed cases of novel coronavirus infection were reported, a big increase in a day.

Another 5,072 new suspected cases were reported on Monday, said the commission, adding that 492 patients became seriously ill.

The commission said that 2,788 patients remained in severe condition and 23,214 people were suspected of being infected with the virus, a pointer that it is increasingly turning virulent.

The overall confirmed cases on the Chinese mainland had reached 20,438 by the end of Monday, the commission said, noting that a total of 425 people had died of the disease.

A total of 632 people had been discharged from hospital after recovery, state-run Xinhua news agency reported As the virus spreads from human to human, 221,015 close contacts had been traced, with 171,329 others still under medical observation.

By the end of Monday, 15 confirmed cases had been reported in Hong Kong, eight in the Macao and 10 in Taiwan.

The Philippines reported the first overseas death from the virus on Sunday while 148 cases have been reported from abroad.

India has reported three cases of the coronavirus. All the three patients from Kerala recently returned from the affected Wuhan city.

Currently, 647 Indians and seven Maldivians who have been evacuated from Wuhan and Hubei are in 14-day quarantine at a medical camp in Manesar, near Delhi.

As the virus continued to spread at an alarming rate, Chinese President Xi Jinping on Monday warned officials of punishment if they shirked responsibility in tackling the virus outbreak.

On Monday, China has opened a 1,000-bed hospital built in record nine days in Wuhan city and started trials for new drug to contain the virus and is set to open another 1,300 bed hospital next to it on Wednesday.

The ruling Communist Party of China on Monday held its political bureau meeting presided by President Xi to review the steps being taken on various fronts to halt the spread of the deadly virus.

The outcome of the epidemic prevention and control directly affects people's lives and health, the overall economic and social stability and the country's opening-up, Xi said.

"Those who disobey the unified command or shirk off responsibilities will be punished," Xi was quoted as saying by the state-run Xinhua news agency.

Xi said that the party and government leaders supervising them would also be held accountable in severe cases.

Chinese armament firms, including those building aircraft carrier and military aircraft, have postponed planned work in order to concentrate on controlling the risk of coronavirus, state-run Global Times reported.

Noted Chinese health expert Zhong Nanshan has said that based on the fresh evidence, the novel coronavirus, which is spreading rapidly in China and the world, may reach its peak in the next 10 to 14 days, contrary to earlier estimates of climaxing sooner.

This means that the cases would drastically increase in the next two weeks before slowing down.

Also, China has begun clinical trials to test a drug to treat the patients of the coronavirus which till now has no cure.

Currently, patients are being treated with a combination of antivirals and other measures, as scientists race to find a vaccine.

Some reports said drugs to treat HIV too was being tried to treat the patients.

The experimental antiviral drug, Remdesivir, to be tested in field trials is developed by US-based Gilead Sciences. It is aimed at treating infectious diseases such as Ebola and SARS, South China Morning Post reported.

It was given to the first US patient last week - a 35-year-old man whose condition appeared to improve within a day, it said.

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