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
July 2,2020

Los Angeles, Jul 2: New daily coronavirus cases in the United States soared past 50,000 for the first time Wednesday, as the World Health Organization delivered a grave warning that the global pandemic is accelerating.

Restaurants, bars and beaches in the world's worst-hit nation closed from California to Florida, as states reeling from yet another surge in the deadly virus braced for Independence Day festivities.

Global infections have hit their highest level in the past week, WHO data showed, with chief Tedros Adhanom Ghebreyesus saying new cases topped "160,000 on every single day."

The grim milestone came as the European Union left the United States, Brazil and Russia off its final list of nations safe enough to allow residents to enter its borders.

With more than 52,000 new COVID-19 cases in the United States alone in the past 24 hours, according to a Johns Hopkins University tally, several US states imposed 14-day quarantines on visitors in the buildup to the long weekend's July 4 celebrations.

California suspended indoor dining at restaurants in Los Angeles and several counties, while New York scrapped plans to allow restaurants to seat customers inside from next week.

President Donald Trump reiterated his belief that the contagion will "at some point... sort of just disappear, I hope."

But the US leader who has yet to be seen in public wearing a face mask during the pandemic added he would have "no problem" doing so.

EU travel ban eased

The rollbacks came as the European Union reopened its borders to visitors from 15 countries.

The bloc hopes relaxing restrictions on countries from Algeria to Uruguay will breathe life into its tourism sector, choked by a ban on non-essential travel since mid-March.

Travelers from China, where the virus first emerged late last year, will be allowed to enter the EU only if Beijing reciprocates.

And Brazil -- which has suffered the most deaths globally for the last week, and is the second-worst affected country overall -- was excluded entirely.

It topped 60,000 total fatalities Wednesday, after suffering 1,000 deaths in just 24 hours.

However, with over 10 million known infections worldwide and more than 500,000 deaths, the pandemic is "not even close to being over", the WHO warned.

Data provided by the UN health agency for the seven days from June 25-July 1 showed the highest number of new daily cases ever recorded came on June 28, when over 189,500 new cases were registered worldwide.

'Dutch brothels reopen'

According to the United Nations, the coronavirus crisis could cost global tourism and related sectors from $1.2 to $3.3 trillion in lost revenue.

Greece, which has suffered fewer than 200 virus deaths, has seen its economy hit hard by lockdowns and travel restrictions -- all but ending its lucrative tourism season before it began.

Romanian Cojan Dragos was "the first tourist" in one Corfu hotel after driving there with his wife and daughter.

"We have the whole hotel just for us," he told news agency.

Separately, Spain and Portugal held a ceremony as they reopened their land border.

The Netherlands also confirmed the reopening Wednesday of another tourist draw -- its brothels and red-light districts.

"I'm totally booked," said sex worker Foxxy, adding that she had held a "little party" when she heard restrictions would be lifted.

Clusters spur new lockdowns

Russia did not make the EU's list of approved countries so its citizens will be absent from the bloc's tourist hot-spots.

The country, however, enjoyed a public holiday Wednesday as it voted in a referendum to approve constitutional changes allowing President Vladimir Putin to stay in power for another 16 years.

Putin was forced to postpone the vote in April as his government tackled an outbreak that has infected almost 650,000 people -- the third-highest in the world.

In other countries, clusters are still causing problems.

Parts of the Australian city of Melbourne suffered sharp rises in infections, spurring new stay-at-home measures.

The Palestinian Authority announced a five-day lockdown across the West Bank after a surge in confirmed cases.

And textile factories in the central British city of Leicester were suggested as the reason for a spike in infections that has prompted the reimposition of local restrictions.

Americas spike

In the United States, spikes across southern and western states are driving a surge in national infections.

Texas, which again smashed its daily COVID-19 record with over 8,000 new cases, joined Florida and California in closing some beaches for the upcoming holiday weekend.

Apple announced it would close another 30 US stores on Thursday, half of them in California.

A further 700 deaths nationwide took the US past 128,000 deaths in total.

The Pan American Health Organization warned that the death count in Latin America and the Caribbean could quadruple to more than 400,000 by October without stricter public health measures.

The US government announced this week it had bought 92 percent of all remdesivir production -- the first drug to be shown to be relatively effective in treating COVID-19.

Britain and Germany, however, said Wednesday they had sufficient stocks of the drug.

'Corona baby'

In Britain, some 1,500 acts from Ed Sheeran and Coldplay to Paul McCartney and The Rolling Stones urged the county's government to save the live music industry, which has been collapsing because of the coronavirus.

But while lockdown measures have been a disaster for many, some have welcomed the chance to spend more quality time with hard-working partners.

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Agencies
February 16,2020

Wuhan, Feb 16: The death toll from China's coronavirus epidemic has climbed to 1,665 after 142 more people died, mostly in the worst-hit Hubei Province, and the confirmed cases jumped to 68,500, officials said on Sunday, as top WHO experts scramble to assist Beijing contain the virus spread.

China's National Health Commission confirmed 2,009 new cases across the country.

Hubei and its provincial capital Wuhan, where the virus first emerged in December, reported 1,843 of the new cases. The latest report brought the total confirmed cases in Hubei to 56,249 cases.

Of the new deaths, 139 were in Hubei, two in Sichuan, and one in Hunan, the state-run Xinhua news agency reported.

The number of new cases, however, appears to have started dropping and a top Chinese health official has said efforts to control the outbreak have reached the “most crucial stage".

The report said 9,419 infected patients had been discharged from hospital after recovery so far.

The coronavirus has posed a severe threat to the medical staff as more than 1,700 Chinese health officials have been infected by the virus while treating the patients and six of them have died.

Experts from the World Health Organisation are expected in Beijing on Sunday to join Chinese health authorities in containing the virus, which has spread to several other countries forcing them to temporarily stop tourist arrivals from China.

The health commission said a joint mission with WHO experts will pay field visits to China's three provincial-level regions to learn the effectiveness of the epidemic control measures.

One task of the mission will be to come up with standard medicine to cure the disease, according to the health commission.

Several antiviral drugs are under clinical trials and Chinese researchers have narrowed down their focus to a few existing drugs, including Chloroquine Phosphate, Favipiravir and Remdesivir, said Zhang Xinmin, director of the China National Centre for Biotechnology Development.

Experts have asked people to frequently wash hands and face, and wear masks.

Authorities have begun quarantining large quantity of bank notes and coins in the affected areas and sanitising them with UV light before releasing them back into circulation to stop the virus from spreading.

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News Network
April 6,2020

New Delhi, April 6: The United States has donated $2.9 million assistance package for India to help the Narendra Modi government brace itself against the coronavirus as countries across the world are coming together to combat the outbreak.

On March 28, the US government, via US Agency for International Development, announced $2.9 million to support India in its response to COVID-19.

"It builds on a foundation of over $1.4 billion in health assistance and nearly $3 billion in total assistance that the US provided to India over the last 20 years," the US Embassy in India said in a statement.

"These new funds will support two organisations, including $2.4 million for USAID's health strengthening project, implemented by Jhpiego, an international non-profit health organisation affiliated with Johns Hopkins University and $500,000 for the World Health Organization (WHO)," the statement said.

The funds will also help India combat the spread of COVID-19, provide care for the affected and support local communities with the tools needed to contain the disease, it added.

Moreover, being a global leader in health and humanitarian response to COVID-19, the US has provided approximately $18.3 million assistance package to ASEAN member countries to fight the contagion.

The funds will be used to prepare laboratories for large-scale testing for the lethal virus, infection prevention and control, enable risk communication, implement public-health emergency plans for border points of entry, activate case-finding and event-based surveillance for influenza-like illnesses, train and equip rapid-responders in investigation and contact-tracing and update training materials for health workers.

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