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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Agencies
February 18,2020

British lawmaker Debbie Abrahams' e-Business visa was revoked as she was involved in anti-India activities and the cancellation was conveyed to her on February 14, government sources said on Tuesday.

Asserting that the grant, rejection or revocation of a visa or electronic travel authorisation is the sovereign right of a country, the sources said Abrahams was issued an e-Business visa on October 7 last year which was valid till October 5, 2020 for attending business meetings.

"Her e-Business visa was revoked on February 14, 2020 on account of her indulging in activities which went against India's national interest. The rejection of the e-Business visa was intimated to her on February 14," a source said.

Abrahams, who chairs a British parliamentary group on Kashmir, was denied entry into India upon her arrival at the New Delhi airport on Monday.

Government officials had said on Monday also that she was informed in advance that her e-visa had been cancelled.

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News Network
March 4,2020

Tokyo, Mar 4: Takeda Pharmaceutical Co said on Wednesday it was developing a drug to treat COVID-19, the flu-like illness that has struck more than 90,000 people worldwide and killed over 3,000.

The Japanese drugmaker is working on a plasma-derived therapy to treat high-risk individuals infected with the new coronavirus and will share its plans with members of the U.S. Congress on Wednesday, it said in a statement.

Takeda is also studying whether its currently marketed and pipeline products may be effective treatments for infected patients.

"We will do all that we can to address the novel coronavirus threat...(and) are hopeful that we can expand the treatment options," Rajeev Venkayya, president of Takeda's vaccine business, said in the statement.

Takeda said it was in talks with various health and regulatory agencies and healthcare partners in the United States, Asia and Europe to move forward its research into the drug.

Its research requires access to the blood of people who have recovered from the respiratory disease or who have been vaccinated, once a vaccine is developed, Takeda said.

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News Network
May 7,2020

United Nations, May 7: An average of 80,000 COVID-19 cases were reported each day in April to the World Health Organization, the top UN health agency has said, noting that South Asian nations like India and Bangladesh are seeing a spike in the infections while the numbers are declining in regions such as Western Europe.

WHO Director-General Tedros Adhanom Ghebreyesus said on Wednesday that countries must also be able to manage any risk of the disease being imported into their territories, and communities should be fully educated to adjust to what will be a "new norm".

He said as the countries press forward in the common fight against COVID-19, they should also lay the groundwork for resilient health systems globally.

"More than 3.5 million cases of COVID-19 and almost 250,000 deaths have now been reported to the WHO. Since the beginning of April, an average of around 80,000 new cases have been reported to the WHO every day," Ghebreyesus said in Geneva yesterday.

Asserting that the virus cases were not just numbers, he said: "every single case is a mother, a father, a son, a daughter, a brother, sister or friend".

He said while the numbers are declining in Western Europe, more cases are being reported every day from Eastern Europe, Africa, South-East Asia, the Eastern Mediterranean and the Americas. Even within regions and within countries, there are divergent trends, the agency added.

While some countries are reporting an increase in COVID-19 cases over time, many have seen caseloads rise because they have ramped up testing, the WHO official said.

"We've also seen in Europe and Western Europe a fundamental decrease in the number of cases, but we have seen an associated increase in the number of cases reported in places like the Russian Federation. Southeast, the Western Pacific areas are relatively on the downward trend like Korea and others, but then we do see in South Asia, in places like Bangladesh, in India, some trends towards increase.

"So it's very difficult to say that any particular region is improving or (not improving). There are individual countries within each region that are having difficulties getting on top of this disease and I am particularly concerned about those countries that have (an) ongoing humanitarian crisis," WHO's Executive Director Michael Ryan said.

The death toll due to COVID-19 in India rose to 1,783 while the number of cases climbed to 52,952 on Thursday, registering an increase of 89 deaths and 3,561 cases in the last 24 hours, the Union Health Ministry said.

The number of active COVID-19 cases stood at 35,902 while 15,266 people have recovered, it said.

Noting that while seeing an increase in the number of cases is not good in terms of transmission, WHO's Emerging Diseases and Zoonoses Unit head Maria Van Kerkhove said: "but I don't want to equate that with something (being) wrong".

"I want to equate that with countries are working very hard to increase their ability to find the virus, to find people with the virus, to have testing in place to identify who has COVID-19, and putting into place what they need to do to care for those patients," Kerkhove said.

With more countries considering easing restrictions implemented to curb the spread of the coronavirus, the WHO has again reminded the authorities of the need to maintain vigilance.

"The risk of returning to lockdown remains very real if countries do not manage the transition extremely carefully, and in a phased approach," Ghebreyesus said.

He urged countries to consider the UN agency's six criteria for lifting stay-at-home measures.

That advice includes ensuring surveillance is strong, cases are declining and transmission is controlled. Health systems also must be able to detect, isolate, test and treat cases, and to trace all contacts.

Additionally, the risk of outbreak in settings such as health facilities and nursing homes needs to be minimised, while schools, workplaces and other public locations should have preventive measures in place.

"The COVID-19 pandemic will eventually recede, but there can be no going back to business as usual. We cannot continue to rush to fund panic but let preparedness go by the wayside," he said.

He said the crisis has highlighted the importance of strong national health systems as the foundation of global health security: not only against pandemics but also against the multitude of health threats that people across the world face every day.

"If we learn anything from COVID-19, it must be that investing in health now will save lives later," Ghebreyesus said.

While the world currently spends around USD 7.5 trillion on health annually, the WHO believes the best investments are in promoting health and preventing disease.

"Prevention is not only better than cure, it's cheaper, and the smartest thing to do," he said.

The deadly coronavirus, which originated from the Chinese city of Wuhan in December last year, has infected over 3.7 million people and killed 263,831 people globally, according to a tally by Johns Hopkins University.

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