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
May 29,2020

Washington, May 29: US President Donald Trump while speaking with reporters at the White House on Thursday said that he is more liked in India than the media in his own country --the United States.

"I know. And they like me in India. I think they like me in India certainly more than the media likes me in this country, " Trump told reporters at his Oval office.

"And I like Modi (Prime Minister Narendra Modi). I like your prime minister a lot. He's a great gentleman. A great gentleman," he added further while briefing the reporters.

But when asked over ties between India and China, the US President said, "They have a big conflict going with India and China. Two countries with 1.4 billion people. Two countries with very powerful militaries. And India is not happy, and probably China is not happy."

Reiterating his offer to mediate between India and China on the border issue, Trump said that he spoke to Prime Minister Narendra Modi, who is not in "good mood" about the ongoing situation with Beijing.

However, informed sources from the Ministry of External Affairs told ANI on Friday that there has been no recent contact between Prime Minister Modi and the US President. The last conversation between them took place on April 4, 2020, on the subject of hydroxychloroquine.

Asked about his Wednesday's tweet regarding his offer to mediate between India and China, Trump said, "I would do that. If they (China and India) thought it would help." However, Trump did not clarify when did he speak to Modi.

Trump on Wednesday tweeted that he is "ready, willing and able to mediate" between India and China."We have informed both India and China that the United States is ready, willing and able to mediate or arbitrate their now raging border dispute," the US President said.

In response to Trump's mediation offer, India said on Thursday that it is engaged with the Chinese side to resolve the border issue peacefully.

India's Ministry of External Affairs spokesperson Anurag Srivastava said that the two sides have established mechanisms both at military and diplomatic levels to resolve situations that may arise in border areas peacefully through dialogue and "continue to remain engaged through these channels."

Indian and Chinese field commanders have been holding talks on de-escalating the tensions.

China has also struck a conciliatory tone on the border issue with India, saying the two countries pose no threat to each other and should resolve their differences through communication, while not allowing them to overshadow bilateral relations.

"We should never let differences overshadow our relations. We should resolve differences through communication. China and India should be good neighbours of harmonious coexistence and good partners to move forward hand in hand," said Chinese Ambassador to India, Sun Weidong, on Wednesday.

The tensions escalated between India and China following a number of confrontations between soldiers of both armies.

Troops of India and China were engaged in two face-offs in Eastern Ladakh and North Sikkim along the disputed Line of Actual Control (LAC), where troops from both sides suffered injuries early this month.

Studies over the anti-malarial drug, which is believed to cure the highly contagious coronavirus, have shown side-effects, according to the Centers for Disease Control and Prevention and the World Health Organisation. But Trump continues to defend his decision to take hydroxychloroquine saying he believes that it gives an additional level of safety.

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News Network
June 6,2020

Islamabad, Jun 6: Pakistan has reported a record 97 COVID-19 deaths in a single day, taking the total number of fatalities to 1,935, while the number of confirmed cases in the country approached 94,000 after over 4,700 infections were detected, the health ministry said on Saturday.

Punjab registered 35,308 COVID-19 cases, Sindh 34,889, Khyber-Pakhtunkhwa 12,459, Balochistan 5,776 Islamabad 4,323, Gilgit-Baltistan 897 and Pakistan-occupied Kashmir 331 cases, the Ministry of National Health Services said.

The total number of COVID-19 cases reached 93,983 after 4,734 new infections were detected across the country, it said.

With a record 97 fatalities in one day, the death toll in the country has reached 1,935, while 32,581 people have recovered from the disease.

The ministry said that the total number of active COVID-19 cases in Pakistan are 59,467, out of which 1,265 patients are in critical condition.

More than 100 labs in the country have so far conducted 660,508 tests, including 22,185 in the last 24 hours.

There are 747 hospitals across the country with COVID-19 treatment facilities where 5,060 patients are being treated. Others have been asked to self-isolate at home.

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News Network
July 18,2020

Global coronavirus infections passed 14 million on Friday, according to a Reuters tally, marking the first time there has been a surge of 1 million cases in under 100 hours.

The first case was reported in China in early January and it took three months to reach 1 million cases. It has taken just four days to climb to 14 million cases from 13 millionrecorded on July 13.

The United States, with more than 3.6 million confirmed cases, is still seeing huge daily jumps in its first wave of Covid-19 infections. The United States reported a daily global record of more than 77,000 new infections on Thursday, while Sweden has reported 77,281 total cases since the pandemic began.

Despite the surging cases, a cultural divide is growing in the country over wearing masks to slow the spread of the virus, a precaution routinely taken in many other nations.

U.S. President Donald Trump and his followers have resisted a full-throated endorsement of masks and have been calling for a return to normal economic activity and reopening schools despite the surging cases.

COVID-19 Pandemic Tracker: 15 countries with the highest number of coronavirus cases, deaths

Other hard-hit countries have “flattened the curve” and are easing lockdowns put in place to slow the spread of the novel virus while others, such as the cities of Barcelona and Melbourne, are implementing a second round of local shutdowns.

The number of cases globally is around triple that of severe influenza illnesses recorded annually, according to the World Health Organization.

The pandemic has now killed more than 590,000 people in almost seven months, edging towards the upper range of yearly influenza deaths reported worldwide. The first death was reported on Jan. 10 in Wuhan, China before infections and fatalities then surged in Europe and later in the United States.

The Reuters tally, which is based on government reports, shows the disease is accelerating the fastest in the Americas, which account for more than half the world’s infections and half its deaths.
In Brazil, more than 2 million people have tested positive including President Jair Bolsonaro, and more than 76,000 people have died.

India, the only other country with more than 1 millioncases, has been grappling with an average of almost 30,000 new infections each day for the last week.

Those countries were the main drivers behind the World Health Organization on Friday reporting a record one-day increase in global coronavirus cases of 237,743.

In countries with limited testing capacity, case numbers reflect only a proportion of total infections. Experts say official data likely under-represents both infections and deaths.

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