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 8,2020

New York, May 8: An Indian-American father and daughter, both doctors in New Jersey, have died due to the COVID-19, with Governor Phil Murphy describing their demise as “particularly tough" and hailed them for dedicating their lives for others.

Satyender Dev Khanna, 78, was a surgeon who served both on staff and as the head of the surgical departments for multiple hospitals across New Jersey for decades.

Priya Khanna, 43, was a double board-certified in both internal medicine and nephrology. She was Chief of Residents at Union Hospital, now part of RWJ Barnabas Health.

"Dr Satyender Dev Khanna and Dr Priya Khanna were father and daughter. They both dedicated their lives to helping others. This is a family dedicated to health and medicine. Our words cannot amply express our condolences," New Jersey Governor Murphy tweeted on Thursday.

“Both dedicated their lives to helping others and we lost both of them to COVID-19,” Murphy said during a press conference on Thursday, saying their demise is a "particularly tough one.”

Satyender passed away at the Clara Maass Medical Center where he had worked for more than 35 years.

Murphy described him as a "pioneering doctor” who was one of the first surgeons to perform laparoscopic surgery in the state. He is being remembered by colleagues as a “gentle and caring physician."

“And for a doctor, I'm not one, but I would bet, I don't think there could be a more fitting way to be remembered, or a nurse or a healthcare worker of any kind,” Murphy said, adding that the doctor had a passion for bicycling, and he often found peace from the hustle of the hospital in biking along the Jersey Shore.

Priya did all of her medical training in New Jersey and then did her fellowship in nephrology in South Jersey with the Cooper Health System. Like her father, she too worked at Clara Maass, where she died.

She was also Medical Director at two dialysis centres in Essex County and “took pride” in teaching the next generation of doctors, Murphy said, adding that the ICU physician who cared for Priya Khanna was trained and taught by her as well.

Follow live developments on the coronavirus pandemic here

“Priya will be remembered as a caring and selfless person who put others first. And even while in the hospital, fighting her own battle, she continued to check up on her mom and dad and her family,” Murphy said.

“This is a family, by the way, dedicated to health and medicine,” he said.

The governor spoke with Satyender's wife Komlish Khanna, who is a paediatrician. The couple has two more daughters - Sugandha Khanna, an emergency medicine physician and Anisha Khanna, a paediatrician.

“Unbelievable. Our words cannot amply express our condolences nor, I am sure, can they express the pain that the Khanna family is feeling. But I hope that the fact that our entire state mourns with them is some small comfort. And we mourn everyone we have lost. We commit in their memory to saving as many lives as we can,” Murphy said.

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News Network
April 16,2020

Brussels/Amsterdam, Apr 16: As the novel coronavirus continues to wreak havoc in the western world since its outbreak in Wuhan last December, researchers believe that the Chinese leadership is trying to absolve President Xi Jinping by using a section of the western media to influence public opinion globally.

"There are clear indications that China is conducting activities in a persistent and systematic manner to influence public opinion-making, academia, think tanks and political decision-making among the member states of the Belt and Road Initiative (BRI) in general and western capital cities in particular," Siegfried O Wolf, Director of Research at Brussels-based think tank South Asia Democratic Front, said.

Some western media say some Chinese officials were secretly aware that they were facing a pandemic from the new coronavirus but allowed Wuhan to host a mass banquet for tens of thousands of people and millions began their annual trip home for the Lunar New Year celebrations.

The pandemic has since then affected 210 countries and territories around the world. Over 2 million people have been declared positive in which over 134,000 lost their lives.

"The frequency and extra-ordinary large scale of Chinese sponsored events in European political hubs, like in Brussels, and the subsequent media coverage can be seen as evidence for Beijing's public diplomacy efforts. However, the rising skepticism within the EU regarding Xi Jinping's development projects and the emerging questioning of Chinese sources funding Free Universities, like the one in Berlin, shows that this strategy produced mixed results so far," Wolf said.

He added, "However, one must also state that these efforts helped China to gain certain leverage among many non-Chinese media, western as well as non-western ones. Today, we can observe that China's political leadership tries to instrumentalise this influence for a major image campaign to distract from the fact that it carries the initial responsibility for the dramatic spread of COVID-19 by holding back key information."

Wolf also said that the current internal dynamics in China, like the shirking of responsibilities by the local authorities, are most-likely part of a twofold strategy. Firstly, there is the strategic component - namely, to reaffirm to the general public that the Communist Party of China is still in full control of the situation. The second strategic pillar is one of 'whitewashing'.

"Concretely, Beijing's obvious aim is to distract the domestic and international attention from the real, but hidden causes of the Coronavirus outbreak and its potential reputational and political consequences for Xi Jinping and his BRI," he stated.

Yoana Barakova, a Research Analyst at European Foundation for South Asian Studies (EFSAS), an Amsterdam-based think-tank, said, "The death of Dr. Li Wenliang, one of the very few medical professionals who tried to warn the world in December 2019 about the looming threat, sparked widespread condemnation around the international community in early February. Yet, little did he know that his legacy would continue much later after his demise, with the emboldened Chinese government trying to cover up its missteps through hardcore censorship after being exposed for undermining and underestimating the initial danger."

The researchers believe that the deterioration in press freedom under Jinping's regime has become more evident in recent days, with local authorities trying to control the state narrative by cosmetically placing media's focus on government's superficial attempts to tackle the crisis.

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News Network
June 12,2020

Jun 12: The global number of COVID-19 cases has increased to over 7.5 million, while the death toll was nearing 421,000, according to the Johns Hopkins University.

As of Friday morning, the overall number of cases stood at 7,500,777, while the deaths increased to 420,993, the University's Center for Systems Science and Engineering (CSSE) revealed in its latest update.

The US continues with the world's highest number of confirmed cases and deaths at 2,022,488 and 113,803, respectively, according to the CSSE.

In terms of cases, Brazil comes in the second place with 802,828 infections.

This was followed by Russia (501,800), the UK (292,860), India (286,605), Spain (242,707), Italy (236,142), Peru (214,788), France (192,493), Germany (186,691), Iran (180,156), Turkey (174,023), Chile (154,092), Mexico (133,974), Pakistan (125,933) and Saudi Arabia (116,021), the CSSE figures showed.

Regarding fatalities, the UK continues in the second position after the US with 41,364 COVID-19 deaths, which also accounts for the highest number of fatalities in Europe.

The other countries with over 10,000 deaths are Brazil (40,919), Italy (34,167), France (29,349), Spain (27,136) and Mexico (15,944).

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