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
April 30,2020

Los Angeles, Apr 30: Los Angeles will begin offering coronavirus">coronavirus testing for free to all citizens regardless of whether they have symptoms, Mayor Eric Garcetti said on Wednesday, adding that LA is the first major US city to take such an initiative.

During the press conference, Garcetti announced that all county residents can now get free coronavirus">coronavirus testing. 

He said the announcement will only apply to city residents for now, but that a similar plan is in development for Los Angeles County,
Garcetti also took to Twitter to announce the same. "Announcing that L.A. is now the first major city in America to offer free COVID-19 testing to all residents. 

While priority will still be given to those with symptoms, individuals without symptoms can also be tested. Sign up at Coronavirus.LACity.org/Testing," he said
Under the new guidelines, priority for the same- or next-day testing will still be given to people with symptoms, such as a fever, cough, and shortness of breath. The free testing will also be prioritized for certain critical frontline workers who interact with the public.

Until now, only residents with symptoms as well as essential workers and those in institutional settings like nursing homes could be tested.

On Wednesday, the LA County reported 1,541 new cases, bringing the total to 22,485 - a seven per cent increase since yesterday.

This includes a backlog of cases that were processed. In the city, there were 683 new cases on Wednesday, bringing the total to 10,380 -- a 7 percent increase since yesterday.

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News Network
May 27,2020

Geneva, May 27: The number of confirmed cases of COVID-19 worldwide has increased by nearly 100,000 over the past 24 hours to surpass 5.4 million, the World Health Organisation (WHO) said.

According to the WHO, the global case tally currently stands at 5,404,512 -- a rise by 99,780 over the past day.

The death count worldwide amounts to 343,514 -- an increase by 1,486.

Most cases of infection are recorded in the Americas -- 2,454,452, with 143,739 deaths.

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April 26,2020

Apr 26: The remarkable story of an airman who overcame prejudice to become one of only a handful of Indian fighter pilots in the First World War has emerged in newly-released archive files by the UK's Commonwealth War Graves Commission (CWGC).

Lieutenant Shri Krishna Chanda Welinkar is one of the thousands of moving stories from the war preserved in family correspondence and being brought alive as part of a digitisation project.

The never-before-published files contain thousands of letters, pictures and other papers sent between the Commission and the next of the kin of First World War dead.

Among them is the story of Welinkar, who hailed from Bombay in colonial India. After much hardship and discrimination, he eventually became a pilot and went missing while on patrol over the skies above the Western Front in June 1918.

His family had to wait nearly three years before they finally knew for certain that he had died, and his grave was located.

“For everyone who died in the First World War, there was inevitably a partner, parent or child back home who had questions. The heartbreaking letters in CWGC's archive give us an insight into what it was like for those families trying to come to terms with their loss,” said Andrew Fetherston, chief archivist for CWGC.

“They are stories that show desperate searches for closure, former enemies uniting and, on many occasions, the sad realisation that a missing loved one would always remain so. We are pleased to be able to make this invaluable piece of World War history accessible to a new generation and help deepen our understanding of how the First World War impacted those who were left behind,” he said.

Welinkar was one of the 1.3 million Indians who answered the call to fight for the British Empire. Nearly 74,000 never saw their homeland again and are remembered today in cemeteries and memorials throughout the world, including France, Belgium, the Middle East and Africa.

Welinkar was a well-educated man studying at Cambridge University. He trained to become an aviator in Middlesex and wished to join the Royal Flying Corps, later known as the Royal Air Force.

Upon attempting to enlist, Welinkar encountered the same prejudices as his other fellow Indian airmen and was encouraged to become an air mechanic instead.

He was eventually given a commission in the Royal Flying Corps as an Officer. In 1918, he was posted to France and patrolled the skies above the Western Front.

In June 1918, Lieutenant Welinkar embarked on what would be his final patrol; he did not return and was reported missing. His fate remained unknown for many months afterwards.

The newly-released e-files chronicle the remarkable discovery of Welinkar and his final resting place long after the war had ended. Colonel Barton, who knew Welinkar, acted on behalf of his mother and helped find her missing son. They spoke to former enemies and honed their search to the grave of an unidentified man, buried by the Germans as “Oberleutnant S.C. Wumkar” in a grave in Rouvroy, Belgium.

The body was later moved and reinterred in Hangard Communal Cemetery Extension but it wasn't until the vital clue, found in the original German burial records in February 1921, that it was confirmed beyond doubt this grave was of Welinkar's.

In May 1921, Colonel Barton, on behalf of Welinkar's mother, requested that a Commission headstone be placed on the grave with the following personal inscription: “To the Honoured Memory of One of the Empire's Bravest Sons”.

This records – known as Enquiry Files – are part of a collection of nearly 3,000 files which have never been made available to the public before. Nearly half have been digitised so far, alongside a previously unreleased collection of more than 16,000 photographs held in negatives in the Commission's archive.

The files, internally referred to simply as E-Files, contain correspondence between the CWGC and the next of kin of the war dead. They often contain letters, typed memos between Commission staff and on occasion photos, maps and diagrams.

CWGC only holds an enquiry file for a small proportion of the 1.7 million people it commemorates from the Commonwealth. Today it is only possible to release those surviving records from the First World War because correspondence with families of Second World War casualties often involves people still alive today and cannot be made public for many years, due to the UK's data protection rules.

To date, more than 1,300 of the surviving 3,000 First World War enquiry files have been digitised.

The CWGC commemorates the 1.7 million Commonwealth servicemen and women who died during the two World Wars. It also holds and updates an extensive and accessible records archive, while operating over 23,000 locations in more than 150 countries and territories.

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