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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May 6,2020

Singapore, May 6: Oil prices slipped back Wednesday after two days of gains, although Brent crude remained above $30 a barrel, as renewed US-China tensions offset optimism about the easing of coronavirus lockdowns.

Brent, the international benchmark, fell 1.1 per cent to $30.63 a barrel in early Asian trade. On Tuesday, the contract surged 14 per cent and rose above $30 for the first time since mid-April.

US marker West Texas Intermediate slipped 1.9 per cent and was changing hands for $24.13 a barrel.

Oil markets have been battered as the virus strangled demand due to business closures and travel restrictions, with US crude falling into negative territory last month for the first time.

They started rallying strongly this week as countries from Europe to Asia ease curbs and economies start shuddering back to life.

But gains were capped Wednesday as dealers follow a brewing US-China row after Donald Trump hit out at Beijing over its handling of the outbreak, saying it began in a Wuhan lab, but so far offering no evidence.

"Traders are incredibly cautious this morning, weighing all the possible China responses," said Stephen Innes, chief global market strategist at AxiCorp.

"And the one that would hurt the most would be for China to reduce imports of US oil."

This week's rally was in part driven by a deal agreed between top producers to reduce output by almost 10 million barrels a day, which came into effect on May 1.

There have also been signs that the massive oversupply in the market is starting to ease as demand slowly comes back.

Energy data provider Genscape said earlier this week that stockpiles at the main US oil depot in Cushing, Oklahoma had increased by only 1.8 million barrels last week following weeks of major rises.

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May 12,2020

May 12: Gunmen stormed a hospital on Tuesday in an ongoing attack in the Afghan capital Kabul, as a suicide blast killed 15 people at a funeral in the country's restive east.

Special forces rescued 80 people including mothers and babies from the Kabul hospital after three gunmen launched a morning assault, killing at least four people, the interior ministry said in a statement.

Heavily armed forces were seen carrying babies wrapped in blankets away from the scene, as the clearance operation continued.

The facility, which has a large maternity ward, is located in the west of the city, home to the capital's minority Shiite Hazara community -- a frequent target of Sunni militants from the Islamic State group.

The flare-up in violence comes as Afghanistan grapples with myriad crises including a rise in militant operations across the country and a surge in coronavirus infections.

A paediatrician who fled the hospital told AFP he heard a loud explosion at the entrance of the building.

"The hospital was full of patients and doctors, there was total panic inside," he said, asking not to be named.

The maternity services at the hospital are supported by humanitarian organisation Doctors Without Borders (MSF).

"Hospitals and health workers must not be attacked. We call on all sides to stop attacking hospitals and health workers," said deputy health minister in the city, Waheed Majroh.

Around an hour later, a suicide bomber killed at least 15 people at the funeral of a local police commander in the country's eastern Nangarhar province, according to provincial spokesman Ataullah Khogyani.

The attacker detonated his explosives in the middle of the ceremony.

Zaher Adel, spokesman for the government hospital in Jalalabad, earlier said 12 bodies had arrived from the blast site and more than 50 people were being treated for injuries.

Amir Mohammad, who was wounded in the blast, said thousands of people had gathered for the funeral, an event which often draws huge crowds in Afghanistan.

The violence comes just a day after four roadside bombs exploded in a northern district of Kabul, wounding four civilians including a child.

The bombings were later claimed by the Islamic State group, according to the SITE intelligence group.

They were just the latest in a string of IS attacks on the capital.

In March, at least 25 people were killed by a gunman at a Sikh temple in Kabul, which was later claimed by the group.

IS is also responsible for an infamous attack in March 2017 on one of the country's largest hospitals, when gunmen disguised as doctors stormed the Kabul building and killed dozens.

In recent months, the jihadist group has suffered mounting setbacks after being hunted by US and Afghan forces as well as Taliban offensives targeting their fighters, but it still retains the ability to launch major assaults on urban centres.

The Taliban have largely refrained from launching large attacks on Afghan cities since February when they signed a landmark withdrawal deal with the US meant to pave the way for peace talks with the Kabul government.

Under the agreement, the Taliban promised not to target forces from the US-led coalition, but made no such pledge toward Afghan troops and have stepped up attacks in the provinces.

The Taliban have denied involvement in both of Tuesday's attacks.

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April 24,2020

Paris, Apr 24: The worldwide death toll from the coronavirus pandemic crossed 190,000 on Friday, with nearly two-thirds of the fatalities in Europe, according to an AFP tally compiled from official sources at 0740 GMT.

A total of 190,089 people have died and 2,698,733 been infected since the virus emerged in China in December. The hardest hit continent is Europe, with 116,221 deaths and 1,296,248 cases.

The country with the most deaths is the United States with 49,963, followed by Italy with 25,549, Spain with 22,157, France with 21,856 and Britain 18,738.

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