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
April 20,2020

Hong Kong, Apr 20: Oil prices collapsed to more than two-decade lows Monday as traders grow concerned that storage facilities are reaching their limits, while equities were mixed, with some support coming from signs that the coronavirus may have peaked in Europe and the United States.

US crude benchmark West Texas Intermediate briefly plunged almost 20 percent to below 15 -- its lowest since 1999 -- as stockpiles continue to build owing to a crash in demand caused by the COVID-19 pandemic.

Analysts said this month's agreement between top producers to slash output by 10 million barrels a day was having little impact on the oil crisis because of lockdowns and travel restrictions that are keeping billions of people at home.

WTI was hit particularly hard as its main US storage facilities in Cushing, Oklahoma, were filling up.

ANZ said "crude oil prices remained under pressure, as projections of weaker demand weigh on sentiment".

"Despite the OPEC+ alliance agreeing to an unprecedented cut in output, the physical market is awash with oil," it said, referring to the Organization of the Petroleum Exporting Countries and non-OPEC partners.

And AxiCorp's Stephen Innes added: "It's a dump at all cost as no one... wants delivery of oil, with Cushing storage facilities filling by the minute.

"It hasn't taken long for the market to recognise that the OPEC+ deal will not, in its present form, be enough to balance oil markets." Stock traders were in slightly more buoyant mood as governments start to consider how and when to ease lockdowns that have crippled the global economy.

Italy, Spain, France and Britain reported drops in daily death tolls and slowing infection rates.

"We are scoring points against the epidemic," said Prime Minister Edouard Philippe, while insisting "we are not out of the health crisis yet".

Meanwhile, in the US, Andrew Cuomo, governor of badly hit New York state, said the disease was "on the descent", though he cautioned it was "no time to get cocky".

Mounting evidence suggests that the lockdowns and social distancing are slowing the spread of the virus.

That has intensified planning in many countries to begin loosening curbs on movement and easing the crushing pressure on national economies.

Adding to the sense of hope was a report indicating promising research on a drug to treat coronavirus.

Hong Kong, Shanghai and Seoul were each up 0.1 percent, while Wellington added 0.4 percent.

However, Tokyo went into the break 0.9 percent lower, while Sydney and Manila dropped one percent apiece. There were also losses in Taipei, Singapore and Jakarta.

"The longer investors have to contemplate future economic issues while they wait for more countries to be on the downward slope of the pandemic curve, the more scope there is of risk assets pricing in a difficult future," Chris Iggo, of AXA Investment Managers UK, said.

Investors are keeping an eye on Washington, where Congress and the White House are working towards a 450 billion economic relief plan for small business to add to the trillions already pledged to support the economy.

Big-name companies including IBM, Netflix and Coca-Cola are due to deliver their earnings reports.

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News Network
March 21,2020

United Nations, Mar 21: The UN has called on all nations to stop the use of capital punishment or put a moratorium on it, a day after four men convicted of gang-raping and murdering a 23-year-old woman were hanged in India.

Seven years after the rape and murder of the young medical student, who came to be known as 'Nirbhaya', sent shock waves across the country, the four convicts - Mukesh Singh (32), Pawan Gupta (25), Vinay Sharma (26) and Akshay Kumar Singh (31) - were hanged to death on Friday at 5.30 am in New Delhi's Tihar Jail.

Responding to the hanging, UN Secretary-General Antonio Guterres' spokesperson Stephane Dujarric said the world organisation calls on all nations to stop the use of capital punishment or put a moratorium on it.

"Our position has been clear, is that we call on all States to halt the use of capital punishment or at least put a moratorium on this," Dujarric said at the daily press briefing on Friday.

The horrific gang-rape and murder of the physiotherapy intern on December 16, 2012, who came to be known as Nirbhaya, the fearless, had seared the nation's soul and triggered countrywide outrage.

This was the first time that four men have been hanged together in Tihar Jail, South Asia's largest prison complex that houses more than 16,000 inmates.

The executions were carried out after the men exhausted every possible legal avenue to escape the gallows. Their desperate attempts only postponed the inevitable by less than two months after the first date of execution was set for January 22.

The execution of the four convicts brings the curtains down on the case that shook not just India but also the world with the details of its brutality The widespread protests subsequently paved the way for a change in India's rape laws.

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Agencies
June 28,2020

Paris, Jun 28: More than 10 million cases of the new coronavirus have been officially declared around the world, half of them in Europe and the United States, according to an AFP tally on Sunday based on official sources.

At least 10,003,942 infections, including 498,779 deaths, have been registered globally.

Europe remains the hardest hit continent with 2,637,546 cases including 195,975 fatalities, while the United States has 2,510,323 infections including 125,539 deaths.

The rate of infections worldwide continues to rise, with one million new cases recorded in just six days.

The tallies, using data collected by AFP from national authorities and information from the World Health Organization (WHO), probably reflect only a fraction of the actual number of infections.

Many countries are testing only symptomatic or the most serious cases and some do not have the capacity to carry out widescale testing.

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