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
January 21,2020

Beijing, Jan 21: The Chinese official investigating a pneumonia outbreak stemming from a new coronavirus said the disease can spread from person to person but can be halted with increased vigilance, as authorities on Tuesday confirmed a fourth death.

Zhong Nanshan said there was no danger of a repeat of the Severe Acute Respiratory Syndrome (SARS) epidemic that killed nearly 800 people globally during a 2002-2003 outbreak, which started in China, as long as precautions were taken.

"It took only two weeks to identify the novel coronavirus," state news agency Xinhua quoted Zhong as saying late on Monday.

The outbreak was still in its early stages and China had good surveillance and quarantine systems to help control it, he added.

The outbreak has spread from the central city of Wuhan to cities including Beijing and Shanghai, with more than 200 cases reported so far. Four cases have been reported outside China - in South Korea, Thailand and Japan.

Australia on Tuesday said it would screen passengers on flights from Wuhan amid rising concerns that the virus will spread globally as Chinese travellers take flights abroad for the Lunar New Year holiday starting this week.

Authorities around the globe, including in the United States and many Asian countries, have stepped up screening of travellers from Wuhan.

Chinese authorities confirmed a total of 217 cases of the virus in China as of 6 p.m. (1000 GMT) on Monday, state television reported, 198 of which were in Wuhan.

A fourth person died on Jan. 19, the Wuhan Municipal Health Commission said. The 89-year-old man, who had underlying health diseases including coronary heart disease, developed symptoms on Jan. 13 and was admitted to hospital five days later, it added.

Zhong, who is renowned in China for his work fighting SARS in 2003, confirmed that the virus can pass from person-to-person.

Fifteen medical workers in Wuhan had been diagnosed with pneumonia, with one other suspected case, the Wuhan Municipal Health Commission said. Of the infected staff, one was in critical condition.

In Shanghai, officials on Tuesday confirmed a second case involving a 35-year-man who had visited Wuhan in early January, and said they were monitoring four other suspected cases.

The virus causes a type of pneumonia and belongs to the same family of coronaviruses as SARS. Symptoms include fever and difficulty in breathing, which are similar to many other respiratory diseases and pose complications for screening efforts.

The World Health Organisation (WHO) said on Monday an animal source appeared most likely to be the primary origin of the outbreak and that some "limited human-to-human transmission" occurred between close contacts.

The Geneva-based U.N. agency convened an emergency committee for Wednesday to assess whether the outbreak constitutes an international health emergency and what measures should be taken to manage it.

So far, the WHO has not recommended trade or travel restrictions, but a panel of independent experts could do so or make other recommendations to limit spread.

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News Network
June 2,2020

Washington, Jun 2: US President Donald Trump said that peaceful protests following the death of African-American man George Floyd in police custody were derailed by acts of domestic terrorism.

"These are not acts of peaceful protests, these are acts of domestic terror - the destruction of innocent life, and the spilling of innocent blood is an offence to humanity and a crime against God," Trump said during a press briefing on Monday.

Trump also added that the chaos is the work of professional agitators and provocateurs - anarchists and the far-left movement Antifa, among others - and put them on notice, vowing to enforce law and order.

He further said, "Those who threaten innocent life and property will be arrested, detained and prosecuted to the fullest extent of the law. I want the organizers of this terror to be on notice that you will face severe criminal penalties and lengthy sentences in jail. This includes Antifa and others who are leading instigators."

The US president also that he is invoking an 1807 law to mobilize the military around the country to "quickly solve the problem."

"I am also taking swift and decisive action to protect our capital Washington DC. As we speak, I am dispatching thousands and thousands of heavily armed soldier, military personnel and enforcement officers to stop the rioting," Trump said during a press briefing.

"I am mobilizing all available federal resources, civilian and military, to stop the rioting and looting, to end the destruction and arson. And to protect the rights of law-abiding Americans, including your Second Amendment rights," he added.

Trump said mayors and governors must establish an "overwhelming law enforcement presence until the violence has been quelled." If the city or state refuses to take the actions, Trump said he would deploy the US military.

Trump on Monday also said that all Americans are rightly 'sickened by the brutal death' of George Floyd and his administration is fully committed to providing justice to George and his family.

"All Americans were rightly sickened and revolted by the brutal death of George Floyd. My administration is fully committed, the justice will be fully served for George and his family and He will not have died in vain," Trump said.

"My first and highest duty as president is to defend and protect the great country and the American people. I have sworn an oath to uphold the laws of our nation and that is exactly what I will do," he added.

After the media address, Trump made a surprise visit to the damaged St Johns church near White House, walking through park violently cleared of protesters. He walked to the church across the street from the White House after tear gas was fired at protesters in the area.

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January 3,2020

Washington, Jan 3: US President Donald Trump ordered the killing of Iran Revolutionary Guards commander Qasem Soleimani, who died in Baghdad "in a decisive defensive action to protect US personnel abroad," the Pentagon said Thursday.

"General Soleimani was actively developing plans to attack American diplomats and service members in Iraq and throughout the region. General Soleimani and his Quds Force were responsible for the deaths of hundreds of American and coalition service members and the wounding of thousands more," the Department of Defense said.

Following Soleimani's death, Trump tweeted an image of the US flag without any further explanation.

"US' act of international terrorism, assassinating General Soleimani—the most effective force fighting Daesh (ISIS), Al Nusrah,Al Qaeda, is extremely dangerous & foolish escalation. US bears responsibility for all consequences of rogue adventurism." said Iran Foreign Minister Javad Zarif.

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