American mathematicians solve Ramanujan's “deathbed” puzzle

[email protected] (The Hindu)
December 30, 2012

sr


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 26,2020

Seoul, Apr 26: A train presumed to belong to North Korean's Kim Jong-un has been spotted at a station in the state's eastern coastal town of Wonsan amid speculation about the leader's health, a US monitor said on Sunday, citing commercial satellite imagery on the region, Yonhap news agency reported.

According to 38 North-- a website devoted to analysis about North Korea, the imagery showed a train "probably belonging to Kim Jong Un parked at the Leadership Railway Station servicing his Wonsan compound since at least April 21."

"The approximately 250-metre long train, although partially covered by the station's roof, can be seen at a railway station reserved for use by the Kim family. It was not present on April 15 but was present on both April 21 and 23," it said.

"The train's presence does not prove the whereabouts of the North Korean leader or indicate anything about his health, but it does lend weight to reports that Kim is staying at an elite area on the country's eastern coast," it added.

The report came as rumours about his health have spread as Kim apparently skipped an important annual visit to the Kumsusan Palace of the Sun on the occasion of the April 15 birthday of late state founder and his grandfather, Kim Il-sung.

CNN intensified the speculation by reporting earlier last week that the United States is looking into intelligence that Kim is "in grave danger" after surgery.

Seoul officials have disputed recent media reports about Kim, saying there have been no unusual signs from the North. Some said that Kim is presumed to be staying in Wonsan for unspecified reasons.

Washington has also dismissed the reports, with US President Donald Trump calling such reports "incorrect" in a press briefing late last week.

On Saturday, other media reports stated that China has dispatched a team of medical doctors and officials to North Korea "to advise on" Kim, citing multiple unnamed people familiar with the situation.

North Korea's state media, however, has not made any mention of Kim's public activity for two weeks since he was last seen in April 11 presiding over a major party meeting, though it has reported on his handling of routine state affairs, such as sending diplomatic letters.
But not all speculation has proven to be false.

When he was absent from public for about a month in 2014, speculation arose about his health and a political crisis in the secretive state. He later reemerged with a cane and a limp reportedly after having a cyst removed from his ankle.

The 36-year-old leader is known to have various health problems apparently caused by obesity and heavy smoking. He took office as leader of the communist state after his father, Kim Jong-il, died of a heart attack in late 2011.

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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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News Network
July 1,2020

As Peru begins to ease its strict coronavirus lockdown, the country's biggest LGBTQ nightclub opened its doors on Tuesday, but there will be no nighttime revellers; its dance floor will instead be filled with shelves stocked with groceries.

Instead of slinging cocktails at the bar or dancing on stage, ValeTodo Downtown's famed staff of drag queens will sell customers daily household products as the space reopens as a market while nightclubs are ordered to remain closed.

The Peruvian government will lift the lockdown in most regions of the country at the beginning of July but will keep borders closed, as well as nightclubs and bars.

The lockdown has been a struggle for the club's 120 employees like drag queen Belaluh McQueen. Her life completely changed when the government announced the quarantine. Her nights were spent at home, rather than performing as a dancer at the club in vivid-coloured costumes.

"I was very depressed because I have been doing this art for years, but you have to adapt to new challenges for the future," said McQueen, who is identified by her stage name.

Now McQueen is back to work as a grocery store employee, wearing a sequined suit, high heels and a mask. A DJ will play club music as patrons shop. "We have a new job opportunity," McQueen added.

Renamed as Downtown Market, the club, which has been a mainstay hallmark of the local LGBTQ community, ushered in its reopening with an inauguration ceremony.

"Before, I used to come here to dance and have a good time, but now we come to buy," said Alexandra Herrera, a regular attendee of the club. "The thing is to reinvent yourself."

The club's general manager, Claudia Achuy, said that the pandemic impacted the heart of Lima nightlife, but she chose to reopen as a market rather than risk cutting staff. "If we had just stayed as a nightclub we did not have a close horizon or a way of working," Achuy said.

Peru's confirmed coronavirus cases rose to 282,364 with 9,504 associated deaths on Monday, according to government data. It has the second-highest outbreak in Latin America after Brazil, according to a Reuters tally.

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