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
May 25,2020

Beijing, May 25: China has reported 51 new coronavirus cases including 40 asymptomatic infections, majority of them in the contagion's first epicentre Wuhan, where over six million tests have been conducted in the last 10 days, health officials said on Monday.

The country's National Health Commission (NHC) said that 11 new imported cases were reported on Sunday.

While no new domestically-transmitted COVID-19 cases were reported in China on Sunday, 11 imported cases including 10 in the Inner Mongolia Autonomous Region and one in Sichuan province were reported, the NHC said in its daily report.

Out of the 40 new asymptomatic cases, 38 were reported in Wuhan, which is currently undergoing mass testing of its over 11.2 million people after a spike in the asymptomatic cases.

Currently, 396 people with asymptomatic symptoms are under medical observation in China, including 326 in Wuhan, according to the health authority.

Asymptomatic cases refer to the patients who have tested COVID-19 positive but develop no symptoms such as fever, cough or sore throat. However, they pose a risk of spreading the disease to others.

Wuhan, which earlier had over 50,000 cases between January and March, started a campaign on May 14 to expand the nucleic acid testing in order to better know the number of asymptomatic cases or people who show no clear symptoms despite carrying the virus.

According to the latest figures released by the Wuhan municipal health commission, the city conducted more than 6 million nucleic acid tests between May 14 and 23.

On Saturday, the city carried out nearly 1.15 million tests, state-run Xinhua news agency reported on Monday.

Nucleic acid testing is a molecular technique for screening blood donations to reduce the risk of transfusion transmitted infections.

As of Sunday, a total of 82,985 confirmed COVID-19 cases have been reported in China with 4,634 fatalities, the NHC added.

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News Network
February 22,2020

Johannesburg, Feb 22: To meet shortage of skilled nursing staff, private hospitals in South Africa are recruiting senior Indian nurses for their good work ethics and ability to become efficient trainers for the local staff, according to a media report.

A report at a 2018 jobs summit indicated that the country had a shortage of more than 47,000 nurses.

The shortage of the skilled nursing staff has been attributed to several factors, including preference of highly qualified nurses to emigrate or take up contract employment in countries such as the UK, the United Aarb Emirates, Saudi Arabia or New Zealand for want of higher salaries, a report in the weekly Business Times said.

Mediclinic, one of South Africa's largest private hospital groups, confirmed that it is recruiting 150 nurses from India this year.

“To supplement our training, as an internal strategy, we will continue to recruit senior registered nurses from India,” a Mediclinic spokesperson told the Business Times.

Mediclinic started recruiting nurses from India in 2005 but could not provide details about how many among the more than 8,800 nurses it employs at its hospitals are from India.

Another company, Life Healthcare SA, said it employed 135 Indian nurses between 2008 and 2014.

Top managements at the hospital groups lauded senior Indian nurses as being very efficient trainers for local staff.

“But we find that many of them prefer coming here on short-term contracts due to family commitments," a hospital executive said on the basis of anonymity.

The official said that the few who apply for long-term positions are usually young newly-qualified nurses, which is not the group in demand.

“They work hard, with a patient-oriented work ethic, and do not have the nine-to-five approach of many local nurses, especially those who are unionised," the official said.

“We would be very happy to take in more nursing staff from India," the official added.

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Agencies
June 10,2020

Houston, Jun 10: George Floyd was fondly remembered Tuesday as “Big Floyd” — a father and brother, athlete and neighborhood mentor, and now a catalyst for change — at a funeral for the black man whose death has sparked a global reckoning over police brutality and racial prejudice.

More than 500 mourners wearing masks against the coronavirus packed a Houston church a little more than two weeks after Floyd was pinned to the pavement by a white Minneapolis police officer who put a knee on his neck for what prosecutors said was 8 minutes and 46 seconds.

Cellphone video of the encounter, including Floyd’s pleas of “I can’t breathe,” ignited protests and scattered violence across the U.S. and around the world, turning the 46-year-old Floyd — a man who in life was little known beyond the public housing project where he was raised in Houston’s Third Ward — into a worldwide symbol of injustice.

“Third Ward, Cuney Homes, that’s where he was born at,” Floyd’s brother, Rodney, told mourners at the Fountain of Praise church. “But everybody is going to remember him around the world. He is going to change the world.”

The funeral capped six days of mourning for Floyd in three cities: Raeford, North Carolina, near where he was born; Houston, where he grew up; and Minneapolis, where he died. The memorials have drawn the families of other black victims whose names have become familiar in the debate over race and justice — among them, Eric Garner, Michael Brown, Ahmaud Arbery and Trayvon Martin.

After the service, Floyd’s golden casket was taken by hearse to the cemetery in the Houston suburb of Pearland to be entombed next to his mother, for whom he cried out as he lay dying. A mile from the graveyard, the casket was transferred to a glass-sided carriage drawn by a pair of white horses. A brass band played as his casket was taken inside the mausoleum.

Hundreds of people, some chanting, “Say his name, George Floyd,” gathered along the procession route and outside the cemetery entrance in the mid-90s heat.

“I don’t want to see any black man, any man, but most definitely not a black man sitting on the ground in the hands of bad police,” said Marcus Brooks, 47, who set up a tent with other graduates of Jack Yates High School, Floyd’s alma mater.

In the past two weeks, amid the furor over Floyd’s death, sweeping and previously unthinkable things have taken place: Confederate statues have been toppled, and many cities are debating overhauling, dismantling or cutting funding for police departments. Authorities in some places have barred police from using chokeholds or are otherwise rethinking policies on the use of force.

Dozens of Floyd’s family members, most dressed in white, took part in the four-hour service. Grammy-winning singer Ne-Yo was among those who sang.

The mourners included actors Jamie Foxx and Channing Tatum, J.J. Watt of the NFL’s Houston Texans, rapper Trae tha Truth, Rep. Sheila Jackson Lee, Houston Police Chief Art Acevedo and Houston Mayor Sylvester Turner, who brought the crowd to its feet when he announced he will sign an executive order banning chokeholds in the city.

“I know you have a lot of questions that no child should have to ask, questions that too many black children have had to ask for generations: Why? Why is Daddy gone?” former Vice President Joe Biden, the Democratic presidential candidate, said, addressing Floyd’s 6-year-old daughter in a video eulogy played at the service. “Now is the time for racial justice. That’s the answer we must give to our children when they ask why.”

Biden made no mention of his opponent in November. But other speakers took swipes at President Donald Trump, who has ignored demands to address racial bias and has called on authorities to crack down hard on lawlessness.

“The president talks about bringing in the military, but he did not say one word about 8 minutes and 46 seconds of police murder of George Floyd,” said the Rev. Al Sharpton, the civil rights activist. “He challenged China on human rights. But what about the human right of George Floyd?”

Most of the pews were full, with relatively little space between people.

“So much for social distancing today,” the Rev. Remus Wright told mourners, gently but firmly instructing those attending to wear face masks.

Texas has no limit on how many people can gather in places of worship during the pandemic, though Republican Gov. Greg Abbott has encouraged churches to follow federal health guidelines.

Although the church service was private, at least 50 people gathered outside to pay their respects.

“There’s a real big change going on, and everybody, especially black, right now should be a part of that,” said Kersey Biagase, who traveled more than three hours from Port Barre, Louisiana, with his girlfriend, Brandy Pickney. They wore T-shirts printed with Floyd’s name and “I Can’t Breathe.”

Floyd served nearly five years in prison for robbery with a deadly weapon before becoming a mentor and a church outreach volunteer in Houston. He moved to Minnesota several years ago through a program that tried to change men’s lives by helping them find work in new settings.

At the time of his death, Floyd was out of work as a bouncer at a Minneapolis club that had closed because of the coronavirus outbreak. He was seized by police after being accused of passing a counterfeit $20 bill at a convenience store.

Four Minneapolis officers were arrested in his death: Derek Chauvin, 44, was charged with second-degree murder. J. Alexander Kueng, Thomas Lane and Tou Thao were charged with aiding and abetting. All four could get up to 40 years in prison.

Some of the mostly peaceful demonstrations that erupted after Floyd’s death were marked by bursts of arson, assaults, vandalism and smash-and-grab raids on businesses, with more than 10,000 people arrested. But protests in recent days have been overwhelmingly peaceful.

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