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
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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News Network
February 12,2020

Feb 12: China on Wednesday reported another drop in the number of new cases of a viral infection and 97 more deaths, pushing the total dead past 1,100 as postal services worldwide said delivery was being affected by the cancellation of many flights to China.

The National Health Commission said 2,015 new cases had been reported over the last 24 hours, declining for a second day. The total number of cases in mainland China reached 44,653, although many experts say a large number of others infected have gone uncounted.

The additional deaths raised the mainland toll to 1,113. Two people have died elsewhere, one in Hong Kong and one in the Philippines.

In the port city of Tianjin, just southeast of Beijing, a cluster of cases has been traced to a department store in Baodi district. One-third of Tianjin’s 104 confirmed cases are in Baodi, the Xinhua state news agency reported.

A salesperson working in the store’s small home appliance section became the first individual in the cluster to be diagnosed on Jan. 31, Xinhua said. The store was already closed at that point, then disinfected on Feb. 1. Nevertheless, several more diagnoses soon followed.

The next to have their infections confirmed were also salespeople at the store. They had not visited Wuhan recently and, with the exception of one married couple, the patients worked in different sections of the store and did not know one another, according to Xinhua.

Japan’s Health Ministry said that 39 new cases have been confirmed on a cruise ship quarantined at Yokohama, bringing the total to 174 on the Diamond Princess.

The U.S. Postal Service said that it was “experiencing significant difficulties” in dispatching letters, parcels and express mail to China, including Hong Kong and Macau.

Both the U.S. and Singapore Post said in notes to their global counterparts that they are no longer accepting items destined for China, “until sufficient transport capacity becomes available.”

The Chinese mail service, China Post, said it was disinfecting postal offices, processing centers and vehicles to ensure the virus doesn’t spread via the mail and to protect staff.

It said the crisis is also impacting mail that transits China to other destinations including North Korea, Kazakhstan, Kyrgyzstan, Mongolia, Tajikistan, Turkmenistan, Uzbekistan and Vietnam.

The World Health Organization has named the disease caused by the virus as COVID-19, avoiding any animal or geographic designation to avoid stigmatization and to show the illness comes from a new coronavirus discovered in 2019.

The illness was first reported in December and connected to a food market in the central Chinese city of Wuhan, where the outbreak has largely been concentrated.

Zhong Nanshan, a leading Chinese epidemiologist, said that while the virus outbreak in China may peak this month, the situation at the center of the crisis remains more challenging.

“We still need more time of hard working in Wuhan,” he said, describing the isolation of infected patients there a priority.

“We have to stop more people from being infected,” he said. “The problem of human-to-human transmission has not yet been resolved.”

Without enough facilities to handle the number of cases, Wuhan has been building prefabricated hospitals and converting a gym and other large spaces to house patients and try to isolate them from others.

China’s official media reported Tuesday that the top health officials in Hubei province, of which Wuhan is the capital, have been relieved of their duties. No reasons were given, although the province’s initial response was deemed slow and ineffective. Speculation that higher-level officials could be sacked has simmered, but doing so could spark political infighting and be a tacit admission of responsibility.

The virus outbreak has become the latest political challenge for the party and its leader, Xi Jinping, who despite accruing more political power than any Chinese leader since Mao Zedong, has struggled to handle crises on multiple fronts. These include a sharply slowing domestic economy, the trade war with the U.S. and pushback on China’s increasingly aggressive foreign policies.

China is struggling to restart its economy after the annual Lunar New Year holiday was extended to try to curb the spread of the virus. About 60 million people are under virtual quarantine and many others are still working at home.

In Hong Kong, the diagnosis of four people living in an apartment building prompted worried comparisons with the deadly SARS pandemic of 17 years ago.

More than 100 people were evacuated from the building after a 62-year-old woman diagnosed with the virus was found living 10 floors directly below a man who was earlier confirmed with the virus.

Health officials called it a precautionary measure and sought to assuage fears of an epidemic, dismissing similarities to the SARS community outbreak at the Amoy Gardens housing estate in 2003.

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News Network
February 12,2020

Saint Martin's Island, Feb 12: At least 15 women and children drowned and more than 50 others were missing after a boat overloaded with Rohingya refugees sank off southern Bangladesh as it tried to reach Malaysia Tuesday, officials said.

Some 138 people -- mainly women and children -- were packed on a trawler barely 13 metres (40 feet) long, trying to cross the Bay of Bengal, a coast guard spokesman told news agency.

"It sank because of overloading. The boat was meant to carry maximum 50 people. The boat was also loaded with some cargo," another coast guard spokesman, Hamidul Islam, added.

Nearly one million Rohingya live in squalid camps near Bangladesh's border with Myanmar, many fleeing the neighbouring country after a 2017 brutal military crackdown.

With few opportunities for jobs and education in the camps, thousands have tried to reach other countries like Malaysia and Thailand by attempting the hazardous 2,000-kilometre journey.

In the latest incident, 71 people have been rescued including 46 women. Among the dead, 11 were women and the rest children.

Anwara Begum said two of her sons, aged six and seven, drowned in the tragedy.

"We were four of us in the boat... Another child (son, aged 10) is very sick," the 40-year-old told news agency.

Fishermen tipped off the coast guard after they saw survivors swimming and crying for help in the sea.

The boat's keel hit undersea coral in shallow water off Saint Martin's Island, Bangladesh's southernmost territory, before it sank, survivors said.

"We swam in the sea before boats came and rescued us," said survivor Mohammad Hossain, 20.

Coast guard commander Sohel Rana said three survivors, including a Bangladeshi, were detained over human trafficking allegations.

An estimated 25,000 Rohingya left Bangladesh and Myanmar on boats in 2015 trying to get to Thailand, Malaysia and Indonesia. Hundreds drowned when overloaded boats sank.

Begum said her family paid a Bangladeshi trafficker $450 per head to be taken to Malaysia.

"We're first taken to a hill where we stayed for five days. Then they used three small trawlers to take us to a large trawler, which sank," she said.

Shakirul Islam, a migration expert whose group works with Rohingya to raise awareness against trafficking, said desperation in the camps was making refugees want to leave.

"It was a tragedy waiting to happen," he said.

"They just want to get out, and fall victim to traffickers who are very active in the camps."

Islam said in the past two months dozens of Rohingya reported approaches from traffickers to his OKUP migration rights group.

"Human smuggling and trafficking in the Bay of Bengal is particularly difficult to address as it requires concerted effort from multiple states," the Bangladesh head of UN agency the International Organization for Migration, Giorgi Gigauri, told news agency.

"The gaps in coordination are easily exploited by criminal networks."

Since last year, Bangladeshi authorities have picked up over 500 Rohingya from rickety fishing trawlers or coastal villages as they waited to board boats.

Trafficking often increases during the November-March period when the sea is safest for the small trawlers used by traffickers.

Bangladesh and Myanmar signed a repatriation deal to send back some Rohingya to their homeland, but none have agreed to return because of safety fears.

The charity Save the Children called on Myanmar to "take all necessary steps to ensure the Rohingya community can return to their homes in a safe and dignified manner".

"The tragic drowning of women and children... should be a wake-up call for us all," the group's Athena Rayburn said in a statement.

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