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
July 2,2020

Naypyitaw, Jul 2: A landslide at a jade mine in northern Myanmar has killed at least 113 people, officials say, warning the death toll is likely to rise further.

The incident took place early on Thursday in the jade-rich Hpakant area of Kachin state after a bout of heavy rainfall, the Myanmar Fire Services Department said on Facebook.

"The jade miners were smothered by a wave of mud," the statement said. "A total of 113 bodies have been found so far," it added, raising the death toll from at least 50.

Photos posted on the Facebook page showed a search and rescue team wading through a valley apparently flooded by the mudslide.

'No one could help them'

Maung Khaing, a 38-year-old miner from the area, said he saw a towering pile of waste that looked on the verge of collapse and was about to take a picture when people began shouting "run, run!"

"Within a minute, all the people at the bottom [of the hill] just disappeared," he told Reuters news agency by phone.

"I feel empty in my heart. I still have goosebumps ... There were people stuck in the mud shouting for help, but no one could help them."

Tar Lin Maung, a local official with the information ministry, said authorities had recovered more than 100 bodies.

"Other bodies are in the mud. The numbers are going to rise," he told Reuters.

Fatal landslides are common in the poorly regulated mines of Hpakant, the victims often from impoverished communities who risk their lives hunting the translucent green gemstone.

The government of Myanmar leader Aung San Suu Kyi pledged to clean up the industry when it took power in 2016, but activists say little has changed.

Official sales of jade in Myanmar were worth $750.4m in 2016-2017, according to data published by the government as part of the Extractive Industries Transparency Initiative.

But experts believe the true value of the industry, which mainly exports to China, is much larger.

Northern Myanmar's abundant natural resources - including jade, timber, gold and amber - have also helped finance both sides of a decades-long conflict between ethnic Kachin and the military.

The fight to control the mines and the revenues they bring frequently traps local civilians in the middle.

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News Network
July 6,2020

Beijing, Jul 6: A city in northern China on Sunday sounded an alert after a suspected case of bubonic plague was reported, according to official media here.

Bayannur, Inner Mongolia Autonomous Region, announced a level III warning of plague prevention and control, state-run People’s Daily Online reported.

The suspected bubonic plague case was reported on Saturday by a hospital in Bayannur. The local health authority announced that the warning period will continue until the end of 2020.

"At present, there is a risk of a human plague epidemic spreading in this city. The public should improve its self-protection awareness and ability, and report abnormal health conditions promptly,” the local health authority said.

On July 1, state-run Xinhua news agency said that two suspected cases of bubonic plague reported in Khovd province in western Mongolia have been confirmed by lab test results.

The confirmed cases are a 27-year-old resident and his 17-year-old brother, who are being treated at two separate hospitals in their province, it quoted a health official as saying.

The brothers ate marmot meat, the health official said, warning people not to eat marmot meat.

A total of 146 people who had contact with them have been isolated and treated at local hospitals, according to Narangerel.

Bubonic plague is a bacterial disease that is spread by fleas living on wild rodents such as marmots. It can kill an adult in less than 24 hours if not treated in time, according to the World Health Organization (WHO).

A couple died of bubonic plague in the western Mongolian province of Bayan-Ulgii last year after eating raw marmot meat.

The news of bubonic plague came after Chinese researchers issued an early warning over another potential pandemic caused by an influenza virus in pigs.

Scientists from China Agricultural University, the Chinese Centre for Disease Control and Prevention and other institutes detected a pig influenza virus bearing genotype 4 (G4), which is contagious among pigs and has the possibility of jumping to humans, as the G4 virus is able to bind with human cells, state-run Global Times reported last week.

The researchers are concerned that it could mutate further so that it can spread easily from person to person, and trigger a global outbreak, BBC reported.

"Controlling the prevailing G4 EA H1N1 viruses in pigs and close monitoring in human populations, especially workers in the swine industry, should be urgently implemented," Chinese researchers warned in the paper.

The new diseases were reported even as China grappled with the second attack of Covid-19 in Beijing after controlling it in Wuhan where it was first reported in December last year.

On Saturday, Beijing reported a single-digit Covid-19, local authorities said Sunday.

The number of newly confirmed Covid-19 cases reached a peak in Beijing on June 13 and 14 and then started declining in general, Xinhua quoted local officials as saying.

From June 11 to July 4, the city reported 334 confirmed locally transmitted cases, 47 per cent of whom are workers of the Xinfadi wholesale food market, the official said.

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Agencies
June 6,2020

Seoul, Jun 6: South Korea on Saturday reported 51 new cases of COVID-19, mostly in the densely populated capital region, as authorities scramble to stem transmissions among low-income workers who can't afford to stay home.

The figures announced by South Korea's Centers for Disease Control and Prevention brought national totals to 11,719 workers and 273 deaths.

At least 34 of the new coronavirus cases were linked to door-to-door sellers hired by Richway, a Seoul-based health product provider.

Vice Health Minister Kim Gang-lip said the spread of the virus among Richway sellers was particularly alarming as most of them are in their 60s and 70s. He called for officials to strengthen their efforts to find and examine workplaces vulnerable to infections.

More than 120 infections have also been linked to a massive warehouse operated by Coupang, a local e-commerce giant, which has been accused of failing to properly implement preventive measures and having employees work even when sick.

South Korea was reporting around 500 new cases per day in early March due to a massive outbreak surrounding the southern city of Daegu, before officials managed to stabilize the situation with aggressive tracking and testing.

But the recent resurgence of COVID-19 in the greater capital area, where about half of South Korea's 51 million people live, is now threatening to erase some of the country's hard-won gains. It has also led to second-guessing whether officials were too quick to ease social distancing and reopen schools.

Health authorities and hospital officials on Friday participated in a table-top exercise for sharing hospital capacities between Seoul and nearby cities and ensure swift transports of patients so that a spike of cases in one area doesn't overwhelm its hospital system. 

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