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
May 20,2020

Kensington (United States), May 20: The world cut its daily carbon dioxide emissions by 17% at the peak of the pandemic shutdown last month, a new study found.

But with life and heat-trapping gas levels inching back toward normal, the brief pollution break will likely be “a drop in the ocean" when it comes to climate change, scientists said.

In their study of carbon dioxide emissions during the coronavirus pandemic, an international team of scientists calculated that pollution levels are heading back up — and for the year will end up between 4% and 7% lower than 2019 levels.

That's still the biggest annual drop in carbon emissions since World War II.

It'll be 7% if the strictest lockdown rules remain all year long across much of the globe, 4% if they are lifted soon.

For a week in April, the United States cut its carbon dioxide levels by about one-third.

China, the world's biggest emitter of heat-trapping gases, sliced its carbon pollution by nearly a quarter in February, according to a study Tuesday in the journal Nature Climate Change. India and Europe cut emissions by 26% and 27% respectively.

The biggest global drop was from April 4 through 9 when the world was spewing 18.7 million tons (17 million metric tons) of carbon pollution a day less than it was doing on New Year's Day.

Such low global emission levels haven't been recorded since 2006. But if the world returns to its slowly increasing pollution levels next year, the temporary reduction amounts to ''a drop in the ocean," said study lead author Corinne LeQuere, a climate scientist at the University of East Anglia.

“It's like you have a bath filled with water and you're turning off the tap for 10 seconds," she said.

By April 30, the world carbon pollution levels had grown by 3.3 million tons (3 million metric tons) a day from its low point earlier in the month. Carbon dioxide stays in the air for about a century.

Outside experts praised the study as the most comprehensive yet, saying it shows how much effort is needed to prevent dangerous levels of further global warming.

“That underscores a simple truth: Individual behavior alone ... won't get us there,” Pennsylvania State University climate scientist Michael Mann, who wasn't part of the study, said in an email.

“We need fundamental structural change.”

If the world could keep up annual emission cuts like this without a pandemic for a couple decades, there's a decent chance Earth can avoid warming another 1.8 degrees (1 degree Celsius) of warming from now, study authors said. But getting the type of yearly cuts to reach that international goal is unlikely, they said.

If next year returns to 2019 pollution levels, it means the world has only bought about a year's delay in hitting the extra 1.8 degrees (1 degree Celsius) of warming that leaders are trying to avoid, LeQuere said. That level could still occur anywhere from 2050 to 2070, the authors said.

The study was carried out by Global Carbon Project, a consortium of international scientists that produces the authoritative annual estimate of carbon dioxide emissions. They looked at 450 databases showing daily energy use and introduced a measurement scale for pandemic-related societal “confinement” in its estimates.

Nearly half the emission reductions came from less transportation pollution, mostly involving cars and trucks, the authors said. By contrast, the study found that drastic reductions in air travel only accounted for 10% of the overall pollution drop.

In the US, the biggest pollution declines were seen in California and Washington with plunges of more than 40%.

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News Network
January 28,2020

Jan 28: China said on Tuesday that 106 people had died from a new coronavirus that is spreading across the country, up from the previous toll of 81.

The number of total confirmed cases in China rose to 4,515 as of Jan. 27, the National Health Commission said in a statement, up from 2,835 reported a day earlier.

The United States warned against travel to China on Monday and Canada issued a more narrow travel warning as the death toll from the spreading coronavirus passed 100, with tens of millions stranded during the biggest holiday of the year and global markets rattled.

Global stocks fell, oil prices hit three-month lows, and China's yuan dipped to its weakest level in 2020 as investors fretted about damage to the world's second-biggest economy from travel bans and the Lunar New Year holiday, which China extended in a bid to keep people at home.

The health commission of China's Hubei province said on Tuesday that 100 people had died from the virus as of Jan. 27, according to an online statement, up from the previous toll of 76, with the number of confirmed cases in the province rose to 2,714.

Other fatalities have been reported elsewhere in China, including the first in Beijing, bringing the deal toll to 106 so far, according to the People's Daily. The state newspaper put the total number of confirmed cases in China at 4,193, though some experts suspect a much higher number.

On Monday, US President Donald Trump offered China whatever help it needed, while the State Department said Americans should "reconsider" visiting all of China due to the virus.

Canada, which has two confirmed cases of the virus and is investigating 19 more potential cases, warned its citizens to avoid travel to China's Hubei province, at the heart of the outbreak.

Authorities in Hubei province are taking increasing flak from the public over their initial response to the virus. Chinese Premier Li Keqiang visited the city of Wuhan, epicentre of the outbreak, to encourage medical workers and promise reinforcements.

Visiting Wuhan in blue protective suit and mask, Li praised medics, said 2,500 more workers would join them in the next two days, and visited the site of a new hospital to be built in days.

The most senior leader to visit Wuhan since the outbreak, Li was shown on state TV leading medical workers in chants of "Wuhan jiayou!" - an exhortation to keep their strength up.

China's ambassador to the United Nations, following a meeting with UN Secretary-General António Guterres on Monday, said "the Chinese government attaches paramount importance to prevention and control of the epidemic, and President Xi Jinping has given important instructions. ...

"China has been working with the international community in the spirit of openness, transparency and scientific coordination," he said.

Guterres said in a statement, "The UN appreciates China's effort, has full confidence in China's ability of controlling the outbreak, and stands ready to provide any support and assistance."

MOUNTING ANGER

On China's heavily censored social media, officials have faced mounting anger over the virus, which is thought to have originated from a market where wildlife was sold illegally.

Some criticised the governor of Hubei province, of which Wuhan is the capital, after he corrected himself twice during a news conference over the number of face masks being produced.

"If he can mess up the data multiple times, no wonder the disease has spread so severely," said one user of the Weibo social media platform.

In rare public self-criticism, Wuhan Mayor Zhou Xianwang said the city's management of the crisis was "not good enough" and indicated he was willing to resign.

The central Chinese city of 11 million people is in virtual lockdown and much of Hubei, home to nearly 60 million people, is under travel curbs.

Elsewhere in China, people from the region faced questioning about their movements. "Hubei people are getting discriminated against," a Wuhan resident complained on Weibo.

Cases linked to people who travelled from Wuhan have been confirmed in a dozen countries, from Japan to the United States, where authorities said they had 110 people under investigation in 26 states. Sri Lanka was the latest to confirm a case.

INVESTORS WORRIED

Investors are worried about the impact. The consensus is that in the short term, economic output will be hit as authorities limit travel and extend the week-long New Year holiday — when millions traditionally travel by rail, road and plane - by three days to limit spread of the virus.

Asian and European shares tumbled, with Japan's Nikkei average sliding 2%, its biggest one-day fall in five months. Demand spiked for safe-haven assets such as the Japanese yen and Treasury notes. European stocks fell more than 2%.

The US S&P 500 closed down nearly 1.6%.

"China is the biggest driver of global growth so this couldn't have started in a worse place," said Alec Young, FTSE Russell's managing director of global markets research.

During the 2002-2003 outbreak of Severe Acute Respiratory Syndrome (SARS), which originated in China and killed nearly 800 people globally, air passenger demand in Asia plunged 45%. The travel industry is more reliant on Chinese travellers now.

Chinese-ruled Hong Kong, which has had eight cases, banned entry to people who had visited Hubei recently.

Some European tour operators cancelled trips to China, while governments around the world worked on repatriating nationals.

Officially known as 2019-nCoV, the newly identified coronavirus can cause pneumonia, but it is still too early to know just how dangerous it is and how easily it spreads.

"What we know about this virus it that transmission occurs through human contact but we are speaking of close contact, i.e. less than a meter," said Jerome Salomon, a senior official with France's health ministry.

"Crossing someone (infected) in the street poses no threat," he said. "The risk is low when you spend a little time near that person and becomes higher when you spend a lot of time near that person."

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Agencies
February 20,2020

Tokyo, Feb 20: One more Indian on board the cruise ship Diamond Princess quarantined off the coast of Japan was tested positive for novel coronavirus, the Indian Embassy in Tokyo said on Wednesday, adding that all seven Indian nationals infected with the virus have been shifted to hospitals in Japan for treatment.

"1 Indian crew who tested positive for #COVID19 among 88 new cases yesterday on #DiamondPrincess taken to hospital for treatment. Indians receiving treatment responding well. From today, the disembarkation of passengers only started, likely to continue till 21 Feb," the embassy tweeted.

"As of 2100 JST, altogether 7 Indian nationals (crew members on board #DiamondPrincess) are receiving treatment in hospitals in Japan, after testing positive for #COVID19 over last few days. Their health conditions are improving. 
@MEAIndia," the following tweet read.

A total of 138 Indians, including 132 crew and 6 passengers, were among the 3,711 people on board the luxury cruise ship which was quarantine off Japan on February 5 after it emerged that a former passenger had tested positive for the virus.

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