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
January 24,2020

Beijing, Jan 24: As China stepped up measures to control the spread of coronavirus, locking down Wuhan and Huanggang cities in the Hubei province where several Indians live, the Indian Embassy here has set up hotlines for their assistance.

Chinese officials assured all assistance, including food supply, to the Indians who stayed put in the province, the Indian Embassy here said in a press release on Thursday.

Wuhan and its surrounding area became the epicentre of the coronavirus outbreak as the confirmed cases climbed to over 600 mostly from the city and the province with 17 deaths so far.

China has virtually sealed Wuhan and Huanggang cities, halting all public transport, including flight services, and advised people to stay at home and follow the precautions. The two cities put together have a population of over 17 million people.

Chinese officials said the measures have been taken to prevent the spread of the virus to other cities and the world.

Concerns arose for India too as about 700 Indian students, mostly studying medicine in different Chinese universities, resided in Wuhan and its neighbouring areas.

While many of them were believed to have left home for the Chinese New Year holidays, others remained in the city to complete their academic work. However, the exact number is not yet known.

“The Embassy of India has been receiving queries from Indians in Hubei province as well as their relatives in India in connection with the evolving situation of coronavirus infection in China,” the embassy press release said.

The embassy is in touch with relevant Chinese authorities in Beijing and Wuhan as well as Indians in Hubei Province, especially in Wuhan, it said.

“We are closely monitoring the evolving situation in China, including the advisories issued by the World Health Organisation (WHO),” the embassy said.

According to the embassy, Chinese authorities have assured all assistance to residents of Wuhan, including food supply.

“At present, it is reported that supermarkets (particularly those that are government-run) and e-commerce services, including food delivery, continue to remain operational in Wuhan,” it said.

The embassy has started two hotlines for those who wish to get in touch with the Mission in this regard in the following phone numbers:              +8618612083629 and +8618612083617.

“All are advised to also keep track of the embassy's social media accounts (Twitter:@EoIBeijing; Facebook: India in China) for updates on this evolving situation,” the release said.

Meanwhile, the Chinese Foreign ministry said all assistance would be provided to consular officials of the foreign missions to ensure the safety of the foreigners in the country.

Asked whether China would consider any request from the respective countries to move their citizens out of Wuhan, Chinese Foreign Ministry spokesman Geng Shuang said, “We always help foreign consular officials in China in their official jobs, we offer them all the assistance and convenience necessary and we work to guarantee foreign citizens' legitimate rights and interest in China.”

He said while specific detailed would be provided by local officials, China in principle, has always handled issues according to domestic laws, international laws and bilateral consular agreements.

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Agencies
July 24,2020

Chengdu, Jul 24: China on Friday asked the US to close down its Consulate in Chengdu in retaliation to Washington's decision to shut the Chinese Consulate in Houston.

A statement by the Chinese Foreign Ministry said China has informed the US Embassy of its decision to withdraw its consent for the establishment and operation of the US Consulate General in Chengdu.

This was in response to "unilateral" decision by the US to shut the Houston Consulate. China's decision is legitimate and necessary response to the unreasonable actions of the US, it said.

The US on Wednesday ordered the closure of the Chinese consulate in Houston, a move it said was aimed "to protect American intellectual property and private information."

Reacting strongly to the US move, Chinese Foreign Ministry spokesman Wang Wenbin termed it as an "unprecedented escalation and warned retaliatory measures.

China on Thursday said that "malicious slander" is behind an order by the US government to close its consulate in Houston, Texas, and maintained that its officials have never operated outside ordinary diplomatic norms.

Wang said the order to close the consulate violates international law and basic norms governing international relations, and seriously undermines China-US relations.

This is breaking down the bridge of friendship between the Chinese and American people, Wang said.

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News Network
April 27,2020

Seoul/South Korea, Apr 27: North Korean leader Kim Jong Un is "alive and well", a top security adviser to the South's President Moon Jae-in said, downplaying rumours over Kim's health following his absence from a key anniversary.
"Our government position is firm," said Moon's special adviser on national security Moon Chung-in, in an interview with CNN on Sunday. "Kim Jong Un is alive and well."

The adviser said that Kim had been staying in Wonsan -- a resort town in the country's east -- since April 13, adding: "No suspicious movements have so far been detected."

Conjecture about Kim's health has grown since his conspicuous absence from the April 15 celebrations for the birthday of his grandfather Kim Il Sung, the North's founder -- the most important day in the country's political calendar.

Kim has not made a public appearance since presiding over a Workers' Party politburo meeting on April 11, and the following day state media reported him inspecting fighter jets at an air defence unit.

North Korean leader Kim Jong Un was not gravely ill, two South Korean government sources said on Tuesday, following reports he had undergone a cardiovascular procedure and was now in "grave danger."

His absence unleashed a series of unconfirmed media reports over his condition, which officials in Seoul previously poured cold water on.

"We have nothing to confirm and no special movement has been detected inside North Korea as of now," the South's presidential office said in a statement last week.

South Korea's unification minister Kim Yeon-chul reiterated Monday that remained the case, adding the "confident" conclusion was drawn from "a complex process of intelligence gathering and assessment".

'Grave danger'

Daily NK, an online media outlet run mostly by North Korean defectors, has reported Kim was undergoing treatment after a cardiovascular procedure earlier this month.

Citing an unidentified source inside the country, it said Kim, who is in his mid-30s, had needed urgent treatment due to heavy smoking, obesity and fatigue.

Soon afterwards, CNN reported that Washington was "monitoring intelligence" that Kim was in "grave danger" after undergoing surgery, quoting what it said was an anonymous US official.

US President Donald Trump on Thursday rejected reports that Kim was ailing but declined to state when he was last in touch with him.

On Monday, the official Rodong Sinmun newspaper reported that Kim had sent a message of thanks to workers on the giant Wonsan Kalma coastal tourism project.

It was the latest in a series of reports in recent days of statements issued or actions taken in Kim's name, although none has carried any pictures of him.

Satellite images reviewed by 38North, a US-based think tank, showed a train probably belonging to Kim at a station in Wonsan last week.

It cautioned that the train's presence did not "indicate anything about his health" but did "lend weight" to reports he was staying on the country's eastern coast.

Reporting from inside the isolated North is notoriously difficult, especially regarding anything to do with its leadership, which is among its most closely guarded secrets.

Previous absences from the public eye on Kim's part have prompted speculation about his health.

In 2014 he dropped out of sight for nearly six weeks before reappearing with a cane. Days later, the South's spy agency said he had undergone surgery to remove a cyst from his ankle.

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