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 29,2020

Washington, May 29: Reiterating his offer to mediate on the border dispute between India and China, US President Donald Trump has said that he spoke with Narendra Modi about the "big conflict" and asserted that the Indian Prime Minister is not in a "good mood" over the latest flare-ups between the two countries.

Speaking with the reporters in the Oval Office of the White House on Thursday, Trump said a "big conflict" was going on between India and China.

"I like your prime minister a lot. He is a great gentleman," the president said.

"Have a big conflict …India and China. Two countries with 1.4 billion people (each). Two countries with very powerful militaries. India is not happy and probably China is not happy," he said when asked if he was worried about the border situation between India and China.

"I can tell you; I did speak to Prime Minister Modi. He is not in a good mood about what is going on with China," Trump said.

A day earlier, the president offered to mediate between India and China.

Trump on Wednesday said in a tweet that he was "ready, willing and able to mediate" between the two countries.

Responding to a question on his tweet, Trump reiterated his offer, saying if called for help, "I would do that (mediate). If they thought it would help" about "mediate or arbitrate, I would do that," he said.

India on Wednesday said it was engaged with China to peacefully resolve the border row, in a carefully crafted reaction to Trump's offer to arbitrate between the two Asian giants to settle their decades-old dispute.

"We are engaged with the Chinese side to peacefully resolve it," External Affairs Ministry Spokesperson Anurag Srivastava said, replying to a volley of questions at an online media briefing.

While the Chinese Foreign Ministry is yet to react to Trump's tweet which appears to have caught Beijing by surprise, an op-ed in the state-run Global Times said both countries did not need such a help from the US President.

"The latest dispute can be solved bilaterally by China and India. The two countries should keep alert on the US, which exploits every chance to create waves that jeopardise regional peace and order," it said.

In Beijing, Chinese Foreign Ministry spokesman Zhao Lijian said on Wednesday that both China and India have proper mechanisms and communication channels to resolve the issues through dialogue and consultations.

Trump previously offered to mediate between India and Pakistan on the Kashmir issue, a proposal which was rejected by New Delhi.

The situation in eastern Ladakh deteriorated after around 250 Chinese and Indian soldiers were engaged in a violent face-off on the evening of May 5 which spilled over to the next day before the two sides agreed to "disengage" following a meeting at the level of local commanders.

Over 100 Indian and Chinese soldiers were injured in the violence.

The incident in Pangong Tso was followed by a similar incident in north Sikkim on May 9.

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Agencies
March 1,2020

Washington, Mar 1: Beginning April 1, Indians wishing to immigrate to America will now have to pay an additional $50,000 for the EB-5 or the US investor visa, a media report said.

Although, this additional tax would impact all visa categories, it will predominantly create a barrier for people investing in the EB-5 visa programme, the American Bazaar daily said in the report on Friday.

In 2019, the EB-5 investor visa programme, for the first time since the 1990's, increased the minimum investment amount to $900,000.

With this increase in minimum investment, the new 5 per cent additional tax would mean that applicants would have to pay the extra $50,000, when they move money to an escrow account in the US to fulfil their application criterion.

"The changes to the tax on remittances is a reminder to Indians to carefully plan their tax position before making the move to the US," the American Bazaar quoted Mark Davies, Global Chairman, Davies & Associates LLC, as saying.

"People seeking to emigrate who do not wish to pay this tax at source and rather account for it later may wish to move their money ahead of the new rules coming into effect.

"It is possible to pre-emptively move money into an escrow account in the US until such a time as they are ready to proceed with emigration process," he added.

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Agencies
June 29,2020

Tehran, Jun 29: Iran has issued an arrest warrant and asked Interpol for help in detaining President Donald Trump and dozens of others it believes carried out the drone strike that killed a top Iranian general in Baghdad, a local prosecutor reportedly said Monday.

While Trump faces no danger of arrest, the charges underscore the heightened tensions between Iran and the United States since Trump unilaterally withdrew America from Tehran’s nuclear deal with world powers.

Tehran prosecutor Ali Alqasimehr said Trump and more than 30 others whom Iran accuses of involvement in the Jan. 3 strike that killed Gen. Qassem Soleimani in Baghdad face “murder and terrorism charges,” the semiofficial ISNA news agency reported.

Alqasimehr did not identify anyone else sought other than Trump, but stressed that Iran would continue to pursue his prosecution even after his presidency ends.

Interpol, based in Lyon, France, did not immediately respond to a request for comment.

Alqasimehr also was quoted as saying that Iran requested a “red notice” be put out for Trump and the others, which represents the highest level arrest request issued by Interpol. Local authorities end up making the arrests on behalf of the country that request it. The notices cannot force countries to arrest or extradite suspects, but can put government leaders on the spot and limit suspects’ travel.

After receiving a request, Interpol meets by committee and discusses whether or not to share the information with its member states. Interpol has no requirement for making any of the notices public, though some do get published on its website.

It is unlikely Interpol would grant Iran’s request as its guideline for notices forbids it from “undertaking any intervention or activities of a political” nature.

The U.S. killed Soleimani, who oversaw the Revolutionary Guard’s expeditionary Quds Force, and others in the January strike near Baghdad International Airport. It came after months of incidents raising tensions between the two countries and ultimately saw Iran retaliate with a ballistic missile strike targeting American troops in Iraq.

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