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
May 7,2020

Mumbai, May 7: Maharashtra Minister Nawab Malik on Wednesday accused the BJP-led Uttar Pradesh and Karnataka governments of adopting an uncooperative approach in taking back migrant workers hailing from these two states.

Mr Malik said that such a problem has not arisen with other states like Bihar, Rajasthan and another BJP-ruled state, Madhya Pradesh.

"They are creating new hurdles. There are no such problems in case of other states like Bihar, Rajasthan, Madhya Pradesh and West Bengal though.

"The process (of sending back migrants) has been smooth in the case of these states," Mr Malik said.

The NCP leader alleged that the Uttar Pradesh and Karnataka governments either don't want the people hailing from their states to return or are deliberately creating hurdles so that out of job workers do not go back in big numbers.

The Uttar Pradesh and Karnataka government should understand that the migrant workers are not ready mentally to stay back in Maharashtra and want to return to their native states, Mr Malik said.

The NCP minister said the Maharashtra government has been sending the applications received from migrant workers to the nodal officers of their respective native districts.

Once the nodal officers (of the native districts) concerned approve the applications, the workers are sent back either by trains or private vehicles following their medical tests, Mr Malik added.

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Agencies
January 4,2020

Tel Aviv, Jan 4: Israeli Prime Minister Benjamin Netanyahu on Friday came out in the support of Trump administration for carrying out the strike near Baghdad's international airport which led to the killing of Iran's elite IRGC Qassem Soleimani, saying that "The US has the right of self-defence."

"Just as Israel has the right of self-defence, the United States has exactly the same right. Qassem Soleimani is responsible for the death of American citizens and many other innocent people. He was planning more such attacks," PM Benjamin Netanyahu wrote on Twitter.

In another tweet, Netanyahu also credited US President Donald Trump for acting decisively in the operation of Iraq that led to the killing of Qassem Soleimani -- a US-designated terrorist, along with six others.

"President Donald Trump deserves all the credit for acting swiftly, forcefully and decisively. Israel stands with the United States in its just struggle for peace, security and self-defence," he added.

Meanwhile, Iran on Friday vowed to take a "vigorous revenge" over the killing of General Qassem Soleimani, the head of Iran's elite IRGC.

The US had accused Soleimani of orchestrating several attacks on coalition bases in Iraq including the December 27 attack in which American and Iraqi personnel were killed. 

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Agencies
March 26,2020

Washington, Mar 26: Indian-American hoteliers have come forward to rescue the stranded Indian students in the US following implementation of lockdown measures in the country in response to the rapidly-spreading coronavirus pandemic, offering them free accommodation and free meals.

With the students scrambling for a roof over their heads after being asked to vacate their hostels and India banning international flights for a week from March 22 due to the coronavirus pandemic, more than 6,000 rooms in nearly 700 hotels were offered to them by Wednesday following a call from the Indian Embassy.

The Indian Embassy have been running a round-the-clock helpline since last week for the students in the US, who number over 2,50,000.

Most of these hotels offered are in and around universities and colleges, but the hotel owners from across the country have come up in large numbers to the call given by community leaders, who have roped in Asian American Hotel Owners Association (AAHOA) for the purpose.

India's Ambassador to the US Taranjit Singh Sandhu said in a tweet, "It is heartening to see that Indian; Indian-American and other hotel owners are coming forward to help people with accommodation in these testing times. Together we can overcome the fight against COVID19!"

"The Indian community has come together to help the student and many hotel owners have offered their rooms free of cost to them. Many of them are also offering free meals to these students," Chicago-based community leader Nirav Patel told PTI.

Indian-American hotelier couple K K Mehta and Chandra Mehta have offered more than 100 rooms to Indian students at their two prime properties each near the Times Square and Barclays Center in New York City, said Jaipur Foot USA chairman Prem Bhandari on behalf of the hotels.

The Indian Consulate in New York had contacted them about this 10 days ago, he said.

"These students are the future of both India and the United States. All the top Indian-American CEOs, scientists and doctors came to this country as a student. It's our moral duty to help them with our resources," Bhandari said.

Regional director of AAHOA Upper Midwest Kalpesh Joshi said they had created a master list of the availability hotel rooms, which was being constantly updated.

Free accommodation would be allocated in coordination with the Indian Embassy and its consulates, he said.

"The Indian Embassy and its consulates are working tirelessly to get these students rooms," he added.

Joshi has also sent out a video message to his hotelier colleagues: "Because of the coronavirus outbreak, our Indian students in the US are out of shelter. Let's work together. As a hotelier, I would like to request all my hotelier friends to come forward... let's provide some rooms to the students."

Boston-based Computer Society of India (North America) has collaborated with AAHOA to help students and Indian IT professionals searching for emergency accommodation due to the COVID-19 lockdown.

Anyone who is having financial hardship will be given hotel accommodation either free of cost or the rates will not be more than USD 50, said the Computer Society of India (North America).

Minesh Patel, the chairman of Virginia Asian American Store Association, said between Richmond, Norfolk, and Virginia Beach, Indian-American hotel owners can help in arranging accommodation for over 500 Indian students.

Florida-based Vipul Patel, the national president of Asian American Store Owners Association, said support for the Indian students have been pouring in from the Indian-American hoteliers.

"I have not come across any hotel owner who said no to us," Patel said.

Rooms would be allocated to students on the recommendation of the Indian Embassy and its consulates in Houston, Chicago, Atlanta, San Francisco and New York.

The Indian Consulate in New York was the first to take a lead in this regard. It has worked with Hammock Worldwide Hotels and Resorts to provide temporary accommodation for the students at a flat rate of USD 50 per night.

Joshi said that initially there was a suggestion to charge a convenience fee of USD 20-25 per day from the students.

"But when a few of them offered free rooms and free meals, everyone agreed to it," he said.

According to Johns Hopkins University coronavirus tracker, the number of deaths caused by the novel coronavirus in the US rose to 1,031 with 68,572 confirmed cases. The US has the third highest number of confirmed cases behind China and Italy.

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