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
July 1,2020

Melbourne, July 1: Authorities will lock down around 300,000 people in suburbs north of Melbourne for a month from late on Wednesday to contain the risk of infection after two weeks of double-digit rises in new coronavirus cases in Australia's second-most populous state.

Australia has fared better than many countries in the pandemic, with around 7,830 cases and 104 deaths, but the recent surge has stoked fears of a second wave of COVID-19, echoing concerns expressed in other countries.

Globally, coronavirus cases exceeded 10 million on Sunday, a major milestone in the spread of a disease that has killed more than half a million people in seven months.

From midnight, more than 30 suburbs in Australia's second-biggest city will return to stage three restrictions, the third-strictest level in curbs to control the pandemic. That means residents will be confined to home except for grocery shopping, health appointments, work or caregiving, and exercise.

The restrictions will be accompanied by a testing blitz that authorities hope will extend to half the population of the area affected, and for which borders will be patrolled, authorities said. The measures come as curbs ease across the rest of the state of Victoria, with restaurants, gyms and cinemas reopening in recent weeks.

Victoria recorded 73 fresh cases on Tuesday from 20,682 tests, following an increase of 75 cases on Monday. State premier Daniel Andrews warned on Wednesday that the return of broader restrictions across city remained a possibility.

"If we all stick together these next four weeks, we can regain control of that community transmission ... across metropolitan Melbourne," Andrews said at a briefing. "Ultimately if I didn't shut down those postcodes I'd be shutting down all postcodes. We want to avoid that."

Victoria's spike in cases has been linked to staff members at hotels housing returned travellers for which quarantine protocols were not strictly followed. Victorian state authorities have announced an investigation into the matter.

Some other Australian states and territories are preparing to open borders, but applying limits and quarantine measures to citizens of Victoria as the school holiday season gets under way.

South Australia, the country's fifth most populous state, has had just three new cases in the past month. But citing the spike in coronavirus infections, on Tuesday it cancelled its scheduled reopening to other parts of the nation.

New South Wales (NSW), Australia's most populous state, has stopped short of closing its borders to all Victorians, but those holidaying from hotspot areas - not permitted under NSW rules - can be handed a fine of A$11,000 ($7,596) or jailed if they are detected, state authorities said.

The delays reopening internal borders cast doubts over a federal plan to set up "travel bubble" with neighbouring New Zealand that would allow movement between the two countries.

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Agencies
February 23,2020

Washington, Feb 23: U.S. president Donald Trump on Saturday said he was looking forward to being with his "great friends" in India next week as he retweeted a short video in which his face was superimposed on the hit movie-character Bahubali, showing the president as a great saviour bringing peace to his kingdom.

Trump will pay a state visit to India on February 24 and 25, accompanied by a high-level delegation including first lady Melania Trump, his daughter Ivanka, son-in-law Jared Kushner and a galaxy of top American officials.

"Look so forward to being with my great friends India!" Trump said in the tweet.

Along with the tweet, Trump retweeted an 81-second video by a Twitter account identified as "Sol" with the handle Solmemes1.

"To celebrate Trump's visit to India I wanted to make a video to show how in my warped mind it will go... USA and India united!" the handle Solmemes1 tweeted in the original post with the video.

Trump appears as a great saviour, in the short animated clip, riding on a chariot with Melania. A few stills later, Trump is seen riding a horse carrying on his shoulders his son Donald Jr and daughter Ivanka.

Later, he is welcomed by Narendra Modi in a village setting. Hundreds and thousands of people are seen welcoming Trump in the video.

"This week Trump will visit India and in celebration I have created a new meme for the occasion... You few, who are my patrons, get to see it first!" Sol told viewers on subscription content service Patreon on Saturday. A few hours later, Trump retweeted the video.

In the Twitter description, Sol describes herself as "award winning master memetician, professor of memology at University of GFY, my views are my own and not associated with real life."

The Trump-Bahubali video, which ends with "USA and India United", went viral after Trump retweeted it. In a few hours, it was seen by nearly 6 lakh people.

Sol in one of her previous posts, dated January 23, writes she was inspired by a video of Bahubali sent to her by a friend, which is the story of 'good defeating evil.'

This inspired Sol to create her first Bahubali-theme meme. The video, lasting 93 seconds, is titled "Jiyo Re Baahu Trump", in which the first lady is seen wearing a saree. "Jiyo Re Bahubali," is the theme song of the video.

"I just loved this video when I saw it! A friend sent it to me and he told me that it is the story of good defeating evil... it was so fitting I had to make it (meme)..." Sol wrote in her post.

Sol's posts show that she is an admirer of Trump. Sol's January 23 video was released at the peak of Trump's impeachment proceedings.

Trump is seen being greeted by an elephant, which bears the logo of the Republican Party.

Towards the end of the video, Trump is seen riding the elephant, and putting on fire the effigy of "Raavan" marked as "D" in a big circle representing the opposition Democratic Party.

An arrow is given by warrior Narendra Modi to the First Lady, who then passes it on to Trump, before he lights the effigy.

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News Network
January 27,2020

Shanghai, Jan 27: The death toll from a coronavirus outbreak in China rose to 81 on Monday, as the government extended the Lunar New Year holiday and more big businesses shut down or told staff to work from home in an effort to curb the spread.

Chinese Premier Li Keqiang visited the central city of Wuhan, the epicenter of the outbreak, as the government sought to signal it was responding seriously to the crisis.

The total number of confirmed cases in China rose about 30% to 2,744, about half of them in Hubei province, whose capital is Wuhan.

As worries grew around the world, Chinese-ruled Hong Kong, which has had eight confirmed cases, banned entry to people who had visited Hubei in the past 14 days. The ban did not cover Hong Kong residents.

The number of deaths from the flu-like virus in Hubei climbed to 76 from 56, health officials said, with five deaths elsewhere in China, including the southern island province of Hainan, which reported its first fatality on Monday.

While a small number of cases have been confirmed in more than 10 countries, linked to people who traveled from Wuhan, no deaths have been reported elsewhere.

Li is the most senior leader to visit Wuhan since the outbreak began. Clad in a blue protective suit and mask, he inspected efforts to contain the epidemic and spoke to patients and medical staff, the government said.

The government is extending the week-long Lunar New Year holiday by three days to February 2, in a bid to slow the spread of the virus. The Lunar New Year is usually a time for millions of people to travel, but many have had to cancel their plans because of travel curbs over the virus.

Incubation

Wuhan is already in virtual lockdown and severe limits on movement are in place in several other Chinese cities.

The city of 11 million clamped down further on Monday, announcing the suspension of visa and passport services until January 30.

Despite the curbs, the mayor of Wuhan said on Sunday that five million people had left the city for holidays and other reasons.

Images from Wuhan showing hospital corridors packed with people seeking treatment have circulated on social media, along with complaints of soaring prices for essentials such as vegetables.

Chinese leaders have urged transparency in the crisis, after public trust was eroded by the cover-up of the spread of Severe Acute Respiratory Syndrome (SARS), a coronavirus that originated in China and killed nearly 800 people globally in 2002 and 2003.

Much is not known about the newly identified coronavirus, including how easily it spreads and just how dangerous it is. It can cause pneumonia, which has been deadly in some cases.

National Health Commission minister Ma Xiaowei said on Sunday the incubation period could range from one to 14 days, and the virus was infectious during incubation, unlike SARS.

That compares with a World Health Organization (WHO) estimate of two to 10 days for the incubation period.

“Understanding the time when infected patients may transmit the virus to others is critical for control efforts,” the WHO said.

The virus is believed to have originated late last year in a Wuhan market illegally selling wildlife. It has spread to other cities, including Beijing and Shanghai, as well as more than 10 countries including France, Japan and the United States.

‘Overwhelmed’

Australia confirmed its fifth case on Monday involving a woman on the last flight out of Wuhan to Sydney before China’s travel ban.

Health minister Greg Hunt told the Australian Broadcasting Corporation (ABC) authorities aimed to get about 100 Australian children and young people out of Wuhan.

One father of two, Nathan Wang, told the ABC his wife was stuck in Wuhan with the children. “We absolutely want the children to come back, because hospitals in Wuhan are overwhelmed,” he said.

Airports around the world have stepped up screening of passengers from China, although some health experts have questioned its effectiveness.

Last week the WHO stopped short of calling the outbreak a global health emergency, but some health experts question whether China can contain the epidemic.

WHO Director-General Tedros Adhanom Ghebreyesus is due to travel to Beijing to meet officials and health experts.

Australia, France, Italy, Japan and the United States have all said they are working to evacuate citizens from Wuhan.

Some of China’s biggest companies have been affected, with hotpot restaurant chain Haidilao International Holding shutting branches nationwide from Sunday until Friday.

Gaming giant Tencent Holdings Ltd advised staff to work from home until February 7, and e-commerce firm Alibaba removed vendors’ offers of overpriced face masks from its online Taobao marketplace as prices surged.

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