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.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
News Network
January 23,2020

Beijing, Jan 23: China is putting on lockdown a city of 11 million people considered the epicenter of the new coronavirus outbreak that has killed 17 and infected nearly 600 people, as health authorities around the world work to prevent a global pandemic.

The previously unknown coronavirus strain is believed to have emerged late last year from illegally traded wildlife at an animal market in the central Chinese city of Wuhan. Cases have been detected as far away as the United States, stoking fears the virus is already spreading worldwide.

Wuhan's local government said it would shut down all urban transport networks and suspend outgoing flights from the city as of 10 a.m. (0200 GMT) Thursday, state media reported, adding that the government is urging citizens to not leave the city in the absence of special circumstances.

Contrasting with its secrecy over the 2002-03 Severe Acute Respiratory Syndrome (SARS), which killed nearly 800 people, China's communist government has this time given regular updates to try to avoid panic as millions of people travel for the Chinese Lunar New Year holiday.

Chinese authorities have confirmed 571 cases and 17 deaths as of end-Wednesday, state television reported on Thursday. There are eight other known cases around the world - Thailand has confirmed four cases, while the United States, Taiwan, South Korea and Japan have each reported one.

Vice Premier Sun Chunlan said during a visit to Wuhan that authorities needed to be open about the spread of the virus and their efforts to contain it, the official Xinhua news agency reported on Thursday, comments likely to reassure global health experts.

After a meeting at its Geneva headquarters on Wednesday, the World Health Organization (WHO) said it would decide on Thursday whether to declare the outbreak a global health emergency, which would step up the international response.

If it does so, it will be the sixth international public health emergency to be declared in the last decade.

WHO Director-General Tedros Adhanom Ghebreyesus told reporters in Geneva that China's actions so far were "very strong" but called in Beijing to take "more and significant measures to limit or minimise the international spread".

"We stressed to them that by having a strong action not only they will control the outbreak in their country but they will also minimise the chances of this outbreak spreading internationally. So they recognise that," he said.

A senior U.S. State Department official also called on China to "play a bigger role in global health so they taking more and significant measures to limit or minimise the international spread".

"The lack of transparency in the past, especially with SARS ... gives us concern that that may be the case here," the official said, adding however that there were "positive signs that they have taken action in Wuhan".

Fears of a pandemic initially spooked markets but they regained their footing on Wednesday, with investors citing the robust response from authorities as reassuring.

VIRUS SPREADING

The outbreak began in Wuhan, a major transportation hub as well as central China's main industrial and commercial centre, and has now spread to other major population centers including Beijing, Shanghai and Hong Kong.

There is no known cure for the virus. Symptoms include fever, difficulty in breathing and cough, similar to many other respiratory illnesses, and can cause pneumonia.

Chinese authorities are still investigating the origins of the virus, though they confirmed the outbreak began at a market in Wuhan with illegal wildlife transactions and that it can spread from one person to another via respiratory transmission. Among confirmed patients are 15 medical workers, further adding to worries about a possible global pandemic.

Many Chinese were canceling trips, buying face masks, avoiding public places such as cinemas and shopping centers, and even turning to an online plague simulation game as a way to cope.

Airports globally stepped up screening passengers from China and the European Centre for Disease Control and Prevention (ECDC) said in a risk assessment that further global spread of the virus was likely.

Britain joined other countries including Australia in advising citizens against all but essential travel to Wuhan.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
Agencies
January 15,2020

Washington, Jan 15: The historic impeachment trial of US President Donald Trump will begin on Tuesday next week, Mitch McConnell, the leader of the Senate's Republican majority, has announced.

Earlier on Tuesday (January 14), Speaker Nancy Pelosi ended the standoff between the Senate and the Democratic-controlled House of Representatives saying that it would vote on next Tuesday to send the impeachment documents to the upper house so it can hold the trial on charges that Trump obstructed Congress and abused presidential powers.

This will be only the third time in the nation's history that a US president is tried after impeachment and Trump can expect to be acquitted like his two predecessors - Bill Clinton in 1998 and Andrew Johnson in 1868 - because there won't be a two-thirds majority to convict and remove him from office.

McConnel told reporters on Tuesday that preparations like swearing in the Senators as jurors for the trial could begin this week ahead of the formal start on next Tuesday.

"This Impeachment Hoax is an outrage," Trump tweeted, repeating his longstanding complaint about it, when the move to hold the trial finally appeared to gain traction.

"The American people deserve the truth and the Constitution demands a trial," Pelosi said.

She had held on to the Articles of Impeachment - the chargesheet against Trump - that the House voted on December 18 in a bid to pressure McConnell to accept her terms for holding the trial and in an attempt to get some Republican senators to break ranks on procedural matters.

But she has agreed to let the process move forward, without an agreement on the main Democratic demand to call in their witnesses at the trial and to introduce new evidence.

The House Intelligence Committee, which conducted the investigation against the president, on Tuesday released what it said was new evidence from Lev Parnas, a former associate of Trump's personal lawyer Rudy Giuliani. Parnas is facing criminal charges.

Pelosi said that starting the trial without witnesses or documents "a pure political cover-up."

The impeachment process is only an investigation by the House and the framing of the chargesheet for the Senate trial that will be presided over by Chief Justice John Roberts with the Senators as jurors and nominees of the House as prosecutors.

While there is no chance for removal of Trump from office, Democrats see the Senate trial as a propaganda mechanism ahead of the elections in November by giving the charges against Trump another public airing and turning voter opinion against Republican senators facing re-election.

Trump called for an outright dismissal of the impeachment by the Senate, but McConnell said, "There is little or no sentiment in the Republican conference for a motion to dismiss."

He added, "Our members feel that we have an obligation to listen to the arguments."

Trump tweeted that by not dismissing the impeachment out of hand, the Senate trial was giving "credence to a trial based on the no evidence, no crime" and "the partisan Democrat Witch Hunt credibility."

Pelosi had hoped to make some Republican senators break ranks with the leaders on the procedures for the trial and has partially succeeded in this as at least four of them appear open to witnesses being called.

While Trump's conviction and ouster from office is virtually impossible because of the two-thirds vote requirement in the 100-member Senate, only a simple majority is required on procedural matters. The Republicans have 53 members and four of them shifting positions could make a difference here.

McConnell appeared confident that he would have a hold on his party senators to set the rules for the trial.

Whether witnesses would be called to testify is still open as the Republicans have said that it would be decided when the trial starts.

The main sticking point is the Democrats demand to call their witnesses to testify at the trial.

The Democrats did not allow the Republicans to call their own witnesses to testify during the impeachment proceeding in the House and Republicans did not seem inclined to oblige them in the Senate.

Trump tweeted, "'We demand fairness' shouts Pelosi and the Do Nothing Democrats, yet the Dems in the House wouldn't let us have 1 witness, no lawyers or even ask questions."

The charges against Trump stem from a July phone call he had with Ukraine's President Volodymyr Zelensky in which he asked him as a "favour" to investigate former Vice President Joe Biden and his son Hunter.

Democrats say that this was an abuse power and amounted to inviting foreign interference in US elections as Biden is the leading candidate for the Democratic nomination to run against Trump in this year's election.

They also say that he withheld crucial military aid to Ukraine, a US ally against Russia, to pressure Zelensky and this endangered US national security. Trump said he delayed the aid to make sure the new government stomped out corruption.

Hunter Biden, who was made to leave the Navy because of alleged drug use and had no experience in the energy industry or in Ukrainian businesses was appointed a director of a gas company there and received monthly payments of $83,000, according to Republicans.

The former vice president, who was looking after Ukrainians affairs, had a prosecutor looking into gas company removed.

He and the Democrats say that it was because the prosecutor was corrupt, while Republicans see it as a conflict of interest.

The obstruction of Congress resulted from Trump's refusal to provide documents that the House demanded and allow some administration officials to testify at the House hearings.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.
News Network
June 6,2020

Washington, Jun 6: US President Donald Trump has said that countries like India and China would have much more coronavirus cases than America, the worst-hit country in the world, if they conduct more tests.

Trump, in his remarks at Puritan Medical Products in Maine, said that the US has carried out 20 million tests.

Compared to the US, Germany is at four million and much talked about South Korea is about three million tests, he said on Friday.

According to Johns Hopkins Coronavirus Resource Center, the US has reported nearly 1.9 million cases and over 1,09,000 deaths, making America the worst affected country, while the total number of coronavirus cases in India and China stand at 2,36,184 and 84,177 respectively.

India has so far conducted over 4 million coronavirus tests, according to the health ministry.

Commenting on the COVID-19 tests in the US, Trump said: "We will be well over 20 million tests. Remember this, when you test more, you have more cases.

"I say to my people every time we test; you find cases because we do more testing. If we have more cases, if we wanted to do testing in China or in India or other places, I promise you there would be more cases... you are doing a fantastic job in getting out the swabs".

Puritan is one of the only manufacturers in the world producing the high-quality medical swabs that are crucial for rapid testing.

"And every swab you make at Puritan is proudly stamped with the beautiful phrase made in the USA."

"Thanks to the testing capacity that you are making possible, our country is reopening and our economy is recovering like nobody would've thought possible," he said.

Referring to the latest monthly employment numbers, Trump said that the economy is now back on track.

"We absolutely shattered expectations, and this is the largest monthly jobs increase in American history, think of that; that's a long time.

"I think it's more than double or about double of what our highest was before so this is the largest monthly job increase in American history. And we're going to have a phenomenal next year. We're going to have a tremendous couple of months prior to the election on November 3 very, very important date," the president said.

Seeking re-election for his second consecutive term, Trump is pitted against Democratic presidential nominee Joe Biden in November 3 presidential elections. Most of the opinion polls shows that Biden is several points ahead of Trump.

"It's going to be a very important election because the only thing that can screw it up is if you get the wrong president and they raise your taxes, and they open up your borders so that everybody pours into our country," Trump said.

Reiterating that he has built a strong economy in the last three years, Trump vowed to bring the economy back on track, which has been badly hit by the coronavirus pandemic.

Describing the fight against coronavirus as the greatest national and industrial mobilisation since the World War II, Trump said that his administration has marshaled the full power of the US government and US industry to defeat the invisible enemy.

"It is indeed an enemy. It came from China, should have been stopped in China. They didn't do that," he alleged.

The administration, he said, has delivered over 1.5 billion pieces of personal protective equipment to doctors and nurses on the front lines. "We slashed the red tape to speed up the development of vaccines. And vaccines are coming along incredibly well, wait till you see, and therapeutics. And we partnered at private sector leaders such as Puritan to build the largest and most advanced testing capacity on the face of the earth, like this one," he said.

The Puritan factory in Maine, he said, quickly ramped up the production to produce nearly 20 million foam tipped swabs each month.

"Then in April, my administration invoked the Defence Production Act to help you scale up even more. Under a USD 75 million public-private partnership, Puritan will soon double production to 40 million swabs per month," Trump added.

Comments

Add new comment

  • Coastaldigest.com reserves the right to delete or block any comments.
  • Coastaldigset.com is not responsible for its readers’ comments.
  • Comments that are abusive, incendiary or irrelevant are strictly prohibited.
  • Please use a genuine email ID and provide your name to avoid reject.