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 7,2020

Dubai/Washington, Jan 7: Iran's Supreme Leader Ayatollah Ali Khamenei wept in grief with hundreds of thousands of mourners thronging Tehran's streets on Monday for the funeral of military commander Qassem Soleimani, killed by a U.S. drone on U.S. President Donald Trump's orders.

The coffins of General Qassem Soleimani and Iraqi militia leader Abu Mahdi al-Muhandis, who also died in Friday's attack in Baghdad, were draped in their national flags and passed from hand to hand over the heads of mourners in central Tehran.

Responding to Trump's threats to hit 52 Iranian sites if Tehran retaliates for the drone strike, Iran's President Hassan Rouhani pointedly wrote on Twitter: "Never threaten the Iranian nation." And Soleimani's successor vowed to expel U.S. forces from the Middle East in revenge.

Khamenei, 80, led prayers at the funeral, pausing as his voice cracked with emotion. Soleimani, 62, was a national hero in Iran, even to many who do not consider themselves supporters of Iran's clerical rulers.

Aerial footage showed people, many clad in black, packing thoroughfares and side streets in the Iranian capital, chanting "Death to America!" - a show of national unity after anti-government protests in November in which many demonstrators were killed.

The crowd, which state media said numbered in the millions, recalled the masses of people that gathered in 1989 for the funeral of the Islamic Republic's founder, Ayatollah Ruhollah Khomeini. Soleimani, architect of Iran's drive to extend its influence across the Middle East, was widely seen as Iran's second most powerful figure behind Khamenei.

His killing of Soleimani has prompted concern around the world that a broader regional conflict could flare.

Trump on Saturday vowed to strike 52 Iranian targets, including cultural sites, if Iran retaliates with attacks on Americans or U.S. assets, and stood by his threat on Sunday, though American officials sought to downplay his reference to cultural targets. The 52 figure, Trump noted, matched the number of U.S. Embassy hostages held for 444 days after the 1979 Iranian Revolution.

Rouhani, regarded as a moderate, responded to Trump on Twitter.

"Those who refer to the number 52 should also remember the number 290. #IR655," Rouhani wrote, referring to the 1988 shooting down of an Iranian airline by a U.S. warship in which 290 were killed.

Trump also took to Twitter to reiterate the White House stance that "Iran will never have a nuclear weapon" but gave no other details.

'ACTIONS WILL BE TAKEN'

General Esmail Ghaani, Soleimani's successor as commander of the Quds Force, the elite unit of Iran's Revolutionary Guards charged with overseas operations, promised to "continue martyr Soleimani's cause as firmly as before with the help of God, and in return for his martyrdom we aim to rid the region of America."

"God the Almighty has promised to take martyr Soleimani's revenge," he told state television. "Certainly, actions will be taken."

Other political and military leaders have made similar, unspecific threats. Iran, which lies at the mouth of the key Gulf oil shipping route, has a range of proxy forces in the region through which it could act.

Iran's demand for U.S. forces to withdraw from the region gained traction on Sunday when Iraq's parliament passed a resolution calling for all foreign troops to leave the country.

Iraqi caretaker Prime Minister Abdel Abdul Mahdi told the U.S. ambassador to Baghdad on Monday that both nations needed to implement the resolution, the premier's office said in a statement. It did not give a timeline.

The United States has about 5,000 troops in Iraq.

Soleimani built a network of proxy militia that formed a crescent of influence - and a direct challenge to the United States and its regional allies led by Saudi Arabia - stretching from Lebanon through Syria and Iraq to Iran. Outside the crescent, Iran nurtured allied Palestinian and Yemeni groups.

He notably mobilised Shi'ite Muslim militia forces in Iraq that helped to crush ISIS, the Sunni militant group that had seized control of swathes of Syria and Iraq in 2014.

Washington, however, blames Soleimani for attacks on U.S. forces and their allies.

The funeral moves to Soleimani's southern home city of Kerman on Tuesday. Zeinab Soleimani, his daughter, told mourners in Tehran that the United States would face a "dark day" for her father's death, adding, "Crazy Trump, don't think that everything is over with my father's martyrdom."

NUCLEAR DEAL

Iran stoked tensions on Sunday by dropping all limitations on its uranium enrichment, another step back from commitments under a landmark deal with major powers in 2015 to curtail its nuclear programme that Trump abandoned in 2018.

In response, European signatories may launch a dispute resolution process against Iran this week that could lead to a renewal of the United Nations sanctions that were lifted as part of the deal, European diplomats said on Monday.

Diplomats said France, Britain and Germany could make a decision ahead of an EU foreign ministers' meeting on Friday that would assess whether there were any ways to salvage the deal.

After quitting the deal, the United States imposed new sanctions on Iran, saying it wanted to halt Iranian oil exports, the main source of government revenues. Iran's economy has been in freefall as the currency has plunged.

Trump adviser Kellyanne Conway said on Monday that he was still confident he could renegotiate a new nuclear agreement "if Iran wants to start behaving like a normal country."

Tehran has said Washington must return to the existing nuclear pact and lift sanctions before any talks can take place.

The United States advised American citizens in Israel and the Palestinian territories to be vigilant, citing the risk of rocket fire amid heightened tensions. As a U.S. ally against Iran, Israel is concerned about possible rocket attacks from Gaza, ruled by Iranian-backed Palestinian Islamists, or major Iran proxy Hezbollah in Lebanon.

Democratic critics of Trump have said the Republican president was reckless in authorising the strike, with some saying his threat to hit cultural sites amounted to a vow to commit war crimes. Trump also threatened sanctions against Iraq and said Baghdad would have to pay Washington for an air base in Iraq if U.S. troops were required to leave.

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News Network
February 11,2020

Feb 11: China reported 108 new coronavirus deaths on February 10, the highest daily toll since the outbreak began in Wuhan late last year, as two senior officials in the hard-hit province of Hubei were removed from their jobs.

The total number of deaths on the mainland reached 1,016 in the 24 hours until midnight, the National Health Commission said on Tuesday.

Some 2,478 new cases were confirmed, bringing the total to 42,638.

Of the new deaths, 103 were in the province of Hubei, including 67 in the provincial capital of Wuhan. The virus is thought to have originated there in a market that sold seafood as well as wild animals.

Two senior health officials in the province - Zhang Jin who was Party Secretary of the health commission for Hubei and Ling Yingzi who was director of the Hubei Provincial Health Commission - were both removed from their posts, state media reported on Tuesday,  a day after Chinese President Xi Jinping visited health facilities in Beijing.

In his first public appearance since the outbreak began, Xi donned a face mask and had his temperature checked while visiting medical workers and patients in the capital.

"We have seen very little of Xi Jinping since the outbreak began but he was out and about in Beijing on Monday," Al Jazeera's Katrina Yu said from Beijing. "He has been trying to rally the troops saying: 'We can win this battle.' But it's also a sign that the battle is far from over."

The other fatalities on Monday were in the provinces of Heilongjiang, Anhui and Henan and the cities of Tianjin and Beijing, the National Health Commission said.

During a meeting chaired by Premier Li Keqiang on Monday, a group of leaders tasked with beating the virus said it would work to solve raw material and labour shortages and boost supplies of masks and protective clothing.

They said nearly 20,000 medical personnel from around the country had already been sent to Wuhan, and more medical teams were also on the way.

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News Network
April 26,2020

Washington/Seoul, Apr 26: A special train possibly belonging to North Korean leader Kim Jong Un was spotted this week at a resort town in the country, according to satellite images reviewed by a Washington-based North Korea monitoring project, amid conflicting reports about Mr. Kim's health and whereabouts.

The monitoring project, 38 North, said in its report on Saturday that the train was parked at the “leadership station” in Wonsan on April 21 and April 23. The station is reserved for the use of the Kim family, it said.

Though the group said it was probably Kim Jong Un's train, Reuters has not been able to confirm that independently, or whether he was in Wonsan.

“The train's presence does not prove the whereabouts of the North Korean leader or indicate anything about his health but it does lend weight to reports that Kim is staying at an elite area on the country's eastern coast,” the report said.

Speculation about Mr. Kim's health first arose due to his absence from the anniversary of the birthday of North Korea's founding father and Mr. Kim's grandfather, Kim Il Sung, on April 15.

North Korea's state media last reported on Mr. Kim's whereabouts when he presided over a meeting on April 11.

China has dispatched a team to North Korea including medical experts to advise on Kim Jong Un, according to three people familiar with the situation.

A third-generation hereditary leader who came to power after his father's death in 2011, Kim has no clear successor in a nuclear-armed country, which could present major international risk.

On Thursday, U.S. President Donald Trump downplayed reports that Mr. Kim was ill. “I think the report was incorrect,” Mr. Trump told reporters, but he declined to say if he had been in touch with North Korean officials.

Mr. Trump has met Mr. Kim three times in an attempt to persuade him to give up a nuclear weapons program that threatens the United States as well as its Asian neighbors. While talks have stalled, Mr. Trump has continued to hail Mr. Kim as a friend.

Reporting from inside North Korea is notoriously difficult because of tight controls on information.

A Trump administration official said continuing days of North Korean media silence on Mr. Kim's whereabouts had heightened concerns about his condition, and that information remained scant from a country U.S. intelligence has long regarded as a ”black box.”

The U.S. State Department did not immediately respond to questions about the situation on Saturday.

Daily NK, a Seoul-based website that reports on North Korea, cited one unnamed source in North Korea on Monday as saying that Kim had undergone medical treatment in the resort county of Hyangsan north of the capital Pyongyang.

It said that Mr. Kim was recovering after undergoing a cardiovascular procedure on April 12.

Since then, multiple South Korean media reports have cited unnamed sources this week saying that Mr. Kim might be staying in the Wonsan area.

On Friday, local news agency Newsis cited South Korean intelligence sources as reporting that a special train for Mr. Kim's use had been seen in Wonsan, while Mr. Kim's private plane remained in Pyongyang.

Newsis reported Mr. Kim may be sheltering from COVID-19, the respiratory disease caused by the novel coronavirus.

Mr. Kim, believed to be 36, has disappeared from coverage in North Korean state media before. In 2014, he vanished for more than a month and North Korean state TV later showed him walking with a limp.

Speculation about his health has been fanned by his heavy smoking, apparent weight gain since taking power and family history of cardiovascular problems.

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