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
March 30,2020

Geneva, Mar 30: The number of confirmed COVID-19 cases worldwide has reached 634,835, among them 29,957 fatalities, the World Health Organization (WHO) said on Sunday.

Over the past 24 hours, 63,159 people were confirmed to be infected with the novel coronavirus and 3,464 people died, the WHO said.

According to the latest situation report, the majority of the confirmed cases - more than 361,000 - are presently concentrated in Europe, with Italy leading the tally with over 92,000 cases, followed by Spain with over 72,000 cases, and Germany with over 52,000 cases.

Italy and Spain are also the countries that top the worldwide death toll from COVID-19, with 10,023 and 5,690 fatalities, respectively.

The second most affected region is currently the Americas with over 120,000 verified COVID-19 cases, of which the majority - over 103,000 - have been found in the United States. The US is also the country with the highest single tally of COVID-19 cases at the moment.
The WHO declared COVID-19 a pandemic on March 11.

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News Network
January 8,2020

New Delhi, Jan 8: Iran will welcome any peace initiative by India for de-escalating its tensions with the US after the killing of Iranian military commander Qasem Soleimani, the Iranian envoy here said on Wednesday.

His comments come hours after Iran launched missile strikes against two US military bases in Iraq in retaliation to the killing of its top commander General Qassem Soleimani.

"India usually plays a very good role in (maintaining) peace in the world. At the same time, India belongs to this region. We welcome all initiatives from all countries, especially India as a good friend for us, to not allow escalation (of tensions)," Iranian Ambassador to India Ali Chegeni told reporters after a condolence meeting for Solemani at the country's embassy here.

"We are not for war, we are looking for peace and prosperity for everybody in this region. We welcome any Indian initiative or any project that can help peace and prosperity in this world," he said.

On the Iranian attack on US targets in Iraq, Chegeni said his country retaliated under its right to defend.

Amid spiralling US-Iran tensions over the killing of Soleimani, External Affairs Minister S Jaishankar on Sunday had a conversation with his Iranian counterpart Javad Zarif and US Secretary of State Mike Pompeo, voicing India's concerns over the escalation of tensions.

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