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 9,2020

Beijing, May 9: Mounting a strong defence of the ruling Communist Party of China, President Xi Jinping has said the COVID-19 fight has once again shown that the CPC leadership and the country's socialist political system can overcome any challenge.

Xi's comments came as China faced global criticism for its initial inaction to act against the novel coronavirus, which according to Chinese officials emerged in the central Chinese city of Wuhan in December last year.

Pressure is also mounting on Beijing to agree for an international probe on the origins of the vicious virus, including from the Wuhan Institute of Virology (WIV), as claimed by the US leadership.

China curbed the spread of the coronavirus in over a month and brought COVID-19 under control at its first epicentre in Wuhan in about three months, Xi, also the General Secretary of the CPC, said at a symposium held on Friday to get suggestions from non-ruling Communist Party of China (CPC) parties on COVID-19 prevention and control.

He termed the curbing of the COVID-19 pandemic as "hard-won achievements" for the world's most populous country and the second-biggest economy.

The COVID-19 fight has once again shown that the CPC leadership, China's socialist system and its governance system can overcome any challenge and make big contributions to the progress of human civilisation, he said.

Xi said China had basically curbed the spread of the virus in over one month, managed to bring the daily number of new domestically-transmitted cases down to single digits in about two months, and secured decisive achievements in protecting epicentres Wuhan and Hubei province in about three months.

"For a huge country with 1.4 billion people, these are hard-won achievements," he said

Besides the top CPC officials, the symposium was attended by members of the central committees of non-CPC parties in China, the All-China Federation of Industry and Commerce, and persons without party affiliation.

The speakers at the symposium praised the Chinese leadership in handling the crisis, saying it fully demonstrated the political advantage of China's socialist system and showed that China was a major responsible country.

Xi, who is also the head of the People's Liberation Army, praised China's one-party political system governed by the CPC.

His comments on the country's political system came as Beijing is also defending the role of the CPC as US President Donald Trump and Secretary of State Mike Pompeo have blamed the ruling party for not being transparent in the fight against the pandemic.

Both Trump and Pompeo have been pressing Beijing to allow American experts for a probe on whether the virus emerged from the WIV, China's premier research lab where viruses of different types are reportedly researched.

At the symposium attended by the top CPC officials, Xi's leadership came for praise for successfully handling the situation, the state-run Xinhua news agency reported.

"Attendees noted the major strategic achievements in the COVID-19 fight under the strong leadership of the CPC Central Committee with Comrade Xi Jinping at the core," the report said.

The meeting was held amid reports of murmurs of internal criticism within the CPC about Xi's handling of the coronavirus crisis.

While China's move of handling the coronavirus from January 23 by locking down Hubei province and its capital Wuhan to prevent the spread of the virus and curbing it by deploying 42000 medical personnel has been praised, Beijing is criticised for its slow reaction after it emerged in December last year.

China used less than a week to identify the full genome sequence of the novel coronavirus and isolate the virus strain, produced various testing kits and swiftly selected a number of effective drugs and treatments. Different types of vaccines have also entered clinical trials.

President Xi said during the COVID-19 fight, China upheld the centralised and unified leadership of the CPC and concentrated the nation's best doctors, the most advanced equipment and the most needed resources to treat patients, with all treatment expenses covered by the state.

It managed to maximise the testing and cure rates while minimising the infection and fatality rates.

As of Friday, the COVID-19 death toll in China remained at 4,633 with no new fatalities reported for several days while the total number of cases stood at 82,887. In contrast, Chinese officials point out the death toll in the US which has crossed 75,000 with over 1.2 million cases, besides the mounting global toll.

Almost all countries in the world have been under lockdown for weeks to control the spread of the virus.

Xi called for mobilising the whole society, leveraging the institutional strength of concentrating resources to get things done and tapping the composite national strength as well as closely relying on science and technology.

On international cooperation, Xi said China had helped countries and international organisations to the best of its ability, demonstrating the nation's sense of responsibility as a major and responsible country.

Xi also stressed fixing the shortcomings in the country's major epidemic prevention and control mechanism and for the national public health system to raise the ability to deal with major public health emergencies.

He emphasised on targeted and effective measures to guard against the importation of cases and prevent a resurgence of the epidemic.

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News Network
May 30,2020

Washington, May 30: President Donald Trump said Friday he would strip several of Hong Kong's special privileges with the United States and bar some Chinese students from US universities in anger over Beijing's bid to exert control in the financial hub.

In a day of concerted action, the United States and Britain also raised alarm at the UN Security Council over a controversial new security law for Hong Kong, angering Beijing which said the issue had no place at the world body.

In a White House appearance that Trump had teased for a day, the US president attacked China over its treatment of the former British colony, saying it was "diminishing the city's longstanding and proud status."

"This is a tragedy for the people of Hong Kong, the people of China and indeed the people of the world," Trump said.

Trump also said he was terminating the US relationship with the World Health Organization, which he has accused of pro-China bias in its management of the coronavirus crisis.

But Trump was light on specifics and notably avoided personal criticism of President Xi Jinping, with whom he has boasted of having a friendship even as the two powers feud over a rising range of issues.

"I am directing my administration to begin the process of eliminating policy that gives Hong Kong different and special treatment," Trump said.

"This will affect the full range of agreements, from our extradition treaty to our export controls on dual-use technologies and more, with few exceptions," he said.

Secretary of State Mike Pompeo on Wednesday informed Congress that the Trump administration would no longer consider Hong Kong to be separate under US law, but it was up to Trump to spell out the consequences.

China this week pressed ahead on a law that would ban subversion and other perceived offenses against its rule in Hong Kong, which was rocked by months of massive pro-democracy protests last year.

US restricts students

In one move that could have long-reaching consequences, Trump issued an order to ban graduate students from US universities who are connected to China's military.

"For years, the government of China has conducted elicit espionage to steal our industrial secrets, of which there are many," Trump said.

Hawkish Republicans have been clamoring to kick out Chinese students enrolled in sensitive fields. The FBI in February said it was investigating 1,000 cases of Chinese economic espionage and technological theft.

But any move to deter students is unwelcome for US universities, which rely increasingly on tuition from foreigners and have already been hit hard by the COVID-19 shutdown.

China has been the top source of foreign students to the United States for the past decade with nearly 370,000 Chinese at US universities, although Trump's order will not directly affect undergraduates.

Critics say Trump has been eager to fan outrage about China to deflect attention from his own handling of the coronavirus pandemic that has killed more than 100,000 people in the United States, the highest number of deaths of any country.

Chuck Schumer, the top Democrat in the Senate, called Trump's announcement "just pathetic."

Eliot Engel, a Democrat who heads the House Foreign Affairs Committee, noted that Trump treaded lightly on Hong Kong during last year's protests as he sought a trade deal with Xi.

"Now, the president wants to shift the blame for his failures onto China, so he's doing the right thing for the wrong reason," Engel said.

Trump's order could also trigger retaliation. China in March expelled US journalists after the Trump administration tightened visa rules for staff at Chinese state media.

Clash at UN

The United States and Britain earlier in the day urged China to reconsider the Hong Kong law during talks at the UN Security Council, where China wields a veto -- making any formal session, let alone action against Beijing, impossible.

The Western allies raised Hong Kong in an informal, closed-door videoconference where China cannot block the agenda.

They said China was violating an international commitment as the 1984 handover agreement with Britain, in which Beijing promised to maintain the financial hub's separate system until at least 2047, was registered with the United Nations.

"The United States is resolute, and calls upon all UN members states to join us in demanding that the PRC immediately reverse course and honor its international legal commitments to this institution and to the Hong Kong people," said US Ambassador Kelly Craft, referring to the People's Republic of China.  

China demanded that the United States and Britain "immediately stop interfering in Hong Kong affairs," saying the law did not fall under the Security Council's mandate.

"Any attempt to use Hong Kong to interfere in China's internal matters is doomed to fail," warned a statement from China's UN mission.

"There was no consensus, no formal discussion in the Security Council, and the US and the UK's move came to nothing," it said.

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News Network
April 6,2020

New Delhi, April 6: The United States has donated $2.9 million assistance package for India to help the Narendra Modi government brace itself against the coronavirus as countries across the world are coming together to combat the outbreak.

On March 28, the US government, via US Agency for International Development, announced $2.9 million to support India in its response to COVID-19.

"It builds on a foundation of over $1.4 billion in health assistance and nearly $3 billion in total assistance that the US provided to India over the last 20 years," the US Embassy in India said in a statement.

"These new funds will support two organisations, including $2.4 million for USAID's health strengthening project, implemented by Jhpiego, an international non-profit health organisation affiliated with Johns Hopkins University and $500,000 for the World Health Organization (WHO)," the statement said.

The funds will also help India combat the spread of COVID-19, provide care for the affected and support local communities with the tools needed to contain the disease, it added.

Moreover, being a global leader in health and humanitarian response to COVID-19, the US has provided approximately $18.3 million assistance package to ASEAN member countries to fight the contagion.

The funds will be used to prepare laboratories for large-scale testing for the lethal virus, infection prevention and control, enable risk communication, implement public-health emergency plans for border points of entry, activate case-finding and event-based surveillance for influenza-like illnesses, train and equip rapid-responders in investigation and contact-tracing and update training materials for health workers.

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