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
May 21,2020

Washington, May 21: US President Donald Trump China is on a "massive disinformation" campaign and is desperately trying to deflect the "pain and carnage" that it spread throughout the world, US President Donald Trump has said, upping the ante on Beijing over its handling of the coronavirus outbreak.

Trump, who has expressed disappointment over China's handling of the COVID-19 pandemic, claimed that it was the "incompetence" of Beijing that led to the mass killing across the globe. 

"China is on a massive disinformation campaign because they are desperate to have Sleepy Joe Biden win the presidential race so they can continue to rip-off the United States, as they have done for decades, until I came along!" Trump said in a tweet on Wednesday.

"Spokesman speaks stupidly on behalf of China, trying desperately to deflect the pain and carnage that their country spread throughout the world. Its disinformation and propaganda attack on the United States and Europe is a disgrace… It all comes from the top. They could have easily stopped the plague, but they didn't," he said in a series of tweets.

Trump blamed China for spreading the coronavirus globally and accused it of being incompetent.
"Some wacko in China just released a statement blaming everybody other than China for the Virus which has now killed hundreds of thousands of people. Please explain to this dope that it was the 'incompetence of China', and nothing else, that did this mass Worldwide killing!" Trump said.

China has denied covering up the extent of its coronavirus outbreak and accused the US of attempting to divert public attention by insinuating that the virus originated from a virology laboratory in Wuhan.

"China was the first country to report the COVID-19 to the World Health Organisation (WHO), (and) that doesn't mean the virus originated from Wuhan... There has never been any concealment, and we'll never allow any concealment," Chinese Foreign Ministry spokesman Zhao Lijian said last month.

"A discerning person will understand at a glance that the purpose is to create confusion, divert public attention, and shirk their responsibility," he said.

The novel coronavirus which first originated in Wuhan in December last year has claimed 328,120 lives and infected nearly 5 million people globally. The Us is the worst affected country with 93,439 deaths and over 1.5 million infections, according to Johns Hopkins University data.

Meanwhile, the US Senate passed a bill boosting oversight of companies based in China and other nations that could lead to their removal from American stock exchanges.

The Holding Foreign Companies Accountable Act, proposes to increase oversight of Chinese and other foreign companies listed on American exchanges and delist and ban over-the-counter trading for firms that are out of compliance with US regulators for a period of three years.

In a related development, a group of top Republican Senators led by Marco Rubio sent a letter to Secretary of the Treasury Steven Mnuchin following disturbing reports that China's state-owned and-directed enterprises were looking to exploit the economic crisis by buying US and foreign companies.

As companies backed by the Chinese Communist Party (CCP) approach banks to identify the purchase of companies in the US and in Europe affected by the pandemic, the senators urged Mnuchin to protect against the China's and the CCP's predatory economic behaviour during the COVID-19 crisis.

"We write to express our concerns related to the People's Republic of China's (PRC) efforts to exploit the economic crisis wrought by the COVID-19 pandemic to gain control of distressed companies or shirking its international responsibilities amidst a worldwide crisis.

"In both Chinese Communist Party (CCP) and PRC policy documents, Beijing has made no secret of its intentions to dominate strategic industrial and emerging technology sectors as well as influence standards at the expense of liberal, rules-based governance," wrote the senators.

As the crisis reverberates across the globe, the PRC's predatory lending practices — including the use of non-disclosure agreements for bilateral loans — not only damage the fiscal situation of recipient countries but also undermine the international community's ability to respond effectively to the crisis, they said.

"Without US and international pressure for accountability and transparency, those countries that are in debt to the PRC will not have the political cover or protection to open their financial books. Such countries will face the risk of default or a currency crisis, leaving the International Monetary Fund (IMF), World Bank, and Western countries to clean up the PRC's mess," the senators said.

During a campaign round table Katrina Pierson, Senior Advisor to the Trump 2020 Campaign, said that only the US President will defeat the coronavirus, hold China accountable for their negligence, and defend the American people from socialism. 

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Agencies
July 1,2020

The ILO has warned that if another Covid-19 wave hits in the second half of 2020, there would be global working-hour loss of 11.9 percent - equivalent to the loss of 340 million full-time jobs.

According to the 5th edition of International Labour Organisation (ILO) Monitor: Covid-19 and the world of work, the recovery in the global labour market for the rest of the year will be uncertain and incomplete.

The report said that there was a 14 percent drop in global working hours during the second quarter of 2020, equivalent to the loss of 400 million full-time jobs.

The number of working hours lost across the world in the first half of 2020 was significantly worse than previously estimated. The highly uncertain recovery in the second half of the year will not be enough to go back to pre-pandemic levels even in the best scenario, the agency warned.

The baseline model – which assumes a rebound in economic activity in line with existing forecasts, the lifting of workplace restrictions and a recovery in consumption and investment – projects a decrease in working hours of 4.9 percent (equivalent to 140 million full-time jobs) compared to last quarter of 2019.

It says that in the pessimistic scenario, the situation in the second half of 2020 would remain almost as challenging as in the second quarter.

“Even if one assumes better-tailored policy responses – thanks to the lessons learned throughout the first half of the year – there would still be a global working-hour loss of 11.9 per cent at the end of 2020, or 340 million full-time jobs, relative to the fourth quarter of 2019,” it said.

The pessimistic scenario assumes a second pandemic wave and the return of restrictions that would significantly slow recovery. The optimistic scenario assumes that workers’ activities resume quickly, significantly boosting aggregate demand and job creation. With this exceptionally fast recovery, the global loss of working hours would fall to 1.2 per cent (34 million full-time jobs).

The agency said that under the three possible scenarios for recovery in the next six months, “none” sees the global job situation in better shape than it was before lockdown measures began.

“This is why we talk of an uncertain but incomplete recovery even in the best of scenarios for the second half of this year. So there is not going to be a simple or quick recovery,” ILO Director-General Guy Ryder said.

The new figures reflect the worsening situation in many regions over the past weeks, especially in developing economies. Regionally, working time losses for the second quarter were: Americas (18.3 percent), Europe and Central Asia (13.9 percent), Asia and the Pacific (13.5 percent), Arab States (13.2 percent), and Africa (12.1 percent).

The vast majority of the world’s workers (93 per cent) continue to live in countries with some sort of workplace closures, with the Americas experiencing the greatest restrictions.

During the first quarter of the year, an estimated 5.4 percent of global working hours (equivalent to 155 million full-time jobs) were lost relative to the fourth quarter of 2019. Working- hour losses for the second quarter of 2020 relative to the last quarter of 2019 are estimated to reach 14 per cent worldwide (equivalent to 400 million full-time jobs), with the largest reduction (18.3 per cent) occurring in the Americas.

The ILO Monitor also found that women workers have been disproportionately affected by the pandemic, creating a risk that some of the modest progress on gender equality made in recent decades will be lost, and that work-related gender inequality will be exacerbated.

The severe impact of Covid-19 on women workers relates to their over-representation in some of the economic sectors worst affected by the crisis, such as accommodation, food, sales and manufacturing.

Globally, almost 510 million or 40 percent of all employed women work in the four most affected sectors, compared to 36.6 percent of men, it said.

The report said that women also dominate in the domestic work and health and social care work sectors, where they are at greater risk of losing their income and of infection and transmission and are also less likely to have social protection.

The pre-pandemic unequal distribution of unpaid care work has also worsened during the crisis, exacerbated by the closure of schools and care services.

Even as countries have adopted policy measures with unprecedented speed and scope, the ILO Monitor highlights some key challenges ahead, including finding the right balance and sequencing of health, economic and social and policy interventions to produce optimal sustainable labour market outcomes; implementing and sustaining policy interventions at the necessary scale when resources are likely to be increasingly constrained and protecting and promoting the conditions of vulnerable, disadvantaged and hard-hit groups to make labour markets fairer and more equitable.

“The decisions we adopt now will echo in the years to come and beyond 2030. Although countries are at different stages of the pandemic and a lot has been done, we need to redouble our efforts if we want to come out of this crisis in a better shape than when it started,” Ryder said. 

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News Network
June 10,2020

Jun 10: Indian-origin California Senator Kamala Harris has joined former vice president and 2020 Democratic presidential nominee Joe Biden to raise USD 3.5 million for the upcoming November elections.

Tuesday's fundraiser is the second-largest single event haul so far for the Biden campaign, which raised USD 4 million at one event earlier this month.

Harris' presence during the virtual mega fund raiser assumes significance as the Democratic Party leaders consider her to be one of the front-runners to be the nominee for vice president. The 55-year-old lawyer-politician was once considered to be a strong opponent of Biden in the 2020 Democratic primaries.

Introducing Harris to the 1,400 supporters present at the event, Biden underlined the history-breaking nature of her past electoral wins.

"For much of her career, she was the only person in the room who looked like she did," he said.

At the start of the campaign last year, Harris was very critical of Biden. She later endorsed him, months after she decided to withdraw herself from the race to the White House.

During the fundraiser, Harris was effusive in her praise for Biden.

Referring to Biden's meeting with George Floyd's family, she said, "He (Biden)is someone who whether one on one or speaking to the nation always has a sense of how people are experiencing this world, and what their needs are...This moment in the history of our country really represents an extraordinary exercise in contrast."

"On the other hand, we have a Donald Trump who had the gall to dispatch the US military to clear the streets so that he could prance down and then, like a prop, hold up the bible for a photo op," Harris said.

The death of African-American Floyd during police confinement in Minneapolis on May 25 has resulted in widespread protests not only in the US but across the world.

"There are so many contrasts between Joe Biden and Donald Trump that really point to the choice that we as Americans have today," Harris said.

California Lt Governor Eleni Kounalakis also joined the fund raiser.

In his remarks, Biden, 77, said the US is reeling in anguish and anger over the brutal killing of Floyd or the systemic racism that still infects every part of the society. "Harris knows better than anybody," he said.

"At the same time, we're facing the worst economic disaster since the Great Depression. American history is not a fairy tale with a guaranteed ending, a happy ending. This is a battle for the soul of the country.

"It's been a constant tug of war between the American ideal that we all are created equal -- and the harsh reality that racism has long torn us apart...I'm going to ask every American to look where we are now and to think, is this who we are? Is this who we want to be?" Biden asked.

Participating in the questions and answers session, Harris said America has still not fully embraced, acknowledged or addressed its history of racism and its current history of racism.

"One can think of this moment as an inflection moment, and it will require bold action and it will require immediate action...This stresses the importance and the immediacy and the urgency of electing Joe Biden," she said.

Replying to a question, Biden said, "Did you see today where the President of the United States while George Floyd was being buried, was condemning the older man who was knocked down with his head bleeding and everyone walking by. Did you see that? I mean, my lord. What have we become if we abide by this? So much we can do and must do."

Harris said the election is going to be rough and tumble.

"There are very powerful forces that thrive off of the hate and division that Donald Trump has been sowing. This is not going to be easy. And we have about just a few months to get this thing done," she said.

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