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
June 23,2020

Jun 23: US President Donald Trump has issued a proclamation to suspend issuing of H-1B visas, which is popular among Indian IT professionals, along with other foreign work visas for the rest of the year.

Trump said the step was essential to help millions of Americans who have lost their jobs due to the current economic crisis.

Issuing the proclamation ahead of the November presidential elections, Trump has ignored the mounting opposition to the order by various business organisations, lawmakers and human rights bodies.

The proclamation that comes into effect on June 24, is expected to impact a large number of Indian IT professionals and several American and Indian companies who were issued H-1B visas by the US government for the fiscal year 2021 beginning October 1.

They would now have to wait at least till the end of the current year before approaching the US diplomatic missions to get stamping. It would also impact a large number of Indian IT professionals who are seeking renewal of their H-1B visas.

“In the administration of our Nation's immigration system, we must remain mindful of the impact of foreign workers on the United States labour market, particularly in the current extraordinary environment of high domestic unemployment and depressed demand for labour,” said the proclamation issued by Trump.

In his proclamation, Trump said that the overall unemployment rate in the United States nearly quadrupled between February and May of 2020 -- producing some of the most extreme unemployment rates ever recorded by the Bureau of Labor Statistics.

While the May rate of 13.3 percent reflects a marked decline from April, millions of Americans remain out of work.

The proclamation also extends till the end of the year his previous executive order that had banned issuing of new green cards of lawful permanent residency.

Green card holders, once admitted pursuant to immigrant visas, are granted "open-market" employment authorisation documents, allowing them immediate eligibility to compete for almost any job, in any sector of the economy, he said.

“American workers compete against foreign nationals for jobs in every sector of our economy, including against millions of aliens who enter the United States to perform temporary work. Temporary workers are often accompanied by their spouses and children, many of whom also compete against American workers,” Trump said.

“Under ordinary circumstances, properly administered temporary worker programmes can provide benefits to the economy. But under the extraordinary circumstances of the economic contraction resulting from the COVID-19 outbreak, certain non-immigrant visa programmes authorising such employment pose an unusual threat to the employment of American workers,” he said.

For example, Trump said, between February and April of 2020, more than 17 million United States jobs were lost in industries in which employers are seeking to fill worker positions tied to H-2B nonimmigrant visas.

“During this same period, more than 20 million United States workers lost their jobs in key industries where employers are currently requesting H-1B and L workers to fill positions,” he said.

“Also, the May unemployment rate for young Americans, who compete with certain J non-immigrant visa applicants, has been particularly high -- 29.9 percent for 16-19-year-olds, and 23.2 percent for the 20-24-year-old group,” he said.

“The entry of additional workers through the H-1B, H-2B, J, and L non-immigrant visa programmes, therefore, presents a significant threat to employment opportunities for Americans affected by the extraordinary economic disruptions caused by the COVID-19 outbreak,” Trump said.

Trump observed that excess labour supply is particularly harmful to workers at the margin between employment and unemployment -- those who are typically "last in" during an economic expansion and "first out" during an economic contraction.

In recent years, these workers have been disproportionately represented by historically disadvantaged groups, including African Americans and other minorities, those without a college degree, and Americans with disabilities, he said.

The proclamation suspends and limits entry into the US of H-1B, H-2B and L visas and their dependents till December 31, 2020. It also includes certain categories of J visas like an intern, trainee, teacher, camp counselor, or summer work travel programme.

The new rule would apply only to those who are outside the US, do not have a valid non-immigrant visa and an official travel document other than a visa to enter the country.

According to the proclamation, it does not have an impact on lawful permanent residents of the United States and foreign nationals who are spouses or child of an American citizen.

Foreign nationals seeking to enter the US to provide temporary labour or services essential to the food supply chain are also exempted from the latest proclamation.

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News Network
April 24,2020

Paris, Apr 24: The worldwide death toll from the coronavirus pandemic crossed 190,000 on Friday, with nearly two-thirds of the fatalities in Europe, according to an AFP tally compiled from official sources at 0740 GMT.

A total of 190,089 people have died and 2,698,733 been infected since the virus emerged in China in December. The hardest hit continent is Europe, with 116,221 deaths and 1,296,248 cases.

The country with the most deaths is the United States with 49,963, followed by Italy with 25,549, Spain with 22,157, France with 21,856 and Britain 18,738.

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Agencies
April 14,2020

The US Commission on International Religious Freedom (USCIRF) has reprimanded the Imran Khan government for denying food aid to Hindus and Christians in Pakistan amid the coronavirus pandemic and warned that it will trigger an additional crisis due to religious discrimination.

The USCIRF is an independent federal government entity set up by the US Congress to monitor and report on religious freedom in the world.

Pakistan continues to be in the tier one of the USCIRF list of the countries whose record on religious freedom remains abysmal.

In a statement issue on Monday, the USCIRF said it was troubled by the reports of food aid being denied to Hindus and Christians in Pakistan amid pandemic.

Citing one of the examples of religious discrimination, the USCIRF said that in Karachi, the Saylani Welfare International Trust, a non-government organization set up to help the homeless and seasonal workers, has been refusing food aid to Hindus and Christians and providing it only Muslims.

Describing such actions "reprehensible", the USCIRF commissioner Anurima Bhargava said: "As COVID-19 continues to spread, vulnerable communities within Pakistan are fighting hunger and to keep their families safe and healthy. Food aid must not be denied because of one's faith."
One of the USCIRF commissioners, Johnnie Moore warned that if the Khan government continued with such policies, Pakistan would add an additional crisis.

"In a recent address by Prime Minister Khan to the international community, he highlighted that the challenge facing governments in the developing world is to save people from dying of hunger while also trying to halt the spread of COVID-19. This is a monumental task laying before many countries.

"Prime Minister Khan's government has the opportunity to lead the way but they must not leave religious minorities behind. Otherwise, they may add on top of it all one more crisis, created by religious discrimination and inter-communal strife."

The organization which makes foreign policy recommendations to the US President, the Secretary of State, and Congress, urged the Pakistani government to ensure that food aid from distributing organizations is shared equally with Hindus, Christians, and other religions minorities.

Last year, in its annual report, the USCIRF had noted that Hindus and Christians in Pakistan "face continued threats to their security and are subjected to various forms of harassment and social exclusion".

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