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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Agencies
April 28,2020

United Nations, Apr 28: UN chief Antonio Guterres has warned that extremist groups are taking advantage of the COVID-19 lockdowns and intensifying efforts on social media to recruit youths online by exploiting their anger and despair, asserting that the world cannot afford a lost generation due to the unprecedented global health crisis.

The UN Secretary-General made the remarks on Monday during a video conference to review the five years since its adoption of a landmark resolution on youth, peace and security.

We can already see such groups taking advantage of the COVID-19 lockdowns, intensifying their efforts on social media to spread hatred and to recruit young people who may be spending more time at home and online, he said.

Guterres told the Security Council that even before the current crisis, young people were facing enormous challenges.

Listing startling numbers, he said one of every five young people was already not in education, training or employment and one of every four is affected by violence or conflict. Every year, 12 million girls become mothers while they themselves are still children.

These frustrations and, frankly, failures to address them by those in power today, fuel declining confidence in political establishments and institutions. And when such a cycle takes hold, it is all too easy for extremist groups to exploit the anger and despair, and the risk of radicalisation climbs, he said.

Issuing a call to action on youth, peace and security, Guterres said the world cannot afford a lost generation of youth, their lives set back by COVID-19 and their voices stifled by a lack of participation. Let us do far more to tap their talents as we tackle the pandemic and chart a recovery that leads to a more peaceful, sustainable and equitable future for all.

With over 1.54 billion children and youth out-of-school and young people acutely feeling the impact of the COVID-19 crisis, Guterres said countries must do more to harness the talents of young people to address the crisis and its aftermath.

In presenting his first report on the Security Council resolution, the UN chief said youth were already confronting numerous challenges even before the pandemic, including in accessing education, or through being affected by violence and conflict. Those pressing for peace or upholding human rights have been threatened.

Despite these obstacles, young people across the world have joined the common fight against the coronavirus disease, supporting both frontline workers and people in need. And they continue to push for change.

UN Youth Envoy Jayathma Wickramanayake spoke of the need for more meaningful partnerships between young people and the civil society organisations and government institutions that work on the youth, peace and security (YPS) agenda.

To date, there are no national action plans on YPS but I'm pleased to note that in some countries, these are in the process of development, she said.

For a national roadmap to be successful, a participatory, transparent and youth-led process with adequate resources are needed, she said.

Issuing his four-point call to action for the Council, Guterres urged members to do more to address the various challenges facing young people.

He also called for investment in youth participation, but also in their organisations and initiatives.

We must strengthen human rights protections and protect the civic space on which youth participation depends, he said. And fourth, we must emerge from the COVID-19 crisis with a determination to recover better - massively increasing our investment in young people's capacities as we deliver the Sustainable Development Goals.

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News Network
January 3,2020

New Delhi, Jan 3: US aviation regulator Federal Aviation Administration on Thursday warned America's airlines and their pilots that there is risk involved in operating flights in Pakistan airspace due to "extremist or militant activity", according to an official document.

"Exercise caution during flight operations. There is a risk to US civil aviation operating in the territory and airspace of Pakistan due to extremist/militant activity," said the US Federal Aviation Administration (FAA) in a notice to airmen (NOTAM) dated December 30, 2019.

The NOTAM is applicable to all US-based airlines and US-based pilots.

The US regulator said in its NOTAM that there continues to be a risk to US civil aviation sector from attacks against airports and aircraft in Pakistan, particularly for aircraft on the ground and aircraft operating at low altitudes, including during the arrival and departure phases of flights.

"The ongoing presence of extremist/militant elements operating in Pakistan poses a continued risk to US civil aviation from small-arms fire, complex attacks against airports, indirect weapons fire, and anti-aircraft fire, any of which could occur with little or no warning," it said.

The FAA said that while, to date, there have been no reports of man-portable air defense systems or Manpads being used against the civil aviation sector in Pakistan, some extremist or terrorist groups operating there are suspected of having access to these Manpads.

"As a result, there is potential risk for extremists/militants to target civil aviation in Pakistan with Manpads," it said.

The regulator added that pilots or airlines must report safety or security incidents - which may happen in Pakistan - to the FAA.

Pakistan on July 16 last year opened its airspace for India after about five months of restrictions imposed in the wake of a standoff with New Delhi.

Following the Balakot airstrikes by the Indian Air Force, Pakistan had closed its airspace on February 26 last year.

Pakistan in October last year had denied India's request to allow Prime Minister Narendra Modi's VVIP flight to use its airspace for his visit to Saudi Arabia over the Jammu and Kashmir issue.

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News Network
June 2,2020

Jun 2: A new female billionaire has emerged from one of Asia's most-expensive breakups.

Du Weimin, the chairman of Shenzhen Kangtai Biological Products Co., transferred 161.3 million shares of the vaccine maker to his ex-wife, Yuan Liping, according to a May 29 filing, immediately catapulting her into the ranks of the world's richest.

The stock was worth $3.2 billion as of Monday's close.

Yuan, 49 this year, owns the shares directly, but signed an agreement delegating the voting rights to her ex-husband, the filing shows. The Canadian citizen, who resides in Shenzhen, served as a director of Kangtai between May 2011 and August 2018. She's now the vice general manager of subsidiary Beijing Minhai Biotechnology Co. Yuan holds a bachelor's degree in economics from Beijing's University of International Business and Economics.

Kangtai shares have more than doubled in the past year and have continued their ascent since February, when the company announced a plan to develop a vaccine to fight the coronavirus. They slipped for a second day Tuesday following news of the divorce terms, losing 3.1% as of 9:43 a.m. in Hong Kong and bringing the company's market value to $12.9 billion.

Du's net worth has now dropped to about $3.1 billion from $6.5 billion before the split, excluding his pledged shares.

The 56-year-old was born into a farming family in China's Jiangxi province. After studying chemistry in college, he began working in a clinic in 1987 and became a sales manager for a biotech company in 1995, according to the prospectus of Kangtai's 2017 initial public offering. In 2009, Kangtai acquired Minhai, the company Du founded in 2004, and he became the chairman of the combined entity.

China's rapidly growing economy has been an engine for the country's richest, and Du is not the only tycoon who's had to pay a steep price for a divorce. In 2012, Wu Yajun, at one point the nation's richest woman, transferred a stake worth about $2.3 billion to her ex-husband, Cai Kui, who co-founded developer Longfor Group Holdings Ltd. In 2016, tech billionaire Zhou Yahui gave $1.1 billion of shares in his online gaming company, Beijing Kunlun Tech Co., to ex-wife Li Qiong after a civil court settlement.

Sometimes, a goodbye can be time-consuming too. South Korean tycoon Chey Tae-won's wife filed a lawsuit in December asking for a 42.3% stake in SK Holdings Co. valued at $1.2 billion. That would make her the second-largest shareholder of the company should she win the case, which is still ongoing.

The most expensive divorce in history is that of Jeff and MacKenzie Bezos. The Amazon.com Inc. founder gave 4% of the online retailer to Mackenzie, who now has a $48 billion fortune and is the world's fourth-richest woman.

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