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 24,2020

Jun 24: The coronavirus tally in Pakistan reached 188,926 with the detection of 3,892 new cases in the last 24 hours, the health ministry said on Wednesday.

Sixty more people died due to the viral infection, taking the death toll to 3,755.

As many as 3,337 patients are in critical condition across the country, the ministry said.

With the detection of 3,892 new cases in the last 24 hours, the coronavirus tally in the country now stands at 188,926, it said.

Sindh reported the maximum number of 72,656 cases, followed by 69,536 in Punjab, 23,388 in Khyber-Pakhtunkhwa, 11,483 in Islamabad, 9,634 in Balochistan, 1,337 in Gilgit-Baltistan and 892 in Pakistan-occupied Kashmir (Pok).

Health authorities have so far conducted 1,150,141 coronavirus tests, including 23,380 in the last 24 hours.

A total of 77,754 patients have recovered so far from the disease.

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News Network
February 6,2020

Beijing, Feb 6: The number of confirmed fatalities from China's coronavirus outbreak rose to at least 560, after authorities in hardest-hit Hubei province reported 70 new deaths on February 6.

In its daily update, the health commission in Hubei also confirmed the number of confirmed infections in the outbreak has reached 28,018 nationwide with 3,694 new cases reported.

The epidemic, which has spiralled into a global health emergency, is believed to have emerged in December from a market that sold wild game in Hubei's capital Wuhan.

Hu Lishan, an official in Wuhan, warned Wednesday that despite building a hospital from scratch and converting public buildings to accommodate thousands of extra patients, there was still a "severe" lack of beds in the region.

There was also a shortage of "equipment and materials," he told reporters, adding that officials were looking to convert other hotels and schools in the city into treatment centres.

Authorities in several other cities in China have placed restrictions on the number of people allowed to leave their homes.

Global concerns have also risen about the virus, with cases confirmed in more than 20 countries.

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April 2,2020

United Nations, Apr 2: The global economy could shrink by up to one per cent in 2020 due to the coronavirus pandemic, a reversal from the previous forecast of 2.5 per cent growth, the UN has said, warning that it may contract even further if restrictions on the economic activities are extended without adequate fiscal responses.

The analysis by the UN Department of Economic and Social Affairs (DESA) said the COVID-19 pandemic is disrupting global supply chains and international trade. With nearly 100 countries closing national borders during the past month, the movement of people and tourism flows have come to a screeching halt.

"Millions of workers in these countries are facing the bleak prospect of losing their jobs. Governments are considering and rolling out large stimulus packages to avert a sharp downturn of their economies which could potentially plunge the global economy into a deep recession. In the worst-case scenario, the world economy could contract by 0.9 per cent in 2020," the DESA said, adding that the world economy had contracted by 1.7 per cent during the global financial crisis in 2009.

It added that the contraction could be even higher if governments fail to provide income support and help boost consumer spending.

The analysis noted that before the outbreak of the COVID-19, world output was expected to expand at a modest pace of 2.5 per cent in 2020, as reported in the World Economic Situation and Prospects 2020.

Taking into account rapidly changing economic conditions, the UN DESA's World Economic Forecasting Model has estimated best and worst-case scenarios for global growth in 2020.

In the best-case scenario with moderate declines in private consumption, investment and exports and offsetting increases in government spending in the G-7 countries and China global growth would fall to 1.2 per cent in 2020.

"In the worst-case scenario, the global output would contract by 0.9 per cent instead of growing by 2.5 per cent in 2020," it said, adding that the scenario is based on demand-side shocks of different magnitudes to China, Japan, South Korea, the US and the EU, as well as an oil price decline of 50 per cent against our baseline of USD 61 per barrel.

The severity of the economic impact will largely depend on two factors - the duration of restrictions on the movement of people and economic activities in major economies; and the actual size and efficacy of fiscal responses to the crisis.

A well-designed fiscal stimulus package, prioritising health spending to contain the spread of the virus and providing income support to households most affected by the pandemic would help to minimise the likelihood of a deep economic recession, it said.

According to the forecast, lockdowns in Europe and North America are hitting the service sector hard, particularly industries that involve physical interactions such as retail trade, leisure and hospitality, recreation and transportation services. Collectively, such industries account for more than a quarter of all jobs in these economies.

The DESA said as businesses lose revenue, unemployment is likely to increase sharply, transforming a supply-side shock to a wider demand-side shock for the economy.

Against this backdrop, the UN-DESA is joining a chorus of voices across the UN system calling for well-designed fiscal stimulus packages which prioritize health spending and support households most affected by the pandemic.

Urgent and bold policy measures are needed, not only to contain the pandemic and save lives, but also to protect the most vulnerable in our societies from economic ruin and to sustain economic growth and financial stability, Under-Secretary-General for Economic and Social Affairs Liu Zhenmin said.

The analysis also warns that the adverse effects of prolonged economic restrictions in developed economies will soon spill over to developing countries via trade and investment channels.

A sharp decline in consumer spending in the European Union and the United States will reduce imports of consumer goods from developing countries.

Developing countries, particularly those dependent on tourism and commodity exports, face heightened economic risks. Global manufacturing production could contract significantly, and the plummeting number of travellers is likely to hurt the tourism sector in small island developing States, which employs millions of low-skilled workers, it said.

Meanwhile, the decline in commodity-related revenues and a reversal of capital flows are increasing the likelihood of debt distress for many nations. Governments may be forced to curtail public expenditure at a time when they need to ramp up spending to contain the pandemic and support consumption and investment.

UN Chief Economist and Assistant Secretary-General for Economic Development Elliot Harris said the collective goal must be a resilient recovery which puts the planet back on a sustainable track. We must not lose sight how it is affecting the most vulnerable population and what that means for sustainable development, he said.

The alarms raised by UN-DESA echo another report, released on March 31, in which UN experts issued a broad appeal for a large-scale, coordinated, comprehensive multilateral response amounting to at least 10 per cent of global gross domestic product (GDP).

According to estimates by the Johns Hopkins University, confirmed coronavirus cases across the world now stand at over 932,600 and over 42,000 deaths.

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