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
April 13,2020

Manila, Apr 13: The Asian Development Bank (ADB) on Monday tripled the size of its response to novel coronavirus disease (COVID-19) pandemic to 20 billion dollars and approved measures to streamline its operations for quicker and more flexible delivery of assistance.

The package expands ADB's 6.5 billion dollars initial response announced on March 18, adding 13.5 billion dollars in resources to help ADB's developing member countries counter the severe macroeconomic and health impacts caused by COVID-19.

The 20 billion dollar package includes about 2.5 billion dollars in concessional and grant resources.

"This pandemic threatens to severely set back economic, social, and development gains in Asia and the Pacific, reverse progress on poverty reduction and throw economies into recession," said ADB President Masatsugu Asakawa.

"Our expanded and comprehensive package of assistance, made possible with the strong support of our board, will be delivered more quickly, flexibly and forcefully to the governments and the private sector in our developing member countries to help them address the urgent challenges in tackling the pandemic and economic downturn," he said in a statement.

ADB's most recent assessment released on April 3 estimates the global impact of the pandemic at between 2.3 and 4.8 per cent of gross domestic product. Regional growth is forecast to decline from 5.2 per cent last year to 2.2 per cent in 2020.

The new package includes the establishment of a COVID-19 pandemic response option under ADB's countercyclical support facility.

Up to 13 billion dollars will be provided through this new option to help governments of developing member countries implement effective countercyclical expenditure programs to mitigate impacts of the COVID-19 pandemic, with a particular focus on the poor and the vulnerable.

Grant resources will continue to be deployed quickly for providing medical and personal protective equipment and supplies from expanded procurement sources.

Some 2 billion dollars from the 20 billion dollar package will be made available for the private sector. Loans and guarantees will be provided to financial institutions to rejuvenate trade and supply chains.

Enhanced microfinance loan and guarantee support and a facility to help liquidity-starved small and medium-sized enterprises, including those run by female entrepreneurs, will be implemented alongside direct financing of companies responding to or impacted by COVID-19.

The response package includes a number of adjustments to policies and business processes that will allow ADB to respond more rapidly and flexibly to the crisis. These include measures to streamline internal business processes, widen the eligibility and scope of various support facilities and make the terms and conditions of lending more tailored.

All support under the expanded package will be provided in close collaboration with international organisations, including the International Monetary Fund, World Bank Group, World Health Organisation, UNICEF, other UN agencies and the broader global community.

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News Network
May 22,2020

Washington, May 22: The deadly coronavirus came from China and the US is not going to take it lightly, American President Donald Trump said on Thursday.

"It came from China. We are not happy about it. We just signed a trade deal, the ink wasn't dry and all of the sudden this floated in. We are not going to take it lightly,” Trump said participating in a Listening Session with African-American Leaders in Michigan.

Trump in the last several weeks has been very critical of China's inability to control the spread of the novel coronavirus within its territory. By Thursday more than 94,000 Americans have died due to the coronavirus and over 1.6 million have tested positive.

He has so far not given any indication of the steps that he is contemplating taking against China.

Meanwhile, pressure is building on his administration, mainly from the Republican lawmakers on this.

On Thursday, Senators Ted Cruz and Rick Scott, along Mike Braun, Marsha Blackburn, Joni Ernst, Martha McSally and Tom Cotton, introduced the COVID-19 Vaccine Protection Act to prevent the Chinese Communist Party from stealing or sabotaging American COVID-19 vaccine research.

The bill requires a thorough national security evaluation and clearance by the Department of Homeland Security, the Department of State, and the Federal Bureau of Investigation of all Chinese student visa holders taking part in activities related to COVID-19 vaccine research.

"The same Chinese Communist Party that covered up the coronavirus outbreak also routinely engages in state sponsored theft of intellectual property," Cruz said. "We cannot allow China to steal or interfere with American research and development of a vaccine,” he added.

"Communist China is responsible for the coronavirus pandemic, and their lies and misinformation cost American lives," Scott said.

"We cannot let Communist China off the hook for this, and we absolutely cannot allow Communist China to steal or sabotage any American research efforts related to the Coronavirus vaccine. The COVID-19 Vaccine Protection Act protects American efforts to create a vaccine as we work to end this pandemic," he added.

The COVID-19 Vaccine Protection Act, among others requires an enhanced vetting of nationals of the Chinese nationals in the US as nonimmigrants under F, J, or M student visas to determine if any student visa holders are a national security threat.

Once the review is complete, authorizes Department of Homeland Secretary, in consultation with other agencies, to continuously monitor all nonimmigrant student visa holders (F, M, J) who are Chinese nationals while in the US and are engaged in, or have access to, the research of any potential COVID-19 vaccine or COVID-19 related material.

Republican Whip and Ranking Member of the Select Subcommittee on the Coronavirus Crisis Steve Scalise alleged that China lied to the world on coronavirus.

"During a critical period in December and January, China withheld evidence of the virus: evidence that confirmed human to human transmission of the virus, evidence of the extent of the spread. China refused entry of American and other medical experts from around the world for weeks,” he said.

“And during this time, China hoarded medical supplies like masks, gowns, and other life-saving PPE. Chinese exports of surgical masks, gowns, and gloves were stifled by the Chinese Communist Party during this period. China knew the danger posed by the virus and while they hid the truth, they used the time to stock up on vital medical supplies,” Scalise said.

“While Chinese authorities limited domestic flights from Wuhan to other Chinese cities like Beijing and Shanghai, China's government urged international carriers to maintain their flight schedules — seeding the virus throughout the rest of the world,” he alleged.

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Agencies
June 7,2020

Moscow, Jun 7: OPEC, Russia and allies agreed on Saturday to extend record oil production cuts until the end of July, prolonging a deal that has helped crude prices double in the past two months by withdrawing almost 10% of global supplies from the market.

The group, known as OPEC+, also demanded countries such as Nigeria and Iraq, which exceeded production quotas in May and June, compensate with extra cuts in July to September.

OPEC+ had initially agreed in April that it would cut supply by 9.7 million barrels per day (bpd) during May-June to prop up prices that collapsed due to the coronavirus crisis. Those cuts were due to taper to 7.7 million bpd from July to December.

“Demand is returning as big oil-consuming economies emerge from pandemic lockdown. But we are not out of the woods yet and challenges ahead remain,” Saudi Energy Minister Prince Abdulaziz bin Salman told the video conference of OPEC+ ministers.

Benchmark Brent crude climbed to a three-month high on Friday above $42 a barrel, after diving below $20 in April. Prices still remain a third lower than at the end of 2019.

“Prices can be expected to be strong from Monday, keeping their $40 plus levels,” said Bjornar Tonhaugen from Rystad Energy.

Saudi Arabia, OPEC’s de facto leader, and Russia have to perform a balancing act of pushing up oil prices to meet their budget needs while not driving them much above $50 a barrel to avoid encouraging a resurgence of rival U.S. shale production.

It was not immediately clear whether Saudi Arabia, the United Arab Emirates and Kuwait would extend beyond June their additional, voluntary cuts of 1.18 million bpd, which are not part of the deal.

BULGING INVENTORIES

The April deal was agreed under pressure from U.S. President Donald Trump, who wants to avoid U.S. oil industry bankruptcies.

Trump, who previously threatened to pull U.S. troops out of Saudi Arabia if Riyadh did not act, spoke to the Russian and Saudi leaders before Saturday’s talks, saying he was happy with the price recovery.

While oil prices have partially recovered, they are still well below the costs of most U.S. shale producers. Shutdowns, layoffs and cost cutting continue across the United States.

“I applaud OPEC-plus for reaching an important agreement today which comes at a pivotal time as oil demand continues to recover and economies reopen around the world,” U.S. Energy Secretary Dan Brouillette wrote on Twitter after the extension.

As global lockdowns ease, oil demand is expected to exceed supply sometime in July but OPEC has yet to clear 1 billion barrels of excess oil inventories accumulated since March.

Rystad’s Tonhaugen said Saturday’s decisions would help OPEC reduce inventories at a rate of 3 million to 4 million bpd in July-August. “The quicker stocks fall, the higher prices will get,” he said.

Nigeria’s petroleum ministry said Abuja backed the idea of compensating for its excessive output in May and June.

Iraq, with one of the worst compliance rates in May, agreed to extra cuts although it was not clear how Baghdad would reach agreement with oil majors on curbing Iraqi output.

Iraq produced 520,000 bpd above its quota in May, while overproduction by Nigeria was 120,000 bpd, Angola’s was 130,000 bpd, Kazakhstan’s was 180,000 bpd and Russia’s was 100,000 bpd, OPEC+ data showed.

OPEC+’s joint ministerial monitoring committee, known as the JMMC, will meet monthly until December to review the market, compliance and recommend levels of cuts. JMMC’s next meeting is scheduled for June 18.

OPEC and OPEC+ will hold their next scheduled meetings on Nov. 30-Dec. 1.

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