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 9,2020

Islamabad, May 9: A female doctor posted at Pakistan Institute of Medical Sciences (Pims) Mother and Child Hospital (MCH), who was tested Covid-19 positive, has exposed Pakistan's mismanagement in handling the patients affected with the deadly virus.

Identified herself as Dr. Sharbat, she made a video of herself locked in an isolated room when the authorities failed to provide any medical assistance to her.

According to Pakistani media, the Pakistan Institute of Medical Sciences (Pims) Mother and Child Hospital (MCH) and the operating theatre in the Children's Hospital were sealed on Tuesday after 15 people from both facilities were diagnosed with Covid-19.

Dr. Sharbat said that despite having Covid-19 symptoms after her colleague doctor was tested positive, she was forced to perform duty by the hospital authorities.

After she tested positive, Dr. Sharbat has isolated herself in a room and has requested the hospital authorities to provide her a bed in the hospital.

She said, "I am isolated in a small room. There is no toilet and other facilities at this place. I have requested the authorities several times to provide me proper bed because I cannot go home as my son and father is there. I have no other place to go. Its been several hours now and the administration is busy doing meetings. They have no idea about my location. I have called the concerned officials several times and requested for a room in the hospital, but they said that they are looking for it. This is the kind of arrangements we have that a doctor, who was serving the patients, is not able to get proper care".

Dr Sharbat said that she is feeling depressed after seeing the response of authorities tackling with Covid-19 crisis in the country.

She added, "It is unfortunate that the government salutes [health professionals] but is not willing to provide isolation rooms."

Pakistan's position in the global ranking in respect of Covid-19 dropped from 24th to 22nd after the number of positive cases increased to 26,806 (till May 08) with the addition of 1,791 new cases.

However, the National Coordination Committee (NCC), chaired by Prime Minister Imran Khan, had decided to substantially ease the lockdown from Saturday after detailed deliberations and consultations with the provinces.

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News Network
March 28,2020

Berlin, Mar 28: The number of confirmed coronavirus infections worldwide topped 600,000 on Saturday as new cases stacked up quickly in Europe and the United States and officials dug in for a long fight against the pandemic.

The latest landmark came only two days after the world passed half a million infections, according to a tally by John Hopkins University, showing that much work remains to be done to slow the spread of the virus. It showed more than 602,000 cases and a total of over 27,000 deaths.

While the U.S. now leads the world in reported infections — with more than 104,000 cases — five countries exceed its roughly 1,700 deaths: Italy, Spain, China, Iran and France.

“We cannot completely prevent infections at this stage, but we can and must in the immediate future achieve fewer new infections per day, a slower spread,” German Chancellor Angela Merkel, who is in quarantine at home after her doctor tested positive for the virus, told her compatriots in an audio message. “That will decide whether our health system can stand up to the virus.”

The virus already has put health systems in Italy, Spain and France under extreme strain. Lockdowns of varying severity have been introduced across Europe. Merkel's chief of staff, Helge Braun, said that Germany — where authorities closed nonessential shops and banned gatherings of more than two in public — won't relax its restrictions before April 20.

As the epicenter has shifted westward, the situation has calmed in China, where some restrictions on people's lives have now been lifted. Six subway lines restored limited service in Wuhan, where the virus first emerged in December, after the city had its official coronavirus risk evaluation downgraded from high to medium on Friday. Five districts of the city of 11 million people had other restrictions on travel loosened after their risk factor was downgraded to low.

For most people, the coronavirus causes mild or moderate symptoms, such as fever and cough that clear up in two to three weeks. But for others, especially older adults and people with existing health problems, the virus can cause more severe illness, including pneumonia, and lead to death.

More than 130,000 people have recovered, according to Johns Hopkins' tally.

In one way or another, the effects of the COVID-19 outbreak have been felt by the powerful and the poor alike.

On Friday, British Prime Minister Boris Johnson became the first leader of a major country to test positive for the virus. He said he would continue to work from self-quarantine.

Countries are still scrambling bring home some citizens stranded abroad by border closures and a near-shutdown of flights. On Saturday, 174 foreign tourists and four Nepali nationals on the foothills of Mount Everest were flown out days after being stranded on the only airstrip serving the world's highest mountain.

In neighboring India, authorities sent a fleet of buses to the outskirts of the capital to meet an exodus of migrant workers desperately trying to reach their home villages during the world's largest lockdown.

Thousands of people, mostly young male day laborers but also families, had fled their New Delhi homes after Prime Minister Narendra Modi announced a 21-day lockdown that began on Wednesday and effectively put millions of Indians who live off daily earnings out of work.

In a possibly hopeful sign, the U.S. Food and Drug Administration cleared a new rapid test from Abbott Laboratories, which the company says can detect the coronavirus in about 5 minutes. Medical device maker Abbott announced the emergency clearance of its cartridge-based test Friday night, saying the test delivers a negative result in 13 minutes when the virus is not detected.

While New York remained the worst-hit city in the U.S., Americans braced for worsening conditions elsewhere, with worrisome infection numbers being reported in New Orleans, Chicago and Detroit.

New Orleans’ sprawling Ernest N. Morial Convention Center, along the Mississippi River, was being converted into a massive hospital as officials prepared for thousands more patients than they could accommodate.

In New York, where there are more than 44,000 cases statewide, the number of people hospitalized with COVID-19 passed 6,000 on Friday, double what it had been three days earlier.

Gov. Andrew Cuomo called for 4,000 more temporary beds across New York City, where the Jacob K. Javits Convention Center has already been converted into a hospital.

The struggle to defeat the virus will take “weeks and weeks and weeks,” Cuomo told members of the National Guard working at the Javits Center.

President Donald Trump invoked the Defense Production Act on Friday, ordering General Motors to begin manufacturing ventilators. Trump had previously rejected Cuomo's pleas for tens of thousands more of the machines and the governor's calls to implement the Korean War-era production law.

Trump signed a $2.2 trillion stimulus package, after the House approved the sweeping measure by voice vote. Lawmakers in both parties lined up behind the law to send checks to millions of Americans, boost unemployment benefits, help businesses and toss a life preserver to an overwhelmed health care system.

Dr. John Brooks of the U.S. Centers for Disease Control and Prevention warned Americans remained “in the acceleration phase” of the pandemic and that all corners of the country were at risk.

"There is no geographic part of the United States that is spared from this," he said.

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Agencies
April 20,2020

Hong Kong, Apr 20: Oil prices collapsed to more than two-decade lows Monday as traders grow concerned that storage facilities are reaching their limits, while equities were mixed, with some support coming from signs that the coronavirus may have peaked in Europe and the United States.

US crude benchmark West Texas Intermediate briefly plunged almost 20 percent to below 15 -- its lowest since 1999 -- as stockpiles continue to build owing to a crash in demand caused by the COVID-19 pandemic.

Analysts said this month's agreement between top producers to slash output by 10 million barrels a day was having little impact on the oil crisis because of lockdowns and travel restrictions that are keeping billions of people at home.

WTI was hit particularly hard as its main US storage facilities in Cushing, Oklahoma, were filling up.

ANZ said "crude oil prices remained under pressure, as projections of weaker demand weigh on sentiment".

"Despite the OPEC+ alliance agreeing to an unprecedented cut in output, the physical market is awash with oil," it said, referring to the Organization of the Petroleum Exporting Countries and non-OPEC partners.

And AxiCorp's Stephen Innes added: "It's a dump at all cost as no one... wants delivery of oil, with Cushing storage facilities filling by the minute.

"It hasn't taken long for the market to recognise that the OPEC+ deal will not, in its present form, be enough to balance oil markets." Stock traders were in slightly more buoyant mood as governments start to consider how and when to ease lockdowns that have crippled the global economy.

Italy, Spain, France and Britain reported drops in daily death tolls and slowing infection rates.

"We are scoring points against the epidemic," said Prime Minister Edouard Philippe, while insisting "we are not out of the health crisis yet".

Meanwhile, in the US, Andrew Cuomo, governor of badly hit New York state, said the disease was "on the descent", though he cautioned it was "no time to get cocky".

Mounting evidence suggests that the lockdowns and social distancing are slowing the spread of the virus.

That has intensified planning in many countries to begin loosening curbs on movement and easing the crushing pressure on national economies.

Adding to the sense of hope was a report indicating promising research on a drug to treat coronavirus.

Hong Kong, Shanghai and Seoul were each up 0.1 percent, while Wellington added 0.4 percent.

However, Tokyo went into the break 0.9 percent lower, while Sydney and Manila dropped one percent apiece. There were also losses in Taipei, Singapore and Jakarta.

"The longer investors have to contemplate future economic issues while they wait for more countries to be on the downward slope of the pandemic curve, the more scope there is of risk assets pricing in a difficult future," Chris Iggo, of AXA Investment Managers UK, said.

Investors are keeping an eye on Washington, where Congress and the White House are working towards a 450 billion economic relief plan for small business to add to the trillions already pledged to support the economy.

Big-name companies including IBM, Netflix and Coca-Cola are due to deliver their earnings reports.

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