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 11,2020

Kabul, May 11: Four back-to-back roadside bombs exploded in a northern district of Afghanistan's capital Kabul on Monday, wounding four civilians including a child, police said. Kabul police spokesman Ferdaws Faramarz said a clearance team was at the site of the attacks.

Militants have carried out several roadside bombings and rocket attacks in Kabul and other parts of the country in recent weeks, but Monday's four consecutive explosions appeared to be the first coordinated effort for some months.

The Taliban has not carried out any large attacks in the city since they signed a landmark withdrawal deal with the US in February, meant to pave the way for peace in the country. No group has claimed the attacks. The explosions come as authorities are trying to impose a lockdown in the capital to curb the spread of coronavirus in the country.

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News Network
June 4,2020

New York, Jun 4: The Minneapolis police officer who used his knee to pin down George Floyd's neck before his death was the most experienced of the four officers involved in the arrest, with a record that included medals for bravery and 17 complaints against him, including one for pulling a woman out of her car during a speeding stop.

New details about Derek Chauvin and the other now-fired officers emerged Wednesday after prosecutors upgraded Chauvin's charge to second-degree murder and charged the others with aiding and abetting in a case that has convulsed the nation with protests over race and police brutality.

Heavily redacted personnel files show that Chauvin, a 19-year veteran of the force, was initially trained as a cook and served in the Army as a military police officer.

Eleven-year veteran and native Hmong speaker Tou Thao began as a community service officer and was the subject of six complaints.

The other two officers were relative newcomers to the department, including Thomas Lane, a former juvenile detention guard who did volunteer work with Somali refugees, and J. Alexander Kueng, who got his start in law enforcement by patrolling his college campus and a department store.

The files were notable for what they didn't include. Only one of the 17 complaints against Chauvin was detailed, none of the six against Thao were mentioned and there was no further detail about a 2017 excessive force lawsuit against Thao.

Records show that the 44-year-old Chauvin initially studied cooking before taking courses in law enforcement and doing two stints in the Army as a military police officer in the late 1990s, serving at Fort Benning, Georgia, and in Germany.

Chauvin became a Minneapolis police officer in 2001 and the lone reprimand in his file involved a 2007 incident when he was accused of pulling a woman out of her car after stopping her for going 10 mph (16 kph) over the speed limit.

Investigators found it was not necessary for Chauvin to remove the woman from the car and noted that his squad car video was turned off during the stop.

But Chauvin was also singled out for bravery. Files show he won two medals of valor, one in 2006 for being part of a group of officers who opened fire on a stabbing suspect who pointed a shotgun at them, and another in 2008 for a domestic violence incident in which Chauvin broke down a bathroom door and shot a suspect in the stomach.

He also won medals of commendation in 2008 after he and his partner tackled a fleeing suspect who had a pistol in his hand, and in 2009 for single-handedly apprehending a group of gang members while working as an off-duty security guard at the El Nuevo Rodeo, a Minneapolis nightclub.

Since his arrest, the former owner of the club, Maya Santamaria, said Chauvin and Floyd both worked as security guards there at various times but that she wasn't sure if they had known one another.

She said Chauvin was unnecessarily aggressive on nights when the club had a black clientele, quelling fights by dousing the crowd with pepper spray and calling in several police squad cars as backup, a tactic she called “overkill.”

Chauvin's wife, Kellie, a Laotian immigrant who became the first Hmong winner of the Mrs. Minnesota pageant, said shortly after his arrest last week that she intends to divorce him.

Before news of the upgraded charges, an attorney for Chauvin said he was not making any statements at this time. Lawyers for the others did not return messages seeking comment.

In cellphone video of the May 25 arrest of Floyd, Chauvin is shown pressing his knee onto Floyd's neck for more than eight minutes while Floyd cries out “I can't breathe” and eventually stops moving.

During much of the arrest, Kueng and Lane were helping Chauvin restrain Floyd. Thao was standing nearby keeping onlookers back.

According the complaint, at one point during the arrest, as Chauvin held Floyd down with his knee, Lane asked Chauvin twice whether they should roll Floyd over.

“No, staying put where we got him,” Chauvin replied, “I am worried about excited delirium or whatever,” Lane said. And Chauvin replied again, “That's why we have him on his stomach.” None of the three officers moved from their positions.

Lane joined the police early last year as a 35-year-old cadet — much older than most rookies — and became a full-fledged officer last December. He had no complaints in his file during his short time on the force.

On employment forms, the University of Minnesota graduate said he done volunteer work tutoring Somali youth and as a mentor helping at-risk elementary school students with reading and homework.”

Kueng, at 26 the youngest of the four officers, was also a recent recruit to the police force. He completed his year's probation just three months before the Floyd arrest.

His personnel file, which notes that he speaks, reads and writes Russian, did not include any commendations or disciplinary actions during his short time on force.

Kueng was a 2018 graduate of the University of Minnesota, where he worked part-time as part of the campus security force. He also worked nearly three years as a theft-prevention officer at Macy's.

Thao joined the police force part-time in 2008 while attending a community college. Before that, he worked as a security guard, a supermarket stocker and trainer at McDonald's.

City records show six complaints were filed against Thao, but there was no mention of that in the records released Wednesday. There also was no mention of a 2017 federal lawsuit accusing him and another officer of excessive force.

According to the lawsuit, Lamar Ferguson claimed that in 2014, Thao and his partner stopped him and beat him up while he was on his way to his girlfriend's house. The lawsuit was settled for $25,000 ___

Richmond reported from Madison, Wisconsin. Associated Press writer Scott Bauer in Madison and researcher Rhonda Shafner in New York contributed to this report.

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News Network
May 2,2020
Seoul, May 2: North Korean leader Kim Jong Un has made his first public appearance since speculation about his health began last month, cutting the ribbon at the opening of a fertilizer factory, KCNA reported Saturday.
 
Kim attended the event on Friday in Sunchon, near the capital Pyongyang, after nearly three weeks of swirling rumours that the leader of the nuclear-armed nation was seriously ill or possibly dead.
 
The North Korean leader had not made a public appearance since presiding over a Workers' Party politburo meeting on April 11, and the following day state media reported that he had inspected fighter jets.
 
At Friday's event, "all the participants broke into thunderous cheers of 'hurrah!'" when Kim appeared, the Korean Central news agency reported.
 
He inspected the facility and was "briefed about the production processes," the report said.
 
Kim "said with deep emotion" that his grandfather Kim Il Sung and father Kim Jong Il "would be greatly pleased if they heard the news that the modern phosphatic fertilizer factory has been built," it added.
 
Also in attendance were other senior officials, including his sister and close adviser, Kim Yo Jong. Photos from the ceremony were not immediately released.
 
Conjecture over Kim's health had grown since his conspicuous no-show at April 15 celebrations for the birthday of his grandfather, the North's founder -- the most important day in the country's political calendar.
 
His absence unleashed a series of unconfirmed reports over his condition, triggering global fears over the North's nuclear arsenal -- and who would succeed Kim were he unable to lead.
 
A top security advisor to South Korea's President Moon Jae-in said less than a week ago that Kim was "alive and well," downplaying rumors that he was ill or incapacitated.
 
The advisor, Moon Chung-in, told CNN that Kim had been staying in Wonsan -- a resort town in the east of North Korea -- since April 13, adding: "No suspicious movements have so far been detected."
 
South Korea Reports Kim Jong Un Is 'Alive and Well' Amid Rumours of His Death
 
South Korea has told CNN that the rumours of North Korean leader Kim Jong Un's death are untrue.
 
Rumours of ill health
 
Daily NK, an online media outlet run mostly by North Korean defectors, reported that Kim was undergoing treatment after a cardiovascular procedure last month.
 
Citing an unidentified source inside the country, it said Kim -- who is in his mid-30s -- had needed urgent treatment due to heavy smoking, obesity and fatigue.
 
Soon afterwards, CNN reported that Washington was "monitoring intelligence" that Kim was in "grave danger" after undergoing surgery, quoting an anonymous US official.
 
US President Donald Trump appeared to confirm that Kim was alive earlier this week.
 
On Friday, Trump refused to comment on Kim's reported re-emergence.
 
Previous absences from the public eye on Kim's part have prompted speculation about his health.
 
The North is extremely secretive, and doubly so about its leadership.
 
Kim's father and predecessor had been dead for two days before anyone outside the innermost circles of North Korean leadership was any the wiser.
 
In 2014, Kim Jong Un dropped out of sight for nearly six weeks before reappearing with a cane.
 
Days later, the South's spy agency said he had undergone surgery to remove a cyst from his ankle.

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