Ramanujan's 'genius' finally proven by mathematicians

November 10, 2012

ramanujam

London, November 10: Hence proved! A US scientist has finally proven the mathematical relation - discussed by great Indian mathematician Srinivasa Ramanujan with his mentor G H Hardy in one of his last letters.

Ramanujan, the young genius who died at the age of 32, often managed to leap from insight to insight without formally proving the logical steps in between.

Now proof has been found for a connection that he seemed to mysteriously intuit between two types of mathematical functions, the 'New Scientist' reported.

"His ideas as to what constituted a mathematical proof were of the most shadowy description," G H Hardy, Ramanujan's mentor and one of his few collaborators, had once said.

Ken Ono of Emory University in Atlanta, Georgia, who has previously unearthed hidden depths in Ramanujan's work, was prompted by Ramanujan's 125th birth anniversary, to look once more at his writings.

"I wanted to go back and prove something special," Ono said.

Ono settled on a discussion in the last known letter that Ramanujan wrote to Hardy, concerning a type of function now called a modular form.

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

The functions looked unlike any other modular forms, but Ramanujan wrote that their outputs would be very similar to those of modular forms when computed for the roots of 1 like the square root -1.

Characteristically, Ramanujan offered neither proof nor explanation for this conclusion.

It was only 10 years later that mathematicians formally defined this other set of functions, now known as mock modular forms.

However, still no one fathomed what Ramanujan meant by saying the two types of function produced similar outputs for roots of 1.

Now Ono and colleagues have exactly calculated one of Ramanujan's mock modular forms for values very close to -1, and said the difference in the value of the two functions, ignoring the functions signs, is tiny when computed for -1, just like Ramanujan said.

The result confirms Ramanujan's incredible intuition, says Ono.

Born in 1887 in Erode, Tamil Nadu, Ramanujan was self-taught and worked in almost complete isolation from the mathematical community of his time, the report said.


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News Network
June 20,2020

New Delhi, Jun 20: Diesel price on Saturday hit a record high after rates were hiked by 61 paise per litre while petrol price was up 51 paise, taking the cumulative increase in rates in two weeks to Rs 8.28 and Rs 7.62 respectively.

Petrol price in Delhi was hiked to Rs 78.88 per litre from Rs 78.37, while diesel rates were increased to Rs 77.67 a litre from Rs 77.06, according to a price notification of state oil marketing companies.

Rates have been increased across the country and vary from state to state depending on the incidence of local sales tax or VAT.

The 14th daily increase in rates since oil companies on June 7 restarted revising prices in line with costs after ending an 82-day hiatus in rate revision, has taken diesel prices to new high. Petrol price too is at a two-year high.

Prior to the current rally, diesel rate had touched a peak of Rs 75.69 per litre in Delhi on October 16, 2018.

The highest-ever petrol price was on October 4, 2018, when rates soared to Rs 84 a litre in Delhi.

When rates had peaked in October 2018, the government had cut excise duty on petrol and diesel by Rs 1.50 per litre each. State-owned oil companies were asked to absorb another Re 1 a litre to help cut retail rates by Rs 2.50 a litre.

Oil companies had quickly recouped the Re 1 and the government in July 2019 raised excise duty by Rs 2 a litre.

The 82-day freeze in rates this year was imposed in mid-March soon after the government hiked excise duty on petrol and diesel to shore up additional finances.

The government on March 14 hiked excise duty on petrol and diesel by Rs 3 per litre each and then again on May 5 by a record Rs 10 per litre in case of petrol and Rs 13 on diesel. The two hikes gave the government Rs 2 lakh crore in additional tax revenues.

Oil PSUs Indian Oil Corp (IOC), Bharat Petroleum Corp Ltd (BPCL) and Hindustan Petroleum Corp Ltd (HPCL), instead of passing on the excise duty hikes to customers, adjusted them against the fall in retail rates that was warranted because of a decline in international oil prices to two-decade lows.

International oil prices have since rebounded and oil firms are now adjusting retail rates in line with them.

In 14 hikes, petrol price has gone up by Rs 7.62 per litre and diesel by Rs 8.28 a litre.

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News Network
February 6,2020

New Delhi, Feb 6: DMK Lok Sabha member M K Kanimozhi on Wednesday challenged popular actor Rajinikanth to raise his voice for Muslims, saying they have "already been affected" by the Citizenship (Amendment) Act and are protesting on streets against the law.

Reacting to his statements earlier in the day in Chennai that "CAA is no threat to Muslims" and "if they face trouble I will be the first person to raise voice for them," Kanimozhi, daughter of former Tamil Nadu Chief Minister M Karunanidhi, told news agency that "Muslims in India have already been affected due to CAA".

"Let him (Rajinikanth) come forward and raise his voice for the affected Muslims", she said.

She said the members of the community have been protesting as the law leaves out Muslims.,

Asked whether Rajinikanth, through this pro-CAA statement, was moving closer to the BJP, the MP from Tuticorin said, "What he has said is no different from the BJP's narrative which we have been listening in parliament for the last few days".

Under CAA, members of Hindu, Sikh, Buddhist, Jain, Parsi and Christian communities who came to India from Pakistan, Bangladesh and Afghanistan till December 31, 2014, to escape religious persecution there will not be treated as illegal immigrants, and be given Indian citizenship.

Rajinikanth had asserted that the legislation did not pose any threat to Muslims. He wondered as to how Muslims, who chose to stay back in India following Partition will be sent out of the country. Besides, the central government had assured that Indian people will have no issues in view of CAA, he noted.

He charged that some political parties were instigating people against the CAA for their selfish interests.

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News Network
March 12,2020

New Delhi, Mar 12: The coronavirus pandemic could deal a crippling blow to the Indian travel and tourism industry, specially with the government suspending all visas, with the economic impact being assessed to run into thousands of crores of rupees. According to industry chamber CII, this is the one of the worst crises ever to hit the Indian tourism industry impacting all its geographical segments - inbound, outbound and domestic, almost all tourism verticals - leisure , adventure, heritage, MICE, cruise, corporate and niche segments.

The whole tourism value chain across hotels, travel agents, tour operations, destinations, restaurants, family entertainment venues and air, land and sea transportation have been hit.

In an impact assessment of the coronavirus pandemic, CII Tourism Committee said inbound foreign tourism of over USD 28 billion in value terms accounts for an average 60-65 per cent between October to March.

"As the news of the virus started picking up from November, the percentage of cancellations started going up in this segment exponentially and is reaching a peak of almost 80 per cent now in March in many Indian locations. The value at risk from this segment will be in multiples of tens of thousands of crores," the CII assessment report said.

With India cancelling all visas, the chamber said the impact "will be worse".

It further said,"The forward bookings for the inbound season of October 2020-March 2021 which should have started picking are all muted. These are showing highly discouraging signs with cancellations of important global travel marts which are marketplaces for contracting for the next season."

It further said there are reports of large scale forward cancellations from NRI segment from developed markets, which account for over 60 per cent during April to September inbound visits.

"Unless the progression of the virus stops, almost the entire value for the remainder of 2020 season is at risk," the report added.

ANAROCK Property Consultants Chairman Anuj Puri said India's hospitality sector will definitely be impacted by the announcement of a global pandemic, and the mounting numbers of confirmed coronavirus cases in the country.

"The cancellation of visas for foreigners as well as the strong advice issued to Indians to refrain from unnecessary travel will have a marked effect. This is the most unsettling healthcare crisis in recent times and hotel bookings will go south," he added.

On Indians being advised to refrain from unnecessary travel, as per the CII report almost 28 million plus Indians are estimated to have travelled outside in 2019 and there were almost 1.8 billion domestic tourist footfalls.

The holiday season of Indians -- those travelling within the country and outside -- is heavy in April-July, October and December.

"The December holiday season of 2019 took an estimated hit of almost 40-50 per cent, the holiday season of April to July 2020 is likely to take a humongous hit which could be as high as 80-100 per cent, unless there is positive news of the progression of virus decreasing," the CII assessment report said.

There are advanced cancellations and highly reduced forward booking pipelines for the holiday season. Only corporates are flying and that too only on highly essential same day travel. Most of the MNCs are advising work from home, stifling travel, it added.

On suspension of visas, MakeMyTrip Group CEO Rajesh Magow told ,"The period between February till the end of March is typically a lean period because of exam season but we are seeing a demand slowdown for the upcoming summer holiday season especially for international travel. The situation remains dynamic making it hard to quantify the actual impact on our business and industry at large."

He further said,"The decision by the government will have an impact on inbound and outbound international travel. So far there are no restrictions or advisories issued for domestic travel."

VFS Global Regional Group COO - South Asia, Middle East and North Africa, Americas Vinay Malhotra said,"While it is too early to comment on the impact of coronavirus on visa application trends, so far, our visa application processes in India continue on schedule as per the mandates of our client governments."

He also said the company is exploring steps to assuage concerns of people about visiting busy public areas due to the nature of the virus by considering discounted rates on courier return services for visa customers who want to avoid returning to the visa centres to pick up their passports.

Besides, he said,"We are also contemplating lower fees for our Visa at your doorstep service, for those customers who are requesting an alternative to visiting the centres to submit visa applications."

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