New Delhi (PTI): A rare autographed manuscript by renowned physicist Albert Einstein explaining the development of his famous contributions to science -- theories of special relativity (1905) and general relativity (1915) -- fetched Rs 10.7 crore at the recently held Christie's '20th/21st Century Art Evening Sale'.

The auction was held at the Waldorf Astoria Shanghai on September 23.

The manuscript, first published in a special supplement to the New York Times on February 3, 1929, is written in German. Einstein had been commissioned to explain the development of his two most famous contributions to science: the theories of special relativity (1905) and general relativity (1915).

"The rare Einstein manuscript, which marked the Classic Art category's debut in mainland China, was met with great enthusiasm, proving that the collecting appetite here is strong and ever evolving.

"We look forward to reconnecting with collectors at our upcoming previews for the Autumn Auctions in Hong Kong, and at the China International Import Expo this November," said Rebecca Yang, chairman of Christie's China, in a statement.

The 14-page manuscript holds tremendous significance as it recounts the history behind the discovery of relativity, explains its working, and looks to the possibility of completing the cycle of relativity in a 'unified field theory'.

It includes two equations and a diagram illustrating the structure of the space-time continuum, along with two pages of scientific formulae.

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Barcelona (AP): Real Madrid slapped players Federico Valverde and Aurélien Tchouaméni with half-a-million-euro ($588,000) fines on Friday for their altercation during practice.

The massive fines came a day after the midfielders tussled when the team trained. Valverde said in a post on social media on Thursday that no punches were thrown. But Valverde knocked his head on a table and he suffered a small cut that required a brief hospital visit.

On social media, Valverde initially called it a “meaningless fight” with a teammate and said “everything has been blown out of proportion."

His employers, however, considered it a significant enough breach of team discipline to nail both Valverde and Tchouaméni with fines that bite even the bank account of a top soccer player. The half-a-million euro penalties reflect the reputational damage the club was enduring in a chaotic end to a disappointing season.

In a statement, the 15-time European champion said its disciplinary action was concluded after both players expressed to the club “their complete remorse for what happened and apologized to one another.”

Madrid added they also apologized to their teammates, the coaching staff and club supporters, as well as showing their willingness to accept whatever disciplinary action the club deemed “opportune.”

Tchouaméni was back training with Madrid on Friday, two days before they play at Barcelona in a clasico. Madrid has to win otherwise Barcelona will be crowned La Liga champion.

After being notified of the fine, he posted a public apology to the club and its fans on social media.

“What happened this week in training is unacceptable,” Tchouaméni wrote. "I say this while thinking about the example we are expected to set for young people, whether in football or at school.

“Above all, I am sorry for the image we projected of the club.”

Valverde was not at practice due to the head knock.

Both players are set to play in the World Cup next month, with Tchouaméni playing for France and Valverde for Uruguay. 

Chaotic end to a poor season

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The run-in between the players, who for seasons have played side by side in Madrid's midfield, came after they argued this week in previous training sessions. But tempers boiled over on Thursday. Spanish media was rife with reports that the players previously disagreed over the club's decision to let coach Xabi Alonso go after just months on the job.

It was not the only altercation involving Madrid players during training this week. Álvaro Carreras confirmed he was in a “minor” incident with a teammate. Spanish media said he and fellow defender Antonio Rüdiger got into a scuffle.

Álvaro Arbeloa, the coach who was promoted from Madrid's reserve team when Alonso was fired in January, will face tough questions on what went wrong inside the changing room when he gives a press conference on Saturday ahead of the clasico at Camp Nou.

Madrid is facing a second consecutive campaign without a major trophy amid rumors in the Spanish media that club president Florentino Pérez is considering bringing back Jose Mourinho to straighten out his underperforming team.