Perelman's proof uses a modified version of a Ricci flow program developed by Richard Hamilton.

* Perelman's proof of the Poincaré conjecture: a nonlinear PDE perspective by Terence Tao, unpublished arxiv. org preprint ( written for mathematicians ).

* Lectures on Perelman's proof by T. Tao.

This method, with full details leading to the proof of Geometrization, can be found in the exposition by B. Kleiner and J. Lott in ' Notes on Perelman's papers ' in the journal Geometry & Topology.

Also containing proofs of Perelman's Theorem 7. 4, there is a paper of Morgan and Tian, another paper of Kleiner and Lott, and a paper by Cao and Ge.

It is the primary tool used in Grigori Perelman's solution of the Poincaré conjecture, as well as in the proof of the Differentiable sphere theorem by Brendle and Schoen.

Another caricature of Cerf, named Harry Hubris and portrayed by Bert Lahr, appears in Perelman's 1962 play The Beauty Part.

New World faces a major financial slump and the company began to restructure ; first, the Marvel Entertainment Group was sold to financier Ronald Perelman's Andrews Group, in 1989 then New World Entertainment was subsequently acquired by Perelman later in the year.

* Among the funniest of S. J. Perelman's writings is his series of pieces Cloudland Revisited in which as a middle-aged man, he re-reads and describes the risqué novels that had thrilled him as a youth.

He reportedly has since dated Mick Jagger's former wife Bianca Jagger and Ronald Perelman's ex-wife Patricia Duff, as well as conservative talk show host Laura Ingraham, and U. S. Senator Maria Cantwell.

Several teams of mathematicians have verified that Perelman's proof is correct.

Perelman's work survived review and was confirmed in 2006, leading to his being offered a Fields Medal, which he declined.

On December 22, 2006, the journal Science honored Perelman's proof of the Poincaré conjecture as the scientific " Breakthrough of the Year ", the first time this had been bestowed in the area of mathematics.

* Bruce Kleiner and John W. Lott posted a paper on the arXiv in May 2006 which filled in the details of Perelman's proof of the geometrization conjecture.

All three groups found that the gaps in Perelman's papers were minor and could be filled in using his own techniques.

A special case of Perelman's theorems about Ricci flow with surgery is given as follows.

This last part of the proof appeared in Perelman's third and final paper on the subject.

*: Detailed proof, expanding Perelman's papers.

* Bruce Kleiner ( Yale ) and John W. Lott ( University of Michigan ): " Notes & commentary on Perelman's Ricci flow papers ".

In 1980, Ronald Perelman, the son of a wealthy Philadelphia businessman, and future " corporate raider " having made several small but successful buyouts, acquired MacAndrews & Forbes, a distributor of licorice extract and chocolate, that Perelman's father had tried and failed to acquire 10 years earlier.

Using the Pantry Pride subsidiary of his holding company, MacAndrews & Forbes Holdings, Perelman's overtures were rebuffed.

After receiving a higher offer from a white knight, private equity firm Forstmann Little & Company, Perelman's Pantry Pride finally was able to make a successful bid for Revlon, valuing the company at $ 2. 7 billion.

Under Perelman's control, Revlon sold 4 divisions: two of which were sold for $ 1 billion, its vision care division was sold for $ 574 million and its National Health Laboratories division was spun out to the public market in 1988.

He lost out at the last minute to Ronald Perelman's slightly higher bid.

The main difficulty in verifying Perelman's proof of the Geometrization conjecture was a critical use of his Theorem 7. 4 in the preprint ' Ricci Flow with surgery on three-manifolds '.

There are now several different proofs of Perelman's Theorem 7. 4, or variants of it which are sufficient to prove geometrization.

They initially implied the proof was their own achievement based on the " Hamilton-Perelman theory ", but later retracted the original version of their paper, and posted a revised version, in which they referred to their work as the more modest " exposition of Hamilton – Perelman's proof ".

* Bruce Kleiner and John Lott, Notes on Perelman's Papers ( May 2006 ) ( fills in the details of Perelman's proof of the geometrization conjecture ).

Sherwood Lass, 4 ( by Victory Song ) in 2:22 ; ;

The Prince visited the hospital of Operation Brotherhood, supported by the Junior Chamber of Commerce of the Philippines, and fed rice to two pet elephants he kept at his residence at Pak Song.

Choreographed by Mr. Nagrin, the work filled the second half of a program that also offered the first New York showing of Miss Tamiris' `` Once Upon A Time '' as well as her `` Women's Song '' and Mr. Nagrin's `` Indeterminate Figure ''.

In the famous long scroll Along the River During the Qingming Festival painted by Zhang Zeduan ( 1085 – 1145 AD ) during the Song Dynasty ( 960 – 1297 AD ), a suanpan is clearly seen lying beside an account book and doctor's prescriptions on the counter of an apothecary's ( Feibao ).

Seven stories are inspired by a nursery rhyme: And Then There Were None by Ten Little Indians ; One, Two, Buckle My Shoe by One, Two, Buckle My Shoe ; Five Little Pigs by This Little Piggy ; Crooked House by There Was a Crooked Man ; A Pocket Full of Rye by Sing a Song of Sixpence ; Hickory Dickory Dock by Hickory Dickory Dock, and Three Blind Mice by Three Blind Mice.

Weill's score uses a number of styles, including rag-time, jazz and formal counterpoint, notably in the " Alabama Song " ( covered by multiple artists, notably The Doors and David Bowie ).

Grant followed the album with her second Christmas album, Home For Christmas in 1992, which included the song " Breath of Heaven ( Mary's Song )", written by Chris Eaton and Grant, and would later be covered by many artists, including Donna Summer, Jessica Simpson ( who acknowledged Grant as one of her favorite artists ), Vince Gill, Sara Groves, Point of Grace, and Broadway star Barbara Cook.

(" Miracle Song ") It is soon revealed to Cora that the miracle is a fake, controlled by a pump inside the rock.

* Lehrer, Tom, The Tom Lehrer Song Book, introduction by Al Capp ( 1954 ) Crown Publishers

The new songs included in this production had been added during a 1971 Los Angeles production: " Echo Song " ( sung by Hero and Philia ), and " Farewell " ( added for Nancy Walker playing the role of Domina as she and Senex depart for the country ).

French poet Paul Verlaine's " Chanson d ' automne " (" Autumn Song ") is likewise characterised by strong, painful feelings of sorrow.

The works dealing with the Old Testament included Commentary on Samuel, Commentary on Genesis, Commentaries on Ezra and Nehemiah, On the Temple, On the Tabernacle, Commentaries on Tobit, Commentaries on Proverbs, Commentaries on the Song of Songs, Commentaries on the Canticle of Habakkuk, The works on Ezra, the Tabernacle and the Temple were especially influenced by Gregory the Great's writings.

Early descriptions of the production process and glazing techniques used for bricks can be found in the Song Dynasty carpenter's manual Yingzao Fashi, published in 1103 by the government official Li Jie, who was put in charge of overseeing public works for the central government's construction agency.

" This Is My Song ", performed by Petula Clark for A Countess from Hong Kong ( 1967 ), reached # 1 on the UK Charts.

Native Chinese astronomy flourished during the Song Dynasty, and during the Yuan Dynasty became increasingly influenced by medieval Islamic astronomy.

Southern Song experienced a period of great technological development which can be explained in part by the military pressure that it felt from the north.

The Song Dynasty is considered by many to be classical China's high point in science and technology, with innovative scholar-officials such as Su Song ( 1020 – 1101 ) and Shen Kuo ( 1031 – 1095 ).