* In Hal Clement's short story Proof ( 1942 ), neutronium is the only form of solid matter known to Solarians, the inhabitants of the Sun's interior.

Proof: We only give the proof in the simplified case ; the general case is similar.

Note that the relationships above are only valid for the form of the Fourier transform shown in the Proof section below.

Proof: Since p is a prime number the only possible values of gcd ( p < sup > k </ sup >, m ) are 1, p, p < sup > 2 </ sup >, ..., p < sup > k </ sup >, and the only way for gcd ( p < sup > k </ sup >, m ) to not equal 1 is for m to be a multiple of p. The multiples of p that are less than or equal to p < sup > k </ sup > are p, 2p, 3p, ..., p < sup > k − 1 </ sup > p = p < sup > k </ sup >, and there are p < sup > k − 1 </ sup > of them.

As there is no explicit Federal requirement for a two person train crew the Utah Transit Authority's FrontRunner service was originally planned to be operated by an operator only with revenue collection being handled by a Proof of Payment system.

Proof: Using the same sum for R ( p, n ) as in Lemma 2, we see that since p < sup > 2 </ sup > > 2n, in fact only the first term is nonzero ; this term is exactly the right-hand side of the above equation.

In 2002, Bracegirdle co-wrote two songs on Cher's album Living Proof, " You Take It All " and " Alive Again ", the latter which was released as a single in Europe only.

In 1997, Pantera released their first and only official live album titled Official Live: 101 Proof.

Proof: The argument invokes only Fuglede's theoerm.

Proof of this is that he only won fifteen fights by knockout, out of more than seventy professional bouts.

The unusual repudiation of torture is reflected not only in our criminal laws, see e. g. §§ 2340-2340A, but also in international agreements, in centuries of Anglo-American law, see e. g., John H. Langbeen, Torture and the Law of Proof: Europe and England in the Ancien Régime ( 1977 ) (“ Torture and the Law of Proof ”), and in the long standing policy of the United States, repeatedly and recently reaffirmed by the President.

Echo had originally planned to release " Proof " as a single to promote the second album, but after agreeing on artwork and a track listing ( and commissioning a video featuring Christopher Eccleston, directed by Krishna Stott ), the label shelved these ideas and subsequently issued the single as a download only ( though a few copies were issued in Europe on the PIAS imprint ).

Proof of Zocor's efficacy in reducing cardiovascular disease was only presented five years after its original introduction, and then only for secondary prevention.

A closed densely defined operator T is bounded if and only if T < sup >∗</ sup > is bounded .< ref > Proof: We have:.

Birmingham Proof House was built in 1813, then one of only two such proof houses in England, the other being in London.

Proof: Notice that the nim-sum (⊕) obeys the usual associative and commutative laws of addition (+), and also satisfies an additional property, x ⊕ x = 0 ( technically speaking, the nonnegative integers under ⊕ form an Abelian group of exponent 2 ).

Proof: Suppose G = ⟨ H | R ⟩ is a finitely presented, residually finite group.

Proof: If n is a prime-power, then a group of order n has a nontrivial center and, therefore, is not simple.

The dual of Z is isomorphic to the circle group T. Proof:

It was due to his attendance as an honorary pallbearer at the funeral of group member Proof.

Originally known as Maximum, under the moniker " Proof ", Holton first rose to national prominence as a part of the rap group D12, a hip-hop group he was instrumental in forming.

He had been with the group for about six months in the mid 1960s, as well as been a member of The Falcons, The Contours and 100 Proof ( Aged In Soul ).

: Proof of the existence of linear differential equations having a prescribed monodromic group

Just like Swift, Proof complains about the propaganda in his solo part, and says how people that view it this way know nothing about the group ( To back up his point, fans yell out “ Where ’ s Obie and Dre ?”, referring to rappers Obie Trice and Dr. Dre ).

* Proof ( rapper ) ( 1973 – 2006 ), American rapper and member of D12

Since 2006, Eminem's hiatus and the death of the member Proof resulted in them being less active in subsequent years.

In the Summer of 2003, D12 member Proof confronted Royce da 5 ' 9 " outside a club in Detroit.

His brother, Joe Stubbs, was a member of 100 Proof Aged In Soul, The Falcons, The Contours and The Originals and one of his cousins was Jackie Wilson.

Proof is demonstrated through peer review of a financial plan submitted by the prospective NAPFA member.

Denaun is Eminem's current hype man after the death of D12 band member Proof.

Proof appeared as Lil ' Tic, a freestyle rapper who rap battles the lead character, B-Rabbit, played by Eminem.

Fuzz was one of the original members of D12 but left in the year 1999 due to a feud with members Bizarre and Proof.

* Quentin Tarantino's Thunderbolt, the fictitious " original title " of the Quentin Tarantino film Death Proof

Also included are some original pieces such as " Fate to Despair ", " Awake ", and " Proof of Blood ".

Proof for the original koukeri traditions is the insignia of honour, given to the municipality of Razlog by Mr. Henri Van der Kroon, President of the International Federation of European and Mediterranean carnival towns in May 2004.

Proof: If we have a description in, we can convert it into a description in our optimal language by first describing as a computer program ( part 1 ), and then using the original description as input to that program ( part 2 ).

* " Proof ", a song by Coldplay from " Speed of Sound "

* " Proof " ( I Am Kloot song ), a song by I Am Kloot from their eponymous second album

* " Proof ", a song by Paul Simon from The Rhythm of the Saints

* " Proof ", a song by Happy Rhodes from Many Worlds Are Born Tonight

* " Proof ", a song by angela

* " Proof ", a song by Mell

Bikutsi's international renown continued to grow, and the song " Proof " from Paul Simon's Rhythm of the Saints, released to mainstream promotion and success in 1990, gained yet more renown from international audiences.

; Loveline, which Adam hosted ; as well as contributing the song " This Photograph Is Proof ( I Know You Know )" to the soundtrack for Spider-Man 2.

Shortly after his label-mate Proof was shot to death in a Detroit nightclub, a song emerged on the mixtape circuit called " Ride Wit Me ".

The song was dedicated to Proof.

It was also sampled by RJD2 for the song " Weather People Off Cage's Album Weather Proof " and by Army of the Pharaohs in their song " Swords Drawn ".

Intending to record one more song for the album (" Living Proof "), he ended up with ten new songs, which became Lucky Town.

D12, in turn, responded with the song " Instigator ", dissing Natas, while Proof made 2 diss tracks aimed specifically at Esham, " Every Sucker Has A Moment " and " Uh Huh ", though the latter was not released.

Eminem references Big Daddy Kane in the lyrics to his song ‘ Yellow Brick Road ’ from his Encore album, saying, “ we ( Eminem and Proof ) was on the same shit, that Big Daddy Kane shit, where compound syllables sound combined ” and he quotes the same lines in his book, The Way I Am – this illustrates how Big Daddy Kane had an influence on both Eminem ’ s and Proof ’ s rhyme technique.

The RICANstruction will also feature an unreleased collaboration with D12's Proof and a song with Big Pun.

This is arguably best exemplified by the music on Thrust, particularly on the song " Actual Proof ", Mike Clark has established himself as a true innovator of linear style drumming, incorporating jazz and funk.

Although Proof does not appear in the song, he provides a spoken introduction to the video, and is seen alongside his bandmates.

In Quentin Tarantino's segment of the 2007 Grindhouse, Death Proof, the character Jungle Julia ( Sydney Tamiia Poitier ) calls a contact at the radio station where she works, requesting the group's song " Hold Tight ".