According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.

According to (), the first historical mention of the statement of this theorem appears in ().

According to Birkhoff's theorem, it is the only vacuum solution that is spherically symmetric.

According to the theorem, it is possible to expand the power ( x + y )< sup > n </ sup > into a sum involving terms of the form ax < sup > b </ sup > y < sup > c </ sup >, where the exponents b and c are nonnegative integers with, and the coefficient a of each term is a specific positive integer depending on n and b. When an exponent is zero, the corresponding power is usually omitted from the term.

According to the theorem, it is possible to expand any power of x + y into a sum of the form

According to Noether's theorem, the conservation of energy is a consequence of the fact that the laws of physics do not change over time.

According to the theorem, within every sufficiently powerful logical system ( such as Principia ), there exists a statement G that essentially reads, " The statement G cannot be proved.

According to the spin-statistics theorem, particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states ; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics.

According to Rice's theorem, if there is at least one computable function in a particular class C of computable functions and another computable function not in C then the problem of deciding whether a particular program computes a function in C is undecidable.

According to the Rouché – Capelli theorem, the system is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix.

According to the optical Raychaudhuri's theorem, this requires a violation of the averaged null energy condition.

According to the theorem, the reconstructed signal will match the original signal provided that the original signal contains no frequencies at or above this limit.

According to the Nyquist theorem, error-free detection of the line code requires a channel bandwidth of at least the Nyquist rate, which is half the line code pulse rate.

According to Shannon's source coding theorem, the optimal code length for a symbol is − log < sub > b </ sub > P, where b is the number of symbols used to make output codes and P is the probability of the input symbol.

According to the CPT theorem of particle physics, antihydrogen atoms should have many of the characteristics regular hydrogen atoms have ; i. e., they should have the same mass, magnetic moment, and transition frequencies ( see atomic spectroscopy ) between their atomic quantum states.

According to Liouville's theorem, any bounded complex analytic function defined on the whole complex plane is constant.

According to Allen Weiss, in Mirrors of Infinity, this optical effect is a result of the use of the tenth theorem of Euclid ’ s Optics which asserts that “ the most distant parts of planes situated below the eye appear to be the most elevated .” In Fouquet ’ s time, interested parties could cross the canal in a boat, but walking around the canal provides a view of the woods that mark what is no longer the garden and shows the distortion of the grottos previously seen as sculptural.

According to the virial theorem, the gravitational binding energy of a star is about two times its internal thermal energy.

According to the correspondence principle and Ehrenfest's theorem as a system becomes larger or more massive ( action >> Planck's constant ) the classical dynamics tends to emerge, with some exceptions, such as superfluidity.

According to the Kutta – Joukowski theorem, lift is the product of circulation, airspeed, and air density.

According to the Shannon – Hartley theorem, the channel capacity of a properly-encoded signal is proportional to the bandwidth of the channel and the logarithm of the signal-to-noise ratio ( SNR ) ( assuming the noise is additive white Gaussian noise ).

According to Ptolemy's second theorem,

According to the inverse function theorem, the matrix inverse of the Jacobian matrix of an invertible function is the Jacobian matrix of the inverse function.

According to one leading historian of statistics, he may have been the earliest discoverer of Bayes theorem.

According to Nikolay Polyakov, Stalin purportedly created a special " Deportation Commission " to plan the deportation of Jews to these camps.

According to Dan Krutz, former president of CUIC, " Overcoming racism has been a focal point of CUIC since its beginning ... Racism may be the biggest sin that divides churches.

According to Dan Sutter of the University of Oklahoma, a systematic liberal bias in the U. S. media could depend on the fact that owners and / or journalists typically lean to the left.

According to Dan Gill, geological investigations in the early 1990s confirmed earlier observations that the high assault ramp consisted mostly of a natural spur of bedrock that required a ramp only high built atop it in order to reach the Masada defenses.

According to the Bible, when the Jewish exiles returned to Jerusalem following a decree from Cyrus the Great ( Ezra 1: 1-4, 2 Chron 36: 22-23 ), construction started at the original site of Solomon's Temple, which had remained a devastated heap during the approximately 70 years of captivity ( Dan.

According to one family tradition, a schoolteacher once expressed concern over Boone's education, but Boone's father was unconcerned, saying " Let the girls do the spelling and Dan will do the shooting ….

According to conversations with Dan McKinnon and Steve Harfst ( former COO ), there was no desire for the company to compete with the low fare cost structure of JetBlue.

According to the best accepted story, the name " Neptune Beach " originated in 1922 with Dan G. Wheeler, one of the few residents.

According to the story told in the radio series, the group of six ambushed Rangers was headed by Reid's brother, Captain Dan Reid.

According to your last letter Dan has left her quiet up till then, but not without sacrifices .”

According to Martin Woesler trends were ' cult literature ' with Guo Jingming ( 郭敬明 ), 悲伤逆流成河 Cry me a sad river, vagabond literature with Xu Zechen ( 徐则臣 ), 跑步穿过中关村 Peking double quick, Liu Zhenyun ( 刘震云 ), 我叫刘跃 The pickpockets, underground literature Mian Mian ( 棉棉 ), 声名狼籍 Panda Sex, ' longing for something ' literature, divided in historicizing literature with Yu Dan 于丹, 《 论语 》 心得 Confucius in your heart, Yi Zhongtian ( 易中天 ) and in Tibetan literature with Alai, literature of the mega cities, women's literature with Bi Shumin ( 毕淑敏 ), 女儿拳 Women ’ s boxing, 女心理师 The female psychologist, master narratives by narrators like Mo Yan 莫言 with 生死疲勞 Life and Death are Wearing me out.

According to the book " From Can See to Can't " by Thad Sitton and Dan Utley, " Under ideal conditions for reproduction – which fortunately seldom existed – the progeny of a single pair of weevils emerging in the spring could reach something like 134 million before the coming of frost.

According to Romanian political analysts such as Daniel Barbu or Dan Pavel, his election was based almost exclusively on the rural population and disoriented lower class industrial workers, controlled through manipulation from the state-controlled media ( Televiziunea Română, the state television, was the only wide-scale TV channel until 1993 ).

According to Richard Wilhelm, Lü was the founder of the School of the Golden Elixir of Life ( Jin Dan Jiao ), and originator of the material presented in the book " Tai Yi Jin Hua Zong Zhi " (《 太一金華宗旨 》), or The Secret of the Golden Flower.

According to Dan Savage, Cornerstone means when you get high in order to break through a sexual inhibition — like when pot helps you " turn a corner " sexually.

According to scout John C. Cremony and historian Dan L. Thrapp, the howitzer fire sent the Apaches into an immediate retreat.

According to Dan Lusthaus, " Since the progression and development of his thought ... is so strikingly evident in these works, and the similarity of vocabulary and style of argument so apparent across the texts, the theory of Two Vasubandhus has little merit.

Calling themselves Dan Emmett's Virginia Minstrels, the performance was wildly popular and most historians mark this production as the beginning of minstrelsy in the U. S. According to jazz historian Gary Giddins:

According to the Torah, the tribe consisted of descendants of Dan, a son of Jacob and Bilhah, Rachel's maidservant ().

According to the biblical narrative, the tribe had originally tried to settle in the central coastal area of Canaan, but due to enmity with the Philistines who had already settled there, were only able to camp in the hill country overlooking the Sorek Valley, the camp location becoming known as Mahaneh Dan (" Camps of Dan ").

According to the Book of Revelation ( 7: 4-8 ), the tribe of Dan is the only original tribe of Israel which is not included in the list of tribes which are sealed.

According to scholar Dan Grigorescu, his essays of the time fluctuate away from Constructivism, and adopt ideas common in Expressionism, Surrealism, or even the Byzantine revival suggested by anti-modernist reviews.

According to writers on organized crime, the Syndicate was born from an idea of Johnny " The Fox " Torrio and was founded or established at a May 1929 conference in Atlantic City, attended by leading underworld figures throughout the United States, including Torrio, Lucky Luciano, Al Capone, Meyer Lansky, Frank Costello, Joe Adonis, Benjamin " Bugsy " Siegel, Dutch Schultz, Abner " Longy " Zwillman, Louis " Lepke " Buchalter, Vince Mangano, gambler Frank Erickson, Frank Scalice and Albert " Mad Hatter " Anastasia .< ref > Carl Sifakis, < cite > The Mafia Encyclopedia: second edition </ cite >, ( Checkmark Books )</ ref > Others describe the Atlantic City meeting as a coordination and strategy conference for bootleggers .< ref > Dennis Eisenberg, Uri Dan, Eli Landau ,< cite > Meyer Lansky: Mogul of the Mob </ cite > Paddington Press, 1979 </ ref >

According to Kelis's management firm, Three Six Zero Group, the album is due for a late 2012 release and will feature production from Skream, BURNS, Tom Neville, Dan Black and Caspa.