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

According and theorem
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 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 a theorem of Nikolay Nikolov and Dan Segal, in any topologically finitely-generated profinite group ( that is, a profinite group that has a dense finitely-generated subgroup ) the subgroups of finite index are open.
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 and Schwarzschild
According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular Schwarzschild black hole.
According to W. Pauli ( Theory of relativity ), Schwarzschild is the first to introduce the correct Lagrangian formalism of the electromagnetic field as
According to general relativity, this would result in a minimum observed size of at least 5. 2 times the black hole's Schwarzschild radius, which, for a black hole of around 4 million solar masses, corresponds to a minimum observed size of approximately 52 μas.

According and solution
According to another study, when measured in a particular solution, the DNA chain measured 22 to 26 ångströms wide ( 2. 2 to 2. 6 nanometres ), and one nucleotide unit measured 3. 3 Å ( 0. 33 nm ) long.
According to this model the issuer cannot " win " and the only solution is to abruptly stop expanding the currency.
According to Arrhenius theory of electrolyte dissociation, the molecules of an electrolyte in solution are constantly splitting up into ions and the ions are constantly reuniting to form unionized molecules.
According to political scientist Norman Finkelstein transfer was considered as an acceptable solution to the problems of ethnic conflict, up until around World War II and even a little afterward, in certain cases.
According to Fromm, the awareness of a disunited human existence is a source of guilt and shame, and the solution to this existential dichotomy is found in the development of one's uniquely human powers of love and reason.
According to another theory, it is believed that the pointed arch evolved naturally in Western Europe as a structural solution to a purely technical problem, concurrent with its introduction and early use as a stylistic feature in French and English churches.
According to Brown & Wallace the de Broglie-Bohm particles play no role in the solution of the measurement problem.
According to Arrhenius's original definition, an acid is a substance that dissociates in aqueous solution, releasing the hydrogen ion H < sup >+</ sup > ( a proton ):
According to an IUPAC definition, solubility is the analytical composition of a saturated solution expressed as a proportion of a designated solute in a designated solvent.
According to Plutarch it was the citizens of Delos who consulted the oracle at Delphi, seeking a solution for their internal political problems at the time, which had intensified relationships among the citizens.
According to the United States diplomats Robert Keely and John Owens, who were attached to the United States embassy in Greece at the time, Constantine asked United States Ambassador Phillip Talbot what the attitude of the United States government would be to an extra-parliamentary solution to this problem.
According to Carter Golembe, the Banking Act of 1933 was the “ only important piece of legislation during the New Deal ’ s famous ‘ one hundred days ’ which was neither requested nor supported by the new administration .” In their books on banking events in 1933, Susan Eastabrook Kennedy and Helen Burns concluded that, although the 1933 Banking Act was not part of the New Deal, Roosevelt ultimately preferred it to no banking reform bill even thought it did not provide the more “ far reaching ” reforms ( Kennedy ) or “ fuller solution ” ( Burns ) he sought.
According to director Eiji Aonuma, they were " faced with the very difficult question of just what kind of game could follow Ocarina of Time and its worldwide sales of seven million units ", and as a solution, came up with the three-day system to " make the game data more compact while still providing deep gameplay ".
According to Drucker, corporations tend to produce too many products, hire employees they don't need ( when a better solution would be outsourcing ), and expand into economic sectors that they should avoid.
According to the philosophical system of Aristotle and his followers, there are four causes or reasons that describe a thing ; these causes can be analyzed to get to a solution to the paradox.
According to this model the issuer cannot " win " and the only solution is to abruptly stop expanding the currency.
According to Bloch's theorem, the wavefunction solution of the Schrödinger equation when the potential is periodic, can be written as:
According to the amended complaint, it is “ not reasonable to expect that in the future the State of Nebraska will enforce its laws regulating the sale of alcohol at Whiteclay .” Bruning had said he believed the State of Nebraska should not be involved in the suit ; that shutting down the beer stores wasn't the solution ; that reservation residents would drive further afield to purchase alcohol, which might lead to increased drunk driving ; and that any money recovered in damages by the OST, in this suit or others, might be used to buy alcohol.
According to Mountain, " The solution we ended with is a beautiful thing ...
According to Harrington's account of the split, when he opened discussion with racial-separatist rabbi Mayer Schiller ( see section on Harrington's ideological development below ) and advocated a two-state solution to the Israeli-Palestinian conflict, he was attacked as a " Zionist ".
According to them, these emerged as a result of solution processes by water in complex interactions with iron compounds from neighbouring or intrusive magmatic-volcanic rocks.
According to directors of the company, the repair bill could have gone as high as $ 2 million, the quickest solution being to replace the damaged engine.

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