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According and inverse
According to the principle of relativity, there is no privileged frame of reference, so the inverse transformations frame F ′ to frame F must be given by simply negating v.
According to Bandler and Grinder, the meta model is intentionally specific, but the Milton model was described as " artfully vague " and metaphoric — the inverse of the meta model.
* According to the inverse function theorem, a smooth map f: M → N is a local diffeomorphism if and only if the derivative Df < sub > p </ sub >: T < sub > p </ sub > M → T < sub > f ( p )</ sub > N is a linear isomorphism for all points p in M. Note that this implies that M and N must have the same dimension.
According to Whitehall study researchers, " a steep inverse association between social class, as assessed by grade of employment, and mortality from a wide range of diseases " has been demonstrated.

According and function
According to Hailsham, a former chairman of the British Conservative Party, " Conservatism is not so much a philosophy as an attitude, a constant force, performing a timeless function in the development of a free society, and corresponding to a deep and permanent requirement of human nature itself.
According to Carnot's principle, work can only be done when there is a temperature difference, and the work should be some function of the difference in temperature and the heat absorbed.
According to the understanding of quantum mechanics known as the Copenhagen interpretation, measurement causes an instantaneous collapse of the wave function describing the quantum system into an eigenstate of the observable state that was measured.
According to Manolo Sanlúcar E is here the tonic, F has the harmonic function of dominant while Am and G assume the functions of subdominant and mediant respectively.
According to K. F. P. v. Martius the kanaima is a human being who employs poison to carry out his function of blood avenger ; other authorities represent the kanaima as a jaguar, which is either an avenger of blood or the familiar of a cannibalistic sorcerer.
According to the BHK interpretation, this proof itself is essentially the function F that is desired.
According to natural law theory, which holds that morality is a function of human nature and reason can discover valid moral principles by looking at the nature of humanity in society, the content of positive law cannot be known without some reference to natural law ( or something like it ).
According to Rand, " man's mind will not function at the point of a gun.
According to Woolf, there are three classes of pain: nociceptive pain ( see hereunder ), inflammatory pain which is associated with tissue damage and the infiltration of immune cells, and pathological pain which is a disease state caused by damage to the nervous system ( neuropathic pain, see hereunder ) or by its abnormal function ( dysfunctional pain, like in fibromyalgia, irritable bowel syndrome, tension type headache, etc.
According to Barthes the function of a wrestler is not to win: it is to go exactly through the motions which are expected of him and to give the audience a theatrical spectacle.
According to one interpretation, as the result of a measurement the wave function containing the probability information for a system collapses from a given initial state to a particular eigenstate.
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 principles of eurythmy, there are archetypal movements or gestures that correspond to every aspect of speech – the sounds ( or phonemes ), the rhythms, and the grammatical functionto every " soul quality " – joy, despair, tenderness, etc.
According to a 1996 statement from the American Association of Physical Anthropologists, although heredity influences behavior in individuals, it does not affect the ability of a population to function in any social setting, all peoples " possess equal biological ability to assimilate any human culture " and " racist political doctrines find no foundation in scientific knowledge concerning modern or past human populations.
According to Hermann Weyl, the assumption that space is made of finite and discrete units is subject to a further problem, given by the " tile argument " or " distance function problem ".
According to some sources, the older man was expected to function as a kind of substitute father and role model to his junior partner ; however, others believe it was reasonably certain that they had sexual relations ( the exact nature of Spartan pederasty is not entirely clear ).
According to this model, the uncoordinated instinctual trends are the " id "; the organized realistic part of the psyche is the " ego ," and the critical and moralizing function the " super-ego.
According to Tober and Carroll, indigo children may function poorly in conventional schools due to their rejection of rigid authority, being smarter ( or more spiritually mature ) than their teachers, and a lack of response to guilt -, fear-or manipulation-based discipline.
According to Malinowski, magic and religion are also similar in that they often serve the same function in a society.
According to Marxists, even literature itself is a social institution and has a specific ideological function, based on the background and ideology of the author.
According to this theory, the pairing wave function of the HTS should have a d < sub > x < sup > 2 </ sup >− y < sup > 2 </ sup ></ sub > symmetry.
According to two researchers, Nesse and Williams, diarrhea may function as an evolved expulsion defense mechanism.
According to some supporters of Everett's theory, if the ( never collapsing ) wave function is taken to be physically real, then it is natural to interpret the theory as having the same many worlds as Everett's theory.

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

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