According to the CPT Theorem, this means they should also be time irreversible, and so establish an arrow of time.

According to a 1977 Kampuchean document, it was claimed that the General Secretary of the CPT was ' Khamtan ' ( nom de guerre of Phayom Chulanont ).

According to Smith, Walter Christaller erred in his development of CPT in 1930 by using size of population and number of telephones in determining the importance of a city.

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 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 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 consensus among cosmologists, dark matter is composed primarily of a new, not yet characterized, type of subatomic particle.

" According to Heisenberg's uncertainty principle, it is impossible to measure both the momentum and the position of particle B exactly.

According to the BMDO, the research on neutral particle beam accelerators, which was originally funded by the SDIO, could eventually be used to reduce the half-life of nuclear waste products using accelerator-driven transmutation technology.

According to ordinary quantum theory, it is not possible to measure the spin or polarization of a particle directly ; instead, the component in one direction is measured ; the outcome from a single particle may be 1, meaning that the particle is aligned with the measuring apparatus, or-1, meaning that it is aligned the opposite way.

According to this interpretation, the purpose of a quantum-mechanical theory is to predict the relative probabilities of various alternative histories ( for example, of a particle ).

According to this cloud particle charging hypothesis, charges are separated when ice crystals rebound off graupel.

According to quantum mechanics, particle pairs are constantly appearing and disappearing as a quantum foam.

According to the U. S. Department of Agriculture Soil Texture Classification system, the sand-silt distinction is made at the 0. 05 mm particle size.

According to Zehe, Fatio's attempt to increase v to a very high value would actually leave the resistance very small compared with gravity, because the resistance in Fatio's model is proportional to ρuv but gravity ( i. e. the particle pressure ) is proportional to ρv < sup > 2 </ sup >.

According to that equation, the motion of a particle of mass m with velocity v is governed by Newton's second law

According to some authors, the thing which distinguishes ACO algorithms from other relatives ( such as algorithms to estimate the distribution or particle swarm optimization ) is precisely their constructive aspect.

According to the Standard Model of particle physics, the particles that make up an atom — quarks and electrons — are point particles: they do not take up space.

According to special relativity, all Lorentz observers watching a particle move will compute the same value for the quantity

According to pilot wave theory, the point particle and the matter wave are both real and distinct physical entities.

According to the Unified Soil Classification System, silt particle sizes are in the range of 0. 002 mm to 0. 075 mm and sand particles have sizes in the range of 0. 075 mm to 4. 75 mm.

According to the BBC, Năstase may have created a black hole at the Relativistic Heavy Ion Collider particle accelerator in New York.

According to the biography and statistics published on the Hasbro web site, Jetfire is 50 feet tall and his main weapon is his particle beam cannon.

According to de Broglie for all matter and for radiation alike, the energy E of the particle was related to the frequency of its associated wave ν by the Planck relation:

According to the wave particle duality, electrons can also be considered as wave propagations and therefore have associated wave properties such as wavelength, phase and amplitude.

According to Chao, the sentence-final particle is phonetically close to the last word before it, but syntactically it is equidistant from every word in the whole predicate.