According to the OED, this may be the origin of the term Nyquist rate.

According to Daniel Pipes, Golitsyn's publications " had some impact on rightist thinking in the United States ", including political writer Jeffrey Nyquist and Joel Skousen, as well as the John Birch Society.

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 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 Ovid, it was Jupiter ( Zeus ) who took the form of Diana ( Artemis ) so that he might evade his wife Juno ’ s detection, forcing himself upon Callisto while she was separated from Diana and the other nymphs.

According to Holmes, it was an encounter with the father of one of his classmates that led him to take up detection as a profession, and he spent the six years following university working as a consulting detective, before financial difficulties led him to take Watson as a roommate, at which point the narrative of the stories begins.

According to Cochrane Review, routine ultrasound in early pregnancy ( less than 24 weeks ) appears to enable better gestational age assessment, earlier detection of multiple pregnancies and earlier detection of clinically unsuspected fetal malformation at a time when termination of pregnancy is possible.

* According to RadiologyInfo, ultrasounds are useful in the detection of pelvic abnormalities and can involve techniques known as abdominal ( transabdominal ) ultrasound, vaginal ( transvaginal or endovaginal ) ultrasound in women, and also rectal ( transrectal ) ultrasound in men.

According to Plato, the rational detection of error amounts to finding the proof of the antithesis.

According to 2003 figures, Crewe had the lowest crime rate and highest detection levels in Cheshire.

According to a cohort study, single-slice spiral CT may help diagnose detection among people with suspected pulmonary embolism.

According to the National Fire Protection Agency, " photoelectric smoke detection is generally more responsive to fires that begin with a long period of smoldering ( called smoldering fires ).

According to proponents, the Philadelphia Experiment supposedly aimed to render the USS Eldridge invisible to radar detection with disastrous results.

According to Dr. Farwell, the MERMER includes additional features involving changes in the frequency of the EEG signal, but for the purposes of signal detection and practical application the MERMER is sufficiently characterized by the P300 and the following negative component in the brain response ( Farwell 1994, Farwell & Smith 2001, Farwell et al.

According to WHO, " Pharmacovigilance activities are done to monitor detection, assessment, understanding and prevention of any obnoxious adverse reactions to drugs at therapeutic concentration that is used or is intended to be used to modify or explore physiological system or pathological states for the benefit of recipient.

According to Pacific Biosciences, the SMRT technology developer, this methodology allows detection of nucleotide modifications ( such as cytosine methylation ).

According to these sources, the radar shows that one or two Libyan MiG-23 had tried to evade detection by flying close to the airliner.

According to journalist Seymour Hersh, the detection was the third joint Israeli-South African nuclear test in the Indian Ocean, and the Israelis had sent two IDF ships and " a contingent of Israeli military men and nuclear experts " for the test.

According to av-comparatives, Norton Internet Security was " Best Product of 2009 ", Bronze award for 98. 6 % detection rate in 2010 and Norton Internet Security 2010 blocked 99 / 100 internet threats from infecting the user's computer.

According to the LC-NE hypothesis, when a salient, or meaningful stimulus is presented, neurons in the locus coeruleus release norepinephrine, a neurotransmitter that benefits the detection of the stimulus.