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According to Cauchy's functional equation theorem, the logarithm is the only continuous transformation that transforms real multiplication to addition.
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According and functional
According to ISO / IEC 2382-01, Information Technology Vocabulary, Fundamental Terms, interoperability is defined as follows: " The capability to communicate, execute programs, or transfer data among various functional units in a manner that requires the user to have little or no knowledge of the unique characteristics of those units ".
According to FSTs, mental states are the particular " realizers " of the functional role, not the functional role itself.
According to Merton's perception of " functionalism ", all standardized social and cultural beliefs and practices are functional for both society as a whole as well as individuals in society.
According to the books, God recommends many economic and social changes if people want to make a more functional, adaptable, and sustainable world and recommends that more attention should focus on the environment.
According to Lucy Rosenstein: " It is verse of public statement ; its language is functional but aesthetically unappealing.
According to researchers at the University of Chicago who used functional magnetic resonance imaging ( fMRI ), children between the ages of 7 and 12 appear to be naturally inclined to feel empathy for others in pain.
According to BOMA Class C buildings are aimed towards " tenants requiring functional space at rents below the average for the area.
According to the Assistive Technology Act of 1988, assistive technology refers to " any item, piece of equipment, or product that is used to increase, maintain, or improve functional capabilities of individuals with disabilities.
According to the American Society of Pharmacognosy, pharmacognosy is " the study of natural product molecules ( typically secondary metabolites ) that are useful for their medicinal, ecological, gustatory, or other functional properties.
According to the Free-radical theory, oxidative damage initiated by reactive oxygen species is a major contributor to the functional decline that is characteristic of aging.
According to an analysis of data derived from the human genome project, humans have approximately 400 functional genes coding for olfactory receptors and the remaining 600 candidates are pseudogenes.
According Babylonian Talmud Tractate Yoma, the Kodesh Hakodashim is located in the center North-South but significantly to the West from an East-West perspective, with all the major courtyards and functional areas lying to its east.
According to research at Rockefeller University, the gene for dynorphin is present in two versions: a “ high output ” and a “ low output ” functional variation.
According to the Ranger Training Brigade, This phase focuses on the continued development of the Ranger Student's combat arms functional skills.
According to these orders, gave the command of all units on the Sinai Front Kress von Kressenstein until the new command arrangements are functional
According to one study, in the great majority of young adults, the functional outcome of surgical treatment of unresolved Osgood-Schlatter disease is excellent or good, the residual pain intensity is low, and postoperative complications or subsequent reoperations are rare.
According to Exelon Corporation, " many people are surprised when they learn that Three Mile Island is still making electricity, enough to power 800, 000 households " from its undamaged and fully functional reactor unit 1.
According to most recent software architecture models, even when using structured programming, it is usually preferred to make each function behave the same way every time the same arguments are passed to it, therefore following one of the basic principles of functional programming.
According and equation
According to Avogadro ’ s law this volume is same for all ideal gases and if we consider ‘ n ’ moles of an ideal gas at STP, then the equation becomes
According to this equation, minimum feature sizes can be decreased by decreasing the wavelength, and increasing the numerical aperture ( to achieve a tighter focused beam and a smaller spot size ).
According to the Tsiolkovsky equation this results in proportionally higher final velocity of propelled craft.
According to the following equation, derived from Ohm's Law, the value of the resistance ( R ) is given by:
According to the Tsiolkovsky rocket equation, a rocket with higher exhaust velocity needs less propellant mass to achieve a given change of speed.
According to the Copenhagen interpretation of quantum mechanics, quantum evolution is governed by the Schrödinger equation, which is time-symmetric, and by wave function collapse, which is time irreversible.
According to a form of Euler's fluid dynamics equation, known as " pump and turbine equation ," the energy input to the fluid is proportional to the flow's local spinning velocity multiplied by the local impeller tangential velocity.
According to Newton's law of gravitation, the gravitational force,, acting on a mass, due to a mass which is a distance away, obeys the equation
According to Bloch's theorem, the wavefunction solution of the Schrödinger equation when the potential is periodic, can be written as:
According to that equation, the motion of a particle of mass m with velocity v is governed by Newton's second law
According to Gibbs free energy equation, the relation between dissociation equilibrium constant, K < sub > d </ sub >, and the components of free energy was built.
According to Noh-Varr the Kree have a mathematical equation that disproves the existence of any deity, which is taught to all Kree around " the same time we learn not to soil ourselves with excrement ".
According to the Friedmann – Lemaître – Robertson – Walker metric which is used to model the expanding universe, if at the present time we receive light from a distant object with a redshift of z, then the scale factor at the time the object originally emitted that light is given by the equation.
According to the orbital energy conservation equation ( also referred to as vis-viva equation ), it does not vary with time:
According to a dew point calculator at this site ( as an alternative, one may use the Antoine equation to obtain an approximate value ), that partial pressure results in the local dew point of about 0. 86 ° C ; in other words, the new local dew point is about equal to the new local temperature.
According to D ' Alembert's principle, inclusion of inertial forces as additional body forces will give the virtual work equation applicable to dynamical systems.
According to this equation, the efficiency of separation is only limited by diffusion and is proportional to the strength of the electric field.
According to this equation, maximum resolution is reached when the electrophoretic and electroosmotic mobilities are similar in magnitude and opposite in sign.
According and theorem
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 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 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.