Abel's theorem farbin-e Abel Fr.: théorème d'Abel 1) If a → power series → converges
for some nonzero value
x_{0}, then it converges absolutely for any value of x, for
which |x| < |x_{0}|. Named after the Norwegian mathematician Niels Henrik Abel (1802-1829); → theorem. |
absolute measurement andâzegiri-ye avast Fr.: mesure absolue A measurement in which the comparison is directly with quantities whose units are basic units of the system. For example, the measurement of speed by measurements of distance and time is an absolute measurement, but the measurement of speed by a speedometer is not an absolute measurement. Note that the word absolute measurement implies nothing about → precision or → accuracy (IEEE Standard Dictionary of Electrical and Electronics Terms). → absolute; → measurement. |
Balmer decrement kâhe-ye Bâlmer Fr.: décrément de Balmer The intensity ratio among the couple of relatively adjacent → Balmer lines, for example Hα/Hβ and Hβ/Hγ, which have well-known theoretical values. They are used to determine the → interstellar extinction. |
Bayes' theorem farbin-e Bayes Fr.: théorème de Bayes A theorem in probability theory concerned with determining the → conditional probability of an event when another event has occurred. Bayes' theorem allows revision of the original probability with new information. Its simplest form is: P(A|B) = P(B|A) P(A)/P(B), where P(A): independent probability of A, also called prior probability; P(B): independent probability of B; P(B|A): conditional probability of B given A has occurred; P(A|B): conditional probability of A given B has occurred, also called posterior probability. Same as Bayes' rule. Named after its proponent, the British mathematician Reverend Thomas Bayes (1702-1761). However, Bayes did not publish the theorem during his lifetime; instead, it was presented two years after his death to the Royal Society of London. |
Bernoulli's theorem farbin-e Bernoulli Fr.: théorème de Bernoulli A statement of the → conservation of energy in the → steady flow of an → incompressible, → inviscid fluid. Accordingly, the quantity (P/ρ) + gz + (V^{2}/2) is → constant along any → streamline, where P is the fluid → pressure, V is the fluid → velocity, ρ is the mass → density of the fluid, g is the acceleration due to → gravity, and z is the vertical → height. This equation affirms that if the internal velocity of the flow goes up, the internal pressure must drop. Therefore, the flow becomes more constricted if the velocity field within it increases. Same as the → Bernoulli equation. After Daniel Bernoulli (1700-1782), the Swiss physicist and mathematician who put forward the theorem in his book Hydrodynamica in 1738; → theorem. |
binomial theorem farbin-e donâmin Fr.: théorème du binôme A rule for writing an equivalent expansion of an expression such as (a + b)^{n} without having to perform all multiplications involved. → binomial expansion. The general expression is (a + b)^{n} = &Sigma (n,k)a^{k}b^{n - k}, where the summation is from k = 0 to n, and (n,k) = n!/[r!(n - k)!]. For n = 2, (a + b)^{2} = a^{2} + 2ab + b^{2}. Historically, the binomial theorem as applied to (a + b)^{2} was known to Euclid (320 B.C.) and other early Greek mathematicians. In the tenth century the Iranian mathematician Karaji (953-1029) knew the binomial theorem and its accompanying table of → binomial coefficients, now known as → Pascal's triangle. Subsequently Omar Khayyam (1048-1131) asserted that he could find the 4th, 5th, 6th, and higher roots of numbers by a special law which did not depend on geometric figures. Khayyam's treatise concerned with his findings is lost. In China there appeared in 1303 a work containing the binomial coefficients arranged in triangular form. The complete generalization of the binomial theorem for all values of n, including negative integers, was established by Isaac Newton (1642-1727). |
Birkhoff's theorem farbin-e Birkhoff Fr.: théorème de Birkhoff For a four dimensional → space-time, the → Schwarzschild metric is the only solution of → Einstein's field equations which describes the gravitational field created by a spherically symmetrical distribution of mass. The theorem implies that the gravitational field outside a sphere is necessarily static, and that the metric inside a spherical shell of matter is necessarily flat. The theorem was first demonstrated in 1923 by George David Birkhoff (1884-1944), an American mathematician; → theorem |
bremsstrahlung legâm-tâbeš Fr.: rayonnement de freinage, bremsstrahlung The → electromagnetic radiation emitted by a → fast moving → charged particle when it passes within the strong → electric field of an → atomic nucleus and is → decelerated. Bremsstrahlung, from Ger. Bremse "brake" + Strahlung "radiation," from strahlen "to radiate," from Strahl "ray," from O.H.G. strala "arrow, stripe;" PIE *ster- "to spread." |
Cauchy's theorem farbin-e Cauchy Fr.: théorème de Cauchy If f(x) and φ(x) are two → continuous functions on the → interval [a,b] and → differentiable within it, and φ'(x) does not vanish anywhere inside the interval, there will be found, in [a,b], some point x = c, such that [f(b) - f(a)] / [φ(b) - φ(a)] = f'(c) / φ'(c). → Cauchy's equation; → theorem. |
central limit theorem farbin-e hadd-e markazi Fr.: théorème central limite A statement about the characteristics of the sampling distribution of means of → random samples from a given → statistical population. For any set of independent, identically distributed random variables, X_{1}, X_{2},..., X_{n}, with a → mean μ and → variance σ^{2}, the distribution of the means is equal to the mean of the population from which the samples were drawn. Moreover, if the original population has a → normal distribution, the sampling distribution of means will also be normal. If the original population is not normally distributed, the sampling distribution of means will increasingly approximate a normal distribution as sample size increases. |
convolution theorem farbin-e hamâgiš Fr.: théorème de convolution A theorem stating that the → Fourier transform of the convolution of f(x) and g(x) is equal to the product of the Fourier transform of f(x) and g(x): F{f*g} = F{f}.F{g}. → convolution; → theorem. |
Coriolis theorem farbin-e Coriolis Fr.: théorème de Coriolis The → absolute acceleration of a point P, which is moving
with respect to a local → reference frame
that is also in motion, is equal to the vector
sum of: → Coriolis effect; → theorem. |
decrement kâhé Fr.: décrément 1) The amount lost in the process of decreasing. L decrementum, from decre(tus), → decrease + -mentum noun suffix -ment. Kâheh, from kâh- present stem of kâhidan, → decrease + noun suffix -é. |
divergence theorem farbin-e vâgerâyi Fr.: théorème de flux-divergence Same as → Gauss's theorem. → divergence; → theorem. |
existence theorem farbin-e hastumandi, ~ hasti Fr.: théorème d'existence Math: A theorem that asserts the existence of at least one object, such as the → solution to a → problem or → equation. |
extreme ostom Fr.: extrême Farthest from the center or middle; outermost; exceeding the bounds of moderation. → extreme adaptive optics; → extreme HB star; → extreme horizontal branch star; → extreme infrared; → extreme mass ratio inspiral; → extreme ultraviolet; → extremely metal-poor star. From L. extremus "outermost, utmost," superlative of exterus, "outer," comparative of ex "out of," → ex-. Ostom "outermost, utmost" (Av. (ustəma- "outermost, highest, ultimate"), superlative of ost "out," → ex-, + -tom superlative suffix, from Mid.Pers. -tom (xwaštom "most pleasant," nevaktom "best," wattom "worst"), from O.Pers. -tama- (fratama- "first, front"); Av. -təma- (amavastəma- "strongest," hubaiδitəma- "most sweet-scented," baēšazyôtəma- "most healing," fratəma- "first, front"); cf. Skt. tama-. |
extreme adaptive optics nurik-e niyâveši-ye ostom Fr.: optique adaptative extrême An → adaptive optics system with high-contrast imaging and spectroscopic capabilities. Extreme adaptive optics systems enable the detection of faint objects (e.g., → exoplanets) close to bright sources that would otherwise overwhelm them. This is accomplished both by increasing the peak intensity of point-source images and by removing light scattered by the atmosphere and the telescope optics into the → seeing disk. |
extreme HB star setâre-ye EHB Fr.: étoile EBH Same as → extreme horizontal branch star. |
extreme horizontal branch star (EHB) setâre-ye šâxe-ye ofoqi-ye ostom Fr.: étoile de la branche horizontale extrême The hottest variety of stars on the → horizontal branch with temperatures ranging from 20,000 to 40,000 K. EHB stars are distinguished from normal horizontal branch stars by having extremely thin, inert hydrogen envelopes surrounding the helium-burning core. They are hot, dense stars with masses in a narrow range near 0.5 Msun. These stars have undergone such extreme mass loss during their first ascent up the giant branch that only a very thin hydrogen envelope survives. Stars identified as EHB stars are found in low metallicity globular clusters as an extension of the normal HB. → extreme; → horizontal; → branch; → star. |
extreme infrared forusorx-e ostom Fr.: infrarouge extrême A portion of the far infrared radiation, including wavelengths between 100 and 1,000 microns. |