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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. |
Alphekka (α Coronae Borealis) Alfakké (#) Fr.: Alphekka Also known as Gemma, the brightest star in Corona Borealis (visual magnitude 2.23). Alphekka is an A type dwarf lying at about 7 → light-years. Actually it has a faint Sun-like (G5 V) companion, that produces an eclipse of the primary every 17.4 days. Alphekka, from Ar. Nayyir al-Fakkah "the bright of the broken" (ring of star), from Nayyir "bright" + fakkah "broken," from fakk "to disjoin, unloose". |
arborescence šâkedâri Fr.: arborescence 1) In → graph theory, a → rooted tree
that has a natural orientation in which all → paths
are directed away from the → root. More specifically, a
→ directed graph in
which, for a → vertex u, called the
→ root, and any other vertex v,
there is exactly one → directed path
from u to v. From Fr. arborescence, from → arborescent + → -ance. Šâkedâri, nous from šâkedâr, → arborescent. |
arborescent šâkedâr Fr.: arborescent Having the shape or characteristics of a tree in growth, structure, or appearance. From Fr. arborescent, from L. arborescent-, p.p. of arborescere "to grow into a tree," from arbor, arboris "tree." Šâkedâr "having branches," from šâké, from šâxé, → branch, + dâr "having, possessor," from dâštan "to have, to possess," → charged. |
aurora borealis uše-ye hudari Fr.: aurore boréale The aurora in the Northern hemisphere, also called as Northern Lights. |
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 |
Bowen fluorescence mechanism sâzokâr-e fluoresti-ye Bowen Fr.: mécanisme de fluorescence de Bowen A mechanism, made possible by certain chance coincidences between → spectral lines of He II, O III and N III in some → planetary nebulae , that explains the presence with a high intensity of a selected group of O III and N III lines while all other lines of these elements are missing. After I. S. Bowen who first discovered this mechanism in 1935; → fluorescence; → mechanism. |
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. |
cluster core maqze-ye xušé Fr.: cœur d'amas The central part of a cluster (globular, galaxies, etc.) where the spatial density of the objects making up the cluster is much higher than the average value. |
convective core maqze-ye hambazi Fr.: cœur convectif The central region of a → massive star where → convection prevails due to steep gradient of temperature relative to pressure. → convective; → core. |
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. |
core maqzé Fr.: cœur, noyau 1) The central region of a star in which energy is generated by
→ thermonuclear reactions. Probably from O.Fr. cœur "core of fruit," literally "heart," from L. cor "heart," cf. Gk. kardia: P.Gmc. *khertan- (O.E. heorte, E. heart, Ger. Herz, Bret. kreiz "middle"), Skt. hrd-; Av. zərəd-; Mid.Pers. dil; Mod.Pers. del; Baluci zird; Arm. sirt; PIE base *kerd- "heart". Maqzé, from maqz "kernel; brain; marrow" + nuance suffix -é. Mod.Pers. maqz from Mid.Pers. mazg "brain; marrow," Av. mazga- "marrow; brain" cf. Skt. majján- "marrow," P.Gmc. *mazga-, O.E. mearg "marrow," Lith. smagenes "brain," O.H.G. mark "marrow," PIE base *mozgho- "marrow, brain". |
core collapse rombeš-e maqzé Fr.: effondrement de cœur The collapse of a → massive star's core at the → final → stages of its → evolution when the core consists entirely of → iron (→ iron core). Since iron cannot burn in → nuclear reaction, no energy is generated to support the → gravitational collapse. The result will be a → supernova explosion of → Type Ib, → Type Ic, or → Type II. See also → core-collapse supernova. |
core elliptical galaxy kahkešân-e beyzigun-e maqzedâr Fr.: galaxie elliptique à coeur An → elliptical galaxy that displays a → surface brightness profile with a distinct break from a steep outer slope to a shallower inner → cusp. Core profiles mainly occur in very luminous elliptical galaxies and are considered the result of dissipation-less → mergers of two galaxies that have central → supermassive black holes (S. P. Rusli et al., 2013, AJ 146, 160). → core; → elliptical; → galaxy. |
core mass function (CMF) karyâ-ye jerm-e maqzé Fr.: fonction de masse des cœurs The mass distribution of → pre-stellar cores in → star-forming regions. The CMF is usually represented by dN/dM = M^{α}, where dM is the mass interval, dN the number of cores in that interval, and α takes different values in different mass ranges. In the case of → low-mass stars, it is found that the CMF resembles the → Salpeter function, although deriving the masses and radii of pre-stellar cores is not straightforward. The observational similarity between the CMF and the → initial mass function (IMF) was first put forth by Motte et al. (1988, A&A, 336, 150), and since then many other samples of dense cores have been presented in this context. For example, Nutter & Ward-Thompson (2007, MNRAS 374, 1413), using SCUBA archive data of the Orion star-forming regions, showed that the CMF can be fitted to a three-part → power law consistent with the form of the stellar IMF. Recent results, obtained using observations by the → Herschel Satellite, confirm the similarity between the CMF and IMF with better statistics (Könyves et al. 2010, A&A, 518, L106; André et al. 2010, A&A, 518, L102). Moreover, these works show that the CMF has a → lognormal distribution (i.e. dN/dlog M follows a → Gaussian form against log M), as is the case for the IMF at low masses (below about 1 solar mass). |
core overshooting farâzad-e maqzé Fr.: dépassement du cœur → core; → overshooting. |
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