binary system râžmâne dorin Fr.: système binaire Two astronomical objects revolving around their common center of mass. → binary; → system. 
binary tree deraxte dorin Fr.: arbre binaire In → graph theory, an → ordered tree with all → nodes having at most two → children. 
bind bandidan (#) Fr.: lier To tie, to fasten, to cause ti stick together. O.E. bindan "to tie up with bonds," PIE base *bhendh "to bind;" cf. Av./O.Pers. band "to bind, fetter," banda "band, tie," Skt. bandh "to bind, tie, fasten," bandhah "a tying, bandage." Bandidan "to bind, confine" [Mo'in, Dehxodâ], from band "band, tie" + idan infinitive suffix; cognate with E. bind, as explained above. 
binding energy kâruže bandeš, ~ hamgiri Fr.: énergie de liaison 1) Of a gravitational system, the difference
in energies between the hypothetical state where all bodies of
the system are infinitely separated from each other and the actual bound state.

binning bâvineš Fr.: binage Combining a few adjacent CCD pixels in bins, during readout; the method used to assemble the bins and transfer the charge by means of an electronic clock. Binning improves signaltonoise ratio at the expense of spatial resolution. Binning, from → bin. Bâvineš, from bâvin, → bin. 
binoculars docašmi (#), durbine ~ (#) Fr.: binoculaire A small optical instrument with two tubes that is used to magnify the view of distant or astronomical objects. → prism binoculars. From Fr. binoculaire, from binocle, from L. bini "double" (L. bis, bi "twice," Av. biš "twice") + ocularis "of the eye," from oculus "eye" (compare with Av. axš, aš "eye," Skt. akshi "eye," Gk. ops "eye," opsis "sight, appearance," from PIE okw "to see;" also O.E. ege, eage, from P.Gmc. *augon, Goth. augo, Lith. akis, Armenian aku). Docašmi "binocular," from do, → two + cašm, → eye, + i adj. suffix; durbin, → telescope. 
binomial donâmin Fr.: 1) binôme; 2) binomial 1a) An algebraic expression containing 2 terms, as x + y and
2x^{2}  3x. In other words, a → polynomial
with 2 terms. From L.L. binomi(us) "having two names," + → al, → nominal. 
binomial coefficient hamgare donâmin Fr.: coefficient binomial
The factor multiplying the variable in a term of a → binomial expansion. For example, in (x + y)^{4} = x^{4} + 4x^{3}y + 6x^{2}y^{2} + 4xy^{3} + y^{4} the binomial coefficients are 1, 4, 6, 4, and 1. In general, the rth binomial coefficient in the expression (x + y)^{n} is: (n,r) = n!/[r!(n  r)!]. → binomial; → coefficient. 
binomial differential degarsâneye donâmin Fr.: binôme différentiel An expression of the form x^{m}(a + bx^{n})^{p}dx, where m, n, p, a, and b are constants. → binomial; → differential. 
binomial distribution vâbâžeše donâmin Fr.: distribution binomiale A probability distribution for independent events for which there are only two possible outcomes i.e., success and failure. The probability of x successes in n trials is: P(x) = [n!/x!(n  x)!] p^{x}.q^{n  x}, where p is the probability of success and q = 1  p the probability of failure on each trial. These probabilities are given in terms of the → binomial theorem expansion of (p + q)^{n}. → binomial; → distribution. 
binomial expansion sopâneše donâmin Fr.: expansion binomiale A rule for the expansion of an expression of the form (x + y)^{n}. The variables x and y can be any → real numbers and n is an → integer. The general formula is known as the → binomial theorem. 
binomial nomenclature nâmgozâriye donâmin Fr.: nomenclature binomiale A system introduced by Carl von Linné (17071778), the Swedish botanist, in which each organism is identified by two names. The first is the name of the genus (generic name), written with a capital letter. The second is the name of the species (specific name). The generic and specific names are in Latin and are printed in italic type. For example, human beings belong to species Homo sapiens. → binomial; → nomenclature. 
binomial theorem farbine 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 (9531029) knew the binomial theorem and its accompanying table of → binomial coefficients, now known as → Pascal's triangle. Subsequently Omar Khayyam (10481131) 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 (16421727). 
birth binary population (BBP) porineše dorinhâ hengâme zâdmân Fr.: population binaire à la naissance In star formation models, the population of binary components formed via random pairing of stars distributed according to the → canonical IMF. → birth; → binary; → population. 
black hole binary siyah câle dorin Fr.: trou noir binaire A → binary system in which each component is a → black hole. The binary's evolution can be divided into three stages: → inspiral, → merger, and → ringdown. 
Chelyabinsk meteor šahâbe Chelyabinsk Fr.: météore de Tcheliabinsk A → meteor exploded on February 15, 2013 over Chelyabinsk, southern Russia.The explosion occurred at a height of 20 km above Earth, releasing 500 kilotons → TNT equivalent of energy, approximately 30 times the yield of the nuclear bomb over Hiroshima. It caused a → shock wave that damaged 7,200 buildings in six Russian cities and injured some 1,500 people, mainly from flying glass. Later, about five tons of meteoritic material reached the ground, including a 650 kg → meteorite that was recovered by divers from the bottom of Lake Chebarkul, on the slopes of the southern Ural mountains. With an estimated initial mass of about 12,00013,000 metric tons, and measuring about 20 m in diameter, it is the largest known natural object to have entered Earth's atmosphere since the 1908 → Tunguska event. Chelyabinsk, a city in Russia, the capital of the Chelyabinsk region, on the eastern slope of the Ural Mountains on the Miass River, 200 km south of Ekaterinburg and 1,879 km east of Moscow. The population of Chelyabinsk is about 1,183,000 (2015), the area, 530 sq. km; → meteor. 
circumbinary pirâdorini Fr.: circumbinaire Of or relating to an object that revolves around a → binary system. 
circumbinary disk gerdeye pirâdorini, diske ~ Fr.: disque circumbinaire A relatively thin structure of matter composed mainly of gas and dust that orbits both the → primary and → secondary stars in → binary systems. → circumbinary; → disk. 
close binary star setâreye dorine kip Fr.: étoile binaire serrée A binary system in which the separation of the component stars is comparable to their diameters, so that they influence each other's evolution most commonly by the tidal forces. 
close binary system râžmâne dorine kip Fr.: système binaire serré A → binary system in which the distance separating the stars is comparable to their size. Most close binaries are spectroscopic binaries (→ spectroscopic binary) and/or eclipsing binaries (→ eclipsing binary). In most of them → mass transfer occurs at some stage, an event which profoundly affects the → stellar evolution of the components. The evolution of close binaries depends on the → initial masses of the two stars and their → separation. When the more massive star evolves into a → red giant first, material will spill through the inner point onto its companion, thereby affecting its companion's evolution. Mass transfer can also alter the separation and → orbital period of the binary star. 