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Weierstrass approximation theorem farbin-e nazdineš-e Weierstrass Fr.: théorème d'approximation de Weierstrass If a function φ(x) is continuous on a closed interval [a,b], then for every ε > 0 there exists a polynomial P(x) such that |f(x) - P(x)| <ε, for every x in the interval. After German mathematician Karl Wilhelm Theodor Weierstrass (1815-1897); → approximation; → theorem. |
Weierstrass M test âzmun-e M Weierstrass Fr.: Weierstrass A test for uniform convergence of a sequence of functions. If there exists a series of numbers Σ M_{i} (summed from n = 1 to ∞), in which M_{i}≥ Σ |u_{i}(x)| for all x in the interval [a, b] and Σ M_{i} is convergent, the series u_{i}(x) will be uniformly convergent in that interval. → Weierstrass approximation theorem; M referring to
→ majorant; → test. |
weight vazn (#) Fr.: poids 1) The force of attraction of the Earth on a given mass.
→ molecular weight; → weightlessness. M.E., from O.E. gewiht, cf. O.N. vætt, O.Fris. wicht, M.Du. gewicht, Ger. Gewicht. Vazn, loan from Ar. wazn. |
weight concentration dabzeš-e vazni Fr.: concentration en poids of a gas included in the composition of a → gas mixture, the ratio of mass of this gas to the mass of the whole mixture. Same as → weight fraction and → weight-fraction concentration. → weight; → concentration. |
weight fraction barxe-ye vazni Fr.: fraction en poids Same as → weight concentration. |
weight of a tensor density vazn-e cagâli-ye tânsor Fr.: poids d'une densité de tenseur A constant the value of which is characteristic for any given → tensor density. |
weight-fraction concentration barxe-ye vazni-ye dabzeš Fr.: concentration en poids Same as → weight concentration. → weight; → fraction; → concentration. |
weighted mean miyângin-e vazni (#) Fr.: moyenne pondérée An mean which is obtained by combining different numbers according to the relative importance of each. |
weightlessness bivazni (#) Fr.: apesanteur The phenomenon experienced by a body when there is no force of reaction on it. This happens when the body is in → free fall in a → gravitational field or when the net force on it is zero. From → weight + -less suffix meaning "without" + -ness a suffix of quality or state. |
Weizsacker formula disul-e Weizsäcker Fr.: formule de Weizsäcker A → semiempirical → equation
which describes the → binding energy
of the → atomic nucleus. It is essentially a nuclear mass formula
that provides the total binding energy per → nucleon as the sum
of five terms: Named after Carl Friedrich von Weizäcker (1912-2007), German physicist, who derived the formula in 1935, Z. für Physik 96, 431; → formula. |
well 1) xoš, xub; 2) câh Fr.: 1) In a good or satisfactory manner; thoroughly, carefully, or soundly. 1) M.E., from O.E. wel(l) (cognates Du. wel, Ger. wohl). 1) Xoš "good, well, sweet, fair, lovely," probably related to hu-
"good, well," → eu-.
Xub, ultimately from Av. huuāpah-
"doing good work," → operate. |
well-formed formula (wff) disul-e xošdisé (wff) Fr.: formule bien formée (FBF) A string of → symbols from the alphabet of the → formal language that conforms to the grammar of the formal language. → closed wff, → open wff. |
well-ordered set hangard-e xoš-râyé Fr.: ensemble bien ordonné A set in which every → nonempty → subset has a minimum element. |
Werner band bând-e Werner Fr.: bande de Werner A sequence of → permitted transitions in the → ultraviolet from an → excited state (C) of the → molecular hydrogen (H_{2}) to the electronic → ground state, with ΔE > 12.3 eV and λ ranging from 1160 Å to 1250 Å. When a hydrogen molecule absorbs such a photon, it undergoes a transition from the ground electronic state to the excited state (C). The following rapid → decay creates an → absorption band in that wavelength range. See also → Lyman band; → Lyman-Werner photon. Named after the Danish physicist Sven Theodor Werner (1898-1984), who discovered the band (S. Werner, 1926, Proc. R. Soc. London Ser. A, 113, 107); → band. |
west bâxtar (#) Fr.: ouest The direction 90° to the left or 270° to the right of → north. M.E., O.E. "west" "in or toward the west;" cf. O.N. vestr, O.Fris., M.Du., Du. west, Ger. West; PIE base *wes- (Gk. hesperos, L. vesper "evening, west"). Bâxtar "west;" Mid.Pers. apâxtar "north;" Av. apāxtar "northern." |
western bâxtari (#) Fr.: (de l') ouest, occidental Lying toward or situated in the west. → greatest western elongation. Adjective from → west. |
western elongation derâzeš-e bâxtari Fr.: élongation ouest The position of a planet when it is visible in the eastern sky before dawn. → western; → elongation. |
wet xis (#) Fr.: mouillé Consisting of, containing, covered or soaked with water or some other liquid. O.E. wæt "moist, liquid," related to O.Frisian wēt, O.N. vātr, O.E. wæter "water." Xis, xês "wet, moist," related to pašang, pašangidan "sprinkle," ultimately from Proto-Ir. *haic- "to pour (out), moisten;" cf. Av. haēc- "to pour (out); to irrigate;" Khotanese häs- "to wet, besprinkle;" Sogd. šync "to pour" (Cheung 2007). |
wet merger tašk-e porgâz Fr.: fusion avec gaz A merger between → gas-rich galaxies. Wet mergers may lead to enhanced star formation, trigger → active galactic nuclei, and transform a → disk galaxy into an → elliptical galaxy. The larger the → redshift, the wetter mergers should be. |
Weyl's principle parvaz-e Weyl Fr.: principe de Weyl The → world lines of galaxies form in the 4D space-time a bundle of non-intersecting → geodesics orthogonal to a series of space-like hyperstructures (e.g. Narlikar 2002, An Introduction to Cosmology, 3rd Edition, Cambridge Univ. Press). Expressed differently: The world lines of galaxies, or "fundamental particles," form (on average) a space-time filling family of non-intersecting geodesics converging toward the past (Rugh & Zinkernagel, 2010, astro-ph/1006.5848). The statement is sometimes denoted postulate, assumption, or hypothesis. The importance of Weyl's principle is that it asserts that cosmic matter moves according to certain regularity requirements. See also → cosmological principle. First introduced by the German mathematician Hermann Weyl (1885-1955) in 1923 in his Raum, Zeit, Materie; → principle. |
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