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finite series seri-ye karânmand (#) Fr.: série finie A sum a_{1} + a_{2} + a_{3} + · · · + a_{N}, where the a_{i}'s are real numbers. In terms of Σ-notation, it is written as a_{1} + a_{2} + a_{3} + · · · + a_{N} = Σ (n = 1 to N). See also → infinite series. |
finite set hangard-e karânmand Fr.: ensemble fini A → set whose elements can be numbered from 1 to n, for some positive integer n. |
fire âtaš(#), taš (#), âzar (#) Fr.: feu A state, process, or instance of combustion in which a substance combines with oxygen producing heat, light, and flame. O..E. fyr, from P.Gmc. *fuir (cf. O.N. fürr, M.Du. vuur, Ger. Feuer), from PIE *paewr-; cf. Mod.Pers. Lori porpor "blazing charcoal," Gilaki bur, biur "smokeless red fire" (Lori perisk, periska "spark," Kurd. biriske "spark," Lârestâni pelita "spark"); Tokharian por, puwar "fire;" Gk. pyr "fire;" Hitt. pahhur "fire;" Skt. pū- "to cleanse." Âtaš, variants âzar, taš, from Mid.Pers. âtaxš, âtur "fire;" Av. ātar-, āθr- "fire," singular nominative ātarš-; O.Pers. ātar- "fire;" Av. āθaurvan- "fire priest;" Skt. átharvan- "fire priest;" cf. L. ater "black" ("blackened by fire"); Arm. airem "burns;" Serb. vatra "fire;" PIE base *āter- "fire." |
fireball tašguy (#), âzarguy (#) Fr.: boule de feu A → meteor that is brighter than the brightest planets, i.e. with an apparent magnitude of -5 or greater. Fireballs are often followed by → meteorite falls. Also called → bolide. From → fire + ball, from O.E., from O.N. bollr "ball," from P.Gmc. *balluz (cf. O.H.G. ballo, Ger. Ball), from PIE base *bhel- "to swell." Tašguy, from taš "fire," variant of âtaš→ fire + guy "ball, sphere," variants golulé, gullé, goruk, gulu, gudé (cf. Skt. guda- "ball, mouthful, lump, tumour," Pali gula- "ball," Gk. gloutos "rump," L. glomus "ball," globus "globe," Ger. Kugel, E. clot; PIE *gel- "to make into a ball"). |
first naxost (#), naxostin (#), yekom (#), âqâz (#) Fr.: premier Being before all others with respect to time, order, importance, etc., used as the ordinal number of one. O.E. fyrst "foremost," superlative of fore, from P.Gmc. *furisto (cf. O.H.G. furist, O.N. fyrstr, Dan. første, M.Du. vorste "first," Ger. Fürst "prince"), superlative of *fur-/*for-, from PIE *pro- (cf. Av. pouruua- "first," fra- "forward, forth;" Skt. pūrva- "first," pra- "before, formerly," Gk. pro; L. pro; E. fore). Naxost, from Mid.Pers. naxust "the first," Parthian Mid.Pers.
nxwšt, from naxu, Manichean Parthian nwx
"beginning" + -ist superlative suffix, Av. -išta-,
cf. Skt. -istha-, Gk. -istos, O.H.G.
-isto, -osto, O.E. -st, -est, -ost; naxostin,
from naxost + suffix -in. |
first approximation nazdin-e naxost Fr.: première approximation 1) Generally, an expression to indicate that a comment or result is only approximate. → first; → approximation. |
first collapse rombeš-e naxost Fr.: premier effondrement An early phase in the process of star formation which begins when the mass of a → molecular cloud → clump exceeds the → Jeans mass. The collapse is initially → optically thin to the thermal emission from → dust grains, and the compressional heating rate is much smaller than the cooling rate by the → thermal radiation. The collapse proceeds → isothermally. The isothermal condition is broken when the central density reaches about 10^{-13} g cm^{-3} and a small region at the center of the cloud starts to become → opaque. The heat generated by the collapse in this region is no longer freely radiated away, and the compression becomes approximately → adiabatic. The central temperature and pressure then begin to rise rapidly, soon becoming sufficient to decelerate and stop the collapse at the center. There then arises a small central core, called the → first core, in which the material has stopped collapsing and is approaching → hydrostatic equilibrium. Outside this core, the material is still nearly isothermal and continues to fall inward almost in → free fall. Consequently a shock front arises at the boundary of the core, where the infalling material is suddenly stopped. The initial mass and radius of the core are about 10^{31} g and 6 x 10^{13} cm, respectively, and the central density and temperature are about 2 x 10^{-10} g cm^{-3} and 170 K, respectively. As the collapse proceeds, the core grows in mass due to the infall of the surrounding material; at the same time, however, the core radius decreases because of radiative energy losses from the outer layers of the core. The process leads to the → second collapse (R. B. Larson, 1969, MNRAS 145, 271). |
first contact parmâs-e naxost Fr.: premier contact 1) The beginning of a → solar eclipse when the eastern part of
the lunar limb touches the western limb of the Sun, marking
the beginning of an eclipse. |
first core maqze-ye naxost Fr.: premier cœur A first object in → hydrostatic equilibrium predicted to form during early dynamical contraction of a → molecular cloud → clump in the course of the → first collapse. |
first degree equation hamugeš-e daraje-ye yekom Fr.: équiation du premier degré A equation in which the highest → exponent of the → variable is 1. Same as → linear equation. |
first dredge-up borunkašid-e naxost Fr.: premier dragage The → dredge-up occurring after core hydrogen burning as the core contracts before helium burning ignites (on the ascending giant branch). The hydrogen envelope becomes convective and this convective zone penetrates deep into the core dredging up material that has been processed by the central nuclear reactions. As a result the abundances of helium and nitrogen are boosted. |
first law of thermodynamics qânun-e naxost-e garâtavânik Fr.: première loi de la thermodynamique The total energy of a → closed system is constant. This means that energy can be changed from one form to another, or transferred from one system to another, but it cannot be created or destroyed. A mathematical formulation of the first law is: δQ = δU + δW, where δQ is the heat transferred to the system, δU the change in internal energy (resulting in a rise or fall of temperature), and δW is the work done by the system. → first; → law; → thermodynamics. |
first light naxostin foruq, ~ nur Fr.: première lumière The first astronomical observation done with a major newly built telescope. |
First Point of Aries noqte-ye âqâz-e barré (#) Fr.: premier point de Bélier One of the two points on the celestial sphere where the ecliptic and the celestial equator crossed one another at → vernal equinox several thousands years ago. |
First Point of Libra noqte-ye âqâz-e tarâzu (#) Fr.: permier point de Balance One of the two points on the celestial sphere where the ecliptic and the celestial equator crossed one another at → autumnal equinox several thousands years ago. Because of → precession, this equinoctial point no longer lies in Libra but in neighboring Virgo. |
first quarter cârak-e naxost Fr.: premier quartier A → lunar phase that occurs in the middle of the interval between the → new Moon and the → full Moon, when half of the Moon's disk is illuminated. At first quarter, the Moon is situated at 90° east of the Sun. |
first star naxostin setâré Fr.: première étoile A member of the → Population III → massive stars that formed some 500 Myr after the → Big Bang. First stars had a simple chemical composition consisting only of H, He, and traces of ^{7}Li and were very short-lived. They are the most likely sources of → reionization of the Universe, which put an end to the → Cosmic Dark Age. |
first-order differential equation hamugeš-e degarsâne-yi-ye râye-ye naxost Fr.: équation différentielle du premier ordre A → differential equation containing only the first → derivative. For example, dy/dx = 3x and 2y(dy/dx) + 3x = 5. → first; → order; → differential; → equation. |
first-order logic (FOL) guyik-e farâsani-ye râye-ye naxost, ~ farâsanhâ-ye ~ ~ Fr.: logique des prédicats du premier ordre A system of → formal logic that is an extension of → propositional logic. It is also known as → first-order predicate calculus and → predicate logic. FOL eliminates deficiencies of propositional logic by: representing → objects (their properties, relations and statements about them), introducing → variables, and introducing → quantifiers. |
first-order partial derivative vâxane-ye pâri-ye râye-ye naxost Fr.: dérivée partielle du premier degré For a → function with several → variables, the derivative, done only once, with respect to one of the variables. For example ∂u/∂x for u = u(x,y). → first; → order; → partial; → derivative. |
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