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spore hâg (#) Fr.: spore A reproductive body in flowerless plants corresponding to the seeds of flowering ones. From Modern L. spora, from Gk. spora "a seed, a sowing, seed-time," related to speirein "to sow, scatter." Hâg, variant of xâg, → egg. |
Sporer minimum kamine-ye Spörer Fr.: minimum de Spörer A period of low → solar activity that lasted from about A.D. 1420 to 1570. It occurred before → sunspots had been studied, and was discovered by analysis of the proportion of carbon-14 in tree rings, which is strongly correlated with solar activity. Named for the German astronomer Gustav Spörer (1822-1895); → minimum. |
Sporer's law qânun-e Spörer Fr.: loi de Spörer The empirical law that predicts the variation of → sunspot latitudes during a → solar cycle. At the start of a sunspot cycle, sunspots tend to appear around 30° to 45° latitude on the Sun's surface. As the cycle progresses, they appear at lower and lower latitudes, until 5° to 10°, at the end of the cycle. This tendency is revealed on a → butterfly diagram. Although named after Gustav Spörer, the "law" was first discovered by Richard Carrington. → Sporer minimum; → law. |
Steiner's theorem farbin-e Steiner Fr.: théorème de Steiner The → moment of inertia of a body about an arbitrary axis x' is equal to the sum of its moment of inertia about axis x, passing through the center of mass of the body and parallel to axis x', and the product of the mass M of the body by the square of the distance d between axes x and x': I_{x'} = I_{x} + Md^{2}. Same as → parallel axis theorem. Named after Jakop Steiner (1796-1863), a Swiss mathematician who derived this statement; → theorem. |
Taylor-Proudman theorem farbin-e Taylor-Proudman Fr.: théorème de Taylor-Proudman In a rapidly rotating fluid, the fluid velocity is constant along any line parallel to the axis of rotation. → Taylor number; Joseph Proudman (1888-1975), British mathematician and oceanographer. |
theorem farbin Fr.: théorème A → proposition, → statement, or → formula in → mathematics or → logic deduced from → axioms, other propositions, → assumptions, → premises, or formulas. Theorems are statements which can be proved. For example, → Fourier theorem; → Liouville's theorem; → Woltjer's theorem. From M.Fr. théorème, from L.L. theorema, from Gk. theorema "spectacle, speculation," in Euclid "proposition to be proved," from theorein "to look at, speculate, consider." Farbin, from far- intensive prefix "much, abundant; elegantly; forward" (Mid.Pers. fra- "forward, before; much; around;" O.Pers. fra- "forward, forth;" Av. frā, fərā-, fra- "forward, forth; excessive;" cf. Skt. prá- "before; forward, in front;" Gk. pro "before, in front of;" L. pro "on behalf of, in place of, before, for;" PIE *pro-) + bin, present stem of didan "to see," from Mid.Pers. wyn-; O.Pers. vain- "to see;" Av. vaēn- "to see;" cf. Skt. veda "I know;" Gk. oida "I know," idein "to see;" L. videre "to see;" PIE base *weid- "to know, to see." |
theoretical negarik (#) Fr.: théorique Of, pertaining to, or consisting in theory. From L.L. theoreticus "of or pertaining to theory," from Gk. theoretikos "contemplative, pertaining to theory;" → theory. Negarik, contraction of negaréik, from negaré→ theory + -ik, → -ic. |
theoretical astrophysics axtarfizik-e negarik (#) Fr.: astrophysique théorique An astrophysical study or research group mainly concerned with theory rather than observation. → theoretical; → astrophysics. |
theoretician negare-pardâz Fr.: théoricien One who formulates or is expert in the theoretical side of a subject. From theoretic, from theoretics, from → theory + -ian. Negare-pardâz, from negaré, → theory, + pardâz, present stem of pardâxtan "to accomplish; bring to perfection; to attempt, to care; to clean; to free;" Mid.Pers. pardâxtan, pardâzidan "to accomplish; to be done with, freed of" ultimately from Proto-Iranian *para-tāxta-, *para-tāca- "to take away; to expel," from *para- "along, forth," → para-, + tāxta-, tāca- "to run, to flow;" cf. Av. tak- "to run, to flow;" Mod.Pers. tâxtan, tâz- "to flow, to cause to walk," → flow. |
turbulent core model model-e maqze-ye âšubnâk Fr.: modèle de cœur turbulent A star formation scenario whereby → massive stars form from gravitationally bound → pre-stellar cores, which are supersonically → turbulent and in approximate pressure equilibrium with the surrounding protocluster medium. The high → accretion rates that characterize such media allow accretion to overcome the radiation pressure due to the luminosity of the star. The core is assumed to → collapse via an → accretion disk to form a single star or binary. The core density structure adopted is ρ ∝ r^{-k}, with k = 1.5 set from observations. This choice affects the evolution of the accretion rate, which increases linearly with time. The high densities in regions of massive-star formation lead to typical time scales for the formation of a massive star of about 10^{5} years (McKee & Tan 2003, ApJ 585, 850). |
uniqueness theorem farbin-e yektâyi Fr.: théorème d'unicité 1) Physics: A → potential that satisfies both
→ Poisson's equation and the
→ boundary conditions
pertinent to a particular field is the only possible potential. → uniqueness; → theorem. |
Van Cittert-Zernike theorem van farbin-e Cittert-Zernike Fr.: théorème de Cittert-Zernike In → Young's experiment of → interference with double apertures, if a monochromatic source is a considerable distance from the → aperture plane and aperture separation is small, → fringe visibility from an extended source is proportional to the → Fourier transform of the source's spatial distribution. The transform variable is the angular separation of the aperture-plane sampling points divided by the wavelength. The van Cittert-Zernike Theorem is at the heart of → aperture synthesis. Developed independently by Dutch physicists Pieter Hendrick van Cittert (1889-1959) in 1934 and Frits Zernike (1888-1966) in 1939; → theorem. |
Varignon's theorem farbin-e Varignon Fr.: théorème de Varignon The → moment of the resultant of a → coplanar system of → concurrent forces about any center is equal to the algebraic sum of the moments of the component forces about that center. Named after Pierre Varignon (1654-1722), a French mathematician, who outlined the fundamentals of statics in his book Projet d'une nouvelle mécanique (1687). |
virial theorem farbin-e viriyâl Fr.: théorème du viriel A general equation applicable to a gravitationally → bound system of equal mass objects (stars, galaxies, etc.), which is stable against → dynamical disruption. It states that in such a system the average → gravitational potential energy (W_{vir}) is twice the average → kinetic energy (K_{vir}) of the system: W_{vir} = -2K_{vir}. This general proposition, first derived by Rudolf Clausius (1822-1888), has important applications in a variety of fields ranging from statistical mechanics to astrophysics. See also → virialization, → virial equilibrium, → virialized. |
Vogt-Russell theorem farbin-e Vogt-Russell Fr.: théorème de Russell-Vogt The internal structure and all observable characteristics of a star (such as luminosity and temperature) are determined uniquely by its mass, chemical composition, and age. Same as → Russell-Vogt theorem. Named after the German astronomer Heinrich Vogt (1890-1968) and the American astronomer Henry Norris Russell (1877-1957); → theorem. |
von Zeipel theorem farbin-e von Zeipel Fr.: théorème de von Zeipel A theorem that establishes a relation between the → radiative flux at some → colatitude on the surface of a → rotating star and the local → effective gravity (which is a function of the → angular velocity and colatitude). For a rotating star in which → centrifugal forces are not negligible, the → equipotentials where gravity, centrifugal force, and pressure are balanced will no longer be spheres. The theorem states that the radiative flux is proportional to the local effective gravity at the considered colatitude, F(θ) ∝ g_{eff} (θ)^{α}, where α is the → gravity darkening coefficient. As a consequence, the stellar surface will not be uniformly bright, because there is a much larger flux and a higher → effective temperature at the pole than at the equator (T_{eff} (θ) ∝ g_{eff} (θ)^{β}, where β is the → gravity darkening exponent. In → massive stars this latitudinal dependence of the temperature leads to asymmetric → mass loss and also to enhanced average → mass loss rates. Also called → gravity darkening. See also → von Zeipel paradox; → meridional circulation; → baroclinic instability; → Eddington-Sweet time scale. Named for Edvard Hugo von Zeipel, Swedish astronomer (1873-1959), who published his work in 1924 (MNRAS 84, 665); → theorem. |
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. |
Wide-field Infrared Survey Explorer (WISE) puyešgar barâye bardid-e bozorg-meydân dar forusorx Fr.: Explorateur pour l'étude grand champ dans l'infrarouge A → NASA infrared astronomical → space telescope launched in December 2009 to carry out an → all-sky survey from 3 to 22 → microns. With its 40-cm → telescope telescope and → infrared cameras, WISE aimed at a wide variety of studies ranging from the evolution of → protoplanetary disks to the history of → star formation in normal galaxies. In early October 2010, after completing its prime science mission, the spacecraft ran out of → coolant that keeps its instrumentation cold. However, two of its four infrared cameras remained operational. Hence, NASA extended the NEOWISE portion of the WISE mission by four months, with the primary purpose of hunting for more → asteroids and → comets, and to finish one complete scan of the main → asteroid belt. In August 2013, the WISE telescope's mission was extended for more three years to search for asteroids that could collide with Earth. → wide field; → infrared; → survey; → explorer. |
Wiener-Khinchin theorem farbin-e Wiener-Khinchin Fr.: théorème de Wiener-Khintchine A theorem used in signal processing whereby the → spectral density of a random signal is the → Fourier transform of the corresponding → autocorrelation function. In other words, the autocorrelation function and the spectral density function constitute a → Fourier transform pair. The Wiener-Khinchin theorem allows one to estimate the spectral density function from the Fourier transform of the autocorrelation function, which is easier to handle. The theorem has an important application particularly in radio astronomy. The two following → Fourier integrals are called the Wiener-Khinchin relations: K(τ) = ∫ J(f)e^{-iωτ}df and J(f) = ∫ K(τ)e^{iωτ}dτ (both summed over -∞ to +∞), where K(τ) is the autocorrelation function and J(f) is the spectral density. Named after Norbert Wiener (1894-1964), American mathematician, who first published this theorem in 1930, and Aleksandr Khinchin (1894-1959), Russian mathematician, who did so independently in 1934; → theorem. |
Woltjer's theorem farbin-e Woltjer Fr.: théorème de Woltjer In → magnetohydrodynamics, in the limit of zero → resistivity, the → magnetic field B satisfies the → induction equation ∂B/∂t = ∇ x (v x B), then for a → plasma confined by a perfectly conducting boundary, the → magnetic helicity is conserved. If the normal field is fixed on the boundary, the minimum-energy state is the linear → force-free magnetic field that conserves the total magnetic helicity. Named after the Dutch astrophysicist Lodewijk Woltjer (1930-2019), who discovered the phenomenon in 1958 while studying the → Crab Nebula; → theorem. |
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