approximation nazdineš Fr.: approximation 1) General: A guess or estimate; nearness in space, position, degree. Approximation, verbal noun of → approximate. Nazdineš, verbal noun of nazdinidan, → approximate. |
Boussinesq approximation nazdineš-e Boussinesq Fr.: approximation de Boussinesq A simplification in the equations of → hydrodynamics that treats the density as constant except in the → buoyancy term. This approximation is motivated by the fact that when pressure and temperature differences in a flow are small, then it follows from the thermodynamic → equation of state that a change in the density is also small. Named after Joseph Valentin Boussinesq (1842-1929), a French physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat; → approximation. |
first approximation nazdin-e naxost Fr.: première approximation 1) Generally, an expression to indicate that a comment or result is
only approximate. → first; → approximation. |
linear approximation nazdineš-e xatti Fr.: approximation linéaire Taking the first term in the Taylor series as an approximation to a mathematical function at a given point. → first approximation. → linear; → approximation. |
method of successive approximations raveš-e nazdinešhâ-ye payâpey Fr.: méthode d'approximations successives The solution of an equation or by proceeding from an initial approximation to a series of repeated trial solutions, each depending upon the immediately preceding approximation, in such a manner that the discrepancy between the newest estimated solution and the true solution is systematically reduced. → method; → successive; → approximation. |
Milne-Eddington approximation nazdineš-e Milne-Eddington Fr.: approximation de Milne-Eddington The approximation of a stellar atmosphere with a plane parallel grey atmosphere in radiative equilibrium. It is assumed that a spectral is formed in such a way that the ratio of the line absorption coefficient to the continuous absorption coefficient is constant with depth. → Milne Universe; Arthur Stanley Eddington (1882-1944), prominent British astrophysicist; → approximation. |
Newtonian approximation nazdineš-e Newtoni Fr.: approximation newtonienne A particular solution of the → general relativity when the → gravitational mass is small. The → space-time is then approximated to the → Minkowski's and this leads to → Newtonian mechanics. → Newtonian; → approximation. |
on-the-spot (OTS) approximation nazdineš-e darjâ Fr.: An approximation in the treatment of photoionized → H II regions, whereby secondary ionizing photons are absorbed immediately very close to their site of emission. The secondary photons, produced by → radiative recombinations directly to the → ground states, are thus ignored with respect to the ionizing photons emitted by the → exciting star. The OTS approximation requires that the ionized gas be sufficiently dense so that secondary ionizing photons are very likely absorbed within the H II region. → on; → spot; → approximation. Nazdineš, → approximation; dar "in," from Mid.Pers. andar, → intra-. |
quasi-single-scattering approximation nazdineš-e cunân-tak-parâkaneš Fr.: A model of radiative transfer that ignores forward scattering of photons; assuming forward-scattered light as un-scattered. → quasi-; → single; → scattering; → approximation. |
second approximation nazdineš-e dovom Fr.: deuxième approximation Math: In calculus, limiting an equation to its → second derivative, for example: e^{x}≅ 1 + x + x^{2}/2. Also called linear approximation. → first approximation. → second; → approximation. |
Sobolev approximation nazdineš-e Sobolev Fr.: approximation de Sobolev A method allowing for a simplified solution to the → radiative transfer equation at frequencies of spectral lines in media moving with a high velocity gradient. This method assumes that the macroscopic velocity gradients are more important than local random variations of thermal line width: dv/dr > v_{th}/l, where dv/dr is the velocity gradient, v_{th} is the thermal broadening of the line, and l the length scale. The Sobolev approximation is only valid if the conditions of the gas do not change over the → Sobolev length. Under the Sobolev approximation, each point in the medium is isolated from other points, and the → radiative transfer problem becomes a local one and therefore much easier to solve. Named after the Russian astronomer Viktor Viktorovich Sobolev, Moving Envelopes of Stars [in Russian], Leningr. Gos. Univ., Leningrad (1947) [translated by S. Gaposchkin, Harvard Univ. Press, Cambridge, Mass. (1960)]; → approximation. |
Stirling's approximation nazdineš-e Stirling Fr.: approximation de Stirling A mathematical formula yielding an approximate value for → factorial n, when n is large: n! ≅ (2πn)^{1/2}n^{n}e^{-n}, where e is the base of → natural logarithm. Named after James Stirling (1692-1770), a Scottish mathematician; → approximation. |
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. |