1) General: A guess or estimate; nearness in space, position, degree.
Approximation, verbal noun of → approximate.
Nazdineš, verbal noun of nazdinidan, → approximate.
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.
Fr.: première approximation
1) Generally, an expression to indicate that a comment or result is
Fr.: approximation linéaire
Taking the first term in the Taylor series as an approximation to a mathematical function at a given point. → first 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.
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.
Fr.: approximation newtonienne
on-the-spot (OTS) approximation
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.
A model of radiative transfer that ignores forward scattering of photons; assuming forward-scattered light as un-scattered.
Fr.: deuxième approximation
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 > vth/l, where dv/dr is the velocity gradient, vth 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.
Fr.: approximation de Stirling
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.