Fr.: étoile EBH
Same as → extreme horizontal branch star.
Fr.: fonction propre
1) Math.: An → eigenvector for a linear
→ operator on a → vector space
whose vectors are → functions. Also known as
From Ger. Eigenfunktion, from eigen- "characteristic, particular, own" (from P.Gmc. *aigana- "possessed, owned," Du. eigen, O.E. agen "one's own") + → function.
Viž-karyâ, from viž, contraction of vižé "particular, charcteristic" + karyâ, → function. Vižé, from Mid.Pers. apēcak "pure, sacred," from *apa-vēcak "set apart," from prefix apa- + vēcak, from vēxtan (Mod.Pers. bixtan) "to detach, separate, sift, remove," Av. vaēk- "to select, sort out, sift," pr. vaēca-, Skt. vic-, vinakti "to sift, winnow, separate; to inquire."
Fr.: état propre
Fr.: valeur propre
1) Math.: The one of the → scalars λ such
that T(v) = λv, where T is a linear → operator
on a → vector space, and v is an
Fr.: vecteur propre
Math.: A nonzero vector v whose direction is not changed by a given linear transformation T; that is, T(v) = λ v for some scalar λ.
M.E. eighte, from O.E. eahta, æhta, related to O.Norse atta, Swed. åtta, Du. acht, O.H.G. Ahto, Ger. acht; Pars. hašt, as below, from PIE *okto(u) "eight."
Hašt, from Mid.Pers. hašt; Av. ašta; cognate with Skt. asta; Gk. okto; L. octo (from which It. otto, Sp. ocho, Fr. huit).
A unit of radiation energy sometimes used in the investigation of photochemical processes. The unit is defined as NAhν, where NA is → Avogadro's number and hν is the energy of a → quantum of the radiation. One einstein (or Einstein unit) is the energy per → mole of photons carried by a beam of monochromatic light.
Named for Albert Einstein (1879-1955).
Fr.: coefficient d'Einstein
A measure of the probability that a particular atomic transition leading to the formation of an atomic spectral line occurs. The coefficient of spontaneous emission is denoted by Aij, and the coefficient of stimulated emission by Bij, i representing the lower level and j is the upper level.
Named after Albert Einstein (1879-1955) who introduced the coefficients in 1916; → coefficient.
Fr.: croix d'Einstein
An image of a distant quasar (redshift 1.7) formed by a foreground spiral galaxy (redshift 0.039) through gravitational lensing. The image of the quasar is split into four point sources forming a cross at the center of the galaxy.
Einstein equivalence principle
parvaz-e hamug-arzi-ye Einstein
Fr.: principe d'équivalence d'Einstein
The → equivalence principle as stated by Einstein, on which is
based the theory of → general relativity. It comprises
the three following items:
Fr.: modèle d'Einstein
A model for the → specific heat of solids in which the specific heat is due to the vibrations of the atoms of the solids. The vibration energy is → quantized and the atoms have a single frequency, ν. Put forward in 1907 by Einstein, this model was the first application of → quantum theory to the solid state physics. The expression for the specific heat is given by: CV = 3Rx2ex/(ex -1)2, where R is the → gas constant, x = TE/T, TE = hν/k, h is → Planck's constant, and k is → Boltzmann's constant. TE is called the → Einstein temperature. This model could explain the temperature behavior of specific heat but not very satisfactorily at low temperatures. It has therefore been superseded by the → Debye model. See also → Dulong-Petit law.
Albert Einstein in 1907; → model.
Fr.: convention Einstein
A notation convention in → tensor analysis whereby whenever there is an expression with a repeated → index, the summation is done over that index from 1 to 3 (or from 1 to n, where n is the space dimension). For example, the dot product of vectors a and b is usually written as: a.b = Σ (i = 1 to 3) ai.bi. In the Einstein notation this is simply written as a.b = ai.bi. This notation makes operations much easier. Same as Einstein summation convention.
Fr.: modèle d'Einstein
Same as → Einstein model.
Einstein static Universe
giti-ye istâ-ye Einstein
Fr.: Univers stationnaire d'Einstein
A cosmological model in which a static (neither expanding nor collapsing) Universe is maintained by introducing a cosmological repulsion force (in the form of the cosmological constant) to counterbalance the gravitational force.
damâ-ye Einstein (#)
Fr.: température d'Einstein
tânsor-e Einstein (#)
Fr.: tenseur d'Einstein
A mathematical entity describing the → curvature of → space-time in → Einstein's field equations, according to the theory of → general relativity. It is expressed by Gμν = Rμν - (1/2) gμνR, where Rμν is the Ricci tensor, gμν is the → metric tensor, and R the scalar curvature. This tensor is both symmetric and divergence free.
Named after Albert Einstein (1879-1955); → tensor.
Fr.: ascenseur d'Einstein
A → thought experiment, involving an elevator, first conceived by Einstein to show the → principle of equivalence. According to this experiment, it is impossible for an observer situated inside a closed elevator to decide if the elevator is being pulled upward by a constant force or is subject to a gravitational field acting downward on a stationary elevator. Einstein used this experiment and the principle of equivalence to deduce the bending of light by the force of gravity.
Bâlâbar, → lift.
Einstein's field equations
hamugešhâ-ye meydân-e Einstein
Fr.: équations de champ d'Einstein
A system of ten non-linear → partial differential equations in the theory of → general relativity which relate the curvature of → space-time with the distribution of matter-energy. They have the form: Gμν = -κ Tμν, where Gμν is the → Einstein tensor (a function of the → metric tensor), κ is a coupling constant called the → Einstein gravitational constant, and Tμν is the → energy-momentum tensor. The field equations mean that the curvature of space-time is due to the distribution of mass-energy in space. A more general form of the field equations proposed by Einstein is: Gμν + Λgμν = - κTμν, where Λ is the → cosmological constant.
Einstein's gravitational constant
pâyâ-ye gerâneši-ye Einstein (#)
Fr.: constante gravitationnelle d'Einstein
Einstein's theory of specific heat
negare-ye garmâ-ye âbize-ye Einstein
Fr.: théorie de la chaleur spécifique d'Einstein
Same as → Einstein model.