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.: rayon d'Einstein
In gravitational lens phenomenon, the critical distance from the → lensing object for which the light ray from the source is deflected to the observer, provided that the source, the lens, and the observer are exactly aligned. Consider a massive object (the lens) situated exactly on the line of sight from Earth to a background source. The light rays from the source passing the lens at different distances are bent toward the lens. Since the bending angle for a light ray increases with decreasing distance from the lens, there is a critical distance such that the ray will be deflected just enough to hit the Earth. This distance is called the Einstein radius. By rotational symmetry about the Earth-source axis, an observer on Earth with perfect resolution would see the source lensed into an annulus, called Einstein ring, centered on its position. The size of an Einstein ring is given by the Einstein radius: θE = (4GM/c2)0.5 (dLS/(dL.dS)0.5, where G is the → gravitational constant, M is the mass of the lens, c is the → speed of light, dL is the angular diameter distance to the lens, dS is the angular diameter distance to the source, and dLS is the angular diameter distance between the lens and the source. The equation can be simplified to: θE = (0''.9) (M/1011Msun)0.5 (D/Gpc)-0.5. Hence, for a dense cluster with mass M ~ 10 × 1015 Msun at a distance of 1 Gigaparsec (1 Gpc) this radius is about 100 arcsec. For a gravitational → microlensing event (with masses of order 1 Msun) at galactic distances (say D ~ 3 kpc), the typical Einstein radius would be of order milli-arcseconds.
Fr.: anneau d'Einstein
The apparent shape of a background source unsergoing the effect of → gravitational lensing as seen from Earth, provided that the source, the intervening lens, and the observer are in perfect alignement through → Einstein radius.
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.
marpel-e zamâni-ye Einstein
Fr.: échelle de temps d'Einstein
The time during which a → microlensing event occurs. It is given by the equation tE = RE/v, where RE is the → Einstein radius, v is the magnitude of the relative transverse velocity between source and lens projected onto the lens plane. The characteristic time-scale of → microlensing events is about 25 days.
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.