An Etymological Dictionary of Astronomy and Astrophysics
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فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 21 Search : formula
Balmer formula
  دیسول ِ بالمر   
disul-e Bâlmer

Fr.: formule de Balmer   

A special solution of the mathematical formula which represents the wavelengths of the various spectral series of hydrogen in which the lower energy level is n = 2.

Balmer; → formula.

Bekenstein formula
  دیسول ِ بکنشتاین   
disul-e Bekenstein

Fr.: formule de Bekenstein   

The mathematical expression giving the → entropy, S, of a → black hole as a function of the area of its → event horizon, A: S = (kc3A)/(4Għ), where k is → Boltzmann's constant, ħ is the → reduced Planck's constant, and G the → gravitational constant. It can also be expressed by S = (kA)/(4lP2), where lP is the → Planck length. The existence of this entropy led to the prediction of the → Hawking radiation, because an entropy is associated with a temperature and a temperature to a → thermal radiation. The entropy of a black hole increases continuously because the fall of material into it increases its area.

For Jacob D. Bekenstein (1947-), an Israeli theoretical physicist, who contributed to the foundation of black hole thermodynamics; → formula.

Boltzmann's entropy formula
  دیسول ِ درگاشت ِ بولتسمن   
disul-e dargâšt-e Boltzmann

Fr.: formule d'entropie de Boltzmann   

In → statistical thermodynamics, a probability equation relating the → entropy S of an → ideal gas to the quantity Ω, which is the number of → microstates corresponding to a given → macrostate: S = k. ln Ω. Same as → Boltzmann's relation.

Boltzmann's constant; → entropy; → formula.

compound angle formula
  دیسول ِ زاویه‌ی ِ همنات   
disul-e zaviye-ye hamnât

Fr.: formule d'angle composé   

One of eight equations that give the → trigonometric functions of → compound angles.
sin(A± B) = sinA.cosnd angleB± cosA.sinB
cos(A + B) = cosA.cosB - sinA.sinB
cos(A - B) = cosA.cosB + sinA.sinB
tan(A + B) = (tanA + tanB)/(1 - tanA.tanB)
tan(A - B) = (tanA - tanB)/(1 + tanA.tanB).

compound; → angle; → formula.

Descartes' formula
  دیسول ِ دکارت   
disul-e Descartes

Fr.: formule de Descartes   

A formula that gives the position of an image formed by highly → paraxial rays from a → spherical mirror. It is quite accurately given by: 1/xo + 1/xi = 2/xC, where xo is the distance along the → principal axis from the mirror to the object, xi is the distance from mirror to image, and xC is the distance from the mirror to its center of curvature. Any distance measured on the same side of the mirror as the reflecting surface is positive; on the other side, negative. Thus for a → concave mirror  xC is positive; for a → convex mirror, negative.

Descartes; → formula.

dimensional formula
  دیسول ِ وامونی   
disul-e vâmuni

Fr.: formule dimensionnelle   

Symbolic representation of the definition of a physical quantity obtained from its units of measurement. For example, with M = mass, L = length, T = time, area = L2, velocity = LT-1, energy = ML2T-2. → dimensional analysis.

dimensional; → formula.

empirical formula
  دیسول ِ آروینی   
disul-e ârvini

Fr.: formule empirique   

1) In physics, a mathematical equation that predicts observed results, but has no known theoretical basis to explain why it works.
2) In chemistry, a simple expression of the relative number of each type of atom in a chemical compound.

empirical; → formula

Euler's formula
  دیسول ِ اویلر   
disul-e Euler

Fr.: formule d'Euler   

A formula which expresses an → exponential function with an → imaginary number  → exponent in terms of → trigonometric functions:
e = cos θ + i sinθ,
e-iθ = cos θ - i sinθ,
cosθ = (e + e-iθ)/2,
sinθ = (e - e-iθ)/2i.
In the particular case of θ = π, Euler's formula becomes: eiπ + 1 = 0, which is considered by many mathematicians to be the most elegant mathematical equation. → mathematical elegance.

Euler; → formula.

formula
  دیسول   
disul

Fr.: formule   

1) Physics, Math.: A statement of facts in a symbolical or general form, by substitution in which a result applicable to particular data may be obtained.
2) Chemistry: An expression of the constituents of a compound by symbols and figures.

From L. formula "form, rule, method, formula," literally "small form," from forma, → form, + → -ule diminutive suffix.

Disul, from dis, → form, + -ul, → -ule.

formulate
  دیسولیدن   
disulidan

Fr.: formuler   

To express in precise → form; state definitely or systematically. To reduce to or express in a → formula.

Verbal form of → form.

formulation
  دیسولش   
disuleš

Fr.: formulation   

1) The act or process of formulating.
2) A particular expression of an idea, thought, or theory.
3) Something prepared according to a → formula.

formulate; → -tion.

mass formula
  دیسول ِ جرم   
disul-e jerm

Fr.: formule de masse   

An → equation expressing the → atomic mass of a → nuclide as a function of its → mass number and the → atomic mass unit.

mass; → formula.

molecular formula
  دیسول ِ مولکولی   
disul-e molekuli

Fr.: formule moléculaire   

The formula of a chemical compound, showing the kind and arrangement of atoms.

molecular; → formula.

Newton-Leibniz formula
  دیسول ِ نیوتن-لایبنیتس   
disul-e Newton-Leibniz

Fr.: formule de Newton-Leibniz   

The formula expressing the value of a → definite integral of a given function over an interval as the difference of the values at the end points of the interval of any → antiderivative of the function: ∫f(x)dx = F(b) - F(a), summed from x = a to x = b.

Named after Isaac → Newton and Gottfried Wilhelm Leibniz (1646-1716), who both knew the rule, although it was published later; → formula.

Nyquist formula
  دیسول ِ نیکویءیست   
disul-e Nyquist

Fr.: formule de Nyquist   

The mean square noise voltage across a resistance in thermal equilibrium is four times the product of the resistance, Boltzmann's constant, the absolute temperature, and the frequency range within which the voltage is measured. → Johnson-Nyquist noise.

Named after Harry Nyquist (1889-1976), a Swedish-born American physicist, who made important contributions to information theory. → Johnson-Nyquist noise; → formula.

Planck's blackbody formula
  دیسول ِ سیه‌جسم ِ پلانک   
disul-e siyah jesm-e Planck

Fr.: formule du corps noir de Planck   

A formula that determines the distribution of intensity of radiation that prevails under conditions of thermal equilibrium at a temperature T: Bv = (2hν3 / c2)[exp(hν / kT) - 1]-1 where h is Planck's constant and ν is the frequency.

Planck; → blackbody; → formula.

quadratic formula
  دیسول ِ چاروشی   
disul-e câruši

Fr.: formule quadratique   

A formula relating the unknown part of a → quadratic equation to the known parts.

quadratic; → formula.

Rydberg formula
  هموگش ِ رودبَری   
hamugeš-e Rydberg

Fr.: formule de Rydberg   

A formula, used in atomic physics, which describes the wavelengths or frequencies of light in various series of related spectral lines, such as those emitted by hydrogen atoms.

rydberg; → formula.

semiempirical binding energy formula
  دیسول ِ نیمه‌آروینی ِ انرژی ِ بندش   
disul-e nime-ârvini-ye kâruž-e bandeš

Fr.: formule semi-empirique de l'énérgie de liaison   

Same as → Weizsacker formula.

semiempirical; → binding; → energy; → formula.

Weizsacker formula
  دیسول ِ وایتسکر   
disul-e Weizsäcker

Fr.: formule de Weizsäcker   

A → semiempirical → equation which describes the → binding energy of the → atomic nucleus. It is essentially a nuclear mass formula that provides the total binding energy per → nucleon as the sum of five terms:
Eb = aVA - aSA2/3 - aCZ2/A1/3 - aA(N -Z)2/A + δ(A,Z),
where the terms in the right-hand side of this equation are called the volume term, surface term, Coulomb term, asymmetry term, and pairing term, respectively. A, Z, and N are the number of nucleons, → protons, and → neutrons, respectively (see, e.g., Alexi M. Frolov, 2013, arxiv.org/pdf/1212.6768). Also called Bethe-Weizacker formula and → semiempirical binding energy formula.

Named after Carl Friedrich von Weizäcker (1912-2007), German physicist, who derived the formula in 1935, Z. für Physik 96, 431; → formula.

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