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: 20 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 ِ چندساخت   
disul-e zaviye-ye candsâxt

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.

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.

well-formed formula (wff)
  دیسول ِ خوش‌دیسه (wff)   
disul-e xošdisé (wff)

Fr.: formule bien formée (FBF)   

A string of → symbols from the alphabet of the → formal language that conforms to the grammar of the formal language. → closed wff, → open wff.

Wff, pronounced whiff; → well; → form; → formula.