An Etymological Dictionary of Astronomy and Astrophysics

فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory



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Number of Results: 93 Search : equation
linear differential equation
  هموگش ِ دگرسانه‌ای ِ خطی   
hamugeš-e degarsâne-yi-ye xatti

Fr.: équation différentielle linéaire   

An equation in which the → dependent variable y and all its differential coefficients occur only in the first degree. A linear differential equation of → order  order n has the form:
fn(x)y(n) + fn-1(x)y(n-1) + ... + f1(x)y' + f0(x)y = Q(x),
where f0(x), f1(x), ..., fn(x) and Q(x) are each continuous functions of x defined on a common interval I and fn(x)≠ 0 in I. A linear differential equation cannot have, for example, terms such as y2 or (y')1/2. See also: → homogeneous linear differential equation; → nonhomogeneous linear differential equation.

linear; → differential; → equation.

linear equation
  هموگش ِ خطی   
hamugeš-e xatti

Fr.: équation linéaire   

An equation composed of first degree variables and representing a straight line.

linear; → equation.

linearized differential equation
  هموگش ِ دگرسانه‌ای ِ خطی   
hamugeš-e degarsâneyi-ye xatti

Fr.: équation différentielle linéarisée   

A differential equation that has been derived from an original nonlinear equation.

Linearized, p.p. of → linearize; → differential; → equation.

Maxwell's equations
  هموگش‌های ِ ماکسول   
hamugešhâ-ye Maxwell

Fr.: équations de Maxwell   

A set of four fundamental equations that describe the electric and magnetic fields arising from varying electric charges and magnetic fields, electric currents, charge distributions, and how those fields change in time. In their vector differential form, these equations are:
i) ∇.E = ρ/ε0 (→ Gauss's law for electricity),
ii) ∇.B = 0 (→ Gauss's law for magnetism),
iii) x E = -∂B/∂t (→ Faraday's law of induction),
iv) x B = μ0J + μ0ε0E/∂t (→ Ampere's law), with c2 = 1/(μ0ε0), where E is → electric intensity, B is → magnetic flux density, ρ is → charge density, ε0 is → permittivity, μ0 is → permeability, J is → current density, and c is → speed of light.

maxwell. It should be emphasized that the equations originally published by James Clerk Maxwell in 1873 (in A Treatise on Electricity and Magnetism) were 20 in number, had 20 variables, and were in scalar form. The German physicist Heinrich Rudolf Hertz (1857-1894) reduced them to 12 scalar equations (1884). It was the English mathematician/physicist Oliver Heaviside (1850-1925) who expressed Maxwell's equations in vector form using the notations of → gradient, → divergence, and → curl of a vector, thus simplifying them to the present 4 equations (1886). Before Einstein these equations were known as Maxwell-Heaviside-Hertz equations, Einstein (1940) popularized the name "Maxwell's Equations;" → equation.

Navier-Stokes equation
  هموگش ِ ناویه-استوکس   
hamugeš-e Navier-Stokes

Fr.: équation de Navier-Stokes   

One of a set of → differential equations that describes the motion of a → fluid as a function of → pressure, → density, total external force, and → viscosity. See also → Euler equation.

Named after Claude-Louis Navier (1785-1836), a French engineer and physicist, and George Gabriel Stokes, → stokes; → equation.

Newton's equation
  هموگش ِ نیوتن   
hamugeš-e Newton

Fr.: équation de Newton   

In → geometric optics, an expression relating the → focal lengths of an → optical system (f and f') and the object x and image x' distances measured from the respective focal points. Thus, ff' = xx'. Same as Newton's formula.

Newton; → equation.

nondimensional equation
  هموگش ِ ناوامونی   
hamugeš-e nâvâmuni

Fr.: équation non-dimensionnelle   

An equation that is independent of the units of measurement as it only involves nondimensional numbers, parameters, and variables.

non-; → dimensional; → equation.

nonhomogeneous linear differential equation
  هموگش ِ دگرسانه‌ای ِ خطی ناهمگن   
hamugeš-e degarsâne-yi-ye xatti nâhamgen

Fr.: équation différentielle linéaire non homogène   

A → linear differential equation if Q(x)≠ 0 on interval I.

nonhomogeneous; → linear; → differential; → equation.

ordinary differential equation
  هموگش ِ دگرسانه‌ای شونیک   
hamugeš-e degarsâneyi-ye šunik

Fr.: équation différentielle ordinaire   

A → differential equation in which the unknown function depends on only one → independent variable, as contrasted with a → partial differential equation.

ordinary; → differential; → equation.

parametric equation
  هموگش ِ پارامونی   
hamugeš-e pârâmuni

Fr.: équation paramétrique   

Any of a set of equations that defines the coordinates of the dependent variables of a curve or surface in terms of one or more independent variables or parameters.

parametric; → equation.

partial differential equation
  هموگش ِ دگرسانه‌ای با واخنه‌ی ِ پاری   
hamugeš-e degarsâne-yi bâ vâxane-ye pâri

Fr.: équation différentielle aux dérivées partielles   

A type of differential equation involving an unknown function (or functions) of several independent variables and its (or their) partial derivatives with respect to those variables.

partial; → differential; → equation.

personal equation
  هموگش ِ تنومی   
hamugeš-e tanumi

Fr.: équation personnelle   

A systematic observational error due to the characteristics of the observer.

Personal, adj. of → person; → equation.

perturbation equation
  هموگش ِ پرتورش   
hamugeš-e partureš

Fr.: équation de perturbation   

Any equation governing the behavior of a → perturbation.

perturbation; → equation.

Poisson's equation
  هموگش ِ پو‌آسون   
hamugeš-e Poisson

Fr.: équation de Poisson   

An equation (∇2φ = 4πGρ) which relates the gravitational (or electromagnetic) potential to the mass density (or charge density).

Poisson distribution; → equation.

polar equation
  هموگش ِ قطبی   
hamugeš-e qotbi

Fr.: équation polaire   

An equation for a curve written in terms of the → polar coordinates.

polar; → equation.

polynomial equation
  هموگش ِ بلنامین   
hamugeš-e bolnâmin

Fr.: équation polynomiale   

An equation of the form a0 + a1x + a2x2 + ... + anxn, where a0 ... an are → real numbers and an≠ 0. Same as → algebraic equation.

polynomial; → equation.

quadratic equation
  هموگش ِ چاروشی   
hamugeš-e câruši

Fr.: équation quadratique   

An equation with the general form of ax2 + bx +c = 0, in which the highest power of the unknown is the second power (square).

quadratic; → equation.

quartic equation
  هموگش ِ چارُمیک   
hamugeš-e câromik

Fr.: équation quartique   

An equation containing unknowns of the fourth power; the general form: ax4 + bx3 + cx2 + dx + e = 0.

From L. quart(us) "fourth" (→ quarter) + → -ic; → equation.

hamugeš, → equation; câromân, from cârom "fourth," from câr, cahâr "four" + -om "-th" + -ik, → -ic.

quintic equation
  هموگش ِ پنجمیک   
hamugeš-e panjomik

Fr.: équation quintique   

An equation containing unknowns of the fifth power.

quintic; → equation.

radiation transfer equation
  هموگش ِ تراواژ ِ تابش   
hamugeš-e tarâvâž-e tâbeš

Fr.: équation de transfert radiatif, ~ de rayonnement   

radiative transfer equation.

radiation; → transfer; → equation.

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