# An Etymological Dictionary of Astronomy and AstrophysicsEnglish-French-Persian

## فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

### M. Heydari-Malayeri    -    Paris Observatory

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 linear differential equation   هموگش ِ دگرسانه‌ای ِ خطی   hamugeš-e degarsâne-yi-ye xattiFr.: 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 electric quadrupole   چهارقطبه‌ی ِ برقی ِ خطی   cahârqotbe-ye barqi-ye xattiFr.: quadrupôle électrique linéaire   A system of three charges +q, -2q, and +q, arranged along a line to form an axial quadrupole. The → electric potential  V due to a linear quadrupole varies as 1/r3, whereas the → electric intensity  E varies as 1/r4.→ linear; → electric; → quadrupole. linear equation   هموگش ِ خطی   hamugeš-e xattiFr.: équation linéaire   An equation composed of first degree variables and representing a straight line.→ linear; → equation. linear function   کریای ِ خطی   karyâ-ye xattiFr.: fonction linéaire   A function expressed by a → first degree equation that can be graphically represented in the → Cartesian coordinate plane by a → straight line.→ linear; → function. linear instability   ناپایداری ِ خطی   nâpâydâri-ye xatti (#)Fr.: instabilité linéaire   An instability that can be described (to first-order accuracy) by linear (or tangent linear) equations.→ linear; → instability. linear momentum   جنباک ِ خطی   jonbâak-e xattiFr.: quantité de mouvement linéaire   The product of an object's → mass and → velocity. It is a → vector and points in the same direction as the velocity vector. Linear momentum is distinguished from → angular momentum. When there is no opportunity for confusion, usually the term momentum is used instead of linear momentum.→ linear; → momentum. linear perturbation theory   نگره‌ی ِ پرتورش ِ خطی   negare-ye partureš-e xattiFr.: théorie de perturbation linéaire   Assumption that the variations in the plasma parameters, due to the presence of waves, are small (to the first order) as compared to the undisturbed parameters. This makes it possible to linearize equations by dropping out second order (and higher) nonlinear terms.→ linear; → perturbation; → theory. linear polarization   قطبش ِ خطی   qotbeš-e xatti (#)Fr.: polarisation linéaire   Of an electromagnetic radiation, a → polarization in which the electric vibrations are confined to one plane along the direction of propagation. Also called → plane polarization. See also → circular polarization.→ linear; → polarization. linear programming   برنامه‌سازی ِ خطی   barnâme-sâzi-ye xatti (#)Fr.: programmation linéaire   A procedure for finding the maximum or minimum of a → linear function where the → arguments are subject to linear → constraints. For problems involving more than two variables or problems involving a large number of constraints, solution methods used are those that are adaptable to computers. A well-known such → algorithm is the → simplex method.→ linear; → programmings. linear regression   وایازی ِ خطی   vâyâzi-ye xattiFr.: regression linéaire   In statistics, a regression method that establishes a linear relationship between two random variables.→ linear; → regression. linear size   اندازه‌ی ِ خطی   andâze-ye xattiFr.: taille linéaire   The real, physical size, as opposed to angular size.→ linear; → size. linear system   راژمان ِ خطی   râžmân-e xattiFr.: système linéaire   Physics: A → dynamical system whose evolution is a linear process. If a change in any variable at some initial time produces a change in the same or some other variable at some later time, twice as large a change at the same initial time will produce twice as large a change at the same later time.→ linear; → system. linear velocity   تندای ِ خطی   tondâ-ye xattiFr.: vitesse linéaire   The rate of change of the position of an object that is traveling along a straight path. In other words, the velocity of an object when its moving direction is not changing. For a given → angular velocity (ω), the linear velocity v of the particle is directly proportional to the distance of the particle from the center of the circular path: v = ω ×r.→ linear; → velocity. linearity   خطیگی   xattigiFr.: linéarité   The property, condition, or state of being linear. Math.: A relationship between two variables so that when plotted on a graph they yield a straight line.→ linear; → -ity. linearization   خطش، خطانش   xatteš, xattânešFr.: linéarisation   A process of reduction to linear form by appropriate change of variables or by approximation.Verbal noun of → linearize. linearize   خطیدن، خطانیدن   xattidan, xattânidanFr.: linéariser   To make linear; give linear form to.→ linear + → -ize. linearized differential equation   هموگش ِ دگرسانه‌ای ِ خطی   hamugeš-e degarsâneyi-ye xattiFr.: équation différentielle linéarisée   A differential equation that has been derived from an original nonlinear equation.Linearized, p.p. of → linearize; → differential; → equation. linearly   خطانه   xattânéFr.: linéairement   In a manner characterized by first-degree algebraic terms.Adverb of → linear. linearly dependent   خطانه وابسته   xattâné vâbastéFr.: linéairement dépendant   A set of objects x1, x2, ..., xn (→ vectors, → matrices, → polynomials, etc.) on a given set if there is a linear combination of them: a1x1 + a2x2 + ... + anxn, which is zero, but at least one of the coefficients is non-zero. For example the binomials (2x + y) and (6x + 3y) are linearly dependent, since 3(2x + y) - (6x + 3y) = 0.→ linearly; → dependent. linearly independent   خطانه ناوابسته   xattâné nâvâbastéFr.: linéairement indépendant   1) A set of objects x1, x2, ..., xn (→ vectors, → matrices, → polynomials, etc.) if it si not → linearly dependent. 2) Of two particular solutions (y1, y2) of a → homogeneous linear differential equation of the second order (y'' + a1 y' + a2y = 0) on an interval [a, b], if their ratio in this interval is not a constant: y1/y2≠ constant.→ linearly; → independent.