exponential function karyâ-ye nemâyi Fr.: fonction exponentielle A function in the form of y = b^{x} defined for every → real number x, with positive base b > 1. → exponential; → function. |
function karyâ Fr.: fonction A mathematical rule between two sets which assigns to each element of the first exactly one element of the second, as the expression y = ax^{b}. From M.Fr. fonction, from O.Fr. function, from L. functio (gen. functionis) "performance, execution," from functus, p.p. of fungor "to perform, execute." Karyâ, from Av. kairya- "function;" cf. Mod.Pers. Laki karyâ "done," Awromâni kiriyây, kiria "to be done," from kar- "to do" (Mod.Pers. kar-, kardan "to do, to make;" Mid.Pers. kardan; O.Pers./Av. kar- "to do, make, build;" Av. kərənaoiti "he makes;" cf. Skt. kr- "to do, to make," krnoti "he makes, he does," karoti "he makes, he does," karma "act, deed;" PIE base k^{w}er- "to do, to make") + -ya suffix of verbal adjectives and nouns (e.g. išya- "desirable," jivya- "living, fresh," haiθya- "true," maidya- "middle," dadya- "grain"); cf. Skt. kāryá- "work, duty, performance." |
functional 1) karyâyi; 2) karyâl Fr.: 1) fonctionnel; 2) fonctionnelle 1) Math.: Of, relating to, or affecting a function. |
Gaussian function karyâ-ye Gauss Fr.: fonction de Gauss The function e^{-x2}, whose integral in the interval -∞ to +∞ gives the → square root of the → number pi: ∫e^{-x2}dx = √π. It is the function that describes the → normal distribution. |
Gibbs function karyâ-ye Gibbs Fr.: fonction de Gibbs Same as → Gibbs free energy. Named after Josiah Willard Gibbs (1839-1903), an American physicist who played an important part in the foundation of analytical thermodynamics; → function. |
Hamiltonian function karyâ-ye Hâmilton Fr.: fonction de Hamilton A function that describes the motion of a → dynamical system in terms of the → Lagrangian function, → generalized coordinates, → generalized momenta, and time. For a → holonomic system having n degrees of freedom, the Hamiltonian function is of the form: H = Σp_{i}q^{.}_{i} - L(q_{i},q^{.}_{i},t) (summed from i = 1 to n), where L is the Lagrangian function. If L does not depend explicitly on time, the system is said to be → conservative and H is the total energy of the system. The Hamiltonian function plays a major role in the study of mechanical systems. Also called → Hamiltonian. Introduced in 1835 by the Irish mathematician and physicist William Rowan Hamilton (1805-1865); → function. |
hyperbolic function karyâ-ye hozluli Fr.: fonction hyperbolique Any of the six functions sinh, cosh, tanh, coth, csch, and sech that are related to the → hyperbola in the same way the → trigonometric functions relate to the → circle. Many of the formulae satisfied by the hyperbolic functions are similar to corresponding formulae for the trigonometric functions, except for + and - signs. For example: cosh^{2}x - sinh^{2}x = 1. See also: → hyperbolic cosine, → hyperbolic sine. Hyperbolic functions were first introduced by the Swiss mathematician Johann Heinrich Lambert (1728-1777). → hyperbolic; → function. |
identity function karyâ-ye idâni Fr.: fonction d'identité Math.: Any function f for which f(x) = x for all x in the domain of definition. |
implicit function karyâ-ye dartâhi Fr.: fonction implicite A function which contains two or more variables that are not independent of each other. An implicit function of x and y is one of the form f(x,y) = 0, e.g., 4x + y^{2} - 9 = 0. See also → explicit function. |
initial mass function (IMF) karyâ-ye âqâzin-e jerm Fr.: fonction initiale de masse A mathematical expression describing the relative number of stars found in different ranges of mass for a cluster of stars at the time of its formation. It is defined as φ(log M) = dN / dlog M ∝ M^{ -Γ}, where M is the mass of a star and N is the number of stars in a logarithmic mass interval. The value of the slope found by Salpeter (1955) for → low-mass and → intermediate-mass stars in the → solar neighborhood is Γ = 1.35. The IMF can be expressed also in linear mass units: χ(M) = dN / DM ∝ M^{ -α}. Note that χ(M) = (1 / M lm 10) φ(log M), and α = Γ + 1. In this formalism the Salpeter slope is α = 2.35. There is a third way for representing the IMF, in which the exponent is x = -α. The IMF is not a single power law over all masses, from → brown dwarfs to → very massive stars (Kroupa, 2002, Science 295, 82). Different slopes have been found for different mass segments, as follows: α = 1.3 for 0.08 ≤ M_{solar} < 0.5; α = 2.3 for 0.5 ≤ M_{solar} < 1; α = 2.3 for 1 ≤ M_{solar}. The IMF at low masses can be fitted by a → lognormal distribution (See Bastian et al., 2010, ARAA 48, 339 and references therein). See also → canonical IMF. |
instrumental response function karyâ-ye pâsox-e sâzâl Fr.: fonction de la réponse instrumentale The mathematical form of the way an instrument affects the input signal. → instrumental; → response; → function. |
integral function karyâ-ye dorostâli Fr.: fonction intégrale A function whose image is a subset of the integers, i.e. that takes only integer values. |
Lagrangian function karyâ-ye lâgrânž (#) Fr.: Lagrangien, fonction de Lagrange A physical quantity (denoted L), defined as the difference between the → kinetic energy (T) and the → potential energy (V) of a system: L = T - V. It is a function of → generalized coordinates, → generalized velocities, and time. Same as → Lagrangian, → kinetic potential. → Lagrangian; → function. |
likelihood function karyâ-ye šodvâri Fr.: fonction de vraisemblance A function that allows one to estimate unknown parameters based on known outcomes. Opposed to → probability, which allows one to predict unknown outcomes based on known parameters. More specifically, a probability refers to the occurrence of future events, while a likelihood refers to past events with known outcomes. → likelihood; → function. |
linear function karyâ-ye xatti Fr.: fonction linéaire A function expressed by a → first degree equation that can be graphically represented in the → Cartesian coordinate plane by a → straight line. |
luminosity function karyâ-ye tâbandegi Fr.: fonction de luminosité Number → distribution of → stars or galaxies (→ galaxy) with respect to their → absolute magnitudes. The luminosity function shows the → number of stars of a given intrinsic luminosity (or the number of galaxies per integrated magnitude band) in a given → volume of space. → luminosity; → function. |
mass function karyâ-ye jerm Fr.: fonction de masse 1) The number of a class of objects as a function of their mass.
→ initial mass function (IMF);
→ present-day mass function (PDMF). |
membership function karyâ-ye hamvandi Fr.: fonction d'adhésion One of several functions used in the → fuzzification and → defuzzification steps of a → fuzzy logic system to map the → nonfuzzy input values to → fuzzy linguistic terms and vice versa. A membership function is used to quantify a linguistic term. → membership; → function. |
metallicity distribution function (MDF) karyâ-ye vâbâžeš-e felezigi Fr.: fonction de distribution de métallicité A plot representing the number of stars (or systems) per metallicity interval, usually expressed in [Fe/H] (abundance of → iron relative to → hydrogen). → metallicity; → distribution; → function. |
modulation transfer function (MTF) karyâ-ye tarâvaž-e degarâhangeš Fr.: fonction de transfert de modulation A measure of the ability of an optical system to reproduce (transfer) various levels of detail from the object to the image, as shown by the degree of contrast (modulation) in the image. → optical transfer function. → modulation; → transfer; → function. |