Fr.: fonction imbriquée
In computer programing, a function that is defined inside the definition of another function.
Fr.: fonction non algébrique
A → transcendental function. Examples are: exponential, logarithmic, and trigonometric functions.
optical transfer function (OTF)
karyâ-ye tarâvaž-e nuri
Fr.: fonction de transfert optique
The function that provides a full description of the imaging quality of an optical system. A combination of the → modulation transfer function (MTF) and the → phase transfer function (PTF) , the OTF describes the spatial (angular) variation as a function of spatial (angular) frequency.
Fr.: fonctions orthogonales
A set of functions, any two of which, by analogy to orthogonal vectors, vanish if their product is summed by integration over a specified interval.
Fr.: fonction de partition
See → integer partition.
Fr.: fonction périodique
A function f(x) if for all x, f(x + P) = f(x), where P is a positive constant. The least value of P > 0 is called the period of f(x).
Fr.: fonction de phase
The variation in brightness of a target as the phase angle (the angle between Sun and observer as seen from the target) varies between 0° and 180°. The directional distribution of reflected (or scattered) radiation. The phase angle is the supplement of the scattering angle (the angle between the incident ray and the emerging ray); in other words, the sum of the phase angle and the scattering angle is always 180° (Ellis et al., 2007, Planetary Ring Systems, Springer).
phase transfer function (PTF)
karyâ-ye tarâvaž-e fâz
Fr.: fonction de transfert de phase
A measure of the relative phase in the image as function of frequency. It is the phase component of the → optical transfer function. A relative phase change of 180°, for example, results in an image with the black and white areas reversed.
piecewise continuous function
karyâ-ye peyvaste-ye tekke-yi
Fr.: fonction continue par morceaux
A function f(x) in an interval if :1) the interval can be divided into a finite number of pieces in each of which f(x) is continuous, and 2) the limits of f(x) as x approaches the boundary point of each piece are finite. In other words, a piecewise continuous function is one that is made up of a finite number of continuous pieces.
Fr.: fonction de Planck
Same as → Planck's blackbody formula.
point spread function (PSF)
karyâ-ye gostareš-e noqté, ~ ~ pandé
Fr.: fonction d'étalement du point
The two-dimensional intensity distribution about the image of a point source.
Fr.: fonction de puissance
A function of the form f(x) = xn, where n is a → real number.
present-day mass function (PDMF)
karyâ-ye jerm-e konuni, ~ ~ emruzi
Fr.: fonction de masse actuelle
The present number of stars on the → main sequence per unit logarithmic mass interval per square parsec. The PDMF is the basis for deriving the → initial mass function (IMF). This mass function is not corrected for stellar evolution nor losses through stellar deaths.
probability density function
karyâ-ye cagâli-ye šavânâyi
Fr.: fonction de densité de probabilité
A mathematical function whose integral over any interval gives the probability that a continuous → random variable has values in this interval. Also known as → density function, frequency function, → probability function.
Fr.: fonction de probabilité
A function that represents a probability distribution in terms of integrals. Also called probability density function or density function.
Fr.: fonction de rougissement
The normalized interstellar extinction at a given wavelength. It is defined by f(λ) = A(λ)/A(Hβ) - 1, where A(λ) is the extinction at the given wavelength and A(Hβ) the extinction at Hβ, with f(Hβ) = 0. It is used to → de-redden observed fluxes: I(λ)/I(Hβ) = F(λ)/F(Hβ).10c(Hβ).f(λ), where I represents the flux in the absence of extinction and F the observed flux affected by extinction, c(Hβ) being the → reddening coefficient.
Fr.: fonction de régression
A mathematical function that describes the relationship between two or more variables in a set of data.
Fr.: fonction régulière
A function of a complex variable which is single-valued in a domain and which has a finite derivative at every point.
Fr.: équation de Salpeter
The first mathematical description of the → initial mass function (IMF) of newly formed stars of solar to → intermediate-masses. It is proportional to M -2.35, where M is the stellar mass. → Salpeter slope.
Named after the Austrian-Australian-American astrophysicist Edwin Ernest Salpeter (1924-2008); → function.
Fr.: fonction de Schechter
A mathematical expression that describes the → luminosity function of galaxies. The function correctly reflects the facts that the luminosity function decreases with increasing luminosity and that the decrease is particularly marked at high luminosities. It is expressed as: φ(L) = φ*(L/L*)α exp (-L/L*), which has two parts and three parameters: φ* is an empirically determined amplitude, α is an empirically derived exponent, and L* is a characteristic luminosity which separates the low and high luminosity parts. For small luminosities (L much smaller than L*) the Schechter function approaches a power law, while at high luminosities (L much larger than L*) the frequency of galaxies drops exponentially. φ*, L*, and the faint-end slope α depend on the observed wavelength range, on the → redshift, and on the environment where the galaxies are observed.
Named after the American astronomer Paul Schechter (1948-), who proposed the function in 1976 (ApJ 203, 297); → function.