Fr.: fonction algébrique
A function expressed in terms of → polynomials and/or roots of polynomials. In other words, any function y = f(x) which satisfies an equation of the form P0(x)yn + P1(x)yn - 1 + ... + Pn(x) = 0, where P0(x), P1(x), ..., Pn(x) are polynomials in x.
Fr.: fonction analytique
A function which can be represented by a convergent → power series.
Fr.: fonction d'autocorrélation
A mathematical function that describes the correlation between two values of the same variable at different points in time.
karyâ-ye karânmand, ~ karândâr
Fr.: fonction bornée
The function y = f(x) in a given range of the argument x if there exists a positive number M such that for all values of x in the range under consideration the inequality | f(x) | ≤ M will be fulfilled. → unbounded function.
Fr.: fonction de Brillouin
cluster mass function (CMF)
karyâ-ye jerm-e xušé
Fr.: fonction de masse d'amas
An empirical power-law relation representing the number of clusters as a function of their mass. It is defined as: N(M)dM ∝ M -αdM, where the exponent α has an estimated value of about 2 and dM is the mass interval. It is believed that this is a universal law applying to a variety of objects including globular clusters, massive young clusters, and H II regions.
collapse of the wave function
rombeš-e karyâ-ye mowj
Fr.: effondrement de la fonction d'onde
The idea, central to the → Copenhagen Interpretation of quantum theory, whereby at the moment of observation the → wave function changes irreversibly from a description of all of the possibilities that could be observed to a description of only the event that is observed. More specifically, quantum entities such as electrons exist as waves until they are observed, then "collapse" into point-like particles. According to the Copenhagen Interpretation, observation causes the wave function to collapse. However it is not known what causes the wave function to collapse. Same as → wave collapse.
Fr.: fonction continue
The function y = f(x) is called continuous at the point x = x0 if it is defined in some neighborhood of the point x0 and if lim Δy = 0 when Δx → 0.
core mass function (CMF)
karyâ-ye jerm-e maqzé
Fr.: fonction de masse des cœurs
The mass distribution of → pre-stellar cores in → star-forming regions. The CMF is usually represented by dN/dM = Mα, where dM is the mass interval, dN the number of cores in that interval, and α takes different values in different mass ranges. In the case of → low-mass stars, it is found that the CMF resembles the → Salpeter function, although deriving the masses and radii of pre-stellar cores is not straightforward. The observational similarity between the CMF and the → initial mass function (IMF) was first put forth by Motte et al. (1988, A&A, 336, 150), and since then many other samples of dense cores have been presented in this context. For example, Nutter & Ward-Thompson (2007, MNRAS 374, 1413), using SCUBA archive data of the Orion star-forming regions, showed that the CMF can be fitted to a three-part → power law consistent with the form of the stellar IMF. Recent results, obtained using observations by the → Herschel Satellite, confirm the similarity between the CMF and IMF with better statistics (Könyves et al. 2010, A&A, 518, L106; André et al. 2010, A&A, 518, L102). Moreover, these works show that the CMF has a → lognormal distribution (i.e. dN/dlog M follows a → Gaussian form against log M), as is the case for the IMF at low masses (below about 1 solar mass).
Fr.: fonction cubique
cumulative distribution function
karyâ-ye vâbâžeš-e kumeši
Fr.: fonction de distribution cumulée
Fr.: fonction delta
Same as → Dirac function.
dense core mass function
karyâ-ye jerm-e maqze-ye cagâl
Fr.: fonction de masse des cœurs denses
karyâ-ye degarsânipazir, ~ degarsânidani
Property of a mathematical function if it has a → derivative at a given point.
Fr.: fonction de Dirac
A function of x defined as being zero for all values of x other than x = x0 and having the definite integral from x = -∞ to x = +∞ equal to unity.
Fr.: fonction de distance
Same as → metric.
Fr.: fonction de distribution
A function that gives the relative frequency with which the value of a statistical variable may be expected to lie within any specified interval. For example, the Maxwellian distribution of velocities gives the number of particles, in different velocity intervals, in a unit volume.
Fr.: fonction propre
1) Math.: An → eigenvector for a linear
→ operator on a → vector space
whose vectors are → functions. Also known as
From Ger. Eigenfunktion, from eigen- "characteristic, particular, own" (from P.Gmc. *aigana- "possessed, owned," Du. eigen, O.E. agen "one's own") + → function.
Viž-karyâ, from viž, contraction of vižé "particular, charcteristic" + karyâ, → function. Vižé, from Mid.Pers. apēcak "pure, sacred," from *apa-vēcak "set apart," from prefix apa- + vēcak, from vēxtan (Mod.Pers. bixtan) "to detach, separate, sift, remove," Av. vaēk- "to select, sort out, sift," pr. vaēca-, Skt. vic-, vinakti "to sift, winnow, separate; to inquire."
Fr.: fonction explicite
The most usual form of a function in which the dependent variable (written on the left hand side of the Same as → equality sign) is expressed directly in terms of independent variables written on the left (on the right hand side). See also → implicit function.
Fr.: fonction exponentielle
A function in the form of y = bx defined for every → real number x, with positive base b > 1.