An Etymological Dictionary of Astronomy and Astrophysics
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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)y^{n - 1} + ... + P_n(x) = 0, where P₀(x), P₁(x), ..., P_n(x) are polynomials in x.

→ algebraic + → function.

A function which can be represented by a convergent → power series.

→ analytic; → function.

A mathematical function that describes the correlation between two values of the same variable at different points in time.

→ autocorrelation; → function.

The autocovariance function (ACF) is defined as the sequence of covariances of a stationary process.
A mathematical function that expresses the autocovariance of a series in terms of the interval of separation.

→ autocovariance; → function.

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.

→ bounded; → function.

A mathematical function appearing in the → magnetization equation of a → paramagnetic substance.

→ Brillouin zone; → zone.

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.

→ cluster; → mass; → function.

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.

→ collapse; → wave function.

A function whose → variables are → complex numbers.

→ complex; → function.

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.

→ continuous; → function.

The mass distribution of → pre-stellar cores in → star-forming regions. The CMF is usually represented by dN/dM = M^α, 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).

→ core; → mass; → function.

A function defined by a → polynomial of → degree three. Its generalized form is: f(x) = ax³ + bx² + cx + d, where a, b, c and d are constants, and a≠ 0.

→ cubic; → function.

A function that gives the probability that a → random variable X is less than or equal to x, at each possible outcome: F(x) = P(X ≤ x), for -∞ < x < ∞. Same as → distribution function.

→ cumulative; → distribution; → function.

Same as → Dirac function.

→ core mass function.

→ dense; → core; → mass; → function.

Property of a mathematical function if it has a → derivative at a given point.

From → differentiable; → function.

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.

→ Dirac; → function

Same as → metric.

→ distance + → function.

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.

→ distribution; → function.

1) Math.: An → eigenvector for a linear → operator on a → vector space whose vectors are → functions. Also known as proper function.
2) Quantum mechanics: A → wave function corresponding to an → eigenvalue. Eigenfunctions represent the stationary → quantum states of a system.

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."