An Etymological Dictionary of Astronomy and Astrophysics
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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.

For a radiating material, the ratio of emissivity to opacity.

→ source; → function.

A function consisting of several segments, usually → polynomials, joined smoothly together at specific points with an explicitly stated degree of accuracy. Spline functions are used to approximate a given function on an interval.

From East Anglian dialect, maybe related to O.E. splin and to modern splint. A spline was originally a slat or a thin strip of wood. A later meaning was "a long, thin, flexible strip used as a guide for drawing arcs of curves;" → function.

The number of stars born per unit area in the mass range log M to log M + d log M during the time interval t to t + dt. The integration of the creation function over time gives the → present-day mass function (Miller & Scalo, 1797, ApJSS 41, 513).

→ stellar; → creation; → function.

Math.: A function f of a real variable defined on an interval [a,b] so that [a,b] can be divided into a finite number of sub-intervals on each of which f is a constant. The graph of a step function is a series of line segments resembling a set of steps.

Step, from M.E. steppen, O.E. steppan; cf. Du. stap, O.H.G. stapfo, Ger. stapfe "footprint;" → function.

Karyâ, → function; pellé "stair, step;" Mid.Pers. pylg "step," pillagân "steps, staircase;" from *palak, from *padak, from pad-, → foot, + relation suffix -ak.

A function whose value is defined for all possible input values.

→ total; → function.

A function which is not → algebraic. For example y = cosx, y = 10^xx.

→ transcendental; → function.

The mathematical relationship between the output of a control system and its input: for a linear system, it is the Laplace transform of the output divided by the Laplace transform of the input under conditions of zero initial-energy storage.

→ transfer; → function.

The → probability of finding the → Universe in a → state labelled X₂ at a time t₂, if it was in a state X₁ at an earlier time t₁.

→ transition; → function.

A function of an angle, one of six functions (sine, cosine, tangent, cotangent, secant, and cosecant) that represent ratios of sides of right triangles. Also called circular function.

→ trigonometric; → function.

A → total function from → truth values to truth values (a sequence of truth values).

→ truth; → function.

The function y = f(x) in a given range of the argument x if there is no number M such that for all values of x in the range under consideration the inequality | f(x) | ≤ M will be fulfilled. → bounded function.

→ unbound; → function.

A function whose value at each point is n-dimensional, as compared to a scalar function, whose value is one-dimensional.

→ vector; → function.

The → Fourier transform of a source's → brightness distribution, weighted by the characteristics of the → interferometer's antennas.

→ visibility; → function.

In → quantum mechanics, the function of space and time that satisfies → Schrodinger equation. The square of the modulus of its amplitude at any point represents the probability of finding a particle there.

→ wave; → function.

A function whose value is zero outside a given interval. Applications of window functions include signal filtering and spectral analysis. The various types of windw functions include: → rectangular window, cosine window, triangular window, Gaussian window, Hanning window, and so on.

→ window; → function.

The least amount of energy required to remove an electron from the surface of a solid, to a point just outside the solid where the electron has zero kinetic energy. See also → photoelectric effect.

→ work; → function.