An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

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.

→ explicit; → function.

A function in the form of y = b^x defined for every → real number x, with positive base b > 1.

→ exponential; → function.

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^wer- "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."

1) Math.: Of, relating to, or affecting a function.
2) A → function that associates a → real number or → complex number to a function or a → set of functions. A functional can be considered as a function of a set of several infinite and continuous → variables.

→ function; → -al.

The function e^-x2, whose integral in the interval -∞ to +∞ gives the → square root of the → number pi: ∫e^-x2dx = √π. It is the function that describes the → normal distribution.

→ Gaussian; → function.

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.

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_iq^._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.

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: cosh²x - sinh²x = 1. See also: → hyperbolic cosine, → hyperbolic sine. Hyperbolic functions were first introduced by the Swiss mathematician Johann Heinrich Lambert (1728-1777).

→ hyperbolic; → function.

Math.: Any function f for which f(x) = x for all x in the domain of definition.

→ identity; → function.

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 + y² - 9 = 0. See also → explicit function.

→ implicit; → function.

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.

→ initial; → mass; → function.

The mathematical form of the way an instrument affects the input signal.

→ instrumental; → response; → function.

A function whose image is a subset of the integers, i.e. that takes only integer values.

→ integral; → function.

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.

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.

A function expressed by a → first degree equation that can be graphically represented in the → Cartesian coordinate plane by a → straight line.

→ linear; → function.

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.

1) The number of a class of objects as a function of their mass. → initial mass function (IMF); → present-day mass function (PDMF).
2) A numerical relation between the masses of the two components of a → spectroscopic binary that provides information on the relative masses of the two stars when the spectral lines of only one component can be seen. If M_p is the mass of primary (whose spectrum is known), M_s is the mass of secondary, and i the → angle of inclination of the orbit, the mass function is given by: (M_s³. sin³i) / (M_p + M_s)².

→ mass; → function.

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.

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.