harmonic function


Also found in: Wikipedia.

harmonic function

[här′män·ik ′fəŋk·shən]
(mathematics)
A function of two real variables which is a solution of Laplace's equation in two variables.
A function of three real variables which is a solution of Laplace's equation in three variables.
References in periodicals archive ?
In order to explain their ideas and for completeness, they also review the constant rank theorem technique for the space-time Hessian of space-time convex solutions of the heat equation and for the second fundamental form of the convex level sets for harmonic function. (Ringgold, Inc., Portland, OR)
In this novel hierarchical manner of notating harmonic function, Damschroder replaces these with arabic figures that relate the chords to significant structural harmonies.
Necessarily, harmonic function laterally shifts in order to have it match the peaks and troughs of a data series.
The method is based on the reduction of the problem to the Fredholm integral equation of the second kind for the boundary values of the conjugate harmonic function. The singularity of the obtained integral equation is overcome by using the Hilbert formula.
Consequently, a univalent analytic or harmonic function f: E [right arrow] C is said to be convex or close-to-convex in E if f(E) is convex or close-to-convex there.
Let's first recall the Removable Singularity Theorem for a harmonic function (cf.
[[rho].sub.0] denotes the synchronization coefficient that takes a value of 0.2 according to [1, 3], [mathematical expression not reproducible] is the vibration-dependent function that describes the interaction between pedestrian and footbridge vibration response (i.e., the displacement y, velocity [??], and acceleration y), and [xi](t) denotes the stochastic excitation process (or the harmonic function if the deterministic periodic load is considered).
A constant velocity and a harmonic function are also used to define the follower motion law.
The zero term (L = 0) is characterized by a harmonic function [Y.sup.0.sub.0] ([phi], [theta]) = (1/2 [square root of [pi]]) [a.sup.0.sub.0] describing a sphere.
Gunn exhaustively explores each possible affekt and how it is connected to and influenced by formal structure, harmonic function, key, technique, rhythm, dynamics, expression marks, articulation, ornaments, the damper pedal and tempo.
Adding log [[absolute value of [zeta] - z].sup.2] gives a harmonic function of [zeta] [member of] [P.sup.+].