Delta Function


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delta function

[′del·tə ‚fəŋk·shən]
(mathematics)
A distribution δ such that is ƒ(x). Also known as Dirac delta function; Dirac distribution; unit impulse.

Delta Function

 

(also δ function, Dirac delta function, or δ(x)), a symbol used in mathematical physics in solving problems in which there are point magnitudes (for example, point load and point charge). The delta function can be defined as the density of the distribution of masses, for which a unit mass is concentrated at the point x = 0, while the mass at all other points is equal to zero. Therefore, it is assumed that δ(x) = 0, when x ≠ 0 and δ(0) = ∞, while Delta Function (“infinite splash” of a “unit intensity”). More precisely, the delta function is the name of the generalized function defined by the equality

which is valid for all continuous functions φ(x).

In the theory of generalized functions, the delta function is the name of the functional itself, which is defined by this equality.

References in periodicals archive ?
Dirac delta function [delta](x - L) was introduced to describe a distribution of externally applied torque.
The basic idea is to spread out the delta function.
x[less] than or equal to]z[less than or equal to]y] f (x, z) x y) and the identity is given by the delta function [delta](x, y) = [[delta].
It has been proved that the inverse operator is the solution of the related equation of the following form, in which the non-homogeneous term has been substituted by the Dirac's delta function [17]:
Fisher, The delta function and the composition of distributions, Dem.
r]) is the 3-dimensional Dirac's delta function at the origin.
After an introduction to signals and systems, including properties of the delta function and some classical orthogonal functions, the book provides examples and applications of numerous transforms.
0] is the intensity of the laser beam and [delta](t) is the Dirac delta function [10].
m] x [eta](t) is a continuous zero-mean stationary white-noise process with covariance matrix E{[eta](t)[eta](t + [tau])} = Q[delta]([tau]), where Q is the corresponding process disturbance intensity and [delta](x) is the Dirac delta function.
j] is the coherent scattering length, [delta] is the delta function, r is the coordinate of the neutron, and [R.
We present solutions of Burgers equation subject to an instantaneous point input, which is a Dirac delta function to represent the instant negative pressure (suction) applied to the soil around the sampler.
Scientists have use the Dirac delta function potential in three dimensions to approximate particle interactons.