Dirac delta function

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Dirac delta function

[di′rak ′del·tə ‚fəŋk·shən]
(mathematics)
References in periodicals archive ?
Park, "Greens-function approach to two- and three-dimensional delta-function potentials and application to the spin-1/2 Aharonov-Bohm problem," Journal of Mathematical Physics, vol.
Since the degree of homogeneity of the delta-function equals -1, we obtain that limit (21) coincides with
where [delta] is the Delta-function concentrated at x = [x.sub.0].
Now, periodic delta-function corresponding to singularities disposed in the nodes of the lattice A has the following form:
Formula (8) defines a periodic delta-function uniquely.
Putting [[delta].sub.n](x) = n[rho](nx) for n = 1, 2,..., it follows that {[[delta].sub.n](x)} is a regular sequence of infinitely differentiable functions converging to the Dirac delta-function [delta](x).
It corresponds to the current density defined by means of the Dirac delta-function:
the electric current density is defined by using Dirac's delta-function:
This arrangement is in agreement with the fact that we can integrate a delta-function (charge) but we cannot integrate its square (would be energy).
If the acceleration of the source is a delta-function peaked at t = t, r = 0, then the advanced field of the source vanishes everywhere at t; we need to look closely, however, to see if X does as well.
The analyzed the very classical problem of signal processing how the wide spectrum of the single pulse approaches the delta-function like spectrum of the periodic signal.
As one of their defining properties, Fourier transforms of quasiperiodic functions are discrete sets of delta-functions; they can always be expressed as a series of sine and cosine terms, but with incommensurate lengths, or a number of arithmetically independent basis vectors that exceeds the number of independent variables.