Dirac distribution

Dirac distribution

[də¦rak di·strə′byü·shən]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Therefore, the zero-ordered Lognormal distribution L[N.sub.0] is in fact the degenerate Dirac distribution with pole at the location parameter of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (with vanishing threshold density [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
For the negative-ordered Lognormal family of distributions L[N.sub.[gamma]]([mu], [sigma]) with [gamma] < 0, when [gamma] rises, that is, when one moves from Log-Laplace to degenerate Dirac distribution inside the L[N.sub.[gamma]] family, the local minimum (probability) density points of L[N.sub.[gamma]] are
Recently the rth powers of the Dirac distribution and the Heaviside function for negative integers have been defined in [13] and [14], respectively.
where [([[PHI].sup.*]).sup.n] is the convolution of [PHI] with itself n times, [([[PHI].sup.*]).sup.0] = [[delta].sub.0] by convention with [[delta].sub.0] is the Dirac distribution at 0.
Recently, the author and co-workers investigated the problem of thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to solve a boundary value problem of one dimensional semiinfinite medium heated by a laser beam having a temporal Dirac distribution [8].
The problem of thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to solve a boundary value problem of one dimensional semi-infinite medium heated by a laser beam having a temporal Dirac distribution. The surface of the medium is taken as traction free.