Dirac delta function


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Dirac delta function

[di′rak ′del·tə ‚fəŋk·shən]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Then scattering of relativistic fermions due to a single quaternionic Dirac delta function has been studied.
where f is a function of the position vector x and [delta] (x - x') is the Dirac delta function. Also, n is the volume of the integral that contains x.
In (5), [[delta].sub.[epsilon]] ([phi]) is a smooth version of the Dirac delta function, which is defined as
where [L.sub.P] is the number of the multipath components, [mathematical expression not reproducible] is the complex fading coefficient of the ith multipath component, [absolute value of [a.sub.i]] presents the amplitude, [[phi].sub.i] means the phase and obeys a uniform distribution U(0, 2[pi]) [5], [[tau].sub.i] denotes the time delay for the ith multipath component, and [delta] represents the Dirac delta function.
In our endemic model, letting a =1 and h(t) = [delta](t - 1) where [delta] is the Dirac delta function, we note that each infection increases the force of the infectivity by one unit.
We considered the indeterminate beam problem shown in Figure 3, which is a fixed end supported beam applied by a Dirac delta function [12,13].
This is easily inferred by setting the exit slit width to Dirac delta function according to (1).
where [delta](x) is the Dirac delta function, and f is a given function such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for some positive constant c.
The second term on the right-hand side of (B6) can be written in form of (B3), whereas the last term on the right-hand side of the same equation solemnly includes derivatives of the Dirac delta function since [H.sub.j] is not a function of z.
We know from Fourier transform tables given in [9] [12] that u(t) (j2pf)-1 + 0.5d(f) and time reversal property of Fourier transform immediately allows us to write u(-t) (-j2pf)-1 +0.5d(f), where we have used the even property of Dirac delta function. Now, duality property of Fourier transform is utilized to express the inverse Fourier transform of u(f) as (- j2pt)-1 + 0.5d(t) u(f).
Dirac delta function [delta](x - L) was introduced to describe a distribution of externally applied torque.
First, using Dirac Delta Function [13], the concentrated equivalent inertia force [F.sub.g] and inertia moment [M.sub.g] can be represented in the form of distributed loads as