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.

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.

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