Namias V: Singularities in the fields of electric and magnetic multipoles and related singularities involving the

Dirac delta function.

The result indicates that the radio emissions by the nonlinearly oscillating neutron star are periodically pulse-like radiation with the

Dirac delta shape, which is consistent with the general observations of pulsars.

Ozcag, Defining the kth Powers of the

Dirac Delta Distribution for Negative Integers, Appl.

New to this edition is coverage of the application of Laplace transforms, the

Dirac delta function, and the Heaviside function; the Cherkaev, Lurie, and Milton (CLM) stress invariance theorem; and recent developments in thermoelasticity.

is a convolution algebra with the

Dirac delta distribution [delta] as its unit element.

Dirac delta function [delta](x - L) was introduced to describe a distribution of externally applied torque.

All chapters have been revised and updated for this edition, which has an expanded introduction to Green's functions, discussion of the eigenfunction expansion method and sections on the convergence speed of series solutions and the importance of alternate GF, a section on intrinsic verification, new examples and figures, a new chapter on steady-periodic heat conduction, and new appendices on the

Dirac delta function, the Laplace transform, and properties of common materials.

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.

Although it might seem rough, in this work turbulence closure of the source/sink terms appearing in the soot volume fraction and soot number density equations is achieved by using a simple presumed PDF for the temperature composed of two

Dirac delta functions located at [bar.

In particular we introduce a Delta formalism, d la Dirac-Schwartz, for the description of random measures associated with random closed sets of lower dimensions, such that the well known usual

Dirac delta at a point follows as a particular case (see, for instance, Kolmogorov and Fomin, 1970; Vladimirov, 1979; Jones, 1982).

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.

i], H(t), and [delta](x) are the components of the point force source, Heaviside step function, and

Dirac delta function, respectively.