Let ξt be a stochastic process with independent increments. Suppose that ξt is integervalued and its sample functions are continuous to the left and have a finite number of discontinuities with probability 1. It can be proved (see [3], Theorem 6) that if νk is the number of discontinuities of ξt of magnitude k in the time interval I = [a, b], then the random variables νk (k = ±1,±2, . . .) are ...

Stress intensities of a singular near-tip field around the vertex of a triple junction wedge in multilevel thin film packages are calculated using the two-state M-integral. For this calculation the existence of a simple auxiliary field in the sense of the M-integral associated with every eigenfunction for the triple junction vertex is first verified numerically. The auxiliary field is then empl...

We present a method of superposing rectangles. The superposition is under the condition that some of the regions should be visible. We first define a qualitative spatial representation of the rectangles. In particular, direction relations are used to express the positions of the must-be-visible regions. The representation is extendable to accommodate higher degree of granularity, and therefore ...

We introduce a formalism for constructing models of the gravitational lens action of arbitrary elliptical surface mass distributions including varying ellipticity and isodensity-twist. The projected elliptical surface mass distributions are cut to slices of constant surface mass density for which the de ection is easy to compute. The de ection of the total mass distribution is found by superpos...

In this work we construct Gaussian beam approximations to solutions of the high frequency Helmholtz equation with a localized source. Under the assumption of non-trapping rays we show error estimates between the exact outgoing solution and Gaussian beams in terms of the wave number k, both for single beams and superposition of beams. The main result is that the relative local L2 error in the be...

Utilizing the techniques recently developed for N = 1 super YangMills theories by Dijkgraaf, Vafa and collaborators, we derive the linearity principle of Intriligator, Leigh and Seiberg, for the confinement phase of the theories with semisimple gauge groups and matters in a non-chiral representation which satisfies a further technical assumption.

Abstract-To the authors’ knowledge, previous derivations of the fractional diffusion equation are based on stochastic principles [l], with the result that physical interpretation of the resulting fractional derivatives has been elusive [2]. Herein, we develop a fmctional J%Z Iaw relating solute flux at a given point to what might be called the complete (twosided) fractional derivative of the co...

This problem models heat propagation in a rod where the left end is kept at constant temperature T1, the right end is kept at temperature T2, the initial temperature is f(x) and at each point x, there is heat radiating at the rate F (x, t) at time t. Note that the PDE, the boundary conditions, and the initial condition, are nonhomogeneous. We can use the principle of superposition to decompose ...