Questions of flux regulation in biological cells raise a renewed interest in the narrow escape problem. The determination of a higher order asymptotic expansion of the narrow escape time depends on determining the singularity behavior of the Neumann Green's function for the Laplacian in a three-dimensional (3D) domain with a Dirac mass on the boundary. In addition to the usual 3D Coulomb singul...

In boundary integral methods it is often necessary to evaluate layer potentials on or close to the boundary, where the underlying integral is difficult to evaluate numerically. Quadrature by expansion (QBX) is a new method for dealing with such integrals, and it is based on forming a local expansion of the layer potential close to the boundary. In doing so, one introduces a new quadrature error...

In this paper, we consider a class of substitution strategies which correspond to various minor expansion algorithms, and show that the usual expansion by minors, a row at a time, is optimal in this class. Motivation. One of the least understood aspects of symbolic formula manipulation is the problem of substitution, particularly the merits of various strategies. A specific example, where subst...

We consider the standard GI/G/1 queue with unlimited waiting room and the first-in first-out service discipline. We investigate the steady-state waiting-time tail probabilities P(W > x) when the service-time distribution has a long-tail distribution, i.e., when the service-time distribution fails to have a finite moment generating function. We have developed algorithms for computing the waiting...

Heat-kernel expansion and zeta function regularisation are discussed for Laplace type operators with discrete spectrum on non compact domains. Since a general theory is lacking, the heat-kernel expansion is investigated by means of several examples. Generically, it is pointed out that for a class of exponential (analytic) interactions, the non compactness of the domain gives rise to logarithmic...

This paper studies a Laplace operator on semi-discrete surfaces. A semidiscrete surface is represented by a mapping into three-dimensional Euclidean space possessing one discrete and one continuous variable. It can be seen as a limit case of a quadrilateral mesh, or as a semi-discretization of a smooth surface. Laplace operators on both smooth and discrete surfaces have been an object of intere...

‎Several modifications of the Laplace distribution have been introduced and applied in various fields up to this day‎. ‎In this paper‎,  ‎we introduce a modified symmetric version of the classical Laplace distribution‎.  ‎We provide a comprehensive theoretical description of this distribution‎. ‎In particular‎, ‎we derive the formulas for th...

this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

This paper continues the study of metastable behaviour in disordered mean field models initiated in [2], [3]. We consider the generalized Hopfield model with finitely many independent patterns ξ1, . . . , ξP where the patterns have i.i.d. components and the components of patterns ξ1, . . . ξp have absolutely continuous distributions on [−1, 1] whereas the components of patterns ξp+1, . . . , ξP...