The “balayage” method introduced by H. Poincaré in his proof of Theorem 1 relies heavily on tools of Potential theory: maximum principle, Harnack’s inequality, explicit representation formulas for the Dirichlet problem in a ball (Poisson integral), etc. In 1900, D. Hilbert [39], in a celebrated address, followed by a (slightly) more detailed paper in 1904, announced that he had solved the Diric...

The Born–Kirkwood–Onsager ~BKO! model of solvation, where a solute molecule is positioned inside a cavity cut into a solvent, which is considered as a dielectric continuum, is studied within the bounds of nonlocal electrostatics. The nonlocal cavity model is explicitly formulated and the corresponding nonlocal Poisson equation is reduced to an integral equation describing the behavior of the ch...

Krein-de Branges spectral theory establishes a correspondence between the class of differential operators called canonical Hamiltonian systems and measures on real line with finite Poisson integral. We further develop this area by giving description whose have logarithmic integral converging over line. This result can be viewed as version classical Szego theorem in polynomials orthogonal unit c...

Taking up a recent proposal by Stadje and Parthasarathy in the setting of the many-server Poisson queue, we consider the integral ∫∞ 0 [limu→∞E(X(u))− E(X(t))]dt as a measure of the speed of convergence towards stationarity of the process {X(t), t ≥ 0}, and evaluate the integral explicitly in terms of the parameters of the process in the case that {X(t), t ≥ 0} is an ergodic birth-death process...

We study properties of the clusters of a system of fully penetrable balls, a model formed by centering equal-sized balls on the points of a Poisson process. We develop a formal expression for the density of connected clusters of k balls (called k-mers) in the system, rst rigorously derived by Penrose 15]. Our integral expressions are free of inherent redundancies, making them more tractable for...

We present a new method for the solution of the Stokes equations. The main features of our method are: (1) it can be applied to arbitrary geometries in a black-box fashion; (2) it is second-order accurate; and (3) it has optimal algorithmic complexity. Our approach, to which we refer as the embedded boundary integral method (EBI), is based on Anita Mayo s work for the Poisson s equation: ‘‘The ...

1 . I N T R O D U C T I O N THE UNDERSTANDING of neutral hydrogen atom transport in a hydrogen plasma is important in the context of present-day fusion research. SAKHAROV (1961) was the first to point out that neutral hydrogen atoms could penetrate deeply into a hot plasma by repeated charge exchange. Because the plasma scale length can be comparable to the mean-free-path of the neutrals, an ac...