We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, and negative binomial distributions. Our results also establish connections between the entropy functions and to the Riemann z...

We define a class of anticipating flows on Poisson space and compute its RadonNikodym derivative. This result is applied to statistical testing in an anticipating queuing problem. HYPOTHESIS TESTING; QUEUING THEORY; SKOROKHOD INTEGRAL; POINT PROCESSES AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 62F03; 60H07 SECONDARY 60K25; 60J75

For the family of truncations of the gaussian Riesz transforms and Poisson integral we study their rate of convergence through the oscillation and variation operators. More precisely, we search for their Lp(dγ)−boundedness properties, being dγ the Gauss measure. We achieve our results by looking at the oscillation and variation operators from a vector valued point of view.

1) We identify new parameter branches for the ultra-local boundary Poisson bracket in d spatial dimension with a (d− 1)-dimensional spatial boundary. There exist 2 r-dimensional parameter branches for each d-box, r-row Young tableau. The already known branch (hepth/9912017) corresponds to a vertical 1-column, d-box Young tableau. 2) We consider a local distribution product among the so-called b...

This paper presents scaling laws for the integral capacitance of electric double layer capacitors (EDLCs) supported by rigorous analysis and experimental data for porous carbon-based electrodes. First, dimensionless similarity parameters were identified based on dimensional analysis of the modified Poisson–Boltzmann model for binary and symmetric electrolytes. Then, a correlation for the equili...

In the PIC/ MC simulation of materials processing plasmas, (1) one has to solve the Poisson equation in each electron timestep that is very small. Usually this is the rate determining process of numerical simulation. The Poisson equation has been solved using its finite difference form. Since there exists always a thin sheath near a solid boundary, a very fine mesh should be introduced in the s...

Abstract In this article, we first apply the method of combining interpolation theorem and weak-type estimate developed in Chen et al. to derive Hardy-Littlewood-Sobolev inequality with an extended Poisson kernel. By using weighted Hardy inequality, further obtain Stein-Weiss For extremal problem corresponding presence double-weighted exponents not being necessarily nonnegative makes it impossi...