We study the effect of tachyon condensation on a brane antibrane pair in superstring theory separated in the transverse direction. The static properties of the tachyon potential analyzed using level truncated string field theory reproduces the desired property that the dependence of the minimum value of the potential on the initial distance of separation between the branes decreases as we inclu...

Series expansion methods for fractional integrals are important and useful for treating certain problems of pure and applied mathematics. The aim of the present investigation is to obtain certain new fractional calculus formulae, which involve Srivastava polynomials. Several special cases of our main findings which are also believed to be new have been given. For the sake of illustration, we po...

Theorem 2.1. For all n ≥ 1, n log n− n < log(n!) < n log n, so log(n!) ∼ n log n. Proof. The inequality log(n!) < n log n is a consequence of the trivial inequality n! < nn. Here are three methods of showing n log n− n < log(n!). Method 1: A Riemann sum approximation for ∫ n 1 log x dx using right endpoints is log 2+ · · ·+ log n = log(n!), which overestimates, so log(n!) > ∫ n 1 log x dx = n l...

The structure function S(k;β) for the one-dimensional one-component log-gas is the Fourier transform of the charge-charge, or equivalently the density-density, correlation function. We show that for |k| < min (2πρ, 2πρβ), S(k;β) is simply related to an analytic function f(k;β) and this function satisfies the functional equation f(k;β) = f(−2k/β; 4/β). It is conjectured that the coefficient of k...

Many parameters may be expanded as series with terms involving products of expectations and their estimates expanded as series involving products of averages. The computation of moments and cu-mulants of such estimates may be organized if the terms of the series expansions of parameters, estimates and their moments are considered as functions applied to lists. The lists form a vectors space ass...

A two point Padé approximation of the current and quantity of penetrant at the material transport boundary problems in finite membranes is derived from infinite series expansion. These are shown to be in excellent agreement with previous studies

Solving the BKP equation and comparing with the structure function of hadron for deep inelastic scattering processes we are able to find a relation between reggeizedN−gluon states and anomalous dimensions of QCD. To this end we perform analytical continuation of the Reggeon energy and compare exponents of two different twist-series expansions for the hadron structure function. This makes possib...

We consider discrete kinetic models of a gas moving in a small gap with thickness h. Under an appropriate scaling of the variables, we introduce a formal series expansion to study the limit h→ 0. As a necessary condition for the validity of the expansion we derive a nonlinear diffusion equation.

This work presents a review of a number of control results for mechanical systems. The key technical advances derive from the homogeneity properties of affine connections models for a large class of mechanical systems. Recent results on nonlinear controllability and on series expansions are presented in a unified fashion.

This paper examines asymptotic expansions for estimation errors expressed explicitly as functions of underlying random variables. Taylor series expansions are obtained from which "rst and second moment approximations are derived. While the expansions are essentially equivalent to the traditional Nagar type, the terms are expressed in a form which enables moment approximations to be obtained in ...