in the present work‎, ‎a new stochastic algorithm is proposed to solve multiple dimensional fredholm integral equations of the second kind‎. ‎the solution of the‎ integral equation is described by the neumann series expansion‎. ‎each term of this expansion can be considered as an expectation which is approximated by a continuous markov chain monte carlo method‎. ‎an algorithm is proposed to sim...

In the past decade a lot of work has been done on the subject of multivariate Pad6 approximation theory and so it would be interesting to compare some different definitions. Let us first take a look at the univariate case. It is well known that univariate Pad6 approximants can be obtained in several equivalent ways and that they satisfy some typical properties. We will briefly repeat the defini...

Abstract In this paper, we give the series expansion for the stationary probabilities πn of the queue length of an M/D/1 queue based on analytic properties of the probability generating function π(z). We determine the poles and their associated residues of π(z), then give the partial fraction expansion of π(z). The series expansion of πn are given by the poles and residues. We also give an uppe...

With the help of a simple variational procedure it is possible to convert the partial sums of order N of many divergent series expansions f(g) = ∑∞ n=0 ang n into partial sums ∑N n=0 bng −ωn, where 0 < ω < 1 is a parameter that parametrizes the approach to the large-g limit. The latter are partial sums of a strong-coupling expansion of f(g) which converge against f(g) for g outside a certain di...

We develop a simple and e cient algorithm to compute Riemann-Roch spaces of divisors in general algebraic function elds which does not use the Brill-Noether method of adjoints nor any series expansions. The basic idea also leads to an elementary proof of the Riemann-Roch theorem. We describe the connection to the geometry of numbers of algebraic function elds and develop a notion and algorithm ...

We consider the problem of deciding whether a given rational function has a power series expansion with all its coefficients positive. Introducing an elementary transformation that preserves such positivity we are able to provide an elementary proof for the positivity of Szegö’s function 1 (1− x)(1− y)+ (1− y)(1− z)+ (1− z)(1− x) which has been at the historical root of this subject starting wi...

Using a simple transfer matrix approach we have derived very long series expansions for the perimeter generating function of three-choice polygons. We find that all the terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We perform an analysis of the properties of the differential equation.

We derive a measure of firm speed of price adjustment that is directly inversely related to market power and compare this to the measure derived by Martin (1993). However, both measures are incorrect when firms have non-zero price conjectural variations and treat competing price levels as exogenous. This is because Taylor series expansions of the demand function implicitly assume that firms inf...

The electromagnetic field that an overhead infinitely line current produces at the surface of the earth can be expressed as inverse Fourier integrals over a horizontal wave number in terms of the Neumann and Struve functions. These functions have known mathematical properties, including the series expansions. The latter are utilized in this work to derive expressions for the electromagnetic fie...

Suppose that K ⊂ U(n) is a compact Lie group acting on the (2n+1)dimensional Heisenberg group Hn. We say that (K,Hn) is a Gelfand pair if the convolution algebra LK(Hn) of integrable K-invariant functions on Hn is commutative. In this case, the Gelfand space ∆(K,Hn) is equipped with the GodementPlancherel measure, and the spherical transform ∧ : LK(Hn)→ L(∆(K,Hn)) is an isometry. The main resul...