For simplicity, we follow the rules: x, y are sets, N is an element of N, c, i, j, k, m, n are natural numbers, D is a non empty set, s is an element of 2Set Seg(n + 2), p is an element of the permutations of n-element set, p1, q1 are elements of the permutations of (n+ 1)-element set, p2 is an element of the permutations of (n+ 2)-element set, K is a field, a, b are elements of K, f is a finit...

We state and prove a classical version of the Laplace expansion theorem where all submatrices in the expansion are restricted to contain a speci ed common submatrix (CSM). The result states that (accounting for signs) this restricted expansion equals the determinant of the original matrix times the determinant of the CSM. This result (Muir [Mui60], p.132) is one of many such results contained i...

In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale potential problems, a fast multipole boundary element method for the problems of Laplace equation is presented. through the multipole expansion and local expansion for the basic solution of the kernel function of the Laplace equati...

In this paper, Adomian decomposition method (ADM) and Laplace decomposition method (LDM) used to obtain series solutions of Burgers-Huxley and Burgers-Fisher Equations. In ADM the algorithm is illustrated by studying an initial value problem and LDM is based on the application of Laplace transform to nonlinear partial differential equations. In ADM only few terms of the expansion are required t...

In the paper, we discuss the transformation of the asymptotic expansion for the distribution of a statistic admitting Edgeworth expansion if the sample size is replaced by a random variable.We demonstrate that all those statistics that are regarded as asymptotically normal in the classical sense, become asymptotically Laplace or Student if the sample size is random. Thus, the Laplace and Studen...

The optimal conformal mapping of the Borel plane was recently used to accelerate the convergence of the perturbation expansions in QCD. In this work we discuss the relevance of the method for the calculation of the Laplace-Borel integral expressing formally the QCD Green functions. We define an optimal expansion of the Laplace-Borel integral in the principal value prescription and establish con...

an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

Modified Laplace transformation method at finite temperature: application to infra-red problems of N component φ 4 theory ABSTRACT Modified Laplace transformation method is applied to N component φ 4 theory and the finite temperature problem in the massless limit is reexamined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orde...