We demonstrate that substantial computational savings are attainable in electronic structure calculations using a Cholesky decomposition of the two-electron integral matrix. In most cases, the computational effort involved calculating the Cholesky decomposition is less than the construction of one Fock matrix using a direct O(N) procedure. © 2003 American Institute of Physics. @DOI: 10.1063/1.1...

In this paper, we consider the normality or the integer decomposition property (IDP, for short) for Minkowski sums of integral convex polytopes. We discuss some properties on the toric rings associated with Minkowski sums of integral convex polytopes. We also study Minkowski sums of edge polytopes and give a sufficient condition for Minkowski sums of edge polytopes to have IDP.

In this paper, by considering the two-step Laplace decomposition method and the appearance of noise terms, exact solutions are calculated for nonlinear Abel's integral equation and generalized Abel's integral equation. This new method provides us to find the solutions with lees computation as compared with other methods. The method will be described along with several examples. Mathematics Subj...

The goal of this paper is to present a new major release of the program FIESTA (Feynman Integral Evaluation by a Sector decomposiTion Approach). This version presents features like cluster-parallelization, new asymptotic expansion algorithms, calculations in physical regions, new sector-decomposition strategies, as well as multiple speed, memory, and stability improvements.

In this paper, an Adomian decomposition method using Chebyshev orthogonal polynomials is proposed to solve a well-known class of weakly singular Volterra integral equations. Comparison with the collocation method using polynomial spline approximation with Legendre Radau points reveals that the Adomian decomposition method using Chebyshev orthogonal polynomials is of high accuracy and reduces th...

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2 we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel.

A decomposition of identity is given as a complex integral over the coherent states associated with a class of shape-invariant self-similar potentials. There is a remarkable connection between these coherent states and Ramanujan’s integral extension of the beta function. Electronic address: [email protected] Electronic address: [email protected] Electronic address: [email protected]...

1 Raison d’être 1 1.1 Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Schrödinger Operator with Periodic Potential . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Direct Integral Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Bloch Periodic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

This note is about Doob decomposition and the basics of Square integrable martingales Contents 1 Doob-Meyer Decomposition 1 2 Square Integrable Martingales 4 Brownian Motion and Stochastic Calculus Continuout Time Submartingales Usually it’s su¢ ce to only discuss submartingales by symmetry in de…nition and techniques are the same. 1 Doob-Meyer Decomposition Doob-meyer decomposition clears the ...

Regions in an image graph can be described by their spanning tree. A graph pyramid is a stack of image graphs at different granularities. Integral features capture important properties of these regions and the associated trees. We compute the depth of a rooted tree, its diameter and the center which becomes the root in the top-down decomposition of a region. The integral tree is an intermediate...