Related papers: Power series expansions for the planar monomer-dim…
It is shown that the exponential of a complex power series up to order n can be implemented via (23/12+o(1))M(n) binary arithmetic operations over complex field, where M(n) stands for the (smoothed) complexity of multiplication of…
In this paper, we develop a discretization for the non-linear coupled model of classical Darcy-Forchheimer flow in deformable porous media, an extension of the quasi-static Biot equations. The continuous model exhibits a generalized…
Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove an inequality involving the energy and the discriminant and apply it to deduce a result on totally positive…
With the help of mathematical technique of irreducible tensors the multipole expansion for the probability amplitude of spontaneous radiation of a quantum system is derived. It is shown that the found series represents the total radiation…
We construct solutions of the Friedmann equations near a sudden singularity using generalized series expansions for the scale factor, the density, and the pressure of the fluid content. In this way, we are able to arrive at a solution with…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
Calculating free energy differences is a topic of substantial interest and has many applications including molecular docking and hydration, solvation, and binding free energies which is used in computational drug discovery. However, in…
Various procedures for expressing the multipolar expansion of the electromagnetic field are considered with application to the calculation of the radiated power. Some results from literature are discussed and perspective of developing the…
Given the Fourier-Legendre expansions of $f$ and $g$, and mild conditions on $f$ and $g$, we derive the Fourier-Legendre expansion of their product in terms of their corresponding Fourier-Legendre coefficients. In this way, expansions of…
In the past few years we have derived asymptotic expansions for lambda_d of the dimer problem and lambda_d(p) of the monomer-dimer problem. The many expansions so far computed are collected herein. We shine a light on results in two…
It is shown that detailed and accurate information about the mass spectrum of the massive Schwinger model can be obtained using the technique of strong-coupling series expansions. Extended strong-coupling series for the energy eigenvalues…
As it stands, density matrix purification is a powerful tool for linear scaling electronic structure calculations. The convergence is rapid and depends only weakly on the band gap. However, as will be shown in this paper, there is room for…
One of the unresolved questions currently in cosmology is that of the non-linear accelerated expansion of the universe. This has been attributed to the so called Dark Energy (DE). The accelerated expansion of the universe is deduced from…
The density profiles and other quantities of physical interest for spherically symmetric systems are computed by assuming that a collisionless stellar gas may relax to the non-Gaussian power law distribution suggested by the nonextensive…
The accuracy of the Heller's derivative rule to calculate the numerical weights associated with discretized energy spectrum is enhanced by Broad's extension which adds (N-1) more interpolating points to the original N points. The extension…
We work out an effective theory of accelerated expansion to describe general phenomena of inflation and acceleration (dark energy) in the Universe. Our aim is to determine from theoretical grounds, in a physically-motivated and model…
We study the thermodynamics of massless phi-fourth theory using screened perturbation theory. In this method, the perturbative expansion is reorganized by adding and subtracting a thermal mass term in the Lagrangian. We calculate the free…
The problem of dark energy can be roughly stated as the proposition and validation of a cosmological model that can explain the phenomenon of the accelerated expansion of the Universe. This problem is an open discussion topic in modern…
We give an algorithm to compute term by term multivariate Puiseux series expansions of series arising as local parametrizations of zeroes of systems of algebraic equations at singular points. The algorithm is an extension of Newton's method…
An effective power based parallel preconditioner is proposed for general large sparse linear systems. The preconditioner combines a power series expansion method with some low-rank correction techniques, where the Sherman-Morrison-Woodbury…