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As a first step towards a theory of differential equations involving para-Grassmann variables the linear equations with constant coefficients are discussed and solutions for equations of low order are given explicitly. A connection to…
Linear vector equations and inequalities are considered defined in terms of idempotent mathematics. To solve the equations, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces. The…
Isolating the singularity in the Green's function solution of the inhomogeneous, differential equation for the Stermheimer function of a layered electron gas, permits the construction of an approximate solution of the Stermheimer function…
Finite difference method and finite element method are popular methods for solving groundwater flow equations. This paper presents a new method that uses gradually varied functions to solve such equation. In this paper, we have established…
Consider the linear differential equation of $m$-th order with constant coefficients from the valuation ring $K$ of a non-Archimedean field. We get sufficient conditions of uniqueness and existence for the solution of this equation from…
A general formalism to solve nonlinear differential equations is given. Solutions are found and reduced to those of second order nonlinear differential equations in one variable. The approach is uniformized in the geometry and solves…
It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of…
Defects which appear in heterostructure junctions involving topological insulators are sources of gapless modes governing the low energy properties of the systems, as recently elucidated by Teo and Kane [Physical Review B82, 115120 (2010)].…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
We present a rather unknown version of the change of variables formula for non-autonomous functions. We will show that this formula is equivalent to Green's Theorem for regions of the plane bounded by the graphs of two continuously…
We present the variational multiscale (VMS) method for partial differential equations (PDEs) with stochastic coefficients and source terms. We use it as a method for generating accurate coarse-scale solutions while accounting for the effect…
In this paper we prove an asymptotic formula for the number of solutions in prime numbers to systems of simultaneous linear inequalities with algebraic coefficients. For $m$ simultaneous inequalities we require at least $m+2$ variables,…
A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…
A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…
We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…
We consider the discrete, fractional operator $\left(L_a^\nu x\right) (t) := \nabla [p(t) \nabla_{a^*}^\nu x(t)] + q(t) x(t-1)$ involving the nabla Caputo fractional difference, which can be thought of as an analogue to the self-adjoint…
A dynamic 3D Green's function for the homogeneous, isotropic and viscoelastic (of the Zener type) half-space is derived in a closed form. The results obtained here can be used as either stand-alone solutions for simple problems or in…
We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…
In this paper, we are concerned with the sign-changing solutions of variational inequality problems. In order to give the existence results of the sign-changing solutions for variational inequality problems, we first construct a suitable…
A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…