Related papers: Solutions and Green's function of the first order …
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…
Here we obtain bounds on the spectrum of that operator whose inverse, when it exists, gives the Green's function. We consider the wide of physical problems that can be cast in a form where a constitutive equation ${\bf J}({\bf x})={\bf…
We establish existence and various estimates of fundamental matrices and Green's matrices for divergence form, second order strongly parabolic systems in arbitrary cylindrical domains under the assumption that solutions of the systems…
In present paper we suggest exact solution of the Poisson problem which appears in frequently addressed applications regarding calculation of the gravitational potential of spiral galaxies. We suggest an analytical solution for the problem…
The gauge invariant quark Green's function with a path-ordered phase factor along a straight-line is studied in two-dimensional QCD in the large-Nc limit by means of an exact integrodifferential equation. Its spectral functions are…
The first order loss function and its complementary function are extensively used in practical settings. When the random variable of interest is normally distributed, the first order loss function can be easily expressed in terms of the…
The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
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,…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
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…
The standard assumption for proving linear convergence of first order methods for smooth convex optimization is the strong convexity of the objective function, an assumption which does not hold for many practical applications. In this…
We develop and analyse a first-order algorithm for the A-optimal experimental design problem. The problem is first presented as a special case of a parametric family of optimal design problems for which duality results and optimality…
The purpose of this paper is to establish Picard-Lindel\"{o}f theorem for local uniqueness and existence results for first-order systems of nonlinear delay dynamic equations. In the linear case, we extend our results to global existence and…
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…
We study Green's matrices for divergence form, second order strongly elliptic systems with bounded measurable coefficients in two dimensional domains. We establish existence, uniqueness, and pointwise estimates of the Green's matrices.
Algorithms for computing rational generating functions of solutions of one-dimensional difference equations are well-known and easy to implement. We propose an algorithm for computing rational generating functions of solutions of…
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…
A formulation of the Green's function method is presented in the n-pole approximation. Without referring to a specific model we give a general scheme of calculations that easily permits the computation of the "single-particle" Green's…