相关论文: A lower bound for average values of dynamical Gree…
We prove that for a large class of multiplicative functions, referred to as generalized divisor functions, it is possible to find a lower bound for the corresponding variance in arithmetic progressions. As a main corollary, we deduce such a…
We consider branching random walks on the Euclidean lattice in dimensions five and higher. In this non-Markovian setting, we first obtain a relationship between the equilibrium measure and Green's function, in the form of an approximate…
The values of the ordinary Green functions are known for almost all groups of Lie type, a long term achievement by various authors. In this note we solve the last open cases, which are for exceptional groups $E_8(q)$ where $q$ is a power of…
We study small points for the Arakelov height on the projective line. First, we identify the smallest positive value taken by the Arakelov height, and we characterize all cases of equality. Next we solve several archimedean energy…
We consider a formulation of the equation of motion technique for Green's function in which the unknown averages are computed by solving a linear system. This linear system appears solvable for all finite temperatures, but depending on the…
We study Green's function and the large time behavior of the one-dimensional Euler-Maxwell System with relaxation. Firstly, we construct the Green's function of linearized system and obtain the optimal time decay rates of its solutions. And…
The availability of efficient Krylov subspace solvers play a vital role for the solution of a variety of numerical problems in computational science. Here we consider lattice field theory. We present a new general numerical method to…
We present an experiment which aim is to investigate the mechanical properties of a static granular assembly. The piling is an horizontal 3D granular layer confined in a box, we apply a localized extra force at the surface and the spatial…
We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these…
The aim of this paper is to investigate Green's function for parabolic and elliptic systems satisfying a possibly nonlocal Robin-type boundary condition. We construct Green's function for parabolic systems with time-dependent coefficients…
Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…
Let $L$ be a second-order, homogeneous, constant (complex) coefficient elliptic system in ${\mathbb{R}}^n$. The goal of this article is provide a qualitative and quantitative study of the nature of the Green function associated with the…
A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…
The disorder averaged single-particle Green's function of electrons subject to a time-dependent random potential with long-range spatial correlations is calculated by means of bosonization in arbitrary dimensions. For static disorder our…
The purpose of this paper is to find optimal estimates for the Green function of a half-space of {\it the relativistic $\alpha$-stable process} with parameter $m$ on $\Rd$ space. This process has an infinitesimal generator of the form…
We present a generalized dynamical mean-field approach for the nonequilibrium physics of a strongly correlated system in the presence of a time-dependent external field. The Keldysh Green's function formalism is used to study the…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We obtain optimal lower bounds for moments of theta functions. On the other hand, we also get new upper bounds on individual theta values and moments of theta functions on average over primes. The upper bounds are based on bounds of…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…