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We use the newly introduced conformable fractional derivative, which is different from the Caputo and Riemann-Liouville fractional derivatives, to reformulate several common boundary value problems, including those with conjugate,…
In this work we present a three step procedure for generating a closed form expression of the Green's function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the…
We present two methods for computing two-time correlation functions or Green's functions from real time bold-line continuous time quantum Monte Carlo. One method is a formally exact generalized auxiliary lead formalism by which spectral…
Green's function plays a significant role in both theoretical analysis and numerical computing of partial differential equations (PDEs). However, in most cases, Green's function is difficult to compute. The troubles arise in the following…
A formula relating quotients of determinants of elliptic differential operators sharing their principal symbol, with local boundary conditions, to the corresponding Green function is given.
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the…
We calculate the Green function for the Dirac equation describing a spin 1/2 particle in the presence of a potential which is a sum of the Coulomb potential V_C=-A_1/r and a Lorentz scalar potential V_S=-A_2/r. The bound state spectrum is…
Precise asymptotics known for the Green function of the Laplacian have found their analogs for bounded below periodic elliptic operators of the second-order below and at the bottom of the spectrum. Due to the band-gap structure of the…
Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.
In this paper, a regression algorithm based on Green's function theory is proposed and implemented. We first survey Green's function for the Dirichlet boundary value problem of 2nd order linear ordinary differential equation, which is a…
Based on the generating functional method with an external source function, a useful constraint on the source function is proposed for analyzing the one- and two-loop world-line Green functions. The constraint plays the same role as the…
This article addresses the construction and analysis of the Green's function for the Neumann boundary value problem associated with the operator $-\Delta + a$ on a smooth bounded domain $\Omega \subset \mathbb{R}^N$ ($N \geq 3$) with $a\in…
It's proved that a function connected with the Green function of the even order symmetric focal boundary value problem takes its maximal value on the diagonal.
Closed expressions are derived for resonant multidimensional X-ray spectroscopy using the quasiparticle nonlinear exciton representation of optical response. This formalism is applied to predict coherent four wave mixing signals which probe…
In this paper, we investigate the existence of positive solutions for a nonlocal fractional boundary value problem involving Caputo fractional derivative and nonlocal Riemann-Stieltjes integral boundary condition. By using the spectral…
We consider the Cauchy problem for the Burgers hierarchy with general time dependent coefficients. The closed form for the Green's function of the corresponding linear equation of arbitrary order $N$ is shown to be a sum of generalised…
The second-order Green's function method (GF2) was shown recently to be an accurate self-consistent approach for electronic structure of correlated systems since the self-energy accounts for both the weak and some of the strong correlation.…
This paper continues the studies of symbolic integration by focusing on the stability problems on D-finite functions. We introduce the notion of stability index in order to investigate the order growth of the differential operators…
We construct an explicit solution of the Cauchy initial value problem for the one-dimensional Schroedinger equation with a time-dependent Hamiltonian operator for the forced harmonic oscillator. The corresponding Green function (propagator)…