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Green’s Functions and Integral Formulas
An essential tool of our approach to vector and tensor spherical harmonics is the theory of Green’s function on the unit sphere Ω with respect to the...
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Recursion Formulas on Hall Numbers for Weighted Projective Lines
We study the property of Hall numbers for the category of coherent sheaves over a weighted projective line. Several recursion formulas on Hall...
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On Green’s Functions for Isotropic Metamaterials
The Green’s functions are compared for the Maxwell, Beltrami and Helmholtz equations as applied to effective infinite isotropic media, including...
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A Green’s Function Proof of the Positive Mass Theorem
In this paper, a new proof of the Positive Mass Theorem is established through a newly discovered monotonicity formula, holding along the level sets...
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New Green’s functions for a thermoelastic unbounded parallelepiped under a point heat source and their application
This paper presents new analytical expressions for displacements Green’s functions to a steady-state spatial BVP of thermoelasticity for an unbounded...
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Eigenfunction and Green’s Function Asymptotics for Hill’s Equation with Symmetric Single-Well Potential
We determine the asymptotic formulas for eigenfunctions of Hill’s equation with symmetric single-well potential under periodic and semiperiodic...
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Recursive Green’s functions optimized for atomistic modelling of large superlattice-based devices
The Green’s function method is recognized to be a very powerful tool for modelling quantum transport in nanoscale electronic devices. As atomistic...
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Hadamard expansions for powers of causal Green’s operators and “resolvents”
The Hadamard expansion describes the singularity structure of Green’s operators associated with a normally hyperbolic operator P in terms of Riesz...
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Green’s Function of the Riquier–Neumann Problem for the Polyharmonic Equation in the Unit Ball
AbstractThe Green’s function of the Riquier–Neumann problem for the polyharmonic equation in the unit ball is constructed, and an integral...
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Spatial asymptotics of Green’s function and applications
We study the spatial asymptotics of Green’s function for the 1d Schrödinger operator with operator-valued decaying potential. The bounds on the...
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A complete set of the dimension-8 Green’s basis operators in the Standard Model effective field theory
We present a complete and independent off-shell Green’s basis of the dimension 8 operators in the Standard Model effective field theory (SMEFT). We...
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Generalized Surface Green’s Functions for an Elastic Half-Space
Abstract—Using generalized functions, Green’s functions for homogeneous elastic isotropic half-planes and half-spaces are constructed. Airy and...
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Boundary value problems of quaternion-valued differential equations: solvability and Green’s function
This paper is associated with Sturm–Liouville type boundary value problems and periodic boundary value problems for quaternion-valued differential...
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Hierarchical Interpolative Factorization for Self Green’s Function in 3D Modified Poisson-Boltzmann Equations
The modified Poisson-Boltzmann (MPB) equations are often used to describe the equilibrium particle distribution of ionic systems. In this paper, we...
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Evaluation of Two-Dimensional Stresses Near Rigid Inclusions in Anisotropic Media According to the Sherman Integral Equations and Green’s Solutions
We construct regularized Sherman-type integral equations for the plane anisotropic problem of the theory of elasticity with displacements given on...
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Optimal Quadrature Formulas for Curvilinear Integrals of the First Kind
AbstractWe consider the problem on optimal quadrature formulas for curvilinear integrals of the first kind that are exact for constant functions....
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BIEM via graded piezoelectric half-plane Green’s function for wave scattering by curvilinear cracks
This work presents numerical solution for wave motion in a functionally graded piezoelectric half-plane that includes contributions of incident...
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Strong-motion simulation for the 1944 Tonankai earthquake based on the statistical green’s function method and stochastic representation of complex source process
Precisely evaluating the source, path, and site terms in a broadband frequency range is indispensable for quantitatively predicting strong motions....
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Green’s Function and Wave Scattering in Inhomogeneous Anti-plane PEM Half-Plane
Half-plane Green’s functions and wave scattering solutions in quadratically and exponentially graded in respect to depth piezoelectric half-plane...