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A few years ago the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green's functions of QCD, and called effective locality. This feature of QCD is non-perturbative as it…

We propose an analytical framework to model the effect of single and multiple mechanical surface oscillators on the dynamics of vertically polarized elastic waves propagating in a semi-infinite medium. The formulation extends the canonical…

Pad\'e approximants to the many-body Green's function can be built by rearranging terms of its perturbative expansion. The hypothesis that the best use of a finite number of terms of such an expansion is given by the subclass of diagonal…

Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…

In present work, we explore and experiment an alternative approach of studying resonance properties in finite volume. By analytic continuing finite lattice size $L$ into complex plane, the oscillating behavior of finite volume Green's…

We derive formulas for the matrix elements of the two dimensional square lattice Green function along the diagonal, and along the coordinate axes. We also give an asymptotic formula for the diagonal elements.

Unique transformation properties under the hyperspherical inversion of a partial differential equation describing a stationary scalar wave in an $N$-dimensional ($N\geqslant2$) Maxwell fish-eye medium are exploited to construct a closed…

Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting…

In a previous paper, "Generalized Green functions and unipotent classes for finite reductive groups, I", we have determined certain unknown scalars involved in the algorithm of computing generalized Green functions in the case of SL_n. In…

We show that the acoustic Green`s function for a half-space impedance problem in arbitrary spatial dimension d can be written as a sum of two terms, each of which is the product of an exponential function with the eikonal in the argument…

It has been known for some time that the Green's function of a planar domain can be defined in terms of the exit time of Brownian motion, and this definition has been extended to stopping times more general than exit times. In this paper,…

The strong-coupling character expansion of lattice models is reanalyzed in the perspective of its complete algorithmization. The geometric problem of identifying, counting, and grouping together all possible contributions is disentangled…

This report provides Green's functions (classical propagators) of gravitational fields appearing in general relativity. The existence of Green's function of the wave equation in curved space with an indefinite metric is ensured owing to the…

We continue the attempt to develop a theory of character sheaves on a not necessarily connected reductive algebraic group. In this paper we introduce and study the generalized Green functions.

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…

In this short note we review some facts about elliptic differential operators on Riemannian manifolds.

In this survey paper we consider some applications of the Wright function with special emphasis of its key role in the partial differential equations of fractional order. It was found that the Green function of the time-fractional…

We present a new boundary integral formulation for time-harmonic wave diffraction from two-dimensional structures with many layers of arbitrary periodic shape, such as multilayer dielectric gratings in TM polarization. Our scheme is robust…

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…

The study of wave propagation and scattering in time-dependent materials is a rapidly growing field of research. Whereas for 1D applications there is a simple relation between the wave equations for space-dependent and time-dependent…