Related papers: Superposition principle and Kirchhoff's integral t…

Green's general hyperplane restriction theorem gives a sharp upper bound for the Hilbert function of a standard graded algebra over and infinite field K modulo a general linear form. We strengthen Green's result by showing that the linear…

Let Y be a hypersurface in projective space having only ordinary double points as singularities. We prove a variant of a conjecture of L. Wotzlaw on an algebraic description of the graded quotients of the Hodge filtration on the top…

The non-renormalization theorems of chiral vertex functions are derived on the basis of an algebraic analysis. The property, that the interaction vertex is a second supersymmetry variation of a lower dimensional field monomial, is used to…

We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated…

Supersymmetry can be consistently generalized in one and two dimensional spaces, fractional supersymmetry being one of the possible extension. 2D fractional supersymmetry of arbitrary order $F$ is explicitly constructed using an adapted…

Stationary potential scattering admits a formulation in terms of the quantum dynamics generated by a non-Hermitian effective Hamiltonian. We use this formulation to give a proof of the reciprocity theorem in two and three dimensions that…

Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of…

This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…

In this paper the classical theory of spherical harmonics in R^m is extended to superspace using techniques from Clifford analysis. After defining a super-Laplace operator and studying some basic properties of polynomial null-solutions of…

This paper proposes, for wave propagating in a globally perturbed half plane with a perfectly conducting step-like surface, a sharp Sommerfeld radiation condition (SRC) for the first time, an analytic formula of the far-field pattern, and a…

Quantum field theory near thresholds of ultra-heavy particles is considered. We focus especially on the top-antitop and the stop-antistop systems. The question of the possible large corrections due to a running width of the top quark could…

Diffraction is a phenomenon, discussed for centuries from various points of view. The very simple principle, proposed by Huygens [1] and then modified by Fresnel[2], Stokes [3] and Kirchoff [4], allows us to make calculations, substituting…

Based on a canonical approach and functional-integration techniques, a series expansion of Green's function of a scalar field, in the presence of a medium, is obtained. A series expansion for Lifshitz-energy, in finite-temperature, in terms…

We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the…

In order for surface scattering models to be accurate they must necessarily satisfy energy conservation and reciprocity principles. Roughness scattering models based on Kirchoff's approximation or perturbation theory do not satisfy these…

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…

A "spatiotemporal dipole" wave source, as defined by D.A.B. Miller (1991), differs from an ordinary ("spatial") dipole source in that the inverted monopole is delayed relative to the uninverted monopole, the delay being equal to the…

In the absence of the Axiom of Choice, necessary and sufficient conditions for a locally compact Hausdorff space to have all non-empty second-countable compact Hausdorff spaces as remainders are given in $\mathbf{ZF}$. Among other…

We consider the free space Helmholtz Green's function and split it into the sum of oscillatory and non-oscillatory (singular) components. The goal is to separate the impact of the singularity of the real part at the origin from the…

We present a novel procedure for calculating non-equilibrium two-point Green's functions in the $O(N) \phi^{4}$ theory at large $N$. The non-equilibrium density matrix $\rho$ is constructed via the Jaynes-Gibbs principle of maximal entropy…