相关论文: Ans\"atze for Scattering Amplitudes from $p$-adic …
We study various properties of the gradients of solutions to harmonic functions on Lipschitz surfaces. We improve an exponential bound of Naber and Valtorta on the size of the superlevel sets for the frequency function to a sharp quadratic…
We introduce a new generalization of Stirling numbers of the second kind and analyze their properties, including generating functions, integral representations, and recurrence relations. These numbers are used to approximate Riemann zeta…
This paper is a continuation and an extension of our recent work [3] on the geometric structures of Laplacian eigenfunctions and their applications to inverse scattering problems. In [3], the analytic behaviour of the Laplacian…
We show how Stokes' Theorem, in the fashion of the Generalised Cauchy Formula, can be applied for computing double-cut integrals of one-loop amplitudes analytically. It implies the evaluation of phase-space integrals of rational functions…
We prove scattering for the 2D cubic derivative Schr\"odinger equation with small data in the critical Besov space with one degree angular regularity. The main new ingredient is that we prove a spherically averaged maximal function estimate…
The analyticity properties of the scattering amplitude for a massive scalar field is reviewed in this article where the spacetime geometry is $R^{3,1}\otimes S^1$ i.e. one spatial dimension is compact. Khuri investigated the analyticity of…
We present theoretical calculations of the ensemble-averaged (a.k.a. effective or coherent) wavefield propagating in a heterogeneous medium considered as one realization of a random process. In the literature, it is usually assumed that…
It is proved that an inhomogeneous medium whose boundary contains a weakly singular point of arbitrary order scatters every incoming wave. Similarly, a compactly supported source term with weakly singular points on the boundary always…
We introduce a novel technique to generate Benders' cuts from a conic relaxation ("corner") derived from a basis of a higher-dimensional polyhedron that we aim to outer approximate in a lower-dimensional space. To generate facet-defining…
Scattering of refracting Huygens' metasurfaces is revisited. A new analytical closed-form solution is obtained for the two-dimensional problem under transverse electric (TE) plane-wave incidence -- a solution which gives the scattering for…
In this work we study some topological aspects of function spaces arising in Stieltjes differential calculus. Chief among them are compactness results related to the Ascoli-Arzel\`a and Kolmogorov-Riesz theorems, as well as their…
The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and…
Using Zeilberger generating function formula for the values of a discrete analytic function in a quadrant we make connections with the theory of structured reproducing kernel spaces, structured matrices and a generalized moment problem. An…
The standard unitarity-cut method is applied to several massive two-dimensional models, including the world-sheet AdS$_5\times S^5$ superstring, to compute $2\to 2$ scattering S-matrices at one loop from tree level amplitudes. Evidence is…
This paper introduces a new conceptual framework that recasts surface roughness effects as a "ray deflection function" (RDF) which can be statistically represented through a modified Zernike-Fourier hybrid approach that directly connects…
Single-particle resonance parameters and wave functions in spherical and deformed nuclei are determined through analytic continuation in the potential strength. In this method, the analyticity of the eigenvalues and eigenfunctions of the…
An analytic function can be continued across an analytic arc $\Gamma$ with the help of the Schwarz function $S(z)$, the analytic function satisfying $S(z) = \bar z$ for $z\in \Gamma$. We show how $S(z)$ can be computed with the AAA…
In this work the numerical solution of acoustic tomography problem based on the iterative and functional-analytical algorithms is considered. The mathematical properties of these algorithms were previously described in works of R.G.Novikov…
Any homogeneous polynomial $P(x, y, z)$ of degree $d$, being restricted to a unit sphere $S^2$, admits essentially a unique representation of the form $\lambda + \sum_{k = 1}^d [\prod_{j = 1}^k L_{kj}]$, where $L_{kj}$'s are linear forms in…
We examine SERS from two perspectives: as a phenomenon described by the Laplace Equation (the electrostatic or Rayleigh limit) and by the Helmholtz Equation (electrodynamic or Mie limit). We formulate the problem in terms of the scalar…