Related papers: Representation of Integral Dispersion Relations by…
There are two usual computational methods for linear (waves and instabilities) problem: eigenvalue (dispersion relation) solver and initial value solver. In fact, we can introduce an idea of the combination of them, i.e., we keep time…
Four-dimensional renormalized (FDR) integrals play an increasingly important role in perturbative loop calculations. Thanks to them, loop computations can be performed directly in four dimensions and with no ultraviolet (UV) counterterms.…
We introduce a nonperturbative approximation scheme for performing scattering calculations in two dimensions that involves neglecting the contribution of the evanescent waves to the scattering amplitude. This corresponds to replacing the…
Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We study the long time behavior of small solutions to the semi-relativistic Hartree equations in two dimension. The nonlinear term is convolved with the singular potential $|x|^{-\gamma}$ for $1<\gamma<2$, which is referred to as…
This paper presents a class of boundary integral equations for the solution of problems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations,…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
In this paper we study the spectrum of long-range percolation graphs. The underlying geometry is given in terms of a finitely generated amenable group. We prove that the integrated density of states (IDS) or spectral distribution function…
We propose a function-valued evaluation metric for generative models based on the relative density ratio (RDR) designed to characterize distributional differences between real and generated samples. As an evaluation metric, the RDR function…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
The impact-parameter representation of the spin-flip amplitude of hadron elastic scattering is examined in different unitarisation schemes, taking the Born term of the spin-flip amplitude from the Dubna Dynamical Model (DDM). It is shown…
In the large $N_c$ approximation to $QCD$, the leading $\pp$ scattering amplitude is expressed as the sum of an infinite number of tree diagrams. We investigate the possibility that an adequate approximation at energies up to somewhat more…
The overlap integrals of scattering states in potentials of finite widths are expressed with their asymptotic behaviors and those of energies $E_1$ and $E_2$ consist of diagonal terms that are proportional to $\delta(E_1-E_2)$ and…
We discuss a general model for effective quantum field theories (QFTs), which for example comprises quantum chromodynamics and quantum electrodynamics. We assume in the model a perturbative expansion of the Lagrangian with respect to a…
In conventional scattering theory, by large-distance asymptotics, at the cost of losing the information of the distance between target and observer, one imposes a large-distance asymptotics to achieve a scattering wave function which can be…
In this paper, we offer to the reader an essential review of the theory of Fluctuation-Dissipation Relations (FDR), from the first formulations due to Einstein and Onsager, to the recent developments in the framework of stochastic…
We establish a direct connection between scattering amplitudes in planar four-dimensional theories and a remarkable mathematical structure known as the positive Grassmannian. The central physical idea is to focus on on-shell diagrams as…