相关论文: Numerical Quadrature for Singular Integrals on Fra…
Given a spectral triple (A,D,H), the functionals on A of the form a -> tau_omega(a|D|^(-t)) are studied, where tau_omega is a singular trace, and omega is a generalised limit. When tau_omega is the Dixmier trace, the unique exponent d…
The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the…
A class of numerical quadrature rules is derived, with equally-spaced nodes, and unit weights except at a few points at each end of the series, for which "corrections" (not using any further information about the integrand) are added to the…
In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous…
We study various measure theories using the classical approach and then compute the Hausdorff dimension of some simple objects and self-similar fractals. We then develop a nonstandard approach to these measure theories and examine the…
Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers. The distribution of the number of summands converges to a Gaussian, and the individual measures on gaps between…
We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the…
In this article, quadrature rules for the efficient computation of the stiffness matrix for the fractional Laplacian in three dimensions are presented. These rules are based on the Duffy transformation, which is a common tool for…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
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,…
Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters $\beta$ and $\gamma$, equal to one in Einstein theory, can be obtained from static…
The fractal dimensions of polymer chains and high-temperature graphs in the Ising model both in three dimension are determined using the conformal bootstrap applied for the continuation of the $O(N)$ models from $N=1$ (Ising model) to $N=0$…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
In the present work we explore features of single and pairs of solitary waves in a fractional variant of the nonlinear Schr{\"o}dinger equation. Motivated by the recent experimental realization of arbitrary fractional exponents, upon…
Let $\{S_i\}_{i\in \Lambda}$ be a finite contracting affine iterated function system (IFS) on ${\Bbb R}^d$. Let $(\Sigma,\sigma)$ denote the two-sided full shift over the alphabet $\Lambda$, and $\pi:\Sigma\to {\Bbb R}^d$ be the coding map…
This article presents a novel approach to enhance the accuracy of classical quadrature rules by incorporating correction terms. The proposed method is particularly effective when the position of an isolated discontinuity in the function and…
Non-integer dimensions are commonplace in quantum field theories (QFTs) through dimensional regularization. In particular this affects angular calculations involving dot products. The structure of these rises from the generally accepted…
In this paper we present a treatment of hypersingular integrals and integral equations. It is shown the equivalence of different definitions of hypersingular integrals. Then we construct explicit analytical solution to a characteristic…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
It was well known that geometric considerations enter in a decisive way in many questions of harmonic analysis. The main purpose of this paper is to provide the criterion of the boundedness for singular integrals on the Hardy spaces and as…