相关论文: Study of the vacuum matrix element of products of …
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these…
We propose a method to evaluate hadronic matrix elements of QCD gluon operators in the instanton vacuum. We construct the ground state of the interacting instanton ensemble for non-zero $\vartheta$--angle using a variational principle. A…
We develop a scattering-matrix formalism to numerically study the resonant scattering of light on generic assemblies of atoms. Protocols to eliminate the artifacts of the method and extract physical information from the numerical data are…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
In this paper, we will construct the graph free product of noncommutative probability space. This is the attempt to explain and observe the combinatorial-object-depending probabilistic structure.
This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coordinate-wise, elementwise, or element-wise product) is…
We describe a practical procedure to calculate the Coulomb matrix elements of 2D spatially separated and confined charge carriers, which are needed for detailed theoretical descriptions of important condensed matter finite systems. We…
We introduce and study, for a process P delivering edges on the Cartesian product of the vertex sets of a given set of graphs, the P-product of these graphs, thereby generalizing many types of product graph. Analogous to the notion of a…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…
In this paper we introduce a new approach to computing hidden features of sampled vector fields. The basic idea is to convert the vector field data to a graph structure and use tools designed for automatic, unsupervised analysis of graphs.…
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic…
The form factors of integrable models in finite volume are studied. We construct the explicite representations for the form factors in terms of determinants.
Using a complete basis set we have obtained an analytic expression for the matrix elements of the Coulomb interaction. These matrix elements are written in a closed form. We have used the basis set of the three-dimensional isotropic quantum…
In this paper, by using the theory of circulant matrices we study some matrices over finite fields which involve the quadratic character and trinomial coefficients.
The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults,…
We study vector fields generating a local flow by automorphisms of a parabolic geometry with higher order fixed points. We develop general tools extending the techniques of [1], [2], and [3]. We apply these tools to almost Grassmannian,…
We give necessary and sufficient conditions for a family of inner products in a finite-dimensional vector space $V$ over an arbitrary field $\mathbb{K}$ to have an orthogonal basis relative to all the inner products. Some applications to…
The magnetic field is traditionally presented as a (pseudo)vector quantity, tied closely to the cross product. Though familiar to experts, many students find these ideas challenging and full of subtleties. Building on earlier work in…
One may identify the general properties of the neutrino mass matrix by generating many random mass matrices and testing them against the results of the neutrino experiments.