相关论文: Combinatorial Solutions to Normal Ordering of Boso…
Summation-by-parts (SBP) operators are popular building blocks for systematically developing stable and high-order accurate numerical methods for time-dependent differential equations. The main idea behind existing SBP operators is that the…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
The s-ordered form of any product of single-mode boson creation and annihilation operators, containing only a single annihilator, is computed explicitly. The s-ordering concept originated in quantum optics, but subsumes normal, symmetric…
We give combinatorially controlled series solutions to Dyson--Schwinger equations with multiple insertion places using tubings of rooted trees and investigate the algebraic relation between such solutions and the renormalization group…
In the relativistic and the nonrelativistic theoretical treatment of moderate and high-power laser-matter interaction, the generalized Bessel function occurs naturally when a Schr\"odinger-Volkov and Dirac-Volkov solution is expanded into…
In this article we give a computational study of combinatorics of the discriminantal arrangements. The discriminantal arrangements are parametrized by two positive integers n and k such that n>k. The intersection lattice of the…
First we give an introduction to the method of diagonalizing or block-diagonalizing continuously a Hamiltonian and explain how this procedure can be used to analyze the two-dimensional Hubbard model. Then we give a short survey on…
The problem of a differential operator left- and right division is solved in terms of generalized Bell polinomials for nonabelian differential unitary ring. The definition of the polinomials is made by means of recurrent relations. The…
Over the past decade, a combinatorial framework for discrete, finite, and irreversibly aggregating systems has emerged. This work reviews its progress, practical applications, and limitations. We outline the approach's assumptions and…
We present a way to normalize a combinatorial Morse function into an integer-valued canonical representative of the set of discrete Morse functions inducing a given gradient field.
We propose a regularization of the BFKL equation which allows for its solution in each order of perturbation theory by means of a sum over multiple poles. This sum can be presented in a rather simple formula for the Fourier transform in the…
It is often the case in mathematical analysis that solving an open problem can be facilitated by finding a new set of coordinates which may illumniate the known difficulties. In this article, we illustrate how to derive an assortment…
Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
In some previous works, two of the authors have introduced a strategy to develop high-order numerical methods for systems of balance laws that preserve all the stationary solutions of the system. The key ingredient of these methods is a…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
Integral operators of Abel type of order a > 0 arise naturally in a large spectrum of physical processes. Their inversion requires care since the resulting inverse problem is ill-posed. The purpose of this work is to devise and analyse a…
We introduce a novel generalization of deranged Bell numbers by defining the partial deranged Bell numbers $w_{n,r}$, which count the number of set partitions of $\left[ n\right] $ with exactly $r$ fixed blocks, while the remaining blocks…
The $(q,r)$-Whitney numbers were recently defined in terms of the $q$-Boson operators, and several combinatorial properties which appear to be $q$-analogues of similar properties were studied. In this paper, we obtain elementary and…
We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…