相关论文: Polynomial algebras and exact solutions of general…

We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…

We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, like Poincare, Galilei and Euclidean in N dimensions. The action associated to the bicrossproduct structure allows to obtain a…

The polynomial deformations of the Witten extensions of the U(su(2)) and U(osp(1,2)) algebras are three generator algebras with normal ordering, admitting a two generator subalgebra. The modules and the representations of these algebras are…

Multiple orthogonal polynomials are a generalization of orthogonal polynomials in which the orthogonality is distributed among a number of orthogonality weights. They appear in random matrix theory in the form of special determinantal point…

In this short communication we introduce a rather simple autonomous system of 2 nonlinearly-coupled first-order Ordinary Differential Equations (ODEs), whose initial-values problem is explicitly solvable by algebraic operations. Its ODEs…

The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order $n$ requires analyzing…

We define the non-commutative multiple bi-orthogonal polynomial systems, which simultaneously generalize the concepts of multiple orthogonality, matrix orthogonal polynomials and of the bi-orthogonality. We present quasideterminantal…

We define a class of deformed multimode oscillator algebras which possess number operators and can be mapped to multimode Bose algebra.We construct and discuss the states in the Fock space and the corresponding number operators.

Singletons are those unitary irreducible modules of the Poincare or (anti) de Sitter group that can be lifted to unitary modules of the conformal group. Higher-spin algebras are the corresponding realizations of the universal enveloping…

We discuss the necessity of using non-standard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to…

We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusion-exclusion principle.

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…

The purpose of this paper is to describe the images of multilinear polynomials of arbitrary degree on the strictly upper triangular matrix algebra.

We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…

In this paper, we study nonlinear differential equations satisfied by the generating function of Boole numbers. In addition, we derive some explicit and new interesting identities involving Boole numbers and higher-order numbers arising…

P representation techniques, which have been very successful in quantum optics and in other fields, are also useful for general bosonic quantum dynamical many-body calculations such as Bose-Einstein condensation. We introduce a…

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional…

Recently we have started a program to describe the action of Lie algebras associated with Dynkin-type diagrams on generic Verma modules in terms of polynomial vector fields. In this paper we explain that the results for the classical ABCD…

We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the…

It is well recognized that in auxiliary equation methods, the exact solutions of different types of auxiliary equations may produce new types of exact travelling wave solutions to nonlinear partial differential equations in hand. In this…