相关论文: A Chebycheff recursion formula for Coxeter polynom…

Numerical characteristics of identities of finite-dimensional nonassociative algebras are studied. The main result is the construction of a four-dimensional simple unitary algebra with fractional PI-exponent strictly less than its…

By using the Picard-Fuchs equation and the property of Chebyshev space to the discontinuous differential system, we obtain an upper bound of the number of limit cycles for the nongeneric quadratic reversible system when it is perturbed…

We consider the Schrodinger operator on the real line with even quartic potential and study analytic continuation of eigenvalues, as functions of the coefficient of the potential. We prove several properties of this analytic continuation…

In this work, considering a general subclass of bi-univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.

We study the algebraic boundary of a convex semi-algebraic set via duality in convex and algebraic geometry. We generalize the correspondence of facets of a polytope to the vertices of the dual polytope to general semi-algebraic convex…

To each associative unitary finite-dimensional algebra over a normal base, we associative a canonical multiplicative function called its determinant. We give various properties of this construction, as well as applications to the topology…

It is shown that the CMV Laurent polynomials associated to the sieved Jacobi polynomials on the unit circle satisfy an eigenvalue equation with respect to a first order differential operator of Dunkl type. Using this result, the sieved…

We derive orthogonality relations for discrete q-ultraspherical polynomials and their duals by means of operators of representations of the quantum algebra su_q(1,1). Spectra and eigenfunctions of these operators are found explicitly. These…

Results on matrix canonical forms are used to give a complete description of the higher rank numerical range of matrices arising from the study of quantum error correction. It is shown that the set can be obtained as the intersection of…

A family of polynomials parameterized by the conjugacy classes of a finite Coxeter group is investigated. These polynomials, together with the character table of the group, determine the associated generic degrees. The polynomials are…

A many variable $q$-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The…

We show that there exists an atomic representable polyadic equality algebra of finite dimension n\geq 3, such that the cylindric reduct of its completion is not in SNr_n\CA_{n+4}, hence the result in the title. This solves an open problem…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

We construct new families of vector orthogonal polynomials that have the property to be eigenfunctions of some differential operator. They are extensions of the Hermite and Laguerre polynomial systems. A third family, whose first member has…

In this paper, we investigate some properties of Chebyshev polynomials arising from non-linear differential equations. From our investigation, we derive some new and interesting identities on Chebyshev polynomials.

We develop a max-plus spectral theory for infinite matrices. We introduce recurrence and tightness conditions, under which many results of the finite dimensional theory, concerning the representation of eigenvectors and the asymptotic…

Recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced and studied over Clifford algebras and octonions, respectively. In this paper, we further develop the theory of generalized…

In this paper, we find bounds for the eigenvalues of matrix polynomials. In particular, we find generalizations of Cauchy's classical Theorem for distribution of eigenvalues of matrix polynomial.

We determine the support of the irreducible spherical representation (i.e., the irreducible quotient of the polynomial representation) of the rational Cherednik algebra of a finite Coxeter group for any value of the parameter c. In…

For every dimension d, there is an infinite family of convex co-compact reflection groups of isometries of hyperbolic d-space --- the superideal (simplicial and cubical) reflection groups --- with the property that a random group at any…