Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi–orthogonality conditions. We obtain several characterizations for these polynomials including the analogous of the semiclas-sical Pearson differential equation, the structure relation and a differential– difference equation.

Define the transportation polytope Tn,m to be a polytope of non-negative n×m matrices with row sums equal to m and column sums equal to n. We present a new recurrence relation for the numbers fk of the k-dimensional faces for the transportation polytope Tn,n+1. This gives an efficient algorithm for computing the numbers fk , which solves the problem known to be computationally hard in a general...

In this paper, we study the global stability of the difference equation

We study the difference equation xn = [( f × g1 + g2 +h)/(g1 + f × g2 +h)](xn−1, . . . ,xn−r), n = 1,2, . . . , x1−r , . . . ,x0 > 0, where f ,g1,g2 : (R+) → R+ and h : (R+) → [0,+∞) are all continuous functions, and min1≤i≤r{ui,1/ui} ≤ f (u1, . . . ,ur) ≤ max1≤i≤r{ui,1/ui}, (u1, . . . ,ur) T ∈ (R+) . We prove that this difference equation admits c = 1 as the globally asymptotically stable equi...

The purpose of the paper is to introduce mathematicians to a cash-in-advance model from economics. We show that tools from inverse limits and dynamical systems developed in the last forty or so years are applicable to it. © 2007 Elsevier B.V. All rights reserved. MSC: primary 54H20, 39A05, 37N99; secondary 37N40, 37B45

We develop a methodology to extract a quantitative model for behavioral effects in markets from empirical data. A set of 24 asset market experiments are utilized to derive an equation of price and its dependence on momentum, fundamental value, excess bid level and liquidity considerations. A difference equation is derived from a statistical analysis of the data. The methods are quite general an...

The paper provides conditions sufficient for the existence of strictly increasing solutions of the second-order nonautonomous difference equation x n 1 x n n/ n 1 2 x n − x n − 1 h2f x n , n ∈ N, where h > 0 is a parameter and f is Lipschitz continuous and has three real zeros L0 < 0 < L. In particular we prove that for each sufficiently small h > 0 there exists a solution {x n }n 0 such that {...

In this work is presented a study on matrix biorthogonal polynomials sequences that satisfy a nonsymmetric recurrence relation with unbounded coefficients. The ratio asymptotic for this family of matrix biorthogonal polynomials is derived in quite general assumptions. It is considered some illustrative examples.

Discretizations of the Bogoyavlensky lattices are introduced, belonging to the same hierarchies as the continuous–time systems. The construction exemplifies the general scheme for integrable discretization of systems on Lie algebras with r–matrix Poisson brackets. An initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamilt...

Abstract: An important question arising from the Frobenius Coin Problem is to decide whether or not a given monetary sum S can be obtained from N coin denominations. We develop a new Generating Function G(x), where the coefficient of x is equal to the number of ways in which coins from the given denominations can be arranged as a stack whose total monetary worth is i. We show that the Recurrenc...