We start a general study of counting the number of occurrences of ordered patterns in words generated by morphisms. We consider certain patterns with gaps (classical patterns) and those with no gaps (consecutive patterns). Occurrences of the patterns are known, in the literature, as rises, descents, (non-)inversions, squares and p-repetitions. We give recurrence formulas in the general case, th...

Let {φn} be a sequence of rational functions with arbitrary complex poles, generated by a certain three-term recurrence relation. In this paper we show that under some mild conditions the rational functions φn form an orthonormal system with respect to a Hermitian positive-definite inner product.

Asymptotic stability for difference equations with decreasing arguments D. M. Chan , E. R. Chang , M. Dehghan , C. M. Kent , R. Mazrooei-Sebdani & H. Sedaghat To cite this article: D. M. Chan , E. R. Chang , M. Dehghan , C. M. Kent , R. Mazrooei-Sebdani & H. Sedaghat (2006) Asymptotic stability for difference equations with decreasing arguments, Journal of Difference Equations and Applications,...

We extend and give short proofs of some recent results regarding some classes of rational difference equations.

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

In this paper, we investigate the global behavior of the difference equation xn+1 = αxn−1 β + γ t ∑