A family of continuous biorthogonal functions related to an elliptic analog of the Gauss hypergeometric function is constructed. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. The relationship with the Sklyanin algebra and elliptic analogs of the Faddeev modular double are discussed in detail. §

Let S ⊂ R denote a compact set with infinite cardinality and C(S) the set of real continuous functions on S. We investigate the problem of polynomial and orthogonal polynomial bases of C(S). In case of S = {s0, s1, s2, . . .} ∪ {σ}, where (sk)k=0 is a monotone sequence with σ = limk→∞ sk, we give a sufficient and necessary condition for the existence of a so-called Lagrange basis. Furthermore, ...

A 1993 result of J. Llibre, and M. Misiurewicz, (Theorem A [5]), states that if a continuous map f of a graph into itself has an s-horseshoe, then the topological entropy of f is greater than or equal to logs, that is h( f ) ? logs. Also a 1980 result of L.S. Block, J. Guckenheimer, M. Misiurewicz and L.S. Young (Lemma 1.5 [3]) states that if G is an A-graph of f then h(G) ? h( f ). In this pap...

Nonlinear approximation is widely used in signal processing. Real-life signals can be modeled as functions of bounded variation. Thus the variable knot of approximating function could be selfadaptively chosen by balancing the total variation of the target function. In this paper, we adopt continuous piecewise linear approximation instead of the existing piecewise constants approximation. The re...

Let {Xn, n >= 1} be a strictly stationary sequence of negatively associated random variables, with common continuous and bounded distribution function F. In this paper, we consider the estimation of the two-dimensional distribution function of (X1,Xk+1) based on histogram type estimators as well as the estimation of the covariance function of the limit empirical process induced by the se...

In this paper we introduce a new class of mg-continuous mapping and studied some of its basic properties.We obtain some characterizations of such fuctions. Moreover we define subminimal structure and further study certain properties of mg-closed sets.

We construct a family of continuous biorthogonal functions related to an elliptic analogue of the Gauss hypergeometric function. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. Relations to the Sklyanin algebra and elliptic analogues of the Faddeev modular double are discussed in detail.

A population of RNA molecules that catalyze the template-directed ligation of RNA substrates was made to evolve in a continuous manner in the test tube. A simple serial transfer procedure was used to achieve approximately 300 successive rounds of catalysis and selective amplification in 52 hours. During this time, the population size was maintained against an overall dilution of 3 x 10(298). Bo...