We study the map 9: C!C defined by 9(w, z)=(z, z+w) and the associated collection of sequences [zj] satisfying the recurrence zj+2=zj+1+zj . Iteration of 9 is equivalent to the study of such sequences. We analyze growth rates of the sequences, positive sequences, periodic and asymptotically periodic sequences and establish the existence of doubly infinite homoclinic sequences, non-zero sequence...

The linear complexity and the k-error linear complexity of a sequence have been used as important security measures for key stream sequence strength in linear feedback shift register design. By using the sieve method of combinatorics, the k-error linear complexity distribution of 2-periodic binary sequences is investigated based on Games-Chan algorithm. First, for k = 2, 3, the complete countin...

Three-dimensional synchronous instabilities of two-dimensional time-periodic wake flows, such as the so-called modes A and B of the circular cylinder wake, are now well-known. On the other hand, quasi-periodic three-dimensional instabilities are just as generic, but have as yet not received such wide-spread recognition, partly as a consequence of the predominance of attention given to flows, su...

Sinusoidal oscillatory flow around a circular cylinder is simulated to study the periodic streaming in three flow regimes under the low KC and low  number conditions. The first regime of periodic streaming is featured by V-shape jet-like streams towards a fix direction. In the second regime, the V-shaped streams also exist, but the V-shape switches direction with a secondary flow period. The t...

It is often assumed that a warped galaxy can be modeled by a set of rings. This paper verifies numerically the validity of this assumption by the study of periodic orbits populating a heavy self-gravitating warped disk. The phase space structure of a warped model reveals that the circular periodic orbits of a flat disk are transformed in quasi annular periodic orbits which conserve their stabil...

We extend the results obtained for different cases of the product superposition of periodic functions, and the determination of the scattered fields, for the case of circular symmetry. The characteristics of focalization for such cases are studied. We name Cantor-Fresnel zone plate the structures obtained with this method. Also, in this study can be included the focalization by periodic, Cantor...

In this paper we study the existence of almost periodic solution for nonlinear discrete Volterra equation with unbounded delay, as a discrete version of the results for integro-differential equations. 1. Almost periodic sequences and difference equations Bohr’s theory of almost periodic functions has been extensively studied, especially in connection with differential equations. Almost periodic...

We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set X in a metric space, it is proved the existence of an almost periodic sequence {ψk}k∈Z such that {ψk; k ∈ Z} = X and ψk = ψk+lq(k), l ∈ Z for all...

This paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + V(x)u=g(x, v), -triangle v - b(x)nabla v + V(x)v=f(x, u), end{array} right. $$ for $x in {R}^{N}$, where $V $, $b$ and $W$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. In this paper, we give a new technique to show the boundedness of Cerami sequences and estab...

De Bruijn sequences are circular strings of length 2n whose length n substrings are the binary strings of length n. Our focus is on creating circular strings of length (