Statistics of Poincaré recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the statistics of the return times.

We consider the problem of counting the occurrences of patterns of the form xy-z within flattened permutations of a given length. Using symmetric functions, we find recurrence relations satisfied by the distributions on Sn for the patterns 12-3, 21-3, 23-1 and 32-1, and develop a unified approach to obtain explicit formulas. By these recurrences, we are able to determine simple closed form expr...

An (infinite) sequence is a function from the set IN = {0, 1, 2, . . .} of natural numbers to some set S. If a : IN → S is a sequence, we often denote a(n) by an. The values a0, a1, a2, . . . are called the elements or terms of the sequence. A recurrence relation is a way of defining a sequence. A few of the first elements of the sequence are given explicitly. Then, the recurrence relation give...

Electrochemical noise data is commonly used to monitor corrosion of metals in various environments. In this work we use recurrence plots to study electrochemical noise time series of stainless steel AISI 316 samples immersed in mildly corrosive electrolyte. It has been found that current and potential time series reveal different information. Recurrence quantification analysis of current time s...

The problem of summing a set of mutual recurrence relations with constant coefficients is investigated. A method is presented for summing an order d system of the form A(n) = ∑d i=1 MiA(n − i) + G(n), where A,G : N → K and M1, . . . ,Md ∈ Mm(K) for some field K and natural number m. The procedure expresses the sum ∑n i=0 A(i) in terms of A(n), . . . , A(n− d), initial conditions and sums of the...

The computed α particle momentum distributions from the decay of low-lying C resonances are shown. The wave function of the decaying fragments is computed by means of the complex scaled hyperspherical adiabatic expansion method. The large-distance part of the wave functions is crucial and has to be accurately calculated. We discuss energy distributions, angular distributions and Dalitz plots fo...

In a well-known result, Ronald Graham found a Fibonacci-like sequence whose two initial terms are relatively prime and which consists only of composite integers. We generalize this result to nondegenerate second-order recurrences.

Cyclic codes of dimension 2 over a finite field are shown to have at most two nonzero weights. This extends a construction of Rao et al (2010) and disproves a conjecture of Schmidt-White (2002). We compute their weight distribution, and give a condition on the roots of their check polynomials for them to be MDS.

We define new statistics, (c, d)-descents, on the colored permutation groups Zr o Sn and compute the distribution of these statistics on the elements in these groups. We use some combinatorial approaches, recurrences, and generating functions manipulations to obtain our results.