We present several results concerning the number of positions and games of Go. We derive recurrences for L(m,n), the number of legal positions on an m× n board, and develop a dynamic programming algorithm which computes L(m,n) in time O(mnλ) and space O(mλ), for some constant λ < 5.4. An implementation of this algorithm lets us list L(n, n) for n ≤ 17. For bigger boards, we prove existence of a...

This paper presents a dynamic agent model of recurrences of a depression for an individual. Based on several personal characteristics and a representation of events (i.e. life events or daily hassles) the agent model can simulate whether a human agent that recovered from a depression will fall into a relapse or recurrence. A number of well-known relations between events and the course of depres...

The goal of this paper is to prove new recurrences involving 2–colored and 3–colored generalized Frobenius partitions of n similar to the classical recurrence for the partition function p(n). Section

We present an automatic method for mapping a system of linear recurrence equations onto systolic architectures. First, we show that systolic architectures can be derived from linear recurrence equations using the notion of directed recurrence equations. Next, we provide a procedure called CUBIZATION to achieve better performance while mapping such equations. The CUBIZATION procedure is complete...

Quantitative recurrence indicators are defined by measuring the first entrance time of the orbit of a point x in a decreasing sequence of neighborhoods of another point y. It is proved that these recurrence indicators are a.e. greater or equal to the local dimension at y, then these recurrence indicators can be used to have a numerical upper bound on the local dimension of an invariant measure.

written for a particular gain. Then KGH = −1 so that a) when the amplitude of KGH is 1 or 0 dB and b) phase is 180o then we have the system just become unstable. Both the conditions have to be fulfilled. Hence, if we ask the question: How far is the system from instability ? We get two answers. The gain increment required at the frequency where phase is 180o and the phase increment required at ...

In recent work on multivariate elliptic hypergeometric integrals, the author generalized a conjectural integral formula of van Diejen and Spiridonov to a ten parameter integral provably invariant under an action of the Weyl group E7. In the present note, we consider the action of the affine Weyl group, or more precisely, the recurrences satisfied by special cases of the integral. These are of t...

The periodic transference of nucleotide strings in bacterial and archaeal complete genomes is investigated by using the metric representation and the recurrence plot method. The generated periodic correlation structures exhibit four kinds of fundamental transferring characteristics: a single increasing period, several increasing periods, an increasing quasi-period and almost noincreasing period...

The master theorem provides a solution to a well-known divide-and-conquer recurrence, called here the master recurrence. This paper proves two cook-book style generalizations of this master theorem. The first extends the treated class of driving functions to the natural class of exponential-logarithmic (EL) functions. The second extends the result to the multiterm master recurrence. The power a...