How does meaning influence cognitive processes involved in the production and reception of language? The language-game hypothesis (LGH) states that meaning acts to constrain the cognitive processes involved in language comprehension. The degree of constraint can be gauged by measures of structuredness of a process, e.g. using Recurrence Quantification Analysis (RQA). LGH was originally formulat...

Let T be any time scale such that 0, 1 be subset of T. The concept of dynamic equations on time scales can build bridges between differential and difference equations. This concept not only gives us unified approach to study the boundary value problems on discrete intervals with uniform step size and real intervals but also gives an extended approach to study on discrete case with non uniform s...

This paper is devoted for a rigorous investigation of Hahn’s difference operator and the associated calculus. Hahn’s difference operator generalizes both the difference operator and Jackson’s q-difference operator. Unlike these two operators, the calculus associated with Hahn’s difference operator receives no attention. In particular, its right inverse has not been constructed before. We aim to...

* Correspondence: [email protected]; [email protected] Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, P. R. China Full list of author information is available at the end of the article Abstract In this paper, we consider a class of impulsive difference equations with distributed delays. By establishing an impulsive delay difference inequality and using the propertie...

Denote by S the class of standard Sturmian words. It is a class of highly compressible words extensively studied in combinatorics of words, including the well known Fibonacci words. The suffix automata for these words have a very particular structure. This implies a simple characterization (described in the paper by the Structural Lemma) of the periods of runs (maximal repetitions) in Sturmian ...

Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches – recurrence plots and recurrence networks –, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recu...

Based on Riccati transformation and the inequality technique, we establish some new sufficient conditions for oscillation of the second-order neutral delay dynamic equations on time scales. Our results not only extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation ...

In this paper we shall discuss the exponential stability in mean square for a neutral stochastic diierential diierence equation of the form dx(t) ? G(x(t ?))] = f(t; x(t); x(t ?))dt + (t; x(t); x(t ?))dw(t). In the case when (t; x; y) 0 this neutral stochastic diierential diierence equations becomes a deterministic neutral diierential diierence equations d dt x(t)?G(x(t?))] = f(t; x(t); x(t?))....

We consider two decision problems for linear recurrence sequences (LRS) over the integers, namely the Positivity Problem (are all terms of a given LRS positive?) and the Ultimate Positivity Problem (are all but finitely many terms of a given LRS positive?). We show decidability of both problems for LRS of order 5 or less, with complexity in the Counting Hierarchy for Positivity, and in polynomi...

Suppose rate of change of coefficients of a linear time-variant system modeled via a difference equation is restricted. The work presented herein is an attempt at developing an algorithm that determines regions in coefficient-space where such a system is guaranteed to be globally asymptotically stable. Such information can be extremely useful in many applications. Some previously published rela...