Asynchronous cellular automata that hide some of the configurations during evolution

In the light of recent developments in the theory of reversibility for asynchronous cellular automata, we attempt to explore the dynamics of recurrent rules under fully asynchronous updating scheme. Depending on the reachability of the configurations for a communication class during the evolution of the system, we classify the recurrent rules into two classes — partially exposed recurrent system and fully exposed recurrent system.

EXISTENCE AND BOX DIMENSION OF GENERAL RECURRENT FRACTAL INTERPOLATION FUNCTIONS

The notion of recurrent fractal interpolation functions (RFIFs) was introduced by Barnsley et al. [‘Recurrent iterated function systems’, Constr. Approx.5 (1989), 362–378]. Roughly speaking, the graph of an RFIF is the invariant set of a recurrent iterated function system on $\mathbb {R}^2$ . We generalise the definition of RFIFs so that iterated functions in the recurrent system need not be contractive with respect to the first variable. We obtain the box dimensions of all self-affine RFIFs in this general setting.

The experience of representation of the applied terminological system by means of terminological network

The article is devoted to the study of the English-language Digital Photography terminological units by building a terminological network, namely, identifying key categories of special notions and system relations between the corresponding terminological units to prove that the analyzed terminological system is mainly applied. These features of the terminological system are identified and classified by building a terminological network. The primary task was to determine the main categories of special notions that are frequentlyverbalized by the English-language Digital hotography terminological units drawing on the example of the analysis of definitions of key terms, as well as to calculate the types of relations between the designated categories. In this regard, the study of a term as a system unit that occupies a clearly defined place in the subsystem of professional lexis becomes possible with the help of a terminological semantic network, which shows that the relationships and categories which the correlating terms belong to are not random. Digital Photography terminological units in the modern English language, which have been taken from the English-language online dictionaries, reference books, glossaries, and Internet portals dedicated to the topic in question, have served as the material for the research. Terms of one category can be associated with the representatives of other categories by means of recurrent system relationships, thus forming prototypical schemes of interaction between terminological units. During the work the two groups of terms have been allocated: the first one consists of “material” terminological units, verbalizing natural objects/phenomena, natural / artificial substances, loci (places, locations), instruments and tools (parts of tools), simple and complex mechanisms and their components, natural / artificial materials, artificially created loci (places) or constructions. The second group includes non-material terms that nominate the category “actor”, processes, situations, characteristics, ideal phenomena. The predominant categories of notions in the sphere of Digital Photography are components of mechanisms /tools, processes, ideal phenomena, complex mechanisms, characteristics / parameters, which indicates the fact that the Digital Photography terminological system is mainly applied. The study has revealed that the most frequent types of system relations between notions and their verbalizers-the corresponding English-language Digital Photography terms are: AKO (system relations between hyperonym and hyponym), ISA (system relations of coincidence or inclusion in a set), SR (system relations between referents which make up the subject of influence and the result obtained within the same process), which also indicate the predominantly applied nature of the Digital Photography terminological system

SMALL PERTURBATION METHOD TO SOLVE THE PROBLEM OF LAMINAR BOUNDARY LAYER OF INCOMPRESSIBLE VISCOUS FLUID FLOWS

The recurrent system of second order partial differential equations serving for asymptotic approximation to the Stokes equation has been derived by the asymptotic method. The zeroth order and basic approximation is the Prandtl equation used to study the non-steady-state boundary layer. The exact analytical solutions of the Prandtl equation with a pressure gradient have been obtained.

Discrete Pseudo-SINR-Balancing Nonlinear Recurrent System

Being inspired by the Hopfield neural networks (Hopfield (1982) and Hopfield and Tank (1985)) and the nonlinear sigmoid power control algorithm for cellular radio systems in Uykan and Koivo (2004), in this paper, we present a novel discrete recurrent nonlinear system and extend the results in Uykan (2009), which are for autonomous linear systems, to nonlinear case. The proposed system can be viewed as a discrete-time realization of a recently proposed continuous-time network in Uykan (2013). In this paper, we focus on discrete-time analysis and provide various novel key results concerning the discrete-time dynamics of the proposed system, some of which are as follows: (i) the proposed system is shown to be stable in synchronous and asynchronous work mode in discrete time; (ii) a novel concept called Pseudo-SINR (pseudo-signal-to-interference-noise ratio) is introduced for discrete-time nonlinear systems; (iii) it is shown that when the system states approach an equilibrium point, the instantaneous Pseudo-SINRs are balanced; that is, they are equal to a target value. The simulation results confirm the novel results presented and show the effectiveness of the proposed discrete-time network as applied to various associative memory systems and clustering problems.