Computer Sciences

The Geometric Form of Automaton Mappings, Recurrent and Z-recurrent Definition of Sequences

Authors: Tverdokhlebov V. A.

For automaton mappings we present a method to construct geometric images, a method for complexity estimate by geometric forms, a method of Z-recurrent definition of sequences. A method for complexity estimate for finite sequences by recurrent and Z-recurrent numerical indicators is proposed. Numerical indicators of recurrent and Z-recurrent definitions of sequences are systematized into the spectrum of recurrent definitions with 5 levels of numerical indicators.

The Sperner Property for Polygonal Graphs Considered as Partially Ordered Sets

Authors: Salii V. N.

A finite poset is said to have the Sperner property if at least one of its maximum antichains is formed from elements of the same height. A polygonal graph is a directed acyclic graph derived from a circuit by some orientation of its edges. The reachability relation of a polygonal graph is a partial order. A criterion is presented for posets associated with polygonal graphs to have the Sperner property.

On Applications of Wavelets in Digital Signal Processing

Authors: Rodionov E. A.

Discrete Wavelet transform associated with the Walsh functions was defined by Lang in 1998. The article describes an application of Lang’s transform and some its modifications in analysis of financial time series and for the compression of fractal data. It is shown that for the processing of certain signals the studied discrete wavelet transform has advantages over the discrete transforms Haar, Daubechies and the method of zone coding.

Analyticity Conditions of Characteristic and Disturbing Quasipolynomials of Hybrid Dynamical Systems

Authors: Portenko M. S., Melnichuk D. V., Andreichenko D. K.

Hybrid dynamical systems (HDS) are connected by means of the boundary conditions and the constraint’s conditions systems of ordinary differential equations and partial differential equations with the corresponding initial conditions. Check the stability of HDS can be performed on the basis of the "fast"algorithm for the application which requires analytic characteristic and disturbing quasipolynomials of HDS in the right half-plane and near the imaginary axis.