Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.

Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces

* This work was supported by the CNR while the author was visiting the University of Milan.

Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.

Extreme Situations Prediction by MultidimenSional Heterogeneous Time Series Using Logical Decision Functions

* The work is supported by RFBR, grant 04-01-00858-a

Exploration by Means of Computer Simulation of Nonlinear Hierarchical Structure of Neuronal Memory on the Model of Olfactory Bulb

Results of numerical experiments are introduced. Experiments were carried out by means of computer simulation on olfactory bulb for the purpose of checking of thinking mechanisms conceptual model, introduced in [2]. Key role of quasisymbol neurons in processes of pattern identification, existence of mental view, functions of cyclic connections between symbol and quasisymbol neurons as short-term memory, important role of synaptic plasticity in learning processes are confirmed numerically. Correctness of fundamental ideas put in base of conceptual model is confirmed on olfactory bulb at quantitative level.

A Mathematical Apparatus for Domain Ontology Simulation. An Extendable Language of Applied Logic

* This paper was made according to the program of fundamental scientific research of the Presidium of the Russian Academy of Sciences «Mathematical simulation and intellectual systems», the project "Theoretical foundation of the intellectual systems based on ontologies for intellectual support of scientific researches".

On the Error-Free Computation of Fast Cosine Transform

We extend our previous work into error-free representations of transform basis functions by presenting a novel error-free encoding scheme for the fast implementation of a Linzer-Feig Fast Cosine Transform (FCT) and its inverse. We discuss an 8x8 L-F scaled Discrete Cosine Transform where the architecture uses a new algebraic integer quantization of the 1-D radix-8 DCT that allows the separable computation of a 2-D DCT without any intermediate number representation conversions. The resulting architecture is very regular and reduces latency by 50% compared to a previous error-free design, with virtually the same hardware cost.

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

2000 Mathematics Subject Classification: 42B10, 43A32.

Some Fractional Extensions of the Temperature Field Problem in Oil Strata

This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed in terms of a convolution of two special functions of Wright’s type.

Generalized Convolution Transforms and Toeplitz Plus Hankel Integral Equations

Mathematics Subject Classification: 44A05, 44A35

Fekete-Szegö Inequality for Universally Prestarlike Functions

MSC 2010: 30C45

Applications of Subordination Principle to Log-Harmonic Mappings

MSC 2010: 30C45, 30C55

Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

MSC 2010: 30C45, 30C55

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

Finite Symmetric Functions with Non-Trivial Arity Gap

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable. ACM Computing Classification System (1998): G.2.0.