Stabilization by Local Projection for Convection–Diffusion and Incompressible Flow Problems

We give a survey on recent developments of stabilization methods based on local projection type. The considered class of problems covers scalar convection–diffusion equations, the Stokes problem and the linearized Navier–Stokes equations. A new link of local projection to the streamline diffusion method is shown. Numerical tests for different type of boundary layers arising in convection–diffusion problems illustrate the stabilizing properties of the method.     

Solution of systems of linear algebraic equations with preliminary flattening

A method of improving computing properties of matrices of systems of linear algebraic equations is considered. Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 144–149, September–October, 1999.     

Pattern-based abstraction for verifying secrecy in protocols

We present a method based on abstract interpretation for verifying secrecy properties of cryptographic protocols. Our method allows one to verify secrecy properties in a general model allowing an unbounded number of sessions, an unbounded number of principals, and an unbounded size of messages. As abstract domain we use sets of so-called super terms. Super terms are obtained by allowing an interpreted constructor, which we denote by Sup , where the meaning of a term Sup (t) is the set of terms that contain t as subterm. For these terms, we solve a generalized form of the unification problem and introduce a widening operator. We implemented a prototype and were able to verify well-known protocols such as, for instance, Needham–Schroeder–Lowe (0.03 s), Yahalom (12.67 s), Otway–Rees (0.01 s), and Kao–Chow (0.78 s).     

A robust algorithm for solution of the fuzzy clustering problem on the basis of the fuzzy joint points method

The approach called the method of Fuzzy Joint Points (FJP) is considered in which the fuzziness of clusterization lies in the detailedness of taking into account properties of elements in forming sets of similar elements. Based on this approach, a new robust variant of the FJP algorithm is proposed. The properties of this FJP algorithm are analyzed and a sufficient condition for the correct recognition of the hidden structure of clusters is proved. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 10–22, January–February 2008.     

Numerical Solution of Convection–Diffusion Equations Using a Nonlinear Method of Upwind Type

This paper is devoted to the numerical solution of convection–diffusion equations using the Mizukami–Hughes method which is a nonlinear method of upwind type using conforming piecewise linear triangular finite elements. We extend this method to the whole range of the diffusion parameter whereas the original method was introduced for the convection-dominated regime only. We prove that the extended method satisfies the discrete maximum principle and illustrate its properties by means of numerical results.     

Decomposition and composition of the properties of alternatives in multicriteria decision-making problems

It is shown that under the vector approach, the problem of making decisions by decomposing the properties of alternatives can be represented by a hierarchical system of criteria. At the lower hierarchy level, an alternative is evaluated for separate properties on the basis of a criterion vector and, at the upper level, a composition is used to evaluate the alternative as a whole. The problem is solved by the method of nested scalar convolutions of vector-valued criteria. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 117–122, January–February 2009.     

Theoretical study of a numerical method to solve a diffusion-convection problem

The paper analyzes the approximation, stability, convergence, monotonicity, and dissipative and dispersion properties of the diffusion-convection method. The spatial mesh is considered nonuniform. The application of the method to a problem with the third boundary condition is considered. The computational complexity of the algorithm is estimated. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 161–170, March–April 2008.     

On the numerical solution of nonlinear systems of Volterra integro-differential equations with delay arguments

Particular cases of nonlinear systems of delay Volterra integro-differential equations (denoted by DVIDEs) with constant delay τ > 0, arise in mathematical modelling of ‘predator–prey’ dynamics in Ecology. In this paper, we give an analysis of the global convergence and local superconvergence properties of piecewise polynomial collocation for systems of this type. Then, from the perspective of applied mathematics, we consider the Volterra’s integro-differential system of ‘predator–prey’ dynamics arising in Ecology. We analyze the numerical issues of the introduced collocation method applied to the ‘predator–prey’ system and confirm that we can achieve the expected theoretical orders of convergence.      

Analysis and formation of acoustic fields in inhomogeneous waveguides

The problem of numerical modeling and formation of acoustic fields with definite properties in an axisymmetric inhomogeneous underwater waveguide is considered. A numerical method to solve a boundary-value and extremal problems for a parabolic Schr?dinger-type wave equation with a complex nonself-adjoint operator is proposed and investigated. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 62–71, March–April 2009.     

Formation of pseudorandom sequences with improved autocorrelation properties

An original technique is proposed for formation of pseudorandom sequences on the basis of coding methods. The synthesis of large ensembles of signals with improved autocorrelation properties is theoretically substantiated. Methods of correlation analysis are used to study auto-and crosscorrelation properties of sequences being formed. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 3–16, January–February 2007.     

Method of ordering the values of a linear function on a set of permutations

The paper deals with a new method of solving a combinatorial problem with account for the properties of the set of permutations and its structure. Using this method, the values of the linear objective function are sequenced and the set of permutations is decomposed over hyperplanes, with account of element recurrences. This makes it possible to develop an algorithm of finding the point (an element of the set of permutations) at which the objective function attains a given value. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 50–61, March–April 2009.     

A method of multicriteria evaluation and optimization of hierarchical systems

It is shown that any multicriterion problem can be represented by a hierarchical system. Individual properties of the object are evaluated at the lower level of the system, using a criterion vector; and a composition mechanism is used to evaluate the object as a whole at the upper level. The paper proposes a method to solve complex multicriterion problems of evaluation and optimization. It is based on nested scalar convolutions of vector-valued criteria and allows simple structural and parametrical synthesis of multicriterion hierarchical systems. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 84–92, May–June 2007.     

Bioinspired computing nets for directionality in vision

Directional selectivity to local visual stimuli appears in various levels of the visual pathway, being in the retina very conspicuous. Neurophysiology suggests that directionality (as well as other local and quasi-global filtering properties) are based in the space–time interactions of processes with different “memory” (latency). We draw inspiration from the corresponding underlying biological mechanisms to propose two general schemes for directionality computation in nets, compatible with other space–time filtering properties. First, a connectivistic mechanism based on bipolar–amacrine–ganglion cell interaction is proposed, by formalizing the classical proposals of early vision neurophysiologists. Second, inspired initially in the more recently described intrinsic directionality of amacrines, novel schemes are proposed where directionality appear as the computing consequence of adding memory to spatial filtering structures. The mathematical formulations are achieved by means of Newton Filters and Hermite Functionals.     

The Neural Network Approach to Input–Output Analysis for Economic Systems

Economic practitioners in China are giving up the classical Leontief’s Input–Output analysis methods. This paper offers an alternative method of input–output analysis. The proposed method is based on the layered neural network model. It shows that neural networks method can be useful for input–output analysis for a dynamic economic system.       

Stability in impulsive systems with Markov perturbations in averaging scheme. 2. Averaging principle for impulsive Markov systems and stability analysis based on averaged equations

The Bogoliubov–Mitropolsky small parameter method is used to study the behavior of stochastic differential systems in the analysis of the corresponding properties of solutions of averaged systems.     

Stability in impulsive systems with Markov perturbations in averaging scheme. I. Averaging principle for impulsive Markov systems

The Bogoliubov–Mitropolsky small parameter method is used to study the behavior of stochastic differential systems in the analysis of the corresponding properties of solutions of averaged systems.     

Efficient logic design of reliable control units. I

This paper deals with the impact of the properties of transparent flip-flops (latches) and nontransparent flip-flops on the complexity of formal methods for design of control units. Transformations of control unit specifications are described that take into account the timing properties of signals. These transformations make it possible to improve the timing properties of the control units designed and lead to simple, transparent, and easily automated methods of logic synthesis. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 66–83, May–June, 2000.     

A General Reliable Quadratic Form: An Extension of Affine Arithmetic

In this article, a new extension of affine arithmetic is introduced. This technique is based on a quadratic form named general quadratic form. We focus here on the computation of reliable bounds of a function over a hypercube by using this new tool. Some properties of first quadratic functions and then polynomial ones are reported. In order to show the efficiency of such a method, ten polynomial global optimization problems are presented and solved by using an interval branch-and-bound based algorithm. The work of the first author was also supported by the Laboratoire de Mathématiques Appliquées CNRS–FRE 2570, Université de Pau et des Pays de l'Adour, France, and by the Laboratoire d'Electrotechnique et d'Electronique Industrielle CNRS–UMR5828, Group EM³, INPT–ENSEEIHT.