Antiblocking decoding

Based on the notion of an antiblocking system a new decoding algorithm is developed which is comparable with the permutation decoding algorithm, but more efficient.     

PD-sets for the codes related to some classical varieties

We generalize the notion of a PD-set of a code to that of a t-PD-set of an arbitrary permutation set. We find PD-sets for miquelian Benz planes of small order and for the ruled rational normal surface of order 3 in PG(4,3) and in PG(4,4). These results yield PD-sets for the related linear codes.     

Gradient systems and gradient-like systems

We briefly discuss existing results on convergence and nonconvergence to equilibrium of bounded solutions of gradient systems and gradient-like systems. We especially raise the question of the influence of the ambient metric. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Duality theorems for linear systems and convex systems

We show that, if (F →^uX) is a linear system, $\text{Ω ? X}$ a convex target set and $\text{h: X →}\text{R}\text{?}$ a convex functional, then, under suitable assumptions, the computation of inf $\text{h({y ? F ¦ u(y) ? Ω}}$) can be reduced to the computation of the infimum of h on certain strips or hyperplanes in F, determined by elements of $\text{u}{}^1\text{(X}{}^1\text{)}$, or of the infima on F of Lagrangians, involving elements of $\text{u}{}^1\text{(X}{}^1\text{)}$. Also, we prove similar results for a convex system (F →^uX) and the convex cone Ω of all non-positive elements in X.     

Expert systems for planning and scheduling manufacturing systems

In this paper, research and applications of expert systems in production planning and scheduling are reviewed. Components of expert systems are briefly discussed. Relationship between expert system and operations research approaches are presented. Integration of operations research and expert system techniques is explored.     

Nonstandard singular perturbation systems and higher index differential-algebraic systems

In order to obtain trajectory approximation results for a given singular perturbation system (SPS), two systems are derived from it: the slow and the fast one. Tikhonov's theorem gives sufficient conditions on them to ensure a good approximation for a standard SPS, i.e., its corresponding slow system is a differential-algebraic system (DAS) of index 1. In this paper it is shown that a nonstandard SPS with the parameter set to zero can be seen as a DAS of higher index. This connection allows us to obtain a Tikhonov's theorem when this DAS is of index 2.     

Smooth control systems of constant rank and linearizable systems

An exposition of the results of the author and A. A. Agrachev concerning systems of constant rank and bang-bang theorems for these systems. The author also presents a survey of results on the linearization of smooth systems and points out the relationship between systems which are linearizable by smooth feedback and systems of constant rank.Translated from Itogi Nauki i Tekhniki, Seriya Sovremennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 35, pp. 135–178, 1989.     

Target setting,lean systems and viable systems: a systems perspective on control and performance measurement

The paper starts with a critique of the reductionist approach to control and performance measurement that emphasizes the parts of a system in isolation. The critique provides the basis for a shift in focus to a systems perspective that emphasizes the interactions between the parts of a system. It is argued that this shift is important because the behaviour of a system is a product of the interactions of the parts not the behaviour of the parts in isolation. Two systems approaches to control and performance management are compared and critiqued: Beer's viable system model and Seddon's lean systems. The paper concludes with the advancement of a model for control and performance measurement that not only integrates the work of Beer and Seddon but also compensates for the weaknesses in these approaches through the inclusion of a process of boundary critique.     

Discrete infinite-dimensional type-K monotone dynamical systems and time-periodic reaction-diffusion systems

The asymptotic behavior of discrete type-K monotone dynamical systems and reaction-diffusion equations is investigated. The studying content includes the index theory for fixed points, permanence, global stability, convergence everywhere and coexistence. It is shown that the system has a globally asymptotically stable fixed point if every fixed point is locally asymptotically stable with respect to the face it belongs to and at this point the principal eigenvalue of the diagonal partial derivative about any component not belonging to the face is not one. A nice result presented is the sufficient and necessary conditions for the system to have a globally asymptotically stable positive fixed point. It can be used to establish the sufficient conditions for the system to persist uniformly and the convergent result for all orbits. Applications are made to time-periodic Lotka-Volterra systems with diffusion, and sufficient conditions for such systems to have a unique positive periodic solution attracting all positive initial value functions are given. For more general time-periodic type-K monotone reaction-diffusion systems with spatial homogeneity, a simple condition is given to guarantee the convergence of all positive solutions.     

Nondegenerate systems and generic properties of the integrable Hamiltonian systems

The goal of the paper is to clarify whether the nondegenerate Hamiltinian systems are “typical” among all integrable systems. The importance of this problem is emphasized by a theorem of Fomenko-Zieschang, in which an isoenergy invariant determining the nondegenerate systems up to topological equivalence is constructed. Bibliography: 12 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 184–192.     

Characterization of affine Steiner triple systems and Hall triple systems

It is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C₁₄. We find three configurations such that a Steiner triple system is affine if and only if it does not contain any of these configurations. Similarly, we characterize Hall triple systems, a superclass of affine Steiner triple systems, using two forbidden configurations.     

Tilings,substitution systems and dynamical systems generated by them

The object of this work is to study the properties of dynamical systems defined by tilings. A connection to symbolic dynamical systems defined by one- and two-dimensional substitution systems is shown. This is used in particular to show the existence of a tiling system such that its corresponding dynamical system is minimal and topological weakly mixing. We remark that for one-dimensional tilings the dynamical system always contains periodic points.     

Historical systems as complex systems

All social systems are simultaneously historical and systemic. They have rules that govern their operation which are reflected in cyclical rhythms; they have irreversible patterns of development which are reflected in their secular trends, and which account for their eventual demise as systems. There are two varieties of complex historical systems: world-empires and world-economies. The latter variety has come to dominate in the period since 1500, leading to the elimination of all other varieties and creating the new situation of a planet with only one existing historical system. The consequences are explored.     

Dual synchronization based on two different chaotic systems: Lorenz systems and Rössler systems

In this paper, we improve and extend the works of Liu and Davids [Dual synchronization of chaos, Phys. Rev. E 61 (2000) 2176–2179] which only introduce the dual synchronization of 1-D discrete chaotic systems. The dual synchronization of two different 3-D continuous chaotic systems, Lorenz systems and Rössler systems, is discussed. And a sufficient condition of dual synchronization about the two different chaotic systems is obtained. Theories and numerical simulations show the possibility of dual synchronization and the effectiveness of the method.