Class Of Differential Systems Research Articles

The effect of sampling period on the behaviour of systems incorporating state feedback

An exposition of the effects of sampling on the controllability characteristics and the Kronecker invariants of the plant and the input matrices of sampled-data systems is presented. In particular, the effect of sampling period on the feedback matrix for time-optimal control of sampled-data systems is investigated in detail, and it is shown that different classes of systems produce different response characteristics as the sampling period becomes large. Also, simple expressions for A(NT) in terms of A(T), and B(NT) as a function of A(T) and B(T), are derived. These expressions are computationally attractive and therefore facilitate the study of the effect of sampling period on system behaviour. By applying these expressions, the effects of sampling period on the feedback matrices for time-optimal control of three classes of systems whose open-loop plants are asymptotically stable, marginally stable, and unstable, are illustrated by numerical examples.

On stability of the trivial solution of a nonautonomous quasilinear system whose characteristic equation has multiple roots

We obtain sufficient conditions for the Lyapunov stability of the trivial solution of a nonautonomous differential system of a special form ast ↑ ω, ω ≤ + ∞. For this system, the coefficient matrix of a differential system of the first approximation has almost Jordan form with triangular blocks. We indicate methods that enable one to reduce certain classes of differential systems of the general form to special differential systems.

Classical integrable lattice models through quantum group related formalism

We effectively translate our earlier quantum constructions to the classical language and, using Yang-Baxterisation of the Faddeev-Reshetikhin-Takhtajan algebra, are able to construct the Lax operators and associated τ-matrices of classical integrable models. Thus, new as well as known lattice systems of different classes are generated, including new types of collective integrable models and canonical models with nonstandard τ matrices.

Intermediate ordering in a liquid supported monolayer: A molecular dynamics study

We report the results of molecular dynamics simulations of a water supported monolayer of F(CF2)6(CH2)6OC6H4COOH. A grazing incidence x-ray diffraction study of this system showed, unexpectedly, the absence of any strongly ordered condensed phase. We find that the monolayer has a partially ordered structure with a range of order intermediate between that typically found in monolayers of, e.g., arachidic acid, and that expected for a two-dimensional liquid. The calculated width of the first order diffraction peak is about ten times larger than for arachidic acid, yet is ten times smaller than expected for a two-dimensional liquid. We argue that monolayers with intermediate order represent a different class of systems that those heretofore studied, and that these systems may have some unusual properties.

Genesis of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle

We present two hypotheses on the mathematical mechanism underlying bursting dynamics in a class of differential systems: (1) that the transition from continuous firing of spikes to bursting is caused by a crisis which destabilizes a chaotic state of continuous spiking; and (2) that the bursting corresponds to a homoclinicity to this unstable chaotic state. These propositions are supported by a numerical test on the Hindmarsh-Rose model, a prototype of its kind. We conclude by a unified view for three types of complex multi-modal oscillations: homoclinic systems, bursting, and the Pomeau-Manneville intermittency.

THE PROBLEMS OF SOCIAL AUTOPOIESIS

Zelený and Hufford apply the concept of autopoiesis to three different classes of systems—biological. chemical, and social. My response is concerned with the latter and in particular with Zelený and Hufford's claims that social systems are autopoietic and that autopoietic systems are inherently social. I argue that these claims are quite ill-founded. There are a number of general weaknesses with Zelený and Hufford's paper, but, most importantly, the authors fail to see major problems in the ascription of autopoiesis to social systems. These problems are outlined, and the responses of other writers such as Maturana, Varela, and Luhmann are explored. Finally, the importance of and problems with Maturana's and Varela's work is assessed.

Some aspects of the group-theoretic approach in problems of nonlinear mechanics

Two aspects of the application of the asymptotic decomposition method to the decomposition and investigation of nonlinear systems are considered. The first one is the extension of the class of functions in terms of which to form the asymptotic decomposition by applying special functions of mathematical physics. The other aspect is the extension of the asymptotic decomposition method to a new class of differential systems, namely, Pfaffian systems in involution.

Correlation and prediction of vapour13-liquid equilibria in ternary systems formed by weak polar components

The efficiencies of various methods for the correlation and prediction of vapour/3-liquid equilibria (VLE) in ternary systems of different classes of mixture have been compared. The total pressure data for five ternary systems (acetonitrile/3-ethanol/3-water, acetone/3-ethanol/3-water, 1,4-dioxan/3-ethanol/3-water, benzene/3-2/3-butanone-ethanol, acetone/3-acetonitrile/3-methyl acetate) and VLE data for 15 corresponding isothermal binary systems (acetonitrile-ethanol, acetonitrile-water, ethanol-water, acetone-ethanol, acetone-water, ethanol-water, 1,4-dioxan-ethanol, 1,4-dioxan-water, ethanol-water, benzene-2-butanone, 2-butanone-ethanol, benzene-ethanol, acetone-acetonitrile, acetone-methylacetate and acetonitrile-methyl acetate) have been selected and correlated by means of the NRTL, UNIQUAC, Wilson and NRTLMK equations. The ternary VLE data have then been predicted by the use of the binary parameters of the equations calculated from the appropriate binary VLE data. The correlation and the prediction results have been discussed from the point of view of intermolecular interactions, and some recommendations have been made on the use of the equations investigated for such calculations.

Correlation and prediction of vle in ternary systems formed by hydrocarbons and alcohols

The problem of the prediction and correlation of vapour-liquid equilibria (VLE) in ternary systems has been discussed and the limited applicability of the known methods for this purpose pointed out. A comparison of the efficiency of the various methods for ternary systems of different classes of mixtures has been undertaken. As a part of this work, total pressure data for 6 ternary mixtures (cyclohexane-ethanol-toluene, cyclohexane-ethanol-benzene, n-hexane-ethanol-benzene, cyclohexane-2-propanol-benzene, n-hexane-1-propanol-benzene, cyclohexane-methanol-benzene) and 18 appropriate binary mixtures (cyclohexane-ethanol, cyclohexane-toluene, ethanol-toluene, cyclohexane-ethanol, benzene-cyclohexane, benzene-ethanol, ethanol-benzene, n-hexane-benzene, n-hexane-ethanol, benzene-2-propanol, benzene-cyclohexane, cyclohexane-2-propanol, benzene-1-propanol, benzene- n-hexane, n-hexane-1-propanol, cyclohexane-methanol, benzene-cyclohexane, benzene-methanol) were selected and correlated by means of the NRTL, UNIQUAC, Wilson and NRTLMK equations. The ternary VLE data were then predicted using the binary parameters of the equations calculated from appropriate binary VLE data. The correlation and prediction results are fully discussed from the point of view of intermolecular interactions, and a number of recommendations on the use of the equations investigated for such calculations are made.

Properties of the Relaxed Trajectories of Evolution Equations and Optimal Control

This paper considers a class of nonconvex control problems in a Banach space, governed by a semilinear evolution equation and establishes the existence of admissible pairs. Then the introduction of measure-valued controls convexifies the system, and under general assumptions it is shown that the set of trajectories of the original system is dense (in an appropriate topology) in the set of relaxed trajectories. Some useful topological properties of the set of relaxed trajectories are also determined. Furthermore, some optimization problems are solved and in many cases the values of the original and relaxed problems are shown to be equal. Finally, another relaxation result is proved for a different class of systems, described by a general nonlinear evolution equation.

Synthesis of heterochain polymers using chemically activated monomers (“Activated polycondensation”). Review

New polycondensation methods of synthesis of polymers are examined subsumed under the title “activated polycondensation” and based on the interaction of chemically activated bis-electrophiles (diverse activated diesters and diamides) with bis-and poly-functional nucleophiles. It is shown that the new methods are characterized by low proneness to secondary reactions and also wide synthetic possibilities giving new promising macromolecular systems of different classes — polyamides, polyurethanes, polyureas, polyesters and other compounds. Close attention is paid in the review to the nature and mechanism of the activation of the biselectrophiles and also the processes of synthesis of new polymers on which are based reactions not requiring the use of traditional forms of electrophilic monomers.

Note on the relation between pole-zero location and input-output behaviour of SISO systems and its influence on controller design

Linear, time-invariant, completely controllable and observable systems can be described, for example, by state equations, transfer functions or time responses due to specific test signals. All these descriptions are uniquely related for a given system where different state representations are possible by use of equivalence transformations. However, a whole class of different systems, characterized by an infinite number of different pole-zero patterns, exhibits the same input-output behaviour within drawing accuracy, i.e. the plots coincide to the point of indistinguishability. This effect is demonstrated, and it may have implications on such fields as system modelling, model-order reduction and controller design.

Self-Organizing Stochastic Control Systems

The paper develops design methods for joint estimation, detection and control algorythras for stochastic dynamic systems with structural and parametric uncertainty. A general approach to the design of self-organizing systems of different classes and types is suggested. Practically important features of the above systems are then analysed.

Waveguide (integrated) optics. Classification and definitions

A classification is proposed of waveguide-optics (integrated-optics) systems developed up to now in the Soviet Union and abroad. The classification is based on the function of the system and its design features. Several new definitions are also suggested (structure element, functional systems of different classes, spatial zone of a system) and these are used to develop the classification. This classification makes it possible to consider in a systematic manner the systems developed so far, to forecast future systems, and to assign a unique index to a given system, independent of its various applications.

Geometry of matrix differential systems

In this paper we generalize some basic parts of the projective theory of linear homogeneous differential equations of order m, m > 2, from the scalar to the matrix case. In Section 1 we define the (m l)-dimensional left-projective space over the real n x n matrices P = P, ~ [(M,(R)) and, relying on a previous paper [7] and on standard methods of linear algebra, we state the basic properties of this space. In Section 2 the geometry of the matrix differential systems is described. To each basis of matrix solutions of a given system there corresponds a curve in P and a change of basis corresponds to a projective mapping of this curve. A given curve, together with its projective maps, corresponds to a class of differential systems having projectively equivalent solutions. Some simple properties of these curves are established and a new kind of disconjugacy is defined for the matrix differential systems.

How to Plan and Evaluate the Work of Computer Centers

Our country's computer potential is increasing at a rapid rate. Our aggregate computer capacities increased more than fourfold under the Tenth Five-Year Plan compared with the preceding five-year plan. There was a concurrent increase in the number of computer centers as the major organizational form in which computers are used. Computer centers (which now number almost 4,000) have become mass-type organizations. The majority of them serve the more than 5,000 automated control systems of different classes and designations. Under the last five-year plan, a number of branches in the national economy allocated up to 3 % of the capital investments in the development of the branch for the formation of computer centers and automated control systems. Quantitative growth is accompanied by the concentration and centralization of the computerized production of information, by its integration, by the creation of group and collectively used computer centers based on large multicomputer complexes.

The evolution of controllable domains†

Calculations of the domains T-controllable to the origin for a certain class of differential systems are presented. These are shown to have re-entrant sections in the case of the Duffing oscillator, and an explanation of the feature is given

On the classes of differential systems with the desired behavior

A discussion of the affect of perturbations on systems of differential equations is presented. In particular, given a property of the solutions of a differential system, we are interested in finding a class of differential equations related to the original system that have a certain prescribed property. Lyapunov theory is the main technique employed.

Value Differences and Value Consensus by Socioeconomic Levels

Sspecific value differences among socioeconomic levels have been well documented.' study of values among classes has been concerned chiefly with discovering variations and describing them in a context of differentiation. In a study by one of the authors conducted in a midwestern city,2 value differences and differences in evaluating occupations were examined. Specifically, socioeconomic status and ethnicity were analyzed for their impact on health knowledge, values, and practices, with emphasis on discovering variations in values; one set consisting of 14 desiderata, the second set consisting of 14 occupations.3 Each of these, although part of the larger study, was a separate and self-contained entity. Each was designed to contain at least one item directly related to health and medicine, with most of the items, however, referring to other institutional spheres. There are four hypotheses central to this analysis of the data: First, upper socioeconomic level respondents differ in their values from lower socioeconomic level respondents; second, there are fewer value differences between higher and lower level respondents in the rankings of occupations than in the rankings of desiderata; third, all respondents manifest greater consensus in ranking occupations than in ranking desiderata; and finally, the amount of consensus varies directly with socioeconomic status. In the sociological literature on values, a variety of definitions has been used. Central to all of these is the process of evaluation, either by ranking objects in terms of some external standard or in terms of their position with respect to each other. In this study, each respondent was presented 14 cards on which * This article is a slightly expanded version of a paper delivered at the annual meeting of the Pacific Sociological Association, Salt Lake City, Utah, April, 1965. Several colleagues have made valuable suggestions and constructive criticism to an earlier draft of this paper. We wish particularly to thank Gerald R. Leslie, Solomon Sutker, James D. Tarver, and J. Paschal Twyman. 1 For summaries, see Herbert Hyman, The Value Systems of Different Classes: A Social Psychological Contribution to the Analysis of Stratification, in Reinhard Bendix and Seymour Martin Lipset (eds.), Status, and Power: A Reader ir Social Stratification (Glencoe, Illinois: Free Press, 1953), pp. 426-442; Joseph A. Kahl, American Class Structure (New York: Rinehart & Co., 1953), pp. 184-220; Frank Auld, Influence of Social Class on Personality Test Responses, Psychological Bulletin, 49 (July 1952), pp. 318-332; Leonard Reissman, Levels of Aspiration and Social Class, American Sociological Review, 18 (June 1953), pp. 233-242; Bernard C. Rosen, Achievement Syndrome: A Psychocultural Dimension of Social Stratification, American Sociological Review, 21 (April 1956), pp. 203211. 2The data came from field work conducted by Richard F. Larson in South Bend, Indiana, with some financial assistance from project W-108, Michigan State University, Charles P. Loomis, Director. See Richard F. Larson, An Analysis of Selected Health Knowledge, Values, and Practices as Related to Social unpublished Ph.D. dissertation, University of Notre Dame, 1961. 3 Desiderata is a term which best describes our items. These are: being in good health, belonging to a church, having a steady job, having a good education, being clean, being respected by people, having children, having friends, owning a home, having insurance, having savings, living in a good neighborhood, getting ahead, and owning an automobile. occupations are: physician, priest or minister, public school teacher, dentist, nurse in a hospital, pharmacist, lawyer, policeman, banker, businessman, plumber, automobile mechanic, clerk in a store, and waiter or waitress.

Ambition and Social Class: A Respecification

Ambition and Social Class: A Respecification