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  • 1
    Electronic Resource
    Electronic Resource
    A stability investigation for an incompressible simple fluid with fading memory (1980)
    Springer
    Archive for rational mechanics and analysis 72 (1980), S. 203-218 
    Details
    ISSN: 1432-0673
    Keywords: simple fluid ; viscoelastic ; fading memory ; stability ; Liapunov function ; dynamical system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The nonlinear equations of motion for an incompressible simple fluid, occupying a fixed bounded container, are formulated on the basis of the “finitelinear” viscoelasticity theory for materials with fading memory; this formal boundary-initial value problem is then viewed as a nonlinear abstract evolution equation on a certain Hilbert space. It is shown that a linearized version of this evolution equation is associated with a linear dynamical system on this Hilbert space, and several results for stability and asymptotic behavior for this linearized problem are proved through the use of Liapunov stability methods. On the assumption that the original nonlinear evolution equation also is associated with some dynamical system on the same space, it is shown that the rest condition of the fluid is stable and all motions are bounded. The Liapunov function employed for this purpose can be interpreted as a mechanical energy function for the fluid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00281589
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  • 2
    Electronic Resource
    Electronic Resource
    Existence and stability of equilibria in age-structured population dynamics (1984)
    Springer
    Journal of mathematical biology 20 (1984), S. 259-276 
    Details
    ISSN: 1432-1416
    Keywords: Age-structured population dynamics ; equilibria ; stability ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. The local existence and uniqueness of a branch of positive equilibria which bifurcates from the trivial (identically zero) solution at the critical value n=1 are proved by implicit function techniques under very mild smoothness conditions on the death and fertility rates as functional of age and population density. This first requires the development of a suitable linear theory. The lowest order terms in the Liapunov-Schmidt expansions are also calculated. This local analysis supplements earlier global bifurcation results of the author. The stability of both the trivial and the positive branch equilibria is studied by means of the principle of linearized stability. It is shown that in general the trivial solution losses stability as n increases through one while the stability of the branch solution is stable if and only if the bifurcation is supercritical. Thus the McKendrick equations exhibit, in the latter case, a standard exchange of stability with regard to equilibrium states as they depend on the inherent net reproductive rate. The derived lower order terms in the Liapunov-Schmidt expansions yield formulas which explicitly relate the direction of bifurcation to properties of the age-specific death and fertility rates as functionals of population density. Analytical and numerical results for some examples are given which illustrate these results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275988
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  • 3
    Electronic Resource
    Electronic Resource
    Predator-prey relationships: Indiscriminate predation (1984)
    Springer
    Journal of mathematical biology 21 (1984), S. 25-34 
    Details
    ISSN: 1432-1416
    Keywords: Predator-prey ; density dependence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The Gurtin and Levine model5 is studied in this paper under the assumption that the fecundity of prey depends on age as well as on the total population sizes of prey and predators. The purpose of this study is to see the effect of this density dependence on the stability criteria for the equilibria of the model equations. It is shown that there are cases when, due to density dependence, the model which is originally neutrally stable becomes stable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00275220
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  • 4
    Electronic Resource
    Electronic Resource
    Agricultural resource use in an andean coastal ecosystem (1981)
    Springer
    Human ecology 9 (1981), S. 47-78 
    Details
    ISSN: 1572-9915
    Keywords: variation ; management ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Energy, Environment Protection, Nuclear Power Engineering , Ethnic Sciences
    Notes: Abstract Five concurrent systems of agricultural resource management in the Viru Valley in Peru's arid northern coastal plain are discussed as adjustments to microenvironmental variations in soil humidity. Widespread dependence on canal irrigation in an environment characterized by uncertainty in the availability of river water affects the agrarian population in several ways. The upper socioeconomic class has adapted to uncertainty by implementing a deviation-counteracting mechanism (tubular wells) that provides water on demand, giving them flexibility in choice of agricultural activities. Another class of farmers is unable to introduce this mechanism, however, and consequently must depend on a repertoire of inflexible decisions to cope with uncertainty. Each group exploits different opportunity costs to increase economic gain. One pattern provides for expansion, whereas the other at best establishes stability and maintenance. Noncanal techniques permit expansion of cultivation in conditions where canal irrigation is not feasible, thereby improving the overall level of effectiveness of resource use. Alternative techniques do not involve regulatory mechanisms nor do they require complex, interlocking social, economic, and political components. Their presence and persistence in the agricultural system provide variation that may ultimately be amplified as the need to intensify resource exploitation increases in the future.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00887855
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  • 5
    Electronic Resource
    Electronic Resource
    Progressive contextualization: Methods for research in human ecology (1983)
    Springer
    Human ecology 11 (1983), S. 265-281 
    Details
    ISSN: 1572-9915
    Keywords: human ecology research methods ; systems analyses ; people-forest interactions ; flux ; stability ; Man and the Biosphere (MAB) program ; Kalimantan (Borneo)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Energy, Environment Protection, Nuclear Power Engineering , Ethnic Sciences
    Notes: Abstract Theoretically or practically significant research results concerning transitory as well as persistent phenomena can be obtained by human ecologists while avoiding commitment to long-term, expensive projects, rigid frameworks, traditional disciplinary goals, and unwarranted assumptions about the stability and purposiveness of units or systems. The procedures to be followed, as illustrated by research on people-forest interactions in East Kalimantan, involve a focus on significant human activities or people-environment interactions and the explanation of these by their placement within progressively wider or denser contexts. Guides for progressively contextualizing activities or interactions include a rationality principle, comparative knowledge of contexts, and the principle of pursuing the surprising.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00891376
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  • 6
    Electronic Resource
    Electronic Resource
    The response of a harpacticoid copepod community to sediment disturbance in a semi-enclosed lagoon (1984)
    Springer
    Hydrobiologia 118 (1984), S. 127-133 
    Details
    ISSN: 1573-5117
    Keywords: meiofauna ; Harpacticoida ; eutrophication ; stability ; colonisation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The harpacticoid fauna of a sandy sediment in the Sluice Dock of Ostend, Belgium, was dominated by a single species, Canuella perplexa, that attained an average annual density of over 400 ind. 10 cm−2 in 1976 and 1977, whereas other species had a total mean density of less than 10 ind. 10 cm−2. In the summer of 1979 a dystrophic crisis with abundant growth of Ulva occurred and in March 1980 the lagoon was drained. After refilling of the lagoon, the sediment was immediately colonized by good swimming harpacticoids, that attained densities of 200 ind. 10 cm−2. Three months after refilling Canuella perplexa reappeared and the system returned to its original state within one month.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00031795
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  • 7
    Electronic Resource
    Electronic Resource
    Limnology and performance of waste treatment lagoons (1980)
    Springer
    Hydrobiologia 72 (1980), S. 21-30 
    Details
    ISSN: 1573-5117
    Keywords: Sewage ponds ; BOD-removal ; stability ; Daphnia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract By arranging sewage ponds in series, some feedback relationships within the food web are disconnected, but stability may increase. This particularly applies to a persistent ‘clearwater-state’ in the last cell caused by mass growths of Daphnia or other zooplankton in the absence of fish. Microbial pollution in this case is reduced to a level which may permit nearly unrestricted irrigation. The oxygen balance of lagoons is, apart from the diurnal cycle, subject to substantial temporal variations. This also applies to continuous-flow laboratory models with a constant (BOD-load, temperature) or a constant-cycle (light) chemical and physical environment. An example is given illustrating a high adjustment stability of a lagoon in consequence of a catastrophic perturbation. The strong tendency of lagoons towards an oligomictic behaviour is promoted by thermal stratification and by a vertical gradient in the metabolic activity (oxidation/reduction potential). The hydrodynamic conditions oscillate between plug flow in periods of convective overturn and short-circuiting if thermal stratification has developed. Nevertheless, the average performance (BOD removal) for a particular season could be calculated with a reasonable accuracy. As a basis for this calculation, nomographs were developed from which the rate coefficient K1 of BOD removal for a given combination of residence time and BOD load can be read.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00016230
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  • 8
    Electronic Resource
    Electronic Resource
    A comparative study of the sessile, filter-feeding ciliates of several small streams (1983)
    Springer
    Hydrobiologia 98 (1983), S. 125-133 
    Details
    ISSN: 1573-5117
    Keywords: peritrichs ; ciliates ; streams ; aufwuchs ; stability ; diversity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Artificial substrates, consisting of strips of nylon cloth, were used to sample sessile, filter-feeding ciliates at eleven stream sites. These ciliates were common (61 % of samples) and frequently abundant (mean = 95 cm−2). Populations varied widely, even within stream sites, and mean abundance was not related to subjective assessments of the sites. Permanent rural streams and streams below reservoirs, which have relatively stable flow regimes, had a peritrich fauna dominated byVorticella campanula along withCarchesium polypinum andV. striata. Urban and intermittent streams, with less stable flow regimes, showed an increasing number of peritrichs with non-contractile stalks, particularlyEpistylis plicatilis. The commonness and diversity of peritrichs was positively related to aufwuchs stability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02185630
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  • 9
    Electronic Resource
    Electronic Resource
    Method of reduction in convex programming (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 349-378 
    Details
    ISSN: 1573-2878
    Keywords: Convexity ; subdifferentials ; cones of directions of constancy ; equality set of constraints ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present an algorithm which solves a convex program with faithfully convex (not necessarily differentiable) constraints. While finding a feasible starting point, the algorithm reduces the program to an equivalent program for which Slater's condition is satisfied. Included are algorithms for calculating various objects which have recently appeared in the literature. Stability of the algorithm is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933505
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  • 10
    Electronic Resource
    Electronic Resource
    Stability of nondominated solutions in multicriteria decision-making (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 229-253 
    Details
    ISSN: 1573-2878
    Keywords: Point-to-set maps ; domination structures ; parameterized decision-making problems ; solution maps ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Decision-making problems with multiple noncommensurable objectives are specified by two factors, i.e., the set of all feasible solutions and the domination structure. The solutions are characterized as nondominated points. Hence, in these problems, there may exist two parameter vectors, according to which the above two factors change. The stability of the solution set for perturbations of these parameters is investigated in this paper. The analysis is guided by using the concept of continuity of the solution map defined on the two parameter spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934497
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  • 11
    Electronic Resource
    Electronic Resource
    Existence and global asymptotic stability of optimal trajectories for a class of infinite-horizon, nonconvex systems (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 515-533 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; economic systems ; stability ; existence theory ; turnpike property
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sufficient conditions for the existence of optimal trajectories and for the global asymptotic stability of these trajectories are given for a class of nonconvex and nonautonomous systems controlled over an infinite-time horizon. The concept ofG-supported trajectory is introduced. It is shown that, under some assumptions, aG-supported trajectory is overtaking and is globally asymptotically stable. The concept of overtaking trajectory has been previously defined as a notion of optimality on an infinite-time domain. For autonomous systems, under weaker conditions, one guarantees the existence of weakly overtaking trajectories. Finally, it is shown howG-supported trajectories can be obtained, and an application to the study of a pre-predator ecosystem optimally harvested is sketched.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934475
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  • 12
    Electronic Resource
    Electronic Resource
    Stability of compromise solution in multicriteria decision-making problems (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 77-83 
    Details
    ISSN: 1573-2878
    Keywords: Parameterized decision-making problems ; utopia point ; compromise solutions ; Hausdorff distance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Stability is a desirable attribute of the nondominated solution in the decision-making problem with multiple noncommensurable objectives. It is assumed that the decision space is given by a system of inequalitiesG(x)≤b, b ∈ R N . In this paper, sufficient conditions are determined for a compromise solution to be stable with respect to the changes ofb.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934632
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  • 13
    Electronic Resource
    Electronic Resource
    Stochastic scheduling problems I — General strategies (1984)
    Springer
    Mathematical methods of operations research 28 (1984), S. 193-260 
    Details
    ISSN: 1432-5217
    Keywords: Analytic behaviour of strategies ; continuous strategies ; ES strategies ; MES strategies ; machine idleness ; monotonicity behaviour ; optimal strategies ; preselectivity ; regular measure of performance ; scheduling problems ; stability ; stochastic dynamic optimization ; stochastically ordered distributions ; stochastic scheduling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The paper contains an introduction to recent developments in the theory of non-preemptive stochastic scheduling problems. The topics covered are: arbitrary joint distributions of activity durations, arbitrary regular measures of performance and arbitrary precedence and resource constraints. The possible instability of the problem is demonstrated and hints are given on stable classes of strategies available, including the combinatorial vs. analytical characterization of such classes. Given this background, the main emphasis of the paper is on the monotonicity behaviour of the model and on the existence of optimal strategies. Existing results are presented and generalized, in particular w.r.t. the cases of lower semicontinuous performance measures or joint duration distributions having a Lebesgue density.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01919323
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  • 14
    Electronic Resource
    Electronic Resource
    Conflict dissolution by reframing game payoffs using linear perturbations (1983)
    Springer
    Journal of optimization theory and applications 39 (1983), S. 187-214 
    Details
    ISSN: 1573-2878
    Keywords: Self-interest maximization ; self-interest stable solutions ; self-interest cooperative games ; self-interest noncooperative games ; monotonic games ; decomposition theory ; reframing game payoffs ; full cooperation ; targeted solutions ; Pareto optimality ; collective group interest ; stability ; structural departure ; incentives for adopting a new game ; habitual domain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Human beings have a prevailing drive to achieve their self-interest goals or equilibrium states, which may subsume their social interests. An ideal working environment or cooperative game situation would be one in which each participant or player maximizes his/her own interest while maximizing his/her contribution to the collective group interest. This paper addresses the feasibility, methods, and bounds for reframing a generaln-person game into an ideal game in which full cooperation or a targeted solution can be induced and maintained by the players' self-interest maximization. Criteria for good reframing are introduced. Monotonic games, self-interest cooperative and noncooperative games, and a decomposition theory of general games are also introduced to facilitate the study. It is shown that everyn-person game can be written as the sum of a self-interest cooperative game and a self-interest noncooperative game. Everyn-person game can be reframed so that full cooperation can be achieved by the players' self-interest maximization. Everyn-person game can be reframed so that a targeted solution can be obtained and maintained through the players' self-interest maximization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934528
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  • 15
    Electronic Resource
    Electronic Resource
    Decentralized control with overlapping information sets (1981)
    Springer
    Journal of optimization theory and applications 34 (1981), S. 279-310 
    Details
    ISSN: 1573-2878
    Keywords: Decentralized control ; overlapping decompositions ; suboptimality ; stability ; interconnected power systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A decentralized control scheme is proposed for linear systems composed of overlapping subsystems. By expanding the state space of the system, a higher-dimensional space is formed where the subsystems appear as disjoint. In the expanded space, standard optimization techniques can be used to formulate a suboptimal decentralized control law for the overall system. A suitable contraction of the obtained control law, which is compatible with the information constraints imposed by the overlapping subsystems, can be implemented in the original system. The application of the proposed decentralized control scheme is illustrated using a 19th order model for load-frequency control of a two-area interconnected power system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935477
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  • 16
    Electronic Resource
    Electronic Resource
    Contour of complete nonuniqueness as a method of structural optimization with stability constraints (1981)
    Springer
    Journal of optimization theory and applications 35 (1981), S. 23-30 
    Details
    ISSN: 1573-2878
    Keywords: Contour of complete nonuniqueness ; trusses ; stability ; structural optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper develops the concept of a contour of complete nonuniqueness and shows its application to the optimal design (optimal layout) of simple trusses transmitting a concentrated force to a presscribed, arbitrary foundation contour. As an example, a symmetric two-bar truss with compressed bars is considered, and the constraints refer to various kinds of elastic instability of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934701
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  • 17
    Electronic Resource
    Electronic Resource
    Duality for nonlinear multiple-criteria optimization problems (1981)
    Springer
    Journal of optimization theory and applications 35 (1981), S. 367-401 
    Details
    ISSN: 1573-2878
    Keywords: Multiple-criteria decision making ; vector-valued duality ; saddle-point duality ; Kuhn-Tucker conditions ; Pareto optimality ; stability ; efficient points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we develop a duality theory for nonlinear multiple-criteria optimization problems. The theory associates to efficient points a matrix, rather than a vector, of dual variables. We introduce a saddle-point dual problem, study stability concepts and Kuhn-Tucker conditions, and provide an economic interpretation of the dual matrix. The results are compared to the classical approach of deriving duality, by applying nonlinear programming duality theory to a problem obtained by conveniently weighting the criteria. Possible directions for future research are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934908
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