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  • Articles  (237)
  • stability  (237)
  • Mathematics  (237)
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  • Articles  (237)
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  • 1
    Electronic Resource
    Electronic Resource
    Single-locus gametophytic incompatibility: the symmetric equilibrium is globally asymptotically stable (1994)
    Springer
    Journal of mathematical biology 32 (1994), S. 515-520 
    Details
    ISSN: 1432-1416
    Keywords: Gametophytic incompatibility ; model ; equilibrium ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The deterministic dynamics of the classical single-locus multiple-allele model of gametophytic incompatibility is analyzed with the intention to prove the conjecture that the symmetric state (uniform distribution of genotypes) is the only polymorphic equilibrium and that this equilibrium is globally asymptotically stable in the interior of the frequency simplex. It is shown that the minimum allelic frequency increases strictly over the generations as long as a uniform allelic distribution is not realized. Hence, the minimum allelic frequency is a Ljapunov function for the invariant set of genotypic frequencies characterized by a uniform allelic distribution. Within this set, the uniform genotypic distribution is approached in an exponential fashion, which proves the assertion. An evolutionary optimization rule associated with the global convergence to the symmetric state is implied by the fact that at this state the overall amount of pollen elimination resulting from incompatible crosses is minimized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00573457
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  • 2
    Electronic Resource
    Electronic Resource
    Permanent coexistence in general models of three interacting species (1985)
    Springer
    Journal of mathematical biology 21 (1985), S. 285-298 
    Details
    ISSN: 1432-1416
    Keywords: Population dynamics ; coexistence ; mutualism ; persistence ; predator-mediated coexistence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations x i = X i f i (i = 1, 2, 3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the f i , in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276227
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  • 3
    Electronic Resource
    Electronic Resource
    Nondestructive evaluation of corrosion damage using electrostatic measurements (1995)
    Springer
    Journal of nondestructive evaluation 14 (1995), S. 127-136 
    Details
    ISSN: 1573-4862
    Keywords: Nondestructive evaluation ; corrosion monitoring ; electrical impedance tomography ; stability ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract We investigate the problem of detecting and assessing, by means of static electrical measurements, damage due to corrosion in a structure. Corrosion damage, which is assumed to occur in an inaccessible part of a specimen, is modelled as material loss. The detection device consists of electrodes which inject DC current and measure voltage potentials in the accessible part of the specimen. The topography of the damaged surface is estimated from the measured data. This research is meant to evaluate if a method based on static electrical measurements has the potential to be developed into a useful nondestructive evaluation tool. We propose computational methods that take the measured data and estimate the unknown damaged surface. The methods are studied in order to understand their properties. Several example calculations from synthetic data are presented. Our findings indicate that such a device has limited resolution. However, it offers several advantages that make it worthwhile to pursue further research.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01183118
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  • 4
    Electronic Resource
    Electronic Resource
    A mixed dynamics approach for linear corridor policies: A revisitation of dynamic setup scheduling and flow control in manufacturing systems (1995)
    Springer
    Discrete event dynamic systems 5 (1995), S. 59-82 
    Details
    ISSN: 1573-7594
    Keywords: Decentralized scheduling ; manufacturing systems ; corridor policies ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sharifnia, Caramanis, and Gershwin [1991] introduced a class of policies for manufacturing systems, called by themlinear corridor policies. They proved that their stability can be discussed by the study of a simpler subset of such policies (cone policies). This paper revisits their work presenting a different description of the dynamics of the systems under study and explores it to device a necessary and sufficient condition for stability, obtained by the strengthening of the assumptions in Sharifnia et al. (1991). This condition is shown to be simply tested (M −1≥0) and valid for various realizations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01438607
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  • 5
    Electronic Resource
    Electronic Resource
    A bifurcation analysis of the nonlinear parametric programming problem (1990)
    Springer
    Mathematical programming 47 (1990), S. 117-141 
    Details
    ISSN: 1436-4646
    Keywords: Bifurcation ; singularity ; parametric programming ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The structure of solutions to the nonlinear parametric programming problem with a one dimensional parameter is analyzed in terms of the bifurcation behavior of the curves of critical points and the persistence of minima along these curves. Changes in the structure of the solution occur at singularities of a nonlinear system of equations motivated by the Fritz John first-order necessary conditions. It has been shown that these singularities may be completely partitioned into seven distinct classes based upon the violation of one or more of the following: a complementarity condition, a constraint qualification, and the nonsingularity of the Hessian of the Lagrangian on a tangent space. To apply classical bifurcation techniques to these singularities, a further subdivision of each case is necessary. The structure of curves of critical points near singularities of lowest (zero) codimension within each case is analyzed, as well as the persistence of minima along curves emanating from these singularities. Bifurcation behavior is also investigated or discussed for many of the subcases giving rise to a codimension one singularity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580856
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  • 6
    Electronic Resource
    Electronic Resource
    Quantitative stability of variational systems: III.ε-approximate solutions (1993)
    Springer
    Mathematical programming 61 (1993), S. 197-214 
    Details
    ISSN: 1436-4646
    Keywords: Epi-convergence ; epi-distance ; stability ; convex optimization ; approximate solutions ; subgradients ; level sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We prove that theε-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that theε-subgradient mapping is Lipschitz continuous.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582147
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  • 7
    Electronic Resource
    Electronic Resource
    Characterization of stable matchings as extreme points of a polytope (1992)
    Springer
    Mathematical programming 54 (1992), S. 57-67 
    Details
    ISSN: 1436-4646
    Keywords: Matchings ; stability ; extreme points ; polytope
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to extend a modified version of a recent result of Vande Vate (1989) which characterizes stable matchings as the extreme points of a certain polytope. Our proofs are simpler and more transparent than those of Vande Vate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586041
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  • 8
    Electronic Resource
    Electronic Resource
    A generalization of the Nash equilibrium theorem on bimatrix games (1996)
    Springer
    International journal of game theory 25 (1996), S. 1-12 
    Details
    ISSN: 1432-1270
    Keywords: Bimatrix game ; ɛ-equilibrium ; optimal strategies ; vertical linear complementarity problem ; degree ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this article, we consider a two-person game in which the first player picks a row representative matrixM from a nonempty set $$A$$ ofm ×n matrices and a probability distributionx on {1,2,...,m} while the second player picks a column representative matrixN from a nonempty set ℬ ofm ×n matrices and a probability distribution y on 1,2,...,n. This leads to the respective costs ofx t My andx t Ny for these players. We establish the existence of an ɛ-equilibrium for this game under the assumption that $$A$$ and ℬ are bounded. When the sets $$A$$ and ℬ are compact in ℝmxn, the result yields an equilibrium state at which stage no player can decrease his cost by unilaterally changing his row/column selection and probability distribution. The result, when further specialized to singleton sets, reduces to the famous theorem of Nash on bimatrix games.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01254380
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  • 9
    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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  • 10
    Electronic Resource
    Electronic Resource
    Lagrange stability and boundedness of discrete event systems (1995)
    Springer
    Discrete event dynamic systems 5 (1995), S. 383-403 
    Details
    ISSN: 1573-7594
    Keywords: Discrete event systems ; stability ; boundedness ; Petri nets ; manufacturing systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of “logical” discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications including manufacturing systems and computer networks (Passino et al. 1994, Burgess and Passino 1994). In this paper we extend the conventional notions and analysis of uniform boundedness, uniform ultimate boundedness, practical stability, finite time stability, and Lagrange stability so that they apply to the class of logical DES that can be defined on a metric space. Within this stability-theoretic framework we show that the standard Petri net-theoretic notions of boundedness are special cases of Lagrange stability and uniform boundedness. In addition we show that the Petri ent-theoretic approach to boundedness analysis is actually a Lyapunov approach in that the net-theoretic analysis actually produces an appropriate Lyapunov function. Moreover, via the Lyapunov approach we provide a sufficient condition for the uniform ultimate boundedness of General Petri nets. To illustrate the Petri net results, we study the boundedness properties of a rate synchronization network for manufacturing systems. In addition, we provide a detailed analysis of the Lagrange stability of a single-machine manufacturing system that uses a priority-based part servicing policy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01439154
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