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  • Articles  (359)
  • stability  (243)
  • global optimization  (117)
  • Springer  (359)
  • Mathematics  (338)
  • Electrical Engineering, Measurement and Control Technology  (22)
  • 101
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    Perron–Frobenius Theory and Symmetry of Solutions to Nonlinear PDE's (2000)
    Springer
    Letters in mathematical physics 53 (2000), S. 313-320 
    Details
    ISSN: 1573-0530
    Keywords: partial differential equations ; nonlinearities ; symmetries ; stability ; minimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007622208894
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  • 102
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    A structural approach to robust stability of polynomials (1992)
    Springer
    Multidimensional systems and signal processing 3 (1992), S. 421-425 
    Details
    ISSN: 1573-0824
    Keywords: Convex combination ; polynomial ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A sufficient condition for Hurwitz stability of a convex combination of two stable polynomials is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01940234
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  • 103
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    Stability regions of Schur andG-stable polynomials (1993)
    Springer
    Multidimensional systems and signal processing 4 (1993), S. 91-101 
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    ISSN: 1573-0824
    Keywords: Bilinear transformation ; polynomial ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The paper presents a unified approach to calculation, for a given, nominal,G-stable polynomial, a corresponding stability region in the space of perturbed coefficients
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00986008
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  • 104
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    Stability determination of two-dimensional discrete-time systems (1993)
    Springer
    Multidimensional systems and signal processing 4 (1993), S. 331-354 
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    ISSN: 1573-0824
    Keywords: two-dimensional discrete-time systems ; two-dimensional digital filters ; bivariate polynomials ; stability ; Bistritz tabular form ; Jury tabular form ; Schur-Cohn minors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In determining root distribution of univariate polynomials with real or complex-valued coefficients, the Bistritz tabular form offers a significant computational advantage. Stability studies of two-dimensional (2-D) discrete-time systems involve univariate polynomials possessing parameter-dependent coefficients, where the parameter takes values on the unit circle in the complex plane. This paper investigates the application of Bistritz tabular form in determining stability of 2-D discrete-time systems, and for this purpose we present two algorithms. Both algorithms utilize a recent result that has established the relationship between Schur-Cohn minors and the entries of the Bistritz tabular form corresponding to a given polynomial. A comparison between the use of the modified Jury table and the Bistritz table in stability checking of 2-D discrete-time systems is also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00989650
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  • 105
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    Acid-base equilibrium—A thermodynamic study of formation and stability of the Bi-2223 phase (1993)
    Springer
    Journal of superconductivity 6 (1993), S. 55-57 
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    ISSN: 1572-9605
    Keywords: Superconductivity ; Bi-2223 ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract A general acid-base equilibrium theory was proposed to explain the formation and stability of the Bi-2223 phase based on the Lewis acid-base theory, and principle of metallurgical physical chemistry. The acid-base nature of oxide was defined according to the electrostatic force between cation and oxygen anion. A series of experimental facts were systematically explained based on the theory: substitution of Bi for Ca in. the Pb-free 2223 phase, and the effect of substitution of the high-valent cation for Bi3+; oxygen-pressure atmosphere, and the heat-schocking technique on the formation and stability of the 2223 phase.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00618506
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  • 106
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    On the stability of solitary-wave solutions of model equations for long waves (1994)
    Springer
    Journal of nonlinear science 4 (1994), S. 449-470 
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    ISSN: 1432-1467
    Keywords: solitary waves ; stability ; nonlinear dispersive wave equations ; model equations for long waves ; Korteweg-de Vries-type equations ; regularized long-wave equations ; nonlinear Schrödinger equations ; 35B35 ; 35B40 ; 35Q35 ; 35Q51 ; 35Q53 ; 35Q55 ; 35S10 ; 76B15 ; 76B25 ; 76E30 ; 86A05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary After a review of the existing state of affairs, an improvement is made in the stability theory for solitary-wave solutions of evolution equations of Korteweg-de Vries-type modelling the propagation of small-amplitude long waves. It is shown that the bulk of the solution emerging from initial data that is a small perturbation of an exact solitary wave travels at a speed close to that of the unperturbed solitary wave. This not unexpected result lends credibility to the presumption that the solution emanating from a perturbed solitary wave consists mainly of a nearby solitary wave. The result makes use of the existing stability theory together with certain small refinements, coupled with a new expression for the speed of propagation of the disturbance. The idea behind our result is also shown to be effective in the context of one-dimensional regularized long-wave equations and multidimensional nonlinear Schrödinger equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02430641
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  • 107
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    Relative equilibria of Hamiltonian systems with symmetry: Linearization, smoothness, and drift (1995)
    Springer
    Journal of nonlinear science 5 (1995), S. 373-418 
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    ISSN: 1432-1467
    Keywords: Hamiltonian system with symmetry ; relative equilibria ; perturbation ; linearization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary A relative equilibrium of a Hamiltonian system with symmetry is a point of phase space giving an evolution which is a one-parameter orbit of the action of the symmetry group of the system. The evolutions of sufficiently small perturbations of a formally stable relative equilibrium are arbitrarily confined to that relative equilibrium's orbit under the isotropy subgroup of its momentum. However, interesting evolution along that orbit, here called drift, does occur. In this article, linearizations of relative equilibria are used to construct a first order perturbation theory explaining drift, and also to determine when the set of relative equilibria near a given relative equilibrium is a smooth symplectic submanifold of phase space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01212907
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  • 108
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    Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis (1993)
    Springer
    Journal of nonlinear science 3 (1993), S. 477-539 
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    ISSN: 1432-1467
    Keywords: nearly integrable systems ; spectral transform ; attractors ; traveling waves ; stability ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary In this paper we rigorously show the existence and smoothness inε of traveling wave solutions to a periodic Korteweg-deVries equation with a Kuramoto-Sivashinsky-type perturbation for sufficiently small values of the perturbation parameterε. The shape and the spectral transforms of these traveling waves are calculated perturbatively to first order. A linear stability theory using squared eigenfunction bases related to the spectral theory of the KdV equation is proposed and carried out numerically. Finally, the inverse spectral transform is used to study the transient and asymptotic stages of the dynamics of the solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02429875
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  • 109
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    Analysis of stable two-dimensional patterns in contractile cytogel (1991)
    Springer
    Journal of nonlinear science 1 (1991), S. 289-311 
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    ISSN: 1432-1467
    Keywords: cytogel ; mechanochemical ; two-dimensional patterns ; cellular differentiation ; pattern formation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary Contractile actomyosin systems play a central role in the generation of intracellular patterns. Models for pattern formation have benefited greatly from the application of mechanochemical theory. However, investigations of the patterns have been primarily qualitative in nature; the two-dimensional nature of the evolving patterns has not yet been addressed mathematically, nor has the evolution of stable heterogeneous steady-state solutions. We consider these issues, supporting our analytical predictions with numerical simulations in one and two spatial dimensions. We show how, for certain gels, the two and three-dimensional tensor equation which describes a balance of forces can be reduced to a reaction-diffusion equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01238816
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  • 110
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    A generalization of the Nash equilibrium theorem on bimatrix games (1996)
    Springer
    International journal of game theory 25 (1996), S. 1-12 
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    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.
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    URL: http://dx.doi.org/10.1007/BF01254380
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  • 111
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    Computing a closest bifurcation instability in multidimensional parameter space (1993)
    Springer
    Journal of nonlinear science 3 (1993), S. 307-327 
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    ISSN: 1432-1467
    Keywords: bifurcation ; saddle node ; Hopf ; stability ; robustness ; optimization ; numerical methods ; transcritical ; pitchfork ; extended systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary Engineering and physical systems are often modeled as nonlinear differential equations with a vector λ of parameters and operated at a stable equilibrium. However, as the parameters λ vary from some nominal value λ0, the stability of the equilibrium can be lost in a saddle-node or Hopf bifurcation. The spatial relation in parameter space of λ0 to the critical set of parameters at which the stable equilibrium bifurcates determines the robustness of the system stability to parameter variations and is important in applications. We propose computing a parameter vector λ* at which the stable equilibrium bifurcates which is locally closest in parameter space to the nominal parameters λ0. Iterative and direct methods for computing these locally closest bifurcations are described. The methods are extensions of standard, one-parameter methods of computing bifurcations and are based on formulas for the normal vector to hypersurfaces of the bifurcation set. Conditions on the hypersurface curvature are given to ensure the local convergence of the iterative method and the regularity of solutions of the direct method. Formulas are derived for the curvature of the saddle node bifurcation set. The methods are extended to transcritical and pitchfork bifurcations and parametrized maps, and the sensitivity to λ0 of the distance to a closest bifurcation is derived. The application of the methods is illustrated by computing the proximity to the closest voltage collapse instability of a simple electric power system.
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    URL: http://dx.doi.org/10.1007/BF02429868
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  • 112
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    Nondestructive evaluation of corrosion damage using electrostatic measurements (1995)
    Springer
    Journal of nondestructive evaluation 14 (1995), S. 127-136 
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    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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  • 113
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    Estimates for norms of matrix-valued and operator-valued functions and some of their applications (1993)
    Springer
    Acta applicandae mathematicae 32 (1993), S. 59-88 
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    ISSN: 1572-9036
    Keywords: 47A56 ; 47A55 ; 15A54 ; 35A30 ; 34A30 ; Operator-valued functions ; matrices ; nonself-adjoint operators ; spectrum perturbation ; eigenvalues ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A survey is presented of estimates for a norm of matrix-valued and operator-valued functions obtained by the author. These estimates improve the Gel'fand-Shilov estimate for regular functions of matrices and Carleman's estimates for resolvents of matrices and compact operators. From the estimates for resolvents, the well-known result for spectrum perturbations of self-adjoint operators is extended to quasi-Hermitian operators. In addition, the classical Schur and Brown's inequalities for eigenvalues of matrices are improved. From estimates for the exponential function (semigroups), bounds for solution norms of nonlinear differential equations are derived. These bounds give the stability criteria which make it possible to avoid the construction of Lyapunov functions in appropriate situations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00992083
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  • 114
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    On coupling of stochastic processes with embedded point processes (1994)
    Springer
    Acta applicandae mathematicae 34 (1994), S. 71-81 
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    ISSN: 1572-9036
    Keywords: 60F55 ; 60G10 ; 60K15 ; Coupling ; marked-point processes ; regeneration ; stationarity ; stability ; maximal coupling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Criteria for semi-, wide-sense-, traditional regeneration and a coupling construction of stochastic processes with embedded point processes are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00994258
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  • 115
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    Markov Control Processes with the Expected Total Cost Criterion: Optimality, Stability, and Transient Models (1999)
    Springer
    Acta applicandae mathematicae 59 (1999), S. 229-269 
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    ISSN: 1572-9036
    Keywords: (discrete-time) Markov control processes ; expected total cost ; value iteration ; policy iteration ; stability ; transient control models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper studies the expected total cost (ETC) criterion for discrete-time Markov control processes on Borel spaces, and possibly unbounded cost-per-stage functions. It presents optimality results which include conditions for a control policy to be ETC-optimal and for the ETC-value function to be a solution of the dynamic programming equation. Conditions are also given for the ETC-value function to be the limit of the α-discounted cost value function as α ↑ 1, and for the Markov control process to be `stable" in the sense of Lagrange and almost surely. In addition, transient control models are fully analized. The paper thus provides a fairly complete, up-dated, survey-like presentation of the ETC criterion for Markov control processes on Borel spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006368714127
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  • 116
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    Qualitative and numerical analysis of a class of prey-predator models (1985)
    Springer
    Acta applicandae mathematicae 4 (1985), S. 225-258 
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    ISSN: 1572-9036
    Keywords: 92A15 ; Prey ; predator ; competition ; dynamical system ; ordinary differential equation ; phase diagram ; equilibrium ; trajectory ; stability ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a problem of the dynamics of prey-predator populations suggested by the content of a letter of the biologist Umberto D'Ancona to Vito Volterra. The main feature of the problem is the special type of competition between predators of the same species as well as of different species. Two classes of cases are investigated: a first class in which the behaviour of the predator is ‘blind’ and the second one in which the behaviour is ‘intelligent’. A qualitative analysis of the dynamical systems under consideration is followed by a numerical analysis of the most significant cases.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00052462
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  • 117
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    On the Stability of Functional Equations and a Problem of Ulam (2000)
    Springer
    Acta applicandae mathematicae 62 (2000), S. 23-130 
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    ISSN: 1572-9036
    Keywords: stability ; functional equations ; Cauchy difference ; semigroup ; inequalities ; approximate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study the stability of functional equations that has its origins with S. M. Ulam, who posed the fundamental problem 60 years ago and with D. H. Hyers, who gave the first significant partial solution in 1941. In particular, during the last two decades, the notion of stability of functional equations has evolved into an area of continuing research from both pure and applied viewpoints. Both classical results and current research are presented in a unified and self-contained fashion. In addition, related problems are investigated. Some of the applications deal with nonlinear equations in Banach spaces and complementarity theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006499223572
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  • 118
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    Permanent coexistence in general models of three interacting species (1985)
    Springer
    Journal of mathematical biology 21 (1985), S. 285-298 
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    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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  • 119
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    Persistence, stability and level crossings in an integrodifferential system (1994)
    Springer
    Journal of mathematical biology 32 (1994), S. 395-426 
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    ISSN: 1432-1416
    Keywords: Uniform persistence ; stability ; Lyapunov functional ; level-crossing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Dynamical characteristics of an integrodifferential system modelling two species competition with hereditary effects are investigated; in particular we derive sufficient conditions for the persistence of the species, existence of an attracting periodic solution and ‘level-crossings’ of solutions about the periodic solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00160166
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  • 120
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    Single-locus gametophytic incompatibility: the symmetric equilibrium is globally asymptotically stable (1994)
    Springer
    Journal of mathematical biology 32 (1994), S. 515-520 
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    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.
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    URL: http://dx.doi.org/10.1007/BF00573457
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    Existence and stability of equilibria in age-structured population dynamics (1984)
    Springer
    Journal of mathematical biology 20 (1984), S. 259-276 
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    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.
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    URL: http://dx.doi.org/10.1007/BF00275988
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    Predator-prey relationships: Indiscriminate predation (1984)
    Springer
    Journal of mathematical biology 21 (1984), S. 25-34 
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    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.
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    URL: http://dx.doi.org/10.1007/BF00275220
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    Stability of fast travelling pulse solutions of the FitzHugh—Nagumo equations (1985)
    Springer
    Journal of mathematical biology 22 (1985), S. 81-104 
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    ISSN: 1432-1416
    Keywords: FitzHugh-Nagumo equation ; pulse solution ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The FitzHugh-Nagumo equation u t =u xx +f(u)-w, u t =b(u-dw), is a simplified mathematical description of a nerve axon. If the parameters b〉0 and d⩾0 are taken suitably, this equation has two travelling pulse solutions with different propagation speeds. We study the stability of the fast pulse solution when b〉0 is sufficiently small. It is proved analytically by eigenvalue analysis that the fast pulse solution is “exponentially stable” if d〉0, and is “marginally stable” but not exponentially stable if d=0.
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    URL: http://dx.doi.org/10.1007/BF00276548
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    The tabu search metaheuristic: How we used it (1990)
    Springer
    Annals of mathematics and artificial intelligence 1 (1990), S. 111-121 
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    ISSN: 1573-7470
    Keywords: Heuristic ; global optimization ; combinatorial programming ; artificial intelligence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A general description of tabu search is given and various applications to optimization problems are presented. Some guidelines for applying the tabu metaheuristic are exhibited.
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    URL: http://dx.doi.org/10.1007/BF01531073
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  • 125
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    The persistence and stability for a predator-parasite-pest system (1996)
    Springer
    Acta mathematicae applicatae sinica 12 (1996), S. 216-224 
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    ISSN: 1618-3932
    Keywords: Dynamics of populations ; enemy-pest system ; persistence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The model of a kind of predator-parasite-pest system is built in this paper in which the parasite population is controlled by predator in such a way that it preys upon the pest individuals parasitized. A disgusty of predator for preying upon the pest individuals parasitized is introduced in the model to measure the intensity that the parasite population was controlled by the predator. The persistence and the stability are studied for this system mathematically. And the influence of the disgusty on the persistence of the system is also noticed in biology.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02007741
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    A pseudospectral method for vorticity equations on spherical surface (1997)
    Springer
    Acta mathematicae applicatae sinica 13 (1997), S. 176-187 
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    ISSN: 1618-3932
    Keywords: Spherical surface ; pseudospectral method ; vorticity equations ; stability ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual ones, is proposed. Based on such an interpolation, the pseudospectral scheme is constructed. Its generalized stability and convergence are analyzed rigorously. The theoretical analysis and computational skills can also be applied to other nonlinear partial differential equations defined on spherical surface.
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    URL: http://dx.doi.org/10.1007/BF02015139
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    DECUHR: an algorithm for automatic integration of singular functions over a hyperrectangular region (1994)
    Springer
    Numerical algorithms 8 (1994), S. 201-220 
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    ISSN: 1572-9265
    Keywords: Automatic ; adaptive ; cubature ; singularity ; extrapolation ; stability ; 65D30 ; 65-04 ; 65B05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe an automatic cubature algorithm for functions that have a singularity on the surface of the integration region. The algorithm combines an adaptive subdivision strategy with extrapolation. The extrapolation uses a non-uniform subdivision that can be directly incorporated into the subdivision strategy used for the adaptive algorithm. The algorithm is designed to integrate a vector function over ann-dimensional rectangular region and a FORTRAN implementation is included.
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    URL: http://dx.doi.org/10.1007/BF02142691
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    Stability analysis of a general toeplitz systems solver (1995)
    Springer
    Numerical algorithms 10 (1995), S. 225-244 
    Details
    ISSN: 1572-9265
    Keywords: Cholesky factorization error analysis ; Hankel matrix ; least squares ; normal equations ; orthogonal factorization ; QR factorization ; semi-normal equations ; stability ; Toeplitz matrix ; weak stability ; Primary 65F25 ; Secondary 47B35 ; 65F05 ; 65F30 ; 65Y05 ; 65Y10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We show that a fast algorithm for theQR factorization of a Toeplitz or Hankel matrixA is weakly stable in the sense thatR T R is close toA T A. Thus, when the algorithm is used to solve the semi-normal equationsR TRx=AT b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear systemAx=b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem min ||Ax-b||2.
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    Progressive stable interpolation (1997)
    Springer
    Numerical algorithms 14 (1997), S. 343-359 
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    ISSN: 1572-9265
    Keywords: progressive interpolation ; stability ; spline ; shape parameters ; geometric continuity ; 41A05 ; 41A15 ; 65D05 ; 65D07
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we study several interpolating and smoothing methods for data which are known “progressively”. The algorithms proposed are governed by recurrence relations and our principal goal is to study their stability. A recurrence relation will be said stable if the spectral radius of the associated matrix is less than one. The iteration matrices depend on shape parameters which come either from the connection at the knots, or from the nature of the interpolant between two knots. We obtain various stability domains. Moving the parameters inside these domains leads to interesting shape effects.
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    URL: http://dx.doi.org/10.1023/A:1019129400864
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    Numerical solutions for a coupled non-linear oscillator (2000)
    Springer
    Journal of mathematical chemistry 28 (2000), S. 325-340 
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    ISSN: 1572-8897
    Keywords: numerical method ; stability ; Hopf bifurcation ; coupled oscillator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract A second-order accurate numerical method has been proposed for the solution of a coupled non-linear oscillator featuring in chemical kinetics. Although implicit by construction, the method enables the solution of the model initial-value problem (IVP) to be computed explicitly. The second-order method is constructed by taking a linear combination of first-order methods. The stability analysis of the system suggests the existence of a Hopf bifurcation, which is confirmed by the numerical method. Both the critical point of the continuous system and the fixed point of the numerical method will be seen to have the same stability properties. The second-order method is more competitive in terms of numerical stability than some well-known standard methods (such as the Runge–Kutta methods of order two and four).
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    URL: http://dx.doi.org/10.1023/A:1011025104111
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    Multistep methods for differential algebraic equations (1995)
    Springer
    Numerical algorithms 10 (1995), S. 245-260 
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    ISSN: 1572-9265
    Keywords: Multistep methods ; differential-algebraic equations ; stability ; existence and uniqueness ; convergence of iterative method ; 65L06 ; 65L20 ; 65N22
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Multistep methods for the differential/algebraic equations (DAEs) in the form of $$F_1 (x) = 0, F_2 (x,x',z) = 0$$ are presented, whereF 1 maps from ℝ n to ℝ ′ ,F 2 from ℝ n x ℝ n x ℝ m to ℝ s andr〈n≤r+s=n+m. By employing the deviations of the available existence theories, a new form of the multistep method for solutions of (1) is developed. Furthermore, it is shown that this method has no typical instabilities such as those that may occur in the application of multistep method to DAEs in the traditional manner. A proof of the solvability of the multistep system is provided, and an iterative method is developed for solving these nonlinear algebraic equations. Moreover, a proof of the convergence of this iterative method is presented.
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    On an inverse initial-boundary value problem for a one-dimensional hyperbolic system of differential equations (1997)
    Springer
    Acta mathematicae applicatae sinica 13 (1997), S. 33-44 
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    ISSN: 1618-3932
    Keywords: Inverse problem ; hyperbolic equations ; eigenvalue problem ; spectral function ; integral kernel ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the inverse boundary value problem of the hyperbolic system of first-order differential equations is discussed. The estimate of the solution and the quantitative analysis about its stability are obtained, and some stability criteria are established.
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    Stability analysis for two kinds of equations in two-species population dynamics (1991)
    Springer
    Applied mathematics and mechanics 12 (1991), S. 1017-1021 
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    ISSN: 1573-2754
    Keywords: predator ; prey ; patch ; population ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper we study the stability for equilibrium points of equations in two-population dynamics. We discuss two predator-prey-patch models. Model 1 is described by a differential equation. Model 2 is described by an integral differential equation. We obtain the conditions for the stability of their equilibrium points. The results show that the overall population stability despite local extinction is realizable.
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    The theorem of the stability of linear nonautonomous systems under the frequently-acting perturbation and its application in the stability analysis of robot (1991)
    Springer
    Applied mathematics and mechanics 12 (1991), S. 1057-1063 
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    ISSN: 1573-2754
    Keywords: stability ; nonautonomous system ; frequently-acting perturbation ; state transition matrix ; robot
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The necessary and sufficient condition of the stability of linear nonautonomous system under the frequently-acting perturbation has been given and proved on the basis of [1] and [2], and the theorem of the equivalence on the uniform and asymptotical stability in the sense of Liapunov and the stability under the frequently-acting perturbation of linear nonautonomous system has been given in this paper. Besides, the analysis of the dynamic stability of robot has been presented by applying the theorem in this paper, which is closer to reality.
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    The linear stability of plane Poiseuille flow under unsteady distortion (1991)
    Springer
    Applied mathematics and mechanics 12 (1991), S. 539-545 
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    ISSN: 1573-2754
    Keywords: fluid flow ; stability ; unsteady ; plane Poiseuille flow ; multiple scale method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper investigates the linear stability behaviour of plane Poiseuille flow under unsteady distortion by multiscale perturbation method and discusses further the problem proposed by paper [1]. The results show that in the initial period of disturbance development, the distortion profiles presented by paper [1] will make the disturbances grow up, thus augmenting the possibility of instability.
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    The asymptotic stability of the linear discrete large-scale systems (1993)
    Springer
    Applied mathematics and mechanics 14 (1993), S. 95-100 
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    ISSN: 1573-2754
    Keywords: discrete large-scale systems ; stability ; Liapunov function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, we directly use the linear norm Liapunov function to investigate the stability of the linear discrete large-scale systems and obtain some criteria for the asymptotic stability of such a system.
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    URL: http://dx.doi.org/10.1007/BF02451224
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    A study of the construction of lyapunov function for a class of fourth order nonlinear systems (1995)
    Springer
    Applied mathematics and mechanics 16 (1995), S. 195-202 
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    ISSN: 1573-2754
    Keywords: nonlinear ; stability ; Lyapunov function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In the paper Lyapumov function for a fourth order linear system is given and stability of the trivial solutions to a class of fourth order nonlinear systems is studied.
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    Stability for the equilibrium state of Chaplygin's systéms (1995)
    Springer
    Applied mathematics and mechanics 16 (1995), S. 635-642 
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    ISSN: 1573-2754
    Keywords: analytic mechanics ; nonholonomic system ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The stability for the equilibrium states of Chaplygin's systems is considered. The equations of motion of Chaplygin's systems and the existence conditions of their equilibrium states are given. Some criteria of stability for the equilibrium. states of Chaplygin's systems are obtained. Two examples are finally given.
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    Remarks of some problems for rectangular thin plates with free edges on elastic foundations (1991)
    Springer
    Applied mathematics and mechanics 12 (1991), S. 415-420 
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    ISSN: 1573-2754
    Keywords: bending ; flexural function ; stability ; vibration ; critical force ; frequency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract For the bending, stability and vibrations of rectangular thin plates with free edges on elastic foundations, in this paper we give a flexural function which exactly satisfies not only all the boundary conditions on free edges but also the conditions at free corner points. Applying energy variation principle, we give equations defining parameters in flexural function, stability equation, frequency equation, and general formulae of minimum critical force and minimum eigenfrequency as well.
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    The vibration and stability analysis of moderate thick plates by the method of lines (1992)
    Springer
    Applied mathematics and mechanics 13 (1992), S. 523-531 
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    ISSN: 1573-2754
    Keywords: moderate thick plate ; vibration ; stability ; method of lines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The method of lines based on Hu Hai-chang's theory for the vibration and stability of moderate thick plates is developed. The standard nonlinear ordinary differential equation (ODE) system for natural frequencies and critical load is given by use of ODE techniques, and then any indicated eigenvalue could be obtained directly from ODE solver by employing the so-called initial eigenfunction technique instead of the mode orthogonality condition. Numerical examples show that the present method is very effective and reliable.
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    Stability analysis of linear and nonlinear periodic convection in thermohaline double-diffusive systems (1996)
    Springer
    Applied mathematics and mechanics 17 (1996), S. 869-877 
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    ISSN: 1573-2754
    Keywords: thermohaline double-diffusive system ; periodic solution ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A shortout analytic method of stability in strong nonlinear autonomous system is introduced into stability analysis of the thermohaline double-diffusive system. Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions. For linear periodic solution in infinitesimal motion, the existence range of monotomic branch and oscillatory branch are outilined. The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value µ c in this case of 0〈rs-rsc≪1. The stability conclusions under different direction of vortex are drawn out.
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    The auto-adjustable damping method for solving nonlinear equations (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 163-168 
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    ISSN: 1573-2754
    Keywords: nonlinear equation ; stability ; Newton's method ; auto-adjustable damping method ; the vector of damping factors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For the strongly nonlinear problems, the solution obtained in the iterative process is always difficult, even divergent due to the numerical instability. It can not fulfill the engineering requirements. Newton's method and its variants can not settle this problem. As a result, the application of numerical simulation for the strongly nonlinear problems is limited. An auto-adjustable damping method has been presented in this paper. This is a further improvement of Newton's method with damping factor. A set of vector of damping factor is introduced. This set of vector can be adjusted continuously during the iterative process in accordance with the judgement and adjustment. An effective convergence coefficient and quichening coefficient are employed to relax the restricted requirements for the initial values and to shorten the iterative process. Then, the numerical stability will be ensured for the solution of complicated strongly nonlinear equations. Using this method, some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully. It can be used for the numerical simulation of strongly nonlinear problems in engineering such as nonlinear hydrodynamics and aerodynamics, heat transfer and structural dynamic response etc.
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    Disturbances to a rotating fluid with a sphere moving along the axis of rotation (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 861-867 
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    ISSN: 1573-2754
    Keywords: rotating fluids ; motion of body ; small disturbances ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the disturbances to a uniformly rotating ideal fluid with a sphere moving steadily along the axis of rotation are analysed by using linearization theory, the equations of disturbance, pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method of normal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that three are three kinds of possible forms of neutral disturbances.
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    Stability of a class of neural network models with delay (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 912-916 
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    ISSN: 1573-2754
    Keywords: delay ; neural network ; stability ; TN911.23 ; O332
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, by using Liapunov functional, some sufficient conditions are obtained for the stability of the equilibrium of a neural network model with delay of the type $$u'_i \left( t \right) = - b_i u_i \left( t \right) + \sum\limits_{j = 1}^n {T_{ij} f_j } \left( {\mu _j u_j \left( {t - \tau _j } \right)} \right) + c_i ,\tau _j \geqslant 0,i = 1,2 \cdots ,n.$$
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    The stability on the solution of the initial value problem (1991)
    Springer
    Applied mathematics and mechanics 12 (1991), S. 1001-1008 
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    ISSN: 1573-2754
    Keywords: stability ; initial value problem ; differentiability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, using the differentiability of the solution with respect to the initial value and the parameter, we present a method which, different from Liapunov's direct method, will determine the stability of the non-stationary solution of the initial value problem when the non-stationary solution remains unknown.
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    Stability of the Burgers shock wave (1993)
    Springer
    Applied mathematics and mechanics 14 (1993), S. 981-982 
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    ISSN: 1573-2754
    Keywords: Burgers shock wave ; infinitesimal disturbance ; stability ; asymptotically stable
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper considers the stability of the Burgers shock wave solution with respect to infinitesimal disturbance. It is found that the Burgers shock wave is asymptotically stable in the Liapunov sense.
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    The stability in neural networks with interneuronal transmission delays (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 457-462 
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    ISSN: 1573-2754
    Keywords: neural networks ; equilibrium ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, some sufficient conditions are obtained for the global asymptotic stability of the equilibrium of neural networks with interneuronal transmission delays of the type $$x'_i (t) = - b_i x_i (t) + \sum\limits_{j = 1}^n {\omega _{\ddot y} f_j (x_j (t - \tau _j )) + p_i (t 〉 0;i = 1,2, \cdots ,n)} $$
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    A method for following the unstable path between two saddle-node bifurcation points in nonlinear dynamic system (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 1384-1388 
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    ISSN: 1573-2754
    Keywords: nonlinear dynamic system ; bifurcation ; stability ; TB123 ; O322
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A computation algorithm based on the Poincaré Mapping in combination with Pseudo-Arc Length Continuation Method is presented for calculating the unstable response with saddle-node bifurcation, and the singularity, which occurs using the general continuation method combined with Poincaré Mapping to follow the path, is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too. There will be two directions in which the path can be continued at each point, but only one can be used. The method of determining the direction will be presented in the paper. It can be concluded that is method is effective in analysis of nonlinear dynamic system with saddle-node bifurcations.
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    Some dynamical properties of a viscoelastic cylindrical shell (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 233-240 
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    ISSN: 1573-2754
    Keywords: viscoelasticity ; cylindrical shell ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the dynamic stability of a viscoelastic circular cylindrical shell subject to an axial compressive force and a uniformly distributed radial compressive load is discussed. By using the Laplace transformation, stability conditions of viscoelastic shell under constant loads are yielded. By using synthetically the classical dynamic methods, the various dynamical properties for the dynamical system defined by the viscoelastic shell and the effect of parameters on the stability of structure are obtained.
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    An interactive global optimization algorithm for geological problems (1985)
    Springer
    Mathematical geology 17 (1985), S. 703-728 
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    ISSN: 1573-8868
    Keywords: global optimization ; direct search methods ; benthic mixing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A number of problems in geology can be formulated so that they consist of optimizing a real-valued function (termed the objective function) on some interval or over some region. Many methods are available for solution if the function is unimodal within the domain of interest. Direct methods, involving only function evaluations, are particularly useful in geological problems where the objective function may be strongly nonlinear and constructed from sampled data. In practical problems, the objective function often is not unimodal. Standard optimization routines are not capable of distinguishing between local extrema or of locating the global extremum, which is the point of interest in most cases. The usual approach—trying several different starting points in the hope that the best local extremum found is the global extremum—is inefficient and unreliable. An ancillary algorithm has been developed which avoids these problems and which couples with a variety of local optimization routines. The algorithm first constructs a grid of objective function values over some feasible region. The region dimensions and grid spacings are based on specific problem considerations. First differences are then calculated for successive points along each grid line and monitored in sign only, which rapidly locates extrema. User interaction determines how many of these extrema will undergo further investigation, which is carried out by passing locations to a local optimization subroutine. The algorithm has proved successful on a number of problems. A geological example—determination of benthic mixing parameters in deep-sea sediments via minimization of stratigraphic offset between δ 18 O signals from two different species of planktonic foraminifera—is given. FORTRAN code is provided for the global optimization routine, a golden section search subroutine for one-dimensional objective functions, and a simplex subroutine for multidimensional problems.
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    Lagrange stability and boundedness of discrete event systems (1995)
    Springer
    Discrete event dynamic systems 5 (1995), S. 383-403 
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    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.
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    URL: http://dx.doi.org/10.1007/BF01439154
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    Timed Petri Nets in Hybrid Systems: Stability and Supervisory Control (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 137-173 
    Details
    ISSN: 1573-7594
    Keywords: hybrid systems ; switched systems ; timed Petri nets ; stability ; supervisory control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, timed Petri nets are used to model and control hybrid systems. Petri nets are used instead of finite automata primarily because of the advantages they offer in dealing with concurrency and complexity issues. A brief overview of existing results on hybrid systems that are based on Petri nets is first presented. A class of timed Petri nets named programmable timed Petri nets (PTPN) is then used to model hybrid systems. Using the PTPN, the stability and supervisory control of hybrid systems are addressed and efficient algorithms are introduced. In particular, we present sufficient conditions for the uniform ultimate boundness of hybrid systems composed of multiple linear time invariant plants which are switched between using a logical rule described by a Petri net. This paper also examines the supervisory control of a hybrid system in which the continuous state is transfered to a region of the state space in a way that respects safety specifications on the plant's discrete and continuous dynamics.
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    URL: http://dx.doi.org/10.1023/A:1008293802713
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    Some Ergodic Results on Stochastic Iterative Discrete Events Systems (1997)
    Springer
    Discrete event dynamic systems 7 (1997), S. 209-232 
    Details
    ISSN: 1573-7594
    Keywords: Stochastic recurrence equations ; performance evaluation ; ergodicity ; stability ; subadditive ergodic theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the asymptotic behavior of the stochastic dynamics of discrete event systems. In this paper we focus on a wide class of models arising in several fields and particularly in computer science. This class of models may be characterized by stochastic recurrence equations in ℝK of the form T(n+1) = φ n+1(T(n)) where φ n is a random operator monotone and 1—linear. We establish that the behaviour of the extremas of the process T(n) are linear. The results are an application of the sub-additive ergodic theorem of Kingman. We also give some stability properties of such sequences and a simple method of estimating the limit points.
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    URL: http://dx.doi.org/10.1023/A:1008276017457
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    Robust Estimation of Rotation Angles from Image Sequences Using the Annealing M-Estimator (1998)
    Springer
    Journal of mathematical imaging and vision 8 (1998), S. 181-192 
    Details
    ISSN: 1573-7683
    Keywords: deterministic annealing ; global optimization ; M-estimator ; motion analysis ; robust statistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A robust method is presented for computing rotation angles of image sequences from a set of corresponding points containing outliers. Assuming known rotation axis, a least-squares (LS) solution are derived to compute the rotation angle from a clean data set of point correspondences. Since clean data is not guaranteed, we introduce a robust solution, based on the M-estimator, to deal with outliers. Then we present an enhanced robust algorithm, called the annealing M-estimator (AM-estimator), for reliable robust estimation. The AM-estimator has several attractive advantages over the traditional M-estimator: By definition, the AM-estimator involves neither scale estimator nor free parameters and hence avoids instabilities therein. Algorithmically, it uses a deterministic annealing technique to approximate the global solution regardless of the initialization. Experimental results are presented to compare the performance of the LS, M- and AM-estimators for the angle estimation. Experiments show that in the presence of outliers, the M-estimator outperforms the LS estimator and the AM-estimator outperforms the M-estimator.
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    URL: http://dx.doi.org/10.1023/A:1008281429730
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    The Dynamics of Nonlinear Relaxation Labeling Processes (1997)
    Springer
    Journal of mathematical imaging and vision 7 (1997), S. 309-323 
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    ISSN: 1573-7683
    Keywords: relaxation labeling processes ; consistency ; growth transformations ; Liapunov functions ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present some new results which definitively explain thebehavior of the classical, heuristic nonlinear relaxation labelingalgorithm of Rosenfeld, Hummel, and Zucker in terms of theHummel-Zucker consistency theory and dynamical systems theory. Inparticular, it is shown that, when a certain symmetry condition is met,the algorithm possesses a Liapunov function which turns out to be (thenegative of) a well-known consistency measure. This follows almostimmediately from a powerful result of Baum and Eagon developed in thecontext of Markov chain theory. Moreover, it is seen that most of theessential dynamical properties of the algorithm are retained when thesymmetry restriction is relaxed. These properties are also shown tonaturally generalize to higher-order relaxation schemes. Someapplications and implications of the presented results are finallyoutlined.
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    URL: http://dx.doi.org/10.1023/A:1008255111261
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    Stable and Real-Time Scheduling of a Class of Hybrid Dynamic Systems (1999)
    Springer
    Discrete event dynamic systems 9 (1999), S. 45-64 
    Details
    ISSN: 1573-7594
    Keywords: hybrid dynamic systems ; event feedback ; real-time scheduling ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Based on some practical engineering problems arising from process control and space-structure control, this paper studies a class of hybrid dynamic systems in which N plants are controlled by a central controller in sharing time manner, where the plants are described by differential equations and the controller works according to the mechanism of discrete events. An event feedback strategy is suggested to be a scheduling policy such that one and only one plant among N plants is chosen to be controlled at any time. Some conditions of asymptotical and exponential stability are then given and an exponential upper bound of states norm is also estimated for the event feedback scheduling strategy. An algorithm based on event feedback strategy is presented to determine the control laws of the plants to meet the given performance. An example follows to illustrate the application and effect of the results.
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    URL: http://dx.doi.org/10.1023/A:1008320614629
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    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 
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    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.
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    URL: http://dx.doi.org/10.1007/BF01438607
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    Partial Compensation for Mismatched Uncertain Discrete Systems (2000)
    Springer
    Dynamics and control 10 (2000), S. 47-61 
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    ISSN: 1573-8450
    Keywords: stability ; robust control ; Lyapunov approach ; discrete system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Control design of nonlinear discrete-time uncertain systems with (possibly fast) uncertain parameters is considered. We study the effect of only partially compensating the uncertainty. The optimal choice of a design parameter, which indicates the amount of compensation, is recommended.
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    URL: http://dx.doi.org/10.1023/A:1008395928788
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    Optimal Model Reduction with a Frequency Weighted Extension (2000)
    Springer
    Dynamics and control 10 (2000), S. 255-276 
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    ISSN: 1573-8450
    Keywords: continuous-time systems ; frequency weighted model reduction ; gradient flow ; optimization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Inthis paper, a model reduction technique based on optimizationis presented. The objective function minimized is the impulseenergy of the overall system. An extension of the technique tothe frequency weighted case is also presented, where single-sidedor double-sided weightings can be incorporated in the reductionprocedure. The paper proposes an alternative to find an optimizationsolution by solving ordinary differential equations which aregradient flow associated with the objective function to be minimized.Two examples are presented to illustrate the effectiveness ofthe method.
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    URL: http://dx.doi.org/10.1023/A:1008366812002
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    Explicit second-order accurate schemes for the nonlinear Schrödinger equations (1999)
    Springer
    Lithuanian mathematical journal 39 (1999), S. 20-32 
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    ISSN: 1573-8825
    Keywords: Schrödinger equation ; explicit finite-difference schemes ; stability ; energy conservation ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider three-level explicit schemes for solving the nonlinear variable coefficient Schrödinger-type equation. Using spectral and energy methods we establish the stability and convergence of these schemes. The existence of discrete conservation laws is investigated. General results are applied for the DuFort-Frankel and leap-frog diffenrence schemes.
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    URL: http://dx.doi.org/10.1007/BF02465532
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    A Multistage Closed-loop Sigma-Delta modulator (MSCL) (1996)
    Springer
    Analog integrated circuits and signal processing 11 (1996), S. 195-204 
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    ISSN: 1573-1979
    Keywords: A/D converters ; sigma-delta ; modulator ; band-pass ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A new family of high order Sigma Delta modulators called MSCL (Multi Stage Closed-loop) is presented in this paper. They use a global feedback to lower the sensitivity to circuit imperfections. This feedback from the output of the modulator is the sum of the output of each comparator so that no digital prefiltering is required before summing up these signals. However, easy calibration will be required to compensate for the feedback imperfections. MSCL modulators present the same insensitivity to circuit imperfections as classical multi-order one-bit converters, but reach the performance of high-order MASH (MultistAge noise SHaping) modulators. They help make high-order low-pass or band-pass modulators without limit cycles so that their quantizing noise characteristics are similar to those predicted by the linear simplified model.
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    URL: http://dx.doi.org/10.1007/BF00240484
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    On the Global Dynamics of a Controlled Viscous Burgers' Equation (1998)
    Springer
    Journal of dynamical and control systems 4 (1998), S. 457-519 
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    ISSN: 1573-8698
    Keywords: Boundary control ; nonlinear distributed parameter system ; center manifold theorem ; stability ; local attractors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper we consider a boundary control problem for a forced Burgers' equation in a Hilbert state space consisting of square integrable functions on a finite interval. Our first main result consists in proving the global in time existence of solutions of the closed loop boundary control system for arbitrary L 2 initial data and quite general forcing terms (disturbances). For the unforced problem, our main interest is in stability of equilibria, while for the forced problem we are interested in steady state behavior of solutions. We note that the uncontrolled (open loop), unforced problem is not asymptotically stable on L 2. However, for positive gains we show that the unforced closed loop system is globally Lyapunov stable and locally exponentially stable. In addition, for nonzero stationary forcing, we show that there is a local absorbing ball and that the corresponding nonlinear semigroup is compact for all t 〉 0. Using this fact, we are able to deduce several consequences regarding the existence and properties of local attractors. Our method of proof is based on a systematic investigation of the smoothing properties of the controlled dynamics. In particular we establish various regularity results for the dynamics of the closed loop system.
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    URL: http://dx.doi.org/10.1023/A:1021815100868
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    Control of Discrete Fuzzy Systems: Uncertainty and Guaranteed Performance (1998)
    Springer
    Dynamics and control 8 (1998), S. 83-106 
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    ISSN: 1573-8450
    Keywords: fuzzy modeling ; robust control ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Robust control designs for a discrete Takagi and Sugeno (T-S) fuzzy model are proposed. The T-S fuzzy model contains (possibly fast) time-varying uncertainty. First, a switching-type robust control is shown to stabilize the T-S fuzzy model asymptotically. Second, a saturation-type robust control is shown to render the T-S model practically stable. In both designs, only the bound of uncertainty is needed. The effectiveness of proposed designs is analyzed rigorously and illustrated by simulations.
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    URL: http://dx.doi.org/10.1023/A:1008231013911
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    Almost-periodic solutions to systems of differential equations with fast and slow time in the degenerate case (1998)
    Springer
    Mathematical notes 63 (1998), S. 396-400 
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    ISSN: 1573-8876
    Keywords: ordinary differential equations ; fast and slow time ; periodic solutions ; existence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a system of ordinary first-order differential equations. The right-hand sides of the system are proportional to a small parameter and depend almost periodically on fast time and periodically on slow time. With this system, we associate the system averaged over fast time. We assume that the averaged system has a structurally unstable periodic solution. We prove a theorem on the existence and stability of almost periodic solutions of the original system.
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    URL: http://dx.doi.org/10.1007/BF02317788
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    Perturbations of an abstract Euler-Poisson-Darboux equation (1996)
    Springer
    Mathematical notes 60 (1996), S. 269-273 
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    ISSN: 1573-8876
    Keywords: abstract Cauchy problem ; uniform correctness ; perturbation theory ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The stability of the uniform correctness of the Cauchy problem $$u(t) + \frac{k}{t}u'(t) = \mathbb{A}u(t)$$ ,t〉0,u(0)=u 0,u′(0)=0 fork〉0 with respect to perturbations of the operator $$\mathbb{A}$$ is studied.
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    A generalization of the Tikhonov theorem for singularly perturbed differential inclusions (1997)
    Springer
    Journal of dynamical and control systems 3 (1997), S. 291-319 
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    ISSN: 1573-8698
    Keywords: 34D15 ; 34E15 ; 34A60 ; 93C73 ; 93D20 ; 49N99 ; Singular perturbation ; differential inclusion ; control systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract We study the continuity properties of the bundle of solutions to a differential inclusion subject to a singular perturbation, i.e., with respect to a scalar parameter ɛ multiplying a part of the derivatives. We give conditions under which every solution of the singularly perturbed inclusion is close, in a certain sense and for a sufficiently small ɛ, to a solution of the degenerate inclusion obtained for ɛ=0. These conditions include both stability and structural requirements (the later having no counterpart in the case of a differential equation). The main result obtained generalizes the well-known Tikhonov theorem for singularly perturbed differential equations.
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    On Invariant Manifolds in Singularly Perturbed Systems (1999)
    Springer
    Journal of dynamical and control systems 5 (1999), S. 501-507 
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    ISSN: 1573-8698
    Keywords: Singular perturbation ; invariant manifold ; overflowing manifold ; stability ; characteristic numbers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A singularly perturbed system with a small parameter ε at the velocity of the slow variable y and with the fast variable x is considered. The main hypothesis is that for all y from some bounded domain D, the fast subsystem has a stable invariant or overflowing manifold M 0(y) and that the motions in this system going in the directions transversal to M 0(y) are more fast than the mutual approaching of trajectories on M 0(y) (a precise statement is given in terms of appropriate Lyapunov-type characteristic numbers). It is proved that for a sufficiently small ε, the whole system has an invariant manifold close to $$\bigcup\limits_{y \in D} {M_0 (y) \times \{ y\}}$$ the degree of its smoothness is specifed.
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    On the Stability of Nonconservative Systems with Estimation of the Attraction Domain (2000)
    Springer
    Journal of dynamical and control systems 6 (2000), S. 503-510 
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    ISSN: 1573-8698
    Keywords: nonconservative mechanical systems ; stability ; Lyapunov functions ; attraction domain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Mechanical systems subjected to dissipative, gyroscopic, conservative, and also nonconservative positional forces are considered. The question of the effect of dissipative, gyroscopic, and conservative forces on the motion stability of a mechanical systems is determined by classical Kelvin–Chetaev theorems [1]. The presence of nonconservative positional forces considerably complicates the situation and excludes direct application of these theorems. Applying Lyapunov's functions method the condition of asymptotic stability of a mechanical system under the action of all listed above forces is obtained. Moreover, the estimation of the attraction domain in phase space is found. The precession system which is used in the solution of some problems in the applied theory of the gyroscopic systems is also examined. The connection between the stability of origin and precession systems is detected. Theoretical results are applied to the stabilization problem of stationary motion of the balanced gimbal suspension gyro by means of external moments.
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    URL: http://dx.doi.org/10.1023/A:1009500527061
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    Robust Stability of Multivariate Polynomials. Part 1: Small Coefficient Perturbations (1999)
    Springer
    Multidimensional systems and signal processing 10 (1999), S. 7-20 
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    ISSN: 1573-0824
    Keywords: multivariate polynomials ; stability ; robust stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a detailed analysis of some classes of stable multivariate polynomials. The main aim of the analysis is to give conditions under which polynomials preserve stability when they are subjected to small coefficient variations. The maximal class of such polynomials is introduced. Some basic properties of polynomials from this class are obtained.
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    Numerical Investigation of a Stability Theorem Arising from the 2-Dimensional Analysis of an Iterative Optimal Control Algorithm (2000)
    Springer
    Multidimensional systems and signal processing 11 (2000), S. 109-124 
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    ISSN: 1573-0824
    Keywords: 2-D linear systems ; optimal control ; stability ; unit memory linear repetitive processes ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Because many optimal control problems require solution using iterative procedures they fall naturally in the realm of 2-D systems where the two dimensions are response time horizon and iteration index, respectively. The paper uses this observation to employ 2-D systems theory, in the form of unit memory repetitive process techniques, to analyse local stability and convergence behaviour of a continuous optimal control algorithm based on dynamic system optimisation and parameter estimation. Existing work is extended to incorporate unmatched terminal constraints. Necessary and sufficient conditions for stability are obtained whose evaluation require the solution of a difficult eigenvalue problem. The paper shows how solutions can be achieved using numerical and graphical facilities of MATLAB.
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    The Jump Behavior and Stability Analysis for 2-D Singular Systems (2000)
    Springer
    Multidimensional systems and signal processing 11 (2000), S. 339-358 
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    ISSN: 1573-0824
    Keywords: 2-D systems ; descriptor systems ; singular systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, we discussthe jump behavior and stability problems for 2-D linear shift-invariantsingular systems under the standard boundary conditions. It isshown that once a boundary condition or the input is inadmissiblein the classical sense, a group of non-causal or backward jumpsof the system states will be incited. This interpretation releasesthe conventional admissibility constraints on the boundary conditionsand inputs. Based on this observation, a systematic stabilitytheory is developed for 2-D singular systems. The well-knownbasic stability theorem for the 1-D singular systems or 2-D regularsystems is thus extended to the 2-D singular case.
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    Stability tests and performance bounds for a class of 2D linear systems (1993)
    Springer
    Multidimensional systems and signal processing 4 (1993), S. 355-391 
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    ISSN: 1573-0824
    Keywords: repetitive dynamics ; stability ; performance bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Repetitive, or multipass, processes are a class of 2D systems characterized by a recursive action with interaction between successive outputs or pass profiles. This interpass interaction is the source of the unique control problem for these processes in that it can cause the output sequence to exhibit oscillations which increase in amplitude from pass to pass. Previous work has developed an abstract stability theory and applied it to subclasses, such as discrete nonunit memory linear processes which are considered here, to produce basic stability tests. This article begins by reviewing the known stability tests and concludes that, at best, they only produce highly qualitative indicators of relative stability and performance. Hence, unlike (say) Bode and Nyquist tests for standard linear systems, they are of limited appeal as a basis for computer-aided control systems design. To remove this difficulty, step response data is used to develop new simulation-based tests which yield, at no extra cost, unique computable performance measures. Further, the undoubted advantages of having such measures available is clearly shown by developing a (virtually) complete solution to controller design for one subclass.
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    URL: http://dx.doi.org/10.1007/BF00989651
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    Eigenvalue localization ofG-stable matrix polytopes (1994)
    Springer
    Multidimensional systems and signal processing 5 (1994), S. 307-318 
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    ISSN: 1573-0824
    Keywords: Eigenvalue ; matrix ; polytope ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A simple geometric test can be applied to evaluateG-stability of a polytope of matrices. In case of a regionG being a convex subset of the complex plane, it suffices to assume that four (for some regions even less) corner points of a certain rectangle are contained inG.
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    An algorithm for stability determination of two-dimensional delta-operator formulated discrete-time systems (1995)
    Springer
    Multidimensional systems and signal processing 6 (1995), S. 287-312 
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    ISSN: 1573-0824
    Keywords: Two-dimensional discrete-time systems ; two-dimensional digital filters ; δ-operator formulated discrete-time systems ; bivariate polynomials ; Schur-Cohn minors ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The recent interest in delta-operator (or, δ-operator) formulated discrete-time systems (or, δ-systems) is due mainly to (a) their superior finite wordlength characteristics as compared to their more conventional shift-operator (or,q-operator) counterparts (or,q-systems), and (b) the possibility of a more unified treatment of both continuous- and discrete-time systems. With such advantages, design, analysis, and implementation of two-dimensional (2-D) discrete-time systems using the δ-operator is indeed warranted. Towards this end, the work in this paper addresses the development of an easily implementabledirect algorithm for stability checking of 2-D δ-system transfer function models.Indirect methods that utilize transformation techniques are not pursued since they can be numerically unreliable. In developing such an algorithm, a tabular form for stability checking of δ-system characteristic polynomials with complex-valued coefficients and certain quantities that may be regarded as their corresponding Schur-Cohn minors are also proposed.
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    Recent results in mathematical modeling of infectious diseases (1989)
    Springer
    Acta applicandae mathematicae 14 (1989), S. 125-133 
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    ISSN: 1572-9036
    Keywords: 92A07 ; stationary solution ; immune response ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Some results connected with a simple mathematical model of infectious disease are discussed in order to demonstrate the approach to the modelling of such real processes. A more complicated model of antiviral immune response is presented. A new modification of this model in which targets for the viruses are immunocompetent cells is suggested.
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    URL: http://dx.doi.org/10.1007/BF00046679
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    Stability analysis of a rotating flexible system (1989)
    Springer
    Acta applicandae mathematicae 15 (1989), S. 211-234 
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    ISSN: 1572-9036
    Keywords: 70F99 ; 70K20 ; 73C02 ; 35P30 ; Flexible body ; Lagrangian and Hamiltonian dynamics ; stability ; partial differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We analyse here the equations of motion of a planar body consisting of a rigid body with attached flexible rod. These equations take the form of coupled ordinary and partial differential equations. We analyse the equations both with and without centrifugal stiffening effects. Using the ‘energy-momentum’ method, we analyse nonlinear stability of the equilibria in each case. We also analyse the Hamiltonian and Poisson bracket structure of the system as well as the energy-momentum map and associated relative equilibria.
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    URL: http://dx.doi.org/10.1007/BF00047531
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    Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors (1992)
    Springer
    Acta applicandae mathematicae 26 (1992), S. 1-60 
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    ISSN: 1572-9036
    Keywords: 58F13 ; Hausdorff measure ; Hausdorff dimension ; strange attractor ; Lorenz system ; Rössler system ; Lyapunov function ; stability ; chaos ; weakly contracting system ; monostability ; frequency theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper surveys results of the authors and others conceming estimates for the Hausdorff dimension of strange attractors, particularly in the case of (generalized) Lorenz systems and Rössler systems. A key idea is the interpretation of Hausdorff measure as an analogue of a Lyapunov function.
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    URL: http://dx.doi.org/10.1007/BF00046607
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    Outcome-Space Cutting-Plane Algorithm for Linear Multiplicative Programming (2000)
    Springer
    Journal of optimization theory and applications 104 (2000), S. 301-322 
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    ISSN: 1573-2878
    Keywords: global optimization ; multiplicative programming ; cutting plane ; nonconvex programming ; outcome space ; extreme-point search
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    Topics: Mathematics
    Notes: Abstract This article presents an outcome-space pure cutting-plane algorithm for globally solving the linear multiplicative programming problem. The framework of the algorithm is taken from a pure cutting-plane decision set-based method developed by Horst and Tuy for solving concave minimization problems. By adapting this method to an outcome-space reformulation of the linear multiplicative programming problem, rather than applying directly the method to the original decision-set formulation, it is expected that considerable computational savings can be obtained. Also, we show how additional computational benefits might be obtained by implementing the new algorithm appropriately. To illustrate the new algorithm, we apply it to the solution of a sample problem.
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    URL: http://dx.doi.org/10.1023/A:1004657629105
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    Approximation of an Analog Diffusion Network with Applications to Image Estimation (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 391-414 
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    ISSN: 1573-2878
    Keywords: diffusion networks ; image estimation ; global optimization ; simulated annealing ; weak convergence
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    Topics: Mathematics
    Notes: Abstract This work is concerned with a numerical procedure for approximating an analog diffusion network. The key idea is to take advantage of the separable feature of the noise for the diffusion machine and use a parallel processing method to develop recursive algorithms. The asymptotic properties are studied. The main result of this paper is to establish the convergence of a continuous-time interpolation of the discrete-time algorithm to that of the analog diffusion network via weak convergence methods. The parallel processing feature of the network makes it attractive for solving large-scale optimization problems. Applications to image estimation are considered. Not only is this algorithm useful for the image estimation problems, but it is widely applicable to many related optimization problems.
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    URL: http://dx.doi.org/10.1023/A:1026485504384
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    Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 331-354 
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    ISSN: 1573-2878
    Keywords: general quadratic programming problem with quadratic constraints ; global optimization ; branch-and-bound algorithms ; duality bounds
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    Topics: Mathematics
    Notes: Abstract The purpose of this article is to develop a branch-and-bound algorithm using duality bounds for the general quadratically-constrained quadratic programming problem and having the following properties: (i) duality bounds are computed by solving ordinary linear programs; (ii) they are at least as good as the lower bounds obtained by solving relaxed problems, in which each nonconvex function is replaced by its convex envelope; (iii) standard convergence properties of branch-and-bound algorithms for nonconvex global optimization problems are guaranteed. Numerical results of preliminary computational experiments for the case of one quadratic constraint are reported.
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    URL: http://dx.doi.org/10.1023/A:1026437621223
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    Method of reduction in convex programming (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 349-378 
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    ISSN: 1573-2878
    Keywords: Convexity ; subdifferentials ; cones of directions of constancy ; equality set of constraints ; stability
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    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.
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    URL: http://dx.doi.org/10.1007/BF00933505
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    Stability of nondominated solutions in multicriteria decision-making (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 229-253 
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    ISSN: 1573-2878
    Keywords: Point-to-set maps ; domination structures ; parameterized decision-making problems ; solution maps ; stability
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    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.
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    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 
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    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.
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    Stability of compromise solution in multicriteria decision-making problems (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 77-83 
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    ISSN: 1573-2878
    Keywords: Parameterized decision-making problems ; utopia point ; compromise solutions ; Hausdorff distance ; stability
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    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.
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    Bayesian testing of nonparametric hypotheses and its application to global optimization (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 31-50 
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    ISSN: 1573-2878
    Keywords: Bayesian testing ; nonparametric inference ; random distribution functions ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Random distribution functions are the basic tool for solving nonparametric decision-theoretic problems. In 1974, Doksum introduced the family of distributions neutral to the right, that is, distributions such thatF(t 1),[F(t 2)−F(t 1)]/[1 −F(t 1)],...,[F(t k)−F(t k − 1)]/[1 −F(t k − 1)] are independent whenevert 1 〈 ... 〈t kIn practice, application of distributions neutral to the right has been prevented by the lack of a manageable analytical expression for probabilities of the typeP(F(t)〈q) for fixedt andq. A subclass of such distributions can be provided which allows for a close expression of the characteristic function of log[1−F(t)], given the sample. Then, thea posteriori distribution ofF(t) is obtained by numerical evaluation of a Fourier integral. As an application, the global optimization problem is formulated as a problem of inference about the quantiles of the distributionF(y) of the random variableY=f(X), wheref is the objective function andX is a random point in the search domain.
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    Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations (1988)
    Springer
    Journal of optimization theory and applications 57 (1988), S. 265-293 
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    ISSN: 1573-2878
    Keywords: Discrete-time systems ; infinite-horizon optimal control ; moving-horizon control ; state-control constraints ; nonquadratic cost functions ; stability
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    Topics: Mathematics
    Notes: Abstract Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and moving-horizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.
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    URL: http://dx.doi.org/10.1007/BF00938540
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    Stability of linearly constrained convex quadratic programs (1990)
    Springer
    Journal of optimization theory and applications 64 (1990), S. 43-53 
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    ISSN: 1573-2878
    Keywords: Convex quadratic programming ; stability
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    Topics: Mathematics
    Notes: Abstract This paper establishes a simple necessary and sufficient condition for the stability of a linearly constrained convex quadratic program under perturbations of the linear part of the data, including the constraint matrix. It also establishes results on the continuity and differentiability of the optimal objective value of the program as a function of a parameter specifying the magnitude of the perturbation. The results established herein directly generalize well-known results on the stability of linear programs.
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    Fixed-order robust compensators via min-max principle (1994)
    Springer
    Journal of optimization theory and applications 81 (1994), S. 277-296 
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    ISSN: 1573-2878
    Keywords: Robust control ; min-max techniques ; synthesis methods ; stability ; multivariable control systems
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    Topics: Mathematics
    Notes: Abstract An important (some say, the major) reason for using feedback control is the presence of uncertain parameters which are a natural part of any real dynamical model. In this paper, we consider uncertain constant parameters in a time-invariant linear plant and announce some new results concerning robust compensator synthesis. Using the min-max principle, we derive necessary conditions for fixed-order linear robust controllers assuring asymptotic stability or relative stability. These necessary conditions are an extension of the Lagrange multiplier method. This is achieved using a cost function based on the inverse of the so-called critical constraint. We present both matrix and polynomial versions; the latter allows controllers of fixed structure. We suggest a probability-one homotopy algorithm and solve some examples from the literature.
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    Kalman filtering on approximate state-space models (1995)
    Springer
    Journal of optimization theory and applications 84 (1995), S. 415-431 
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    ISSN: 1573-2878
    Keywords: Kalman filtering ; Karhunen-Loève expansion ; stability ; observability ; controllability
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    Topics: Mathematics
    Notes: Abstract Several state-space models for estimating a second-order stochastic process are proposed in this paper on the basis of the approximate Karhunen-Loève expansion. Properties of these models are studied and then the Kalman filtering method is applied. The accuracy of the models on the basis of two different situations, deterministic or random inputs, is studied by means of a simulation of a Brownian motion.
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    Transversality condition for infinite-horizon problems (1996)
    Springer
    Journal of optimization theory and applications 88 (1996), S. 671-688 
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    ISSN: 1573-2878
    Keywords: Infinite-horizon problems ; optimal control ; transversality condition ; stability ; Lyapunov exponents
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    Topics: Mathematics
    Notes: Abstract We present necessary conditions of optimality for an infinitehorizon optimal control problem. The transversality condition is derived with the help of stability theory and is formulated in terms of the Lyapunov exponents of solutions to the adjoint equation. A problem without an exponential factor in the integral functional is considered. Necessary and sufficient conditions of optimality are proved for linear quadratic problems with conelike control constraints.
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    Lagrangian duality of concave minimization subject to linear constraints and an additional facial reverse convex constraint (1996)
    Springer
    Journal of optimization theory and applications 91 (1996), S. 617-641 
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    ISSN: 1573-2878
    Keywords: Lagrangian duality ; global optimization ; concave minimization ; penalty methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the global optimization problem of minimizing a concave function subject to linear constraints and an additional facial reverse convex constraint. Here, the feasible set is the union of some faces of the polyhedron determined by the linear constraints. Several well-known mathematical problems can be written or transformed into the form considered. The paper addresses the Lagrangian duality of the problem. It is shown that, under slight assumptions, the duality gap can be closed with a finite dual multiplier. Finite methods based on solving concave minimization problems are also proposed. We deal with the advantages accrued when outer approximation, cutting plane, or branch-and-bound methods are used for solving these subproblems.
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    Multiplicative Programming Problems: Analysis and Efficient Point Search Heuristic (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 487-510 
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    ISSN: 1573-2878
    Keywords: Multiplicative programming ; global optimization ; concave minimization ; efficient points ; heuristic algorithms ; multiple objectives
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Multiplicative programming problems are difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, finance, economics, and other fields. This article has two purposes. The first is to present an analysis that shows several relationships between concave multiplicative programs and concave minimization problems, and between concave multiplicative programs and certain multiple-objective mathematical programs. The second purpose is to propose and report computational results for a heuristic efficient-point search algorithm that we have designed for use on linear multiplicative programming problems. To our knowledge, this is the first heuristic algorithm of its type. The theoretical and algorithmic results given in the article offer some potentially important new avenues for analyzing and solving multiplicative programming problems of various types.
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    Optimal Control of Nonlinear Fredholm Integral Equations (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 707-729 
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    ISSN: 1573-2878
    Keywords: Nonlinear integral equations ; optimal control in L p-spaces ; relaxation ; existence ; stability ; nonconcentration ; optimality conditions ; Pontryagin maximum principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optimal control problems with nonlinear equations usually do not possess optimal solutions, so that their natural (i.e., continuous) extension (relaxation) must be done. The relaxed problem may also serve to derive first-order necessary optimality condition in the form of the Pontryagin maximum principle. This is done here for nonlinear Fredholm integral equations and problems coercive in an L p-space of controls with p〈+∞. Results about a continuous extension of the Uryson operator play a key role.
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    Reduction of indefinite quadratic programs to bilinear programs (1992)
    Springer
    Journal of global optimization 2 (1992), S. 41-60 
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    ISSN: 1573-2916
    Keywords: Quadratic program ; bilinear program ; global optimization ; reduction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Indefinite quadratic programs with quadratic constraints can be reduced to bilinear programs with bilinear constraints by duplication of variables. Such reductions are studied in which: (i) the number of additional variables is minimum or (ii) the number of complicating variables, i.e., variables to be fixed in order to obtain a linear program, in the resulting bilinear program is minimum. These two problems are shown to be equivalent to a maximum bipartite subgraph and a maximum stable set problem respectively in a graph associated with the quadratic program. Non-polynomial but practically efficient algorithms for both reductions are thus obtaine.d Reduction of more general global optimization problems than quadratic programs to bilinear programs is also briefly discussed.
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    Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions (1995)
    Springer
    Journal of global optimization 6 (1995), S. 179-191 
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    ISSN: 1573-2916
    Keywords: Product of two fractional functions ; global optimization ; branch and bound ; adaptive branching ; efficiency
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    Topics: Mathematics
    Notes: Abstract Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods.
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    A quasiconcave minimization method for solving linear two-level programs (1994)
    Springer
    Journal of global optimization 4 (1994), S. 243-263 
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    ISSN: 1573-2916
    Keywords: Linear two-level program ; global optimization ; Stackelberg game ; quasiconcave minimization ; branch and bound ; outer approximation ; subdivision procedure
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    Topics: Mathematics
    Notes: Abstract In this paper the linear two-level problem is considered. The problem is reformulated to an equivalent quasiconcave minimization problem, via a reverse convex transformation. A branch and bound algorithm is developed which takes the specific structure into account and combines an outer approximation technique with a subdivision procedure.
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    A D.C. optimization method for single facility location problems (1995)
    Springer
    Journal of global optimization 7 (1995), S. 209-227 
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    ISSN: 1573-2916
    Keywords: Facility location ; d.c optimization ; global optimization ; nondifferentiable optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The single facility location problem with general attraction and repulsion functions is considered. An algorithm based on a representation of the objective function as the difference of two convex (d.c.) functions is proposed. Convergence to a global solution of the problem is proven and extensive computational experience with an implementation of the procedure is reported for up to 100,000 points. The procedure is also extended to solve conditional and limited distance location problems. We report on limited computational experiments on these extensions.
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    On the longest circuit in an alterable digraph (1995)
    Springer
    Journal of global optimization 7 (1995), S. 279-295 
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    ISSN: 1573-2916
    Keywords: Alterable digraphs ; global optimization ; approximation ; NP-hardness
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    Topics: Mathematics
    Notes: Abstract Analterable digraph is a digraph with a subset of its edges marked alterable and their orientations left undecided. We say that an alterable digraph has an invariant ofk on the length of the longest circuit if it has a circuit of length at leastk regardless of the orientations over its alterable edges. Computing the maximum invariant on the length of the longest circuit in an alterable digraph is aglobal optimization problem. We show that it is hard to approximate the global optimal solution for the maximum invariant problem.
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    Simulated annealing for constrained global optimization (1994)
    Springer
    Journal of global optimization 5 (1994), S. 101-126 
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    ISSN: 1573-2916
    Keywords: Continuous simulated annealing ; adaptive cooling ; random search ; global optimization ; Monte Carlo optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Hide-and-Seek is a powerful yet simple and easily implemented continuous simulated annealing algorithm for finding the maximum of a continuous function over an arbitrary closed, bounded and full-dimensional body. The function may be nondifferentiable and the feasible region may be nonconvex or even disconnected. The algorithm begins with any feasible interior point. In each iteration it generates a candidate successor point by generating a uniformly distributed point along a direction chosen at random from the current iteration point. In contrast to the discrete case, a single step of this algorithm may generateany point in the feasible region as a candidate point. The candidate point is then accepted as the next iteration point according to the Metropolis criterion parametrized by anadaptive cooling schedule. Again in contrast to discrete simulated annealing, the sequence of iteration points converges in probability to a global optimum regardless of how rapidly the temperatures converge to zero. Empirical comparisons with other algorithms suggest competitive performance by Hide-and-Seek.
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    A generalized duality and applications (1993)
    Springer
    Journal of global optimization 3 (1993), S. 311-324 
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    ISSN: 1573-2916
    Keywords: Nonconvex duality ; zero gap ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.
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