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  • Articles  (410)
  • stability  (304)
  • 81R50
  • Springer  (410)
  • Mathematics  (328)
  • Computer Science  (68)
  • Electrical Engineering, Measurement and Control Technology  (22)
  • 1
    Electronic Resource
    Electronic Resource
    On the stability of wavelet and Gabor frames (Riesz bases) (1999)
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
    Details
    ISSN: 1531-5851
    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01274192
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  • 2
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    Stabilization of smoothness priors time-varying autoregressive models (2000)
    Springer
    Circuits, systems and signal processing 19 (2000), S. 423-435 
    Details
    ISSN: 1531-5878
    Keywords: Time-varying autoregressive models ; stability ; smoothness priors ; Tihkonov regularization ; constrained optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The stability of time-varying autoregressive (AR) models is an important issue in such applications as time-varying spectrum estimation and electroencephalography simulation and estimation. In some cases, such as time-varying spectrum estimation, the models that exhibit roots near unit moduli are difficult to use. Thus a tighter stability condition such as stability with a positive margin is needed. A time-varying AR model is stable with a positive margin if the moduli of the roots of the time-varying characteristic polynomial are somewhat less than unity for every time instant. Recently, a new method for the estimation of the time-varying AR models was introduced. This method is based on the interpretation of the underdetermined time-varying prediction equations as an ill-posed inverse problem that is solved by Tikhonov regularization. The method is referred to as the deterministic regression smoothness priors (DRSP) scheme. In this paper, a stabilization method in which the DRSP scheme is augmented with nonlinear stability constrainst is proposed. The problem is formulated so that stability with a positive margin can also be achieved. The problem is solved iteratively with an exterior point algorithm. The performance of the algorithm is studied with a simulation. It is shown that the proposed approach is well suited to stable modeling of signals containing narrowband transitions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01196156
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  • 3
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    Stability of constant coefficient linear singular systems with delay (2000)
    Springer
    Circuits, systems and signal processing 19 (2000), S. 13-25 
    Details
    ISSN: 1531-5878
    Keywords: Singular systems ; delay ; consistency condition ; stability ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this paper, the general class of singular systems with delay and linear constant coefficient singular systems with delay are discussed. First, several definitions of stability are presented for singular systems with delay, and general sufficient stability conditions and instability conditions are obtained. Second, stability and instability are analyzed for linear constant coefficient singular systems with delay.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01229989
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  • 4
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    On the stability of multistep formulas for Volterra integral equations of the second kind (1980)
    Springer
    Computing 24 (1980), S. 341-347 
    Details
    ISSN: 1436-5057
    Keywords: Numerical analysis ; Volterra integral equations of the second kind ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ziel dieser Arbeit ist es, die Stabilitätseigenschaften einer Klasse Volterrascher Integralgleichungen zweiter Art zu untersuchen. Unsere Behandlung ist der üblichen Stabilitätsanalyse ähnlich, in der die Kernfunktionen zu einer im voraus beschränkten Klasse von Testfunktionen gehören. Wir haben die Klasse der “endlich zerlegbaren” Kerne betrachtet. Stabilitätsbedingungen werden abgeleitet und verglichen mit den Bedingungen für die einfache Testgleichung. Es zeigt sich, daß die neuen Kriteria einschränkender sind als die konventionellen Bedingungen. Der praktische Wert wird getestet durch numerische Experimente mit der Trapezregel.
    Notes: Abstract The purpose of this paper is to analyse the stability properties of a class of multistep methods for second kind Volterra integral equations. Our approach follows the usual analysis in which the kernel function is a priori restricted to a special class of test functions. We consider the class of finitely decomposable kernels. Stability conditions will be derived and compared with those obtained with the simple test equation. It turns out that the new criteria are more severe than the conventional conditions. The practical value is tested by numerical experiments with the trapezoidal rule.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02237819
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  • 5
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    Box schemes on quadrilateral meshes (1993)
    Springer
    Computing 51 (1993), S. 271-292 
    Details
    ISSN: 1436-5057
    Keywords: 65N15 ; 65N99 ; 35A40 ; Box method ; boundary value problem ; finite volume method ; variational formulation ; stability ; error bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Box-Methoden (Finite-Volumen-Methoden) sind verbreitete Verfahren zur Lösung physikalischer Erhaltungsgleichungen, insbesondere in der Strömungsmechanik. In dieser Arbeit werden zwei Methoden für elliptische Differentialgleichungen untersucht, die Diagonal-Boxen und die Schwerpunkt-Boxen. Da die Box-Methoden im Sinne von Petrov-Galerkin-Verfahren interpretiert werden können, erhält man vergleichbar zur Finiten-Element-Methode eine variationsrechnerische Stabilitäts- und Fehleranalyse. Damit werdenO(h)- undO(h 2)-Fehlerabschätzungen hergeleitet. Lokale Eigenwertprobleme führen zu Stabilitätsaussagen. Allerdings ergibt sich eine Abhängigkeit von der Anzahl und Art gestörter Vierecke. Insbesondere die Diagonal-Boxen sind anfällig für lokale Störungen.
    Notes: Abstract Box schemes (finite volume methods) are widely used in fluiddynamics, especially for the solution of conservation laws. In this paper two box-schemes for elliptic equations are analysed with respect to quadrilateral meshes. Using a variational formulation, we gain stability theorems for two different box methods, namely the so-called diagonal boxes and the centre boxes. The analysis is based on an elementwise eigenvalue problem. Stability can only be guaranteed under additional assumptions on the geometry of the quadrilaterals. For the diagonal boxes unsuitable elements can lead to global instabilities. The centre boxes are more robust and differ not so much from the finite element approach. In the stable case, convergence results up to second order are proved with well-known techniques.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238536
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  • 6
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    A note on stability investigations for Rosenbrock-type methods for quasilinear-implicit differential equations (1996)
    Springer
    Computing 56 (1996), S. 47-59 
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    ISSN: 1436-5057
    Keywords: 65 L 05 ; Rosenbrock-type methods ; quasilinear-implicit differential equations ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Bei der Lösung quasilinear-impliziter ODEs mittels Rosenbrock-Typ-Methoden können trotz guter Stabilitätseigenschaften (A- bzw. L-Stabilität) des Grundverfahrens Stabilitätsprobleme auftreten. Diese Schwierigkeiten sind auf Ungenauigkeiten bei der Berechnung künstlich eingeführter Komponenten (Überführung in DAEs) zurückzuführen. Die Arbeit untersucht die Ursachen für diese Effekte und zeigt Möglichkeiten, diese zu überwinden.
    Notes: Abstract The solution of quasilinear-implicit ODEs using Rosenbrock type methods may suffer from stability problems despite stability properties such as A-stability or L-stability, respectively. These problems are caused by inexact computation of artificial introduced components (transformation to DAE system). The paper investigates the source of the numerical difficulties and shows modifications to overcome them.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02238291
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  • 7
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    An analogue of the classical Yang-Baxter equation for general algebraic structures (1995)
    Springer
    Monatshefte für Mathematik 119 (1995), S. 327-346 
    Details
    ISSN: 1436-5081
    Keywords: Primary 81T08 ; Secondary 17B37 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we introduce an analogue of the classical Yang-Baxter equation for general algebraic structures (including nonassociative algebras and vertex operator algebras). Moreover, we give several ways to construct solutions of the equation in case the algebraic structure is graded by an abelian group. In particular, we construct some unitary nondegenerate trignometric solutions of the classical Yang-Baxter equation for affine Lie algebras by means of our equation.
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    URL: http://dx.doi.org/10.1007/BF01293592
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  • 8
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    Reachability of locational Nash equilibria (1998)
    Springer
    OR spectrum 20 (1998), S. 101-107 
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    ISSN: 1436-6304
    Keywords: Competitive location model ; Nash equilibria ; stability ; reachability ; Wettbewerbsmodelle in der Standorttheorie ; Nash Gleichgewicht ; Stabilität ; Erreichbarkeit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In der Arbeit werden die Standorte von Duopolisten in einem Baum untersucht. Unter der Annahme festgesetzter Preise werden notwendige und hinreichende Bedingungen für Nash Gleichgewichte für Standorte auf Bäumen hergeleitet. Unter Verwendung dieser Bedingungen wird dann gezeigt, daß — angenommen Nash Gleichgewichte existieren — diese in einem wiederholt angewandten sequentiellen Standortfindungsprozeß, in dem beide Duopolisten als Zielfunktion kurzfristige Gewinnmaximierung haben, auch erreicht werden.
    Notes: Abstract This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.
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    URL: http://dx.doi.org/10.1007/BF01539861
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  • 9
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    Reachability of locational Nash equilibria (1998)
    Springer
    OR spectrum 20 (1998), S. 101-107 
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    ISSN: 1436-6304
    Keywords: Key words: Competitive location model ; Nash equilibria ; stability ; reachability ; Schlüsselwörter: Wettbewerbsmodelle in der Standorttheorie ; Nash Gleichgewicht ; Stabilität ; Erreichbarkeit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. In der Arbeit werden die Standorte von Duopolisten in einem Baum untersucht. Unter der Annahme festgesetzter Preise werden notwendige und hinreichende Bedingungen für Nash Gleichgewichte für Standorte auf Bäumen hergeleitet. Unter Verwendung dieser Bedingungen wird dann gezeigt, daß– angenommen Nash Gleichgewichte existieren – diese in einem wiederholt angewandten sequentiellen Standortfindungsprozeß, in dem beide Duopolisten als Zielfunktion kurzfristige Gewinnmaximierung haben, auch erreicht werden. “Equilibrium is a place in heaven, but how do we get there from here?”
    Notes: Abstract. This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.
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    URL: http://dx.doi.org/10.1007/s002910050058
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  • 10
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    Stability results for approximately efficient solutions (1994)
    Springer
    OR spectrum 16 (1994), S. 47-52 
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    ISSN: 1436-6304
    Keywords: Vector optimization ; approximately efficient solutions ; stability ; Vektoroptimierung ; Näherungslösungen ; Stabilität
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir führen ein Konzept für Näherungslösungen in der Vektoroptimierung ein und vergleichen dieses mit einem neuen Konzept aus [8]. Weiterhin untersuchen wir Beziehungen zwischen der Menge der Näherungslösungen eines Vektoroptimierungsproblems und den Näherungslösungen eines entsprechenden parametrischen Ersatzproblems. Schließlich beweisen wir Stabilitätseigenschaften des skalaren Ersatzproblems.
    Notes: Abstract We introduce a concept for approximately efficient solutions in vector optimization and compare it with another recent concept given in [8]. Further, we study relations between the set of approximately efficient solutions of a vector optimization problem and the approximate solutions of a corresponding parametric surrogate optimization problem. Finally, we prove stability properties for the scalar surrogate problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01719703
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  • 11
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    Generalized linear complementarity in a problem ofn-person games (1996)
    Springer
    OR spectrum 18 (1996), S. 231-239 
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    ISSN: 1436-6304
    Keywords: Generalized polymatrix games ; generalized linear complementarity problem ; stability ; degree theory ; Verallgemeinerte Polymatrix-Spiele ; verallgemeinertes lineares Komplementaritätsproblem ; Stabilität ; Grad-Theorie
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit führen wir eine Verallgemeinerung des Polymatrix-Spiels (eines Nicht-Nullsummen- und nicht-kooperativenn-Personen-Spiels), das von Howson betrachtet wurde, ein und führen das Problem, eine Gleichgewichtsmenge von Strategien für ein solches Spiel zu berechnen, auf das verallgemeinerte lineare Komplementaritätsproblem von Cottle und Dantzig zurück. Für eine noch allgemeinere Version des Spiels beweisen wir die Existenz einerε-Gleichgewichtsmenge von Strategien. Wir präsentieren auch ein Ergebnis über die Stabilität der Gleichgewichte, das auf der Grad-Theorie beruht.
    Notes: Abstract In this paper, we introduce a generalization of the polymatrix game (a nonzero sum noncooperativen-person game) considered by Howson and relate the problem of computing an equilibrium set of strategies for such a game to the generalized linear complementarity problem of Cottle and Dantzig. For an even more general version of the game we prove the existence of anε-equilibrium set of strategies. We also present a result on the stability of the equilibria based on degree theory.
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    URL: http://dx.doi.org/10.1007/BF01540162
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  • 12
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    A bifurcation analysis of the nonlinear parametric programming problem (1990)
    Springer
    Mathematical programming 47 (1990), S. 117-141 
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    ISSN: 1436-4646
    Keywords: Bifurcation ; singularity ; parametric programming ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The structure of solutions to the nonlinear parametric programming problem with a one dimensional parameter is analyzed in terms of the bifurcation behavior of the curves of critical points and the persistence of minima along these curves. Changes in the structure of the solution occur at singularities of a nonlinear system of equations motivated by the Fritz John first-order necessary conditions. It has been shown that these singularities may be completely partitioned into seven distinct classes based upon the violation of one or more of the following: a complementarity condition, a constraint qualification, and the nonsingularity of the Hessian of the Lagrangian on a tangent space. To apply classical bifurcation techniques to these singularities, a further subdivision of each case is necessary. The structure of curves of critical points near singularities of lowest (zero) codimension within each case is analyzed, as well as the persistence of minima along curves emanating from these singularities. Bifurcation behavior is also investigated or discussed for many of the subcases giving rise to a codimension one singularity.
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    URL: http://dx.doi.org/10.1007/BF01580856
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  • 13
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    Characterization of stable matchings as extreme points of a polytope (1992)
    Springer
    Mathematical programming 54 (1992), S. 57-67 
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    ISSN: 1436-4646
    Keywords: Matchings ; stability ; extreme points ; polytope
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to extend a modified version of a recent result of Vande Vate (1989) which characterizes stable matchings as the extreme points of a certain polytope. Our proofs are simpler and more transparent than those of Vande Vate.
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    URL: http://dx.doi.org/10.1007/BF01586041
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  • 14
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    Quantitative stability of variational systems: III.ε-approximate solutions (1993)
    Springer
    Mathematical programming 61 (1993), S. 197-214 
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    ISSN: 1436-4646
    Keywords: Epi-convergence ; epi-distance ; stability ; convex optimization ; approximate solutions ; subgradients ; level sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We prove that theε-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that theε-subgradient mapping is Lipschitz continuous.
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    URL: http://dx.doi.org/10.1007/BF01582147
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  • 15
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    The spectral accuracy of a fully-discrete scheme for a nonlinear third order equation (1990)
    Springer
    Computing 44 (1990), S. 187-196 
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    ISSN: 1436-5057
    Keywords: 65M10 ; Spectral method ; stability ; stability threshold
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Zur numerischen Lösung einer nichtlinearen Differentialgleichung dritter Ordnung, herrührend aus einem Strömungsproblem bei Gasteilchen, wird ein zeitdiskreter Pseudo-spektral-Algorithmus vorgeschlagen. Stabilität und Konvergenz des neuen Differenzenverfahrens werden analysiert. Numerische Vergleiche mit bestehenden Differenzenschemata sprechen klar zugunsten des neuen Verfahrens.
    Notes: Abstract A time-discrete pseudospectral algorithm is suggested for the numerical solution of a nonlinear third order equation arising in fluidization. The nonlinear stability and convergence of the new scheme are analyzed. Numerical comparisons with available finite-difference methods are also reported which clearly indicate the superiority of the new scheme.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02262215
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  • 16
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    Second-order explicit characteristic difference schemes for quasilinear hyperbolic systems (1985)
    Springer
    Computing 35 (1985), S. 85-91 
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    ISSN: 1436-5057
    Keywords: 65M05 ; 65M10 ; 65M25 ; Second order ; characteristic difference schemes ; quasilinear hyperbolic systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir stellen ein Charakteristikenverfahren zweiter Ordnung für die numerische Lösung der Anfangswertaufgabe von quasilinearen hyperbolischen Systemen vor und beweisen die Stabilität des Verfahrens für Systeme mit konstanten Koeffizienten.
    Notes: Abstract We present two-step, second-order explicit characteristic difference schemes for the numerical solution of initialvalue problems for quasilinear hyperbolic system and show that the method is stable for systems with constant coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02240149
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  • 17
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    Nichtlineare Stabilität und Phasenuntersuchung adaptiver Nyström-Runge-Kutta-Methoden (1985)
    Springer
    Computing 35 (1985), S. 325-344 
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    ISSN: 1436-5057
    Keywords: 65L05 ; Numerical analysis ; Nyström methods ; stiff problems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The stability of adaptive Nyström-Runge-Kutta procedures is studied for a wide class of nonlinear stiff systems of second order differential equations. We show that for a large class of semi-discrete hyperbolic and parabolic problems the restriction of the stepsize is not due to the stiffness of the differential equation. Furthermore we use the scalar test equation $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ to derive conditions which ensure that the numerical forced oscillation is in phase with the analytical forced oscillation. The order of adaptive Nyström-Runge-Kutta methods (with a stability-matrix based on a diagonal Padéapproximation) for which the forced oscillation is in phase with its analytical counterpart cannot be greater than two. This barrier of order is not true forr-stage implicit Nyström methods of orderp=2r.
    Notes: Zusammenfassung Für eine umfangreiche Klasse nichtlinearer steifer Differentialgleichungssysteme zweiter Ordnung wird die Stabilität adaptiver Nyström-Runge-Kutta-Verfahren untersucht. Wir zeigen, daß für eine große Klasse semidiskretisierter hyperbolischer und parabolischer Probleme die Restriktion der Schrittweite unabhängig von der Steifheit des Differentialgleichungssystems ist. Weiterhin verwenden wir die skalare Testgleichung $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ und geben Bedingungen dafür an, daß die numerische erzwungene Schwingung mit der analytischen erzwungenen Schwingung in Phase ist. Die Konsistenzordnung adaptiver Nyström-Runge-Kutta-Verfahren (mit einer Stabilitätsmatrix, die auf einer diagnolen Padé-Approximation beruht), für die die erzwungene Schwingung mit ihrem analytischen Gegenstück in Phase ist, kann nicht größer als zwei sein. Diese Ordnungsbarriere gilt nicht fürr-stufige implizite Nyström-Methoden der Ordnungp=2r.
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    URL: http://dx.doi.org/10.1007/BF02240198
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  • 18
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    The dynamics of coupled planar rigid bodies. II. Bifurcations, periodic solutions, and chaos (1989)
    Springer
    Journal of dynamics and differential equations 1 (1989), S. 269-298 
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    ISSN: 1572-9222
    Keywords: Geometric mechanics ; reduction ; stability ; chaos ; rigid body dynamics ; periodic orbits ; 58F
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.
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    URL: http://dx.doi.org/10.1007/BF01053929
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  • 19
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    Stability and Instability of Fourth-Order Solitary Waves (1998)
    Springer
    Journal of dynamics and differential equations 10 (1998), S. 151-188 
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    ISSN: 1572-9222
    Keywords: Fourth-order solitary waves ; stability ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study ground-state traveling wave solutions of a fourth-order wave equation. We find conditions on the speed of the waves which imply stability and instability of the solitary waves. The analysis depends on the variational characterization of the ground states rather than information about the linearized operator.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022644629950
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  • 20
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    Linear stability of relative equilibria with a dominant mass (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 37-51 
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    ISSN: 1572-9222
    Keywords: Celestial mechanics ; relative equilibria ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A criterion for the linear stability of relative equilibria of the Newtoniann-body problem is found in the case whenn−1 of the masses are small. Several stable periodic orbits of the problem are presented as examples.
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    URL: http://dx.doi.org/10.1007/BF02219187
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  • 21
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    Interval stability and interval covering property in finite posets (1992)
    Springer
    Order 9 (1992), S. 163-175 
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    ISSN: 1572-9273
    Keywords: Primary 06A07 ; secondary 05C70 ; Partial order ; interval ; stability ; covering ; Sperner property ; symmetric chains ; NP-completeness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a finite ranked posetP, let α(P) be the maximum size of a subset ofP such that no two elements of it belong simultaneously to some interval ofP and let ϱ(P) be the minimum number of intervals covering all elements ofP. We say thatP has the strong interval stability property (resp. the strong interval covering property) if for each subposetP′ induced by consecutive levels ofP, i.e.,P′=P (l)∪...∪P (u), one has α(P′)=max{|P (l)|, |P (u)|} (resp. ϱ(P′)=max{|P (l)|, |P (u)|}). We prove these properties for several classes of posets and discuss some general facts concerning the numbers α(P) and ϱ(P), e.g., NP-completeness and min-max relations.
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    URL: http://dx.doi.org/10.1007/BF00814408
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    Stability of Semilinear Delay Equations with Positive Solutions (1997)
    Springer
    Positivity 1 (1997), S. 319-330 
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    ISSN: 1572-9281
    Keywords: delay equations ; stability ; positive solutions ; spectral growth condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove stability for a semilinear delay equation, whose nonlinearity is majorized by a linear positive operator. The key ingredients are a spectral condition, positivity of solutions to the linear problem, and lattice properties of the Banach space.
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    URL: http://dx.doi.org/10.1023/A:1009725823213
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    Some Results on Stability of Retarded Functional Differential Equations Using Dichotomic Map Techniques (1998)
    Springer
    Positivity 2 (1998), S. 229-238 
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    ISSN: 1572-9281
    Keywords: asymptotic stability ; dichotomic maps ; retarded functional differential equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation $$x'(t) = - b(t)x(t - r)$$ and of itsnonlinear generalization $$x'(t) = b(t)f(x(t - r))$$ are established.
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    URL: http://dx.doi.org/10.1023/A:1009742807025
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    Stationary waiting time derivatives (1992)
    Springer
    Queueing systems 12 (1992), S. 369-389 
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    ISSN: 1572-9443
    Keywords: Perturbation analysis ; stability ; stochastic difference equations ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We investigate the stability of waiting-time derivatives when inputs to a queueing system-service times and interarrival times-depend on a parameter. We give conditions under which the sequence of waiting-time derivatives admits a stationary distribution, and under which the derivatives converge to the stationary regime from all initial conditions. Further hypotheses ensure that the expectation of a stationary waiting-time derivative is, in fact, the derivative of the expected stationary waiting time. This validates the use of simulation-based infinitesimal perturbation analysis estimates with a variety of queueing processes. We examine waiting-time sequences satisfying recursive equations. Our basic assumption is that the input and its derivatives are stationary and ergodic. Under monotonicity conditions, the method of Loynes establishes the convergence of the derivatives. Even without such conditions, the derivatives obey a linear difference equation with random coefficients, and we exploit this fact to find stability conditions.
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    URL: http://dx.doi.org/10.1007/BF01158809
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    Re-entrant lines (1993)
    Springer
    Queueing systems 13 (1993), S. 87-110 
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    ISSN: 1572-9443
    Keywords: Manufacturing systems ; semiconductor manufacturing ; thin film lines ; re-entrant lines ; scheduling policies ; queueing networks ; buffer priority policies ; due date policies ; stability ; stochastic control ; mean delay ; variance of delay ; machine failures ; set-up times
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Traditionally, manufacturing systems have mainly been treated as either job shops or flow shops. In job shops, parts may arrive with random routes, with each route having a low volume. In flow shops, the routes are fixed and acyclic, as in assembly lines. With the advent of semiconductor manufacturing plants, and more recently, thin film lines, this dichotomy needs to be expanded to consider another class of systems, which we call “re-entrant lines”. The distinguishing feature of these manufacturing systems is that parts visit some machines more than once at different stages of processing. Scheduling problems arise because several parts at different stages of processing may be in contention with each other for service at the same machine. There may be uncertainties in the form of random service or set-up times, as well as random machine failures and repairs. The goal of scheduling is to improve performance measures such as mean sojourn time in the system, which is also known as the mean “cycle-time”, or the variance of the cycle-time. In this paper we provide a tutorial account of some recent results in this field. We describe several scheduling policies of interest, and provide some results concerning their stability and performance. Several open problems are suggested.
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    URL: http://dx.doi.org/10.1007/BF01158930
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    On pathwise behavior of multiserver queues (1994)
    Springer
    Queueing systems 15 (1994), S. 279-288 
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    ISSN: 1572-9443
    Keywords: Sample-path ; point processes ; workload ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper, by exploiting recent results on the pathwise behavior of the workload process in single server, work conserving queues of theG/G/1/∞ type, we show that the workload of multiserver, work conserving queues ofG/G/m/∞ (m〈∞) (andG/G/∞) queues satisfies an o(t) growth condition, provided that the time average of the work brought into the system is less thanm form 〈 ∞ (and finite form=∞).
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    URL: http://dx.doi.org/10.1007/BF01189241
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    Stability of non-Markovian polling systems (1995)
    Springer
    Queueing systems 21 (1995), S. 67-95 
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    ISSN: 1572-9443
    Keywords: Polling systems ; stability ; stationary regime
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A stationary regime for polling systems with general ergodic (G/G) arrival processes at each station is constructed. Mutual independence of the arrival processes is not required. It is shown that the stationary workload so constructed is minimal in the stochastic ordering sense. In the model considered the server switches from station to station in a Markovian fashion, and a specific service policy is applied to each queue. Our hypotheses cover the purely gated, thea-limited, the binomial-gated and other policies. As a by-product we obtain sufficient conditions for the stationary regime of aG/G/1/∞ queue with multiple server vacations (see Doshi [11]) to be ergodic.
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    URL: http://dx.doi.org/10.1007/BF01158575
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    Pathwise rate- stability for input-output processes (1996)
    Springer
    Queueing systems 22 (1996), S. 47-63 
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    ISSN: 1572-9443
    Keywords: Sample-path analysis ; stability ; rate stability ; ω-rate stability ; input-output process ; queueing ; infinite-server queues
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract An input-output processZ = {Z(t), t ⩾ 0} is said to beω-rate stable ifZ(t) = o(ω(t)) for some non-negative functionω(t). We prove that the processZ is ω-rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions forω-rate-stability can be verified from input data. For example, using input information, we establishω-rate stability of the workload for multiserver queues, an ATM multiplexer, andω-rate stability of queue-length processes for infinite server queues.
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    URL: http://dx.doi.org/10.1007/BF01159392
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    On Whitt's conjecture for queues in which service times and interarrival times depend linearly and randomly upon waiting times (1996)
    Springer
    Queueing systems 22 (1996), S. 345-366 
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    ISSN: 1572-9443
    Keywords: State-dependent service and interarrival times ; Lindley equation ; recursive stochastic equations ; stability ; normal approximations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a modification of the standardG/G/1 queueing system with infinite waiting space and the first-in-first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. When the waiting-time distributions converge to a proper limit, Whitt [10] proposed a normal approximation for this steady-state limit. In this paper we prove a limit theorem for the steady-state limit of the system. Thus, our result provides a solid foundation for Whitt's normal approximation of the steady-state distribution of the system.
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    URL: http://dx.doi.org/10.1007/BF01149178
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    On the stability of a partially accessible multi‐station queue with state‐dependent routing (1998)
    Springer
    Queueing systems 29 (1998), S. 55-73 
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    ISSN: 1572-9443
    Keywords: multi‐server queue ; customer class ; state‐dependent routing ; stability ; Markov chain ; fluid limit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a multi‐station queue with a multi‐class input process when any station is available for the service of only some (not all) customer classes. Upon arrival, any customer may choose one of its accessible stations according to some state‐dependent policy. We obtain simple stability criteria for this model in two particular cases when service rates are either station‐ or class‐independent. Then, we study a two‐station queue under general assumptions on service rates. Our proofs are based on the fluid approximation approach.
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    A stability criterion via fluid limits and its application to a polling system (1999)
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    Queueing systems 32 (1999), S. 131-168 
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    ISSN: 1572-9443
    Keywords: stability ; positive recurrence ; fluid limit ; polling system ; exhaustive service policy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We introduce a generalized criterion for the stability of Markovian queueing systems in terms of stochastic fluid limits. We consider an example in which this criterion may be applied: a polling system with two stations and two heterogeneous servers.
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    URL: http://dx.doi.org/10.1023/A:1019187004209
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    Performance analysis of a slotted-ALOHA protocol on a capture channel with fading (2000)
    Springer
    Queueing systems 34 (2000), S. 1-35 
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    ISSN: 1572-9443
    Keywords: multiple access ; CDMA ; rates of convergence ; stability ; functional limit theorems ; transient analysis ; Markov-modulated capture channel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider the slotted ALOHA protocol on a channel with a capture effect. There are M 〈 ∞ users each with an infinite buffer. If in a slot, i packets are transmitted, then the probability of a successful reception of a packet is q i. This model contains the CDMA protocols as special cases. We obtain sufficient rate conditions, which are close to necessary for stability of the system, when the arrival streams are stationary ergodic. Under the same rate conditions, for general regenerative arrival streams, we obtain the rates of convergence to stationarity, finiteness of stationary moments and various functional limit theorems. Our arrival streams contain all the traffic models suggested in the recent literature, including the ones which display long range dependence. We also obtain bounds on the stationary moments of waiting times which can be tight under realistic conditions. Finally, we obtain several results on the transient performance of the system, e.g., first time to overflow and the limits of the overflow process. We also extend the above results to the case of a capture channel exhibiting Markov modulated fading. Most of our results and proofs will be shown to hold also for the slotted ALOHA protocol without capture.
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    URL: http://dx.doi.org/10.1023/A:1019192600091
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    Stability and continuity of polling systems (1994)
    Springer
    Queueing systems 16 (1994), S. 115-137 
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    ISSN: 1572-9443
    Keywords: Polling systems ; stability ; stochastic continuity ; general arrival process ; functional limit theorems.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The stability of a polling system with exhaustive service and a finite number of users, each with infinite buffers is considered. The arrival process is more general than a Poisson process and the system is not slotted. Stochastic continuity of the stationary distributions, rates of convergence and functional limit theorems for the queue length and waiting time processes have also been proved. The results extend to the gated service discipline.
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    A New ADI Scheme for Solving Three-Dimensional Parabolic Equations with First-Order Derivatives and Variable Coefficients (2000)
    Springer
    Journal of computational analysis and applications 2 (2000), S. 293-308 
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    ISSN: 1572-9206
    Keywords: parabolic equations ; ADI scheme ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An ADI scheme for solving three-dimensional parabolic equations withfirst-order derivatives and variable coefficients has been developed basedon our previous papers and the idea of the modified upwind differencescheme. This ADI scheme is second-order accurate and unconditionallystable. Further, a small parameter can be chosen which makes it suitablefor simulating fast-transient phenomena or for computations on fine spatialmeshes. The method is illustrated with numerical examples.
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    Stability characteristics of transition layer solutions (1993)
    Springer
    Journal of dynamics and differential equations 5 (1993), S. 625-671 
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    ISSN: 1572-9222
    Keywords: Scalar reaction-diffusion equation ; singular perturbation methods ; internal layer ; Neumann layer ; stability ; 35K57 ; 35B25 ; 35B35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The multiple existences and their stability properties of stationary solutions with a single transition layer in some scalar reaction-diffusion equation are shown. Each solution is constructed by using classical singular perturbation methods and its stability property is determined by a simple algebraic quantity, say index, appearing in the construction of a solution.
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    URL: http://dx.doi.org/10.1007/BF01049142
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    Symmetrization properties of parabolic equations in symmetric domains (1994)
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    Journal of dynamics and differential equations 6 (1994), S. 639-658 
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    ISSN: 1572-9222
    Keywords: Symmetry ; parabolic equations ; positive solutions ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Symmetry properties of positive solutions of a Dirichlet problem for a strongly nonlinear parabolic partial differential equation in a symmetric domainD ⊂ R n are considered. It is assumed that the domainD and the equation are invariant with respect to a group {Q} of transformations ofD. In examples {Q} consists of reflections or rotations. The main result of the paper is the theorem which states that any compact inC(D) negatively invariant set which consists of positive functions consists ofQ-symmetric functions. Examples of negatively invariant sets are (in autonomous case) equilibrium points, omega-limit sets, alpha-limit sets, unstable sets of invariant sets, and global attractors. Application of the main theorem to equilibrium points gives the Gidas-Ni-Nirenberg theorem. Applying the theorem to omega-limit sets, we obtain the asymptotical symmetrization property. That means that a bounded solutionu(t) asr→∞ approaches subspace of symmetric functions. One more result concerns properties of eigenfunctions of linearizations of the equations at positive equilibrium points. It is proved that all unstable eigenfunctions are symmetric.
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    Stability-Like Properties of Differential Inclusions (1997)
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    Set-valued analysis 5 (1997), S. 73-88 
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    ISSN: 1572-932X
    Keywords: differential inclusion ; invariance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The properties of invariance, stability, asymptotic stability and attainability of a given compact set $$K \subset \mathbb{R}^n $$ with respect to a differential inclusion, have weak and strong versions: the weak version requires existence of a trajectory with the corresponding property, while the strong one requires this property for all trajectories. The following statement is proven in the paper (under slight restrictions) for each of the above-mentioned properties: if K has the weak property with respect to $$\dot x \in F(x) $$ , then there is a (regulation) mapping G such that G(x) ⊂ F(x) ∀ x and G has the strong property with respect to $${\dot x}$$ ε G(x). In addition, certain regularity of the set of solutions of the last inclusion is claimed.
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    Optimization and Stability Results Through Cone Lower Semicontinuity (1997)
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    Set-valued analysis 5 (1997), S. 365-375 
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    ISSN: 1572-932X
    Keywords: set-valued mappings ; vector optimization ; stability
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    Topics: Mathematics
    Notes: Abstract We establish optimization results for set-valued mappings, with the image space given by a topological vector space partially ordered by a cone. Moreover, we obtain stability results relative to parametrized optimization problems. We use a weak semicontinuity concept related to the order structure of the image space and show how compactness assumptions used in previous papers can be lightened.
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    Bifurcations in parametric nonlinear programming (1990)
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    Annals of operations research 27 (1990), S. 343-369 
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    ISSN: 1572-9338
    Keywords: Bifurcation ; singularities ; continuation ; parametric nonlinear programming ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Bifurcation and continuation techniques are introduced as a class of methods for investigating the parametric nonlinear programming problem. Motivated by the Fritz John first-order necessary conditions, the parametric programming problem is first reformulated as a closed system of nonlinear equations which contains all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points. Since changes in the structure of the solution set and critical point type can occur only at singularities, necessary and sufficient conditions for the existence of a singularity are developed in terms of the loss of a complementarity condition, the linear dependence constraint qualification, and the singularity of the Hessian of the Lagrangian on a tangent space. After a brief introduction to elementary bifurcation theory, some simple singularities in this parametric problem are analyzed for both branching and persistence of local minima. Finally, a brief introduction to numerical continuation and bifurcation procedures is given to indicate how these facts can be used in a numerical investigation of the problem.
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    Stability in multistage stochastic programming (1995)
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    Annals of operations research 56 (1995), S. 79-93 
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    ISSN: 1572-9338
    Keywords: Multistage stochastic programs ; optimization in Banach spaces ; stability ; approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Multistage stochastic programs are regarded as mathematical programs in a Banach spaceX of summable functions. Relying on a result for parametric programs in Banach spaces, the paper presents conditions under which linearly constrained convex multistage problems behave stably when the (input) data process is subjected to (small) perturbations. In particular, we show the persistence of optimal solutions, the local Lipschitz continuity of the optimal value and the upper semicontinuity of optimal sets with respect to the weak topology inX. The linear case with deterministic first-stage decisions is studied in more detail.
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    The Stability of Self-Organized Rule-Following Work Teams (1999)
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    Computational & mathematical organization theory 5 (1999), S. 5-30 
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    ISSN: 1572-9346
    Keywords: network models ; organization theory ; rule following ; self organized ; stability ; work teams ; work routine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Self-organized rule-following systems are increasingly relevant objects of study in organization theory due to such systems&2018; capacity to maintain control while enabling decentralization of authority. This paper proposes a network model for such systems and examines the stability of the networks&2018; repetitive behavior. The networks examined are Ashby nets, a fundamental class of binary systems: connected aggregates of nodes that individually compute an interaction rule, a binary function of their three inputs. The nodes, which we interpret as workers in a work team, have two network inputs and one self-input. All workers in a given team follow the same interaction rule. We operationalize the notion of stability of the team&2018;s work routine and determine stability under small perturbations for all possible rules these teams can follow. To study the organizational concomitants of stability, we characterize the rules by their memory, fluency, homogeneity, and autonomy. We relate these measures to work routine stability, and find that stability in ten member teams is enhanced by rules that have low memory, high homogeneity, and low autonomy.
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    Open queueing networks in discrete time-some limit theorems (1993)
    Springer
    Queueing systems 14 (1993), S. 159-175 
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    ISSN: 1572-9443
    Keywords: Queueing networks ; nonproduct form networks ; stability ; stochastic continuity ; functional limit theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A finite number of nodes, each with a single server and infinite buffers, is considered in discrete time. The service may be FIFO and the service times are constant. The external arrivals and the routing decision variables form a general stationary sequence. Stability of the system is proved under these assumptions. Extension to multiple servers at a node and general stationary distributions holds. If the external input is i.i.d. and the routing is Markovian then stochastic ordering, continuity of stationary distributions, rates of convergence, a functional CLT and a functional LIL and various other limit theorems for the queue length process are also proved. Generalizations to multiple servers at nodes, customers with priority, multiple customer classes, general service length and Markov modulated external arrival cases are discussed.
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    Monotonicity and stability of periodic polling models (1994)
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    Queueing systems 15 (1994), S. 211-238 
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    ISSN: 1572-9443
    Keywords: polling system ; stability ; Markov chain ; stochastic monotonicity ; heavy traffic ; nonpreemptive local priority
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper deals with the stability of periodic polling models with a mixture of service policies. Customers arrive according to independent Poisson processes. The service times and the switchover times are independent with general distributions. The necessary and sufficient condition for the stability of such polling systems is established. The proof is based on the stochastic monotonicity of the state process at the polling instants. The stability of only a subset of the queues is also analyzed and, in case of heavy traffic, the order of explosion of the queues is given. The results are valid for a model with set-up times, and also when there is a local priority rule at the queues.
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    Single-server queues with spatially distributed arrivals (1994)
    Springer
    Queueing systems 17 (1994), S. 317-345 
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    ISSN: 1572-9443
    Keywords: Single-server queue ; spatially distributed arrival points ; travelling server ; Brownian motion ; embedded Markov chain ; stability ; Tweedie's lemma ; regenerative processes ; stochastic decomposition ; equilibrium equations ; mean queue length
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.
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    Piecewise linear test functions for stability and instability of queueing networks (1997)
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    Queueing systems 27 (1997), S. 205-226 
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    ISSN: 1572-9443
    Keywords: multiclass queueing networks ; ergodicity ; stability ; performance analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We develop the use of piecewise linear test functions for the analysis of stability of multiclass queueing networks and their associated fluid limit models. It is found that if an associated LP admits a positive solution, then a Lyapunov function exists. This implies that the fluid limit model is stable and hence that the network model is positive Harris recurrent with a finite polynomial moment. Also, it is found that if a particular LP admits a solution, then the network model is transient.
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    On the guaranteed throughput and efficiency of closed re-entrant lines (1998)
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    Queueing systems 28 (1998), S. 33-54 
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    ISSN: 1572-9443
    Keywords: queueing networks ; throughput ; closed networks ; efficiency ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A closed network is said to be “guaranteed efficient” if the throughput converges under all non-idling policies to the capacity of the bottlenecks in the network, as the number of trapped customers increases to infinity. We obtain a necessary condition for guaranteed efficiency of closed re-entrant lines. For balanced two-station systems, this necessary condition is almost sufficient, differing from it only by the strictness of an inequality. This near characterization is obtained by studying a special type of virtual station called “alternating visit virtual station”. These special virtual stations allow us to relate the necessary condition to certain indices arising in heavy traffic studies using a Brownian network approximation, as well as to certain policies proposed as being extremal with respect to the asymptotic loss in the throughput. Using the near characterization of guaranteed efficiency we also answer the often pondered question of whether an open network or its closed counterpart has greater throughput - the answer is that neither can assure a greater guaranteed throughput.
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    URL: http://dx.doi.org/10.1023/A:1019199022922
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    Stability of token passing rings (1992)
    Springer
    Queueing systems 11 (1992), S. 7-33 
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    ISSN: 1572-9443
    Keywords: Token passing rings ; stability ; substability ; ergodicity ; Markov chains ; Loynes' scheme ; stochastically dominant ; Little's formula ; regenerative processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A sufficient stability condition for the standard token passing ring has been “known” since the seminal paper by Kuehn in 1979. However, this condition was derived without formal proof, and the proof seems to be of considerable interest to the research community. In fact, Watson observed that in the performance evaluation of token passing rings, “it is convenient to derive stability conditions ... (without proof)”. Our intention is to fill this gap, and to provide a formal proof of thesufficient and necessary stability condition for the token passing ring. In this paper, we present the case when the arrival process to each queue is Poisson but service times and switchover times are generally distributed. We consider in depth a gatedl-limited (l≤ ∞) service discipline for each station. We also indicate that the basic steps of our technique can be used to study the stability of some other multiqueue systems.
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    URL: http://dx.doi.org/10.1007/BF01159285
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    Stability of a three‐station fluid network (1999)
    Springer
    Queueing systems 33 (1999), S. 293-325 
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    ISSN: 1572-9443
    Keywords: stability ; fluid models ; multiclass queueing networks ; piecewise linear Lyapunov functions ; linear Lyapunov functions ; monotone global stability ; static buffer priority disciplines
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    Topics: Computer Science
    Notes: Abstract This paper studies the stability of a three‐station fluid network. We show that, unlike the two‐station networks in Dai and Vande Vate [18], the global stability region of our three‐station network is not the intersection of its stability regions under static buffer priority disciplines. Thus, the “worst” or extremal disciplines are not static buffer priority disciplines. We also prove that the global stability region of our three‐station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three‐station network. We also show that the LP proposed by Bertsimas et al. [1] does not characterize either the global stability region or even the monotone global stability region of our three‐station network. Further, we demonstrate that the LP related to the linear Lyapunov function proposed by Chen and Zhang [11] does not characterize the stability region of our three‐station network under a static buffer priority discipline.
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    URL: http://dx.doi.org/10.1023/A:1019184331042
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    A Multiclass Feedback Queueing Network with a Regular Skorokhod Problem (2000)
    Springer
    Queueing systems 36 (2000), S. 327-349 
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    ISSN: 1572-9443
    Keywords: multiclass networks ; networks with feedback ; Skorokhod Problem ; Skorokhod Mapping ; Lipschitz continuity ; stability ; load conditions
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    Topics: Computer Science
    Notes: Abstract We consider a four-class two-station network with feedback, with fluid inputs and a head-of-the-line generalized processor sharing discipline at each station. We derive the Skorokhod Problem associated with the network and obtain algebraic sufficient conditions for Lipschitz continuity of the associated Skorokhod Map. This provides the first example of a multiclass network with feedback for which the associated Skorokhod Problem has been proved to be regular. As an elementary application, we show that under the conditions which guarantee Lipschitz continuity the network is stable if and only if the usual load conditions apply.
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    URL: http://dx.doi.org/10.1023/A:1011037419624
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    Bifurcation Phenomena from Standing Pulse Solutions in Some Reaction-Diffusion Systems (2000)
    Springer
    Journal of dynamics and differential equations 12 (2000), S. 117-167 
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    ISSN: 1572-9222
    Keywords: singular perturbation ; standing pulses ; stability ; Hopf bifurcation ; reaction-diffusion system
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    Topics: Mathematics
    Notes: Abstract Bifurcation phenomena from standing pulse solutions of the problem $$\varepsilon \tau u_t = \varepsilon ^2 u_{xx} + f(u,v),{\text{ }}v_t = v_{xx} + g(u,v)$$ is considered. ε(〉0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g.
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    URL: http://dx.doi.org/10.1023/A:1009098719440
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    Equivariant multiparameter bifurcation via singularity theory (1993)
    Springer
    Journal of dynamics and differential equations 5 (1993), S. 189-218 
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    ISSN: 1572-9222
    Keywords: Equivariant bifurcation ; symmetry ; singularity ; equivariant jets and transversality ; normal forms ; universal unfolding ; stability ; structural stability ; 58F14 ; 58E07 ; 58C27
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    Topics: Mathematics
    Notes: Abstract The theoretical machinery from singularity theory introduced by Golubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problems, is completed and expanded while generalized to the multiple parameter context. In this setting the finite determinacy theorems or normal forms, the stability of equivariant bifurcation problems, and the structural stability of the universal unfolding are discussed.
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    URL: http://dx.doi.org/10.1007/BF01053160
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    A free boundary problem modeling thermal instabilities: Stability and bifurcation (1994)
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    Journal of dynamics and differential equations 6 (1994), S. 447-486 
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    ISSN: 1572-9222
    Keywords: Free boundary problems ; gasless combustion ; stability ; Hopf bifurcation ; 35R35 ; 35B40 ; 80A25
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    Topics: Mathematics
    Notes: Abstract In this paper, we analyze a simple free boundary model associated with solid combustion and some phase transition processes. There is strong evidence that this “one-phase” model captures all major features of dynamical behavior of more realistic (and complicated) combustion and phase transition models. The principal results concern the dynamical behavior of the model as a bifurcation parameter (which is related to the activation energy in the case of combustion) varies. We prove that the basic uniform front propagation is asymptotically stable against perturbations for the bifurcation parameter above the instability threshold and that a Hopf bifurcation takes place at the threshold value. Results of numerical simulations are presented which confirm that both supercritical and subcritical Hofp bifurcation may occur for physically reasonable nonlinear kinetic functions.
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    Discrete time semigroup transformations with random perturbations (1997)
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    Journal of dynamics and differential equations 9 (1997), S. 463-505 
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    ISSN: 1572-9222
    Keywords: Difference equations ; random perturbation ; averaging ; diffusion approximation ; randomly perturbed iterations ; stability ; 3SR60 ; 60H15 ; 60J99
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    Topics: Mathematics
    Notes: Abstract Let (X, ℬ) and (Y,C) be two measurable spaces withX being a linear space. A system is determined by two functionsf(X): X→ X andϕ:X×Y→X, a (small) positive parameterε and a homogeneous Markov chain {y n } in (Y,C) which describes random perturbations. States of the system, say {x n ɛ ∈X, n=0, 1,⋯}, are determined by the iteration relations:x n+1 ɛ =f(x n ɛ )+ɛϕ(x n ɛ ,Yn+1) forn≥0, wherex 0 ɛ =x 0 is given. Here we study the asymptotic behavior of the solutionx n ɛ asε → 0 andn → ∞ under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.
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    On Stability and Boundedness for Lipschitzian Differential Inclusions: The Converse of Lyapunov's Theorems (1997)
    Springer
    Set-valued analysis 5 (1997), S. 377-390 
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    ISSN: 1572-932X
    Keywords: differential inclusions ; stability ; boundedness of solutions ; Lyapunov functions
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    Topics: Mathematics
    Notes: Abstract For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions.
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    URL: http://dx.doi.org/10.1023/A:1008603707291
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    Singularly perturbed differential inclusions: An averaging approach (1996)
    Springer
    Set-valued analysis 4 (1996), S. 361-374 
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    ISSN: 1572-932X
    Keywords: 34A60 ; 34E15 ; 34C29 ; differential inclusion ; singular perturbation ; averaging method ; controlability ; stability
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    Notes: Abstract We consider nonlinear, singularly perturbed differential inclusions and apply the averaging method in order to construct a limit differential inclusion for slow motion. The main approximation result states that the existence and regularity of the limit differential inclusion suffice to describe the limit behavior of the slow motion. We give explicit approximation rates for the uniform convergence on compact time intervals. The approach works under controllability or stability properties of fast motion.
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    Implicit Multifunction Theorems (1999)
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    Set-valued analysis 7 (1999), S. 209-238 
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    ISSN: 1572-932X
    Keywords: nonsmooth analysis ; subdifferentials ; coderivatives ; implicit function theorem ; solvability ; stability ; open mapping theorem ; metric regularity ; multidirectional mean value inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.
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    Perturbed unstable variational inequalities with unbounded operators on approximately given sets (1993)
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    Set-valued analysis 1 (1993), S. 393-402 
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    ISSN: 1572-932X
    Keywords: Primary: 49J40, 65K10, 47A55, 47H05, 65L20 ; Variational inequality ; perturbation ; unbounded and nonsmooth operators ; convex sets ; Hausdorff distance ; regularization ; monotonicity ; convergence ; stability
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains Ω are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.
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    Stability and performance analysis of rate-based feedback flow controlled ATM networks (1998)
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    Queueing systems 29 (1998), S. 129-159 
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    ISSN: 1572-9443
    Keywords: rate-based feedback control ; ATM networks ; stability ; optimal algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Motivated by ABR class of service in ATM networks, we study a continuous time queueing system with a feedback control of the arrival rate of some of the sources. The feedback about the queue length or the total workload is provided at regular intervals (variations on it, especially the traffic management specification TM 4.0, are also considered). The propagation delays can be nonnegligible. For a general class of feedback algorithms, we obtain the stability of the system in the presence of one or more bottleneck nodes in the virtual circuit. Our system is general enough that it can be useful to study feedback control in other network protocols. We also obtain rates of convergence to the stationary distributions and finiteness of moments. For the single botterneck case, we provide algorithms to compute the stationary distributions and the moments of the sojourn times in different sets of states. We also show analytically (by showing continuity of stationary distributions and moments) that for small propagation delays, we can provide feedback algorithms which have higher mean throughput, lower probability of overflow and lower delay jitter than any open loop policy. Finally these results are supplemented by some computational results.
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    Dynamic scheduling in multiclass queueing networks: Stability under discrete-review policies (1999)
    Springer
    Queueing systems 31 (1999), S. 171-206 
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    ISSN: 1572-9443
    Keywords: scheduling ; open multiclass queueing networks ; discrete-review policies ; fluid models ; stability
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    Topics: Computer Science
    Notes: Abstract This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value r k (q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable. In such a policy, system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed. Stability is proved by combining elementary large deviations theory with an analysis of an associated fluid control problem. These results are extended to systems with class dependent setup times as well as systems with alternate routing and admission control capabilities.
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    Queues with service times and interarrival times depending linearly and randomly upon waiting times (1990)
    Springer
    Queueing systems 6 (1990), S. 335-351 
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    ISSN: 1572-9443
    Keywords: State-dependent service and interarrival times ; Lindley equation ; recursive stochastic equations ; stability ; stochastic comparisons ; normal approximations ; scheduling arrivals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a modification of the standardG/G/1 queue with unlimited waiting space and the first-in first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. We determine when the waiting-time distributions converge to a proper limit and we develop approximations for this steady-state limit, primarily by applying previous results of Vervaat [21] and Brandt [4] for the unrestricted recursionY n+1=C n Y n +X n . Particularly appealing for applications is a normal approximation for the stationary waiting time distribution in the case when the queue only rarely becomes empty. We also consider the problem of scheduling successive interarrival times at arrival epochs, with the objective of achieving nearly maximal throughput with nearly bounded waiting times, while making the interarrival time sequence relatively smooth. We identify policies depending linearly and deterministically upon the work in the system which meet these objectives reasonably well; with these policies the waiting times are approximately contained in a specified interval a specified fraction of time.
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    URL: http://dx.doi.org/10.1007/BF02411482
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    Consumer memory and price fluctuations in commodity markets: An integrodifferential model (1989)
    Springer
    Journal of dynamics and differential equations 1 (1989), S. 299-325 
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    ISSN: 1572-9222
    Keywords: Commodity markets ; time delays ; stability ; Hopf bifurcation ; 34K15 ; 45J05 ; 90A16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A model for the dynamics of price adjustment in a single commodity market is developed. Nonlinearities in both supply and demand functions are considered explicitly, as are delays due to production lags and storage policies, to yield a nonlinear integrodifferential equation. Conditions for the local stability of the equilibrium price are derived in terms of the elasticities of supply and demand, the supply and demand relaxation times, and the equilibrium production-storage delay. The destabilizing effect of consumer memory on the equilibrium price is analyzed, and the ensuing Hopf bifurcations are described.
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    Stable steady state of some population models (1992)
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    Journal of dynamics and differential equations 4 (1992), S. 161-190 
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    ISSN: 1572-9222
    Keywords: Delay differential equations ; equilibrium ; stability ; limiting equations ; population dynamics ; 34K20 ; 34K25 ; 92A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Applying an analytical method and several limiting equations arguments, some sufficient conditions are provided for the existence of a unique positive equilibriumK for the delay differential equationx=−γx+D(x t ), which is the general form of many population models. The results are concerned with the global attractivity, uniform stability, and uniform asymptotic stability ofK. Application of the results to some known population models, which shows the effectiveness of the methods applied here, is also presented.
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    The relative variance criterion for stability of delay systems (1993)
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    Journal of dynamics and differential equations 5 (1993), S. 105-128 
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    ISSN: 1572-9222
    Keywords: Delay system ; stability ; relative variance ; dynamical disease
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    Topics: Mathematics
    Notes: Abstract A new approach to the study of delay systems, applicable to physiological control systems and other systems where little information about the time delays is available, is examined. The method is based on the fact that stability information can be deduced from the statistical properties of the probability distribution that encodes the structure of the time delay. The main statistical variables used are the usual expectation parameter,E, and a modified variance, calledrelative variance and denotedR, that is invariant under time scale changes. Recent work of the author has shown that stability often improves asR increases whileE remains fixed. A four-parameter family of delay models is analysed in this paper, and the (E, R) pair is found to be a reliable indicator of stability over the global parameter domain of the family.
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    Stability of standing waves for the generalized Davey-Stewartson system (1994)
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    Journal of dynamics and differential equations 6 (1994), S. 325-334 
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    ISSN: 1572-9222
    Keywords: Nonlinear Schrödinger equations ; anisotropic standing waves ; stability ; concentration compactness principle ; Davey-Stewartson system ; 35Q35 ; 35B35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the stability of standing waves for a nonlinear Schrödinger equation, which derives from the generalized Davey-Stewartson system in the elliptic-elliptic case. We prove the existence of stable standing waves under certain conditions.
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    The index of lyapunov stable fixed points in two dimensions (1994)
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    Journal of dynamics and differential equations 6 (1994), S. 631-637 
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    ISSN: 1572-9222
    Keywords: stability ; fixed point index ; periodic solutions
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    Topics: Mathematics
    Notes: Abstract In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR 2 has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.
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    Stability of Linear Inequality Systems Measured by the Hausdorff Metric (2000)
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    Set-valued analysis 8 (2000), S. 253-266 
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    ISSN: 1572-932X
    Keywords: Hausdorff metric ; linear inequality systems ; stability
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    Topics: Mathematics
    Notes: Abstract In this paper, we propose a Hausdorff metric to measure the “distance” between two linear inequality systems on a real normed space X. For this topology, which comes through a pseudo-metric in the set Σ of linear inequality systems, the closedness of the feasible set mapping is studied, and at the same time a characterization of the stability of the subset Σ c of consistent sytems is given.
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    Stability Properties of a Bond Portfolio Management Problem (2000)
    Springer
    Annals of operations research 99 (2000), S. 251-265 
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    ISSN: 1572-9338
    Keywords: stochastic programming ; bond portfolio management ; interest ratescenarios ; stability ; sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients – the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.
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    Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates (1996)
    Springer
    Queueing systems 24 (1996), S. 37-57 
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    ISSN: 1572-9443
    Keywords: dam ; storage process ; saturation rule ; intermittent production ; state dependent rates ; state dependent jumps ; stability ; positive Harris recurrence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.
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    On the stability of retrial queues (1997)
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    Queueing systems 26 (1997), S. 343-363 
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    ISSN: 1572-9443
    Keywords: retrial queues ; stability ; ergodicity ; renovation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ 〉 λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers.
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    Recurrence and transience properties of some neural networks: an approach via fluid limit models (1999)
    Springer
    Queueing systems 32 (1999), S. 99-130 
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    ISSN: 1572-9443
    Keywords: neural network ; inhibition ; stability ; Markov process ; fluid limit ; Harris-recurrence ; transience
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The subject of the paper is the stability analysis of some neural networks consisting of a finite number of interacting neurons. Following the approach of Dai [5] we use the fluid limit model of the network to derive a sufficient condition for positive Harris-recurrence of the associated Markov process. This improves the main result in Karpelevich et al. [11] and, at the same time, sheds some new light on it. We further derive two different conditions that are sufficient for transience of the state process and illustrate our results by classifying some examples according to positive recurrence or transience.
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    Window flow control in FIFO networks with cross traffic (1999)
    Springer
    Queueing systems 32 (1999), S. 195-231 
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    ISSN: 1572-9443
    Keywords: window flow control ; TCP ; stability ; multiclass networks ; stationary ergodic point processes ; (max,+)-linear system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We focus on window flow control as used in packet-switched communication networks. The approach consists in studying the stability of a system where each node on the path followed by the packets of the controlled connection is modeled by a FIFO (First-In-First-Out) queue of infinite capacity which receives in addition some cross traffic represented by an exogenous flow. Under general stochastic assumptions, namely for stationary and ergodic input processes, we show the existence of a maximum throughput allowed by the flow control. Then we establish bounds on the value of this maximum throughput. These bounds, which do not coincide in general, are reached by time-space scalings of the exogenous flows. Therefore, the performance of the window flow control depends not only on the traffic intensity of the cross flows, but also on fine statistical characteristics such as the burstiness of these flows. These results are illustrated by several examples, including the case of a nonmonotone, nonconvex and fractal stability region.
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    Stability estimates in inverse scattering (1992)
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    Acta applicandae mathematicae 28 (1992), S. 1-42 
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    ISSN: 1572-9036
    Keywords: 35R30 ; Inverse scattering ; stability ; noisy data
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    Topics: Mathematics
    Notes: Abstract An algorithm is given for calculating the solution to the 3D inverse scattering problem with noisy discrete fixed energy data. The error estimates for the calculated solution are derived. The methods developed are of a general nature and can be used in many applications: in nondestructive evaluation and remote sensing, in geophysical exploration, medical diagnostics, and technology.
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    Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations (1999)
    Springer
    Advances in computational mathematics 10 (1999), S. 271-289 
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    ISSN: 1572-9044
    Keywords: delay differential equations ; steady state solutions ; stability ; 34K20 ; 65J10
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    Topics: Mathematics
    Notes: Abstract The characteristic equation of a system of delay differential equations (DDEs) is a nonlinear equation with infinitely many zeros. The stability of a steady state solution of such a DDE system is determined by the number of zeros of this equation with positive real part. We present a numerical algorithm to compute the rightmost, i.e., stability determining, zeros of the characteristic equation. The algorithm is based on the application of subspace iteration on the time integration operator of the system or its variational equations. The computed zeros provide insight into the system’s behaviour, can be used for robust bifurcation detection and for efficient indirect calculation of bifurcation points.
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    On the first eigenvalue of the linearized operator of ther-th mean curvature of a hypersurface (1993)
    Springer
    Annals of global analysis and geometry 11 (1993), S. 387-395 
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    ISSN: 1572-9060
    Keywords: Curvatures of hypersurfaces ; Reilly's inequality ; stability ; 53 A 10 ; 53 C 42
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    Topics: Mathematics
    Notes: Abstract We generalize Reilly's inequality for the first eigenvalue of immersed submanifolds ofIR m +1 and the total (squared) mean curvature, to hypersurfaces ofIR m +1 and the first eigenvalue of the higher order curvatures. We apply this to stability problems. We also consider hypersurfaces in hyperbolic space.
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    Destabilization for quasivariational inequalities of reaction-diffusion type (2000)
    Springer
    Applications of mathematics 45 (2000), S. 161-176 
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    ISSN: 1572-9109
    Keywords: reaction-diffusion system ; unilateral conditions ; quasivariational inequality ; Leray-Schauder degree ; eigenvalue ; stability
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    Topics: Mathematics
    Notes: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
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    A secant method for multiple roots (1977)
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    BIT 17 (1977), S. 321-328 
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    ISSN: 1572-9125
    Keywords: 5.15 ; nonlinear equation ; root finding ; multiple root ; secant method ; Steffensen procedure ; order of convergence ; efficiency ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A superlinear procedure for finding a multiple root is presented. In it the secant method is applied to the given function divided by a divided difference whose increment shrinks toward zero as the root is approached. Two function evaluations per step are required, but no derivatives need be calculated.
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    Numerical experiments with a multistep Radau method (1993)
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    BIT 33 (1993), S. 332-350 
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    ISSN: 1572-9125
    Keywords: AMS(MOS): 65L06 ; Multistep collocation method ; continuous solution ; stability
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    Topics: Mathematics
    Notes: Abstract This paper describes an implementation of multistep collocation methods, which are applicable to stiff differential problems, singular perturbation problems, and D.A.E.s of index 1 and 2. These methods generalize one-step implicit Runge-Kutta methods as well as multistep one-stage BDF methods. We give numerical comparisons of our code with two representative codes for these methods, RADAU5 and LSODE.
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    Meromorphic resolvents and power bounded operators (1996)
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    BIT 36 (1996), S. 531-541 
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    ISSN: 1572-9125
    Keywords: Meromorphic resolvent ; stability ; power bounded
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    Topics: Mathematics
    Notes: Abstract Tools to estimate resolvents are developed and a model result is given for power bounded operators: the dimension showing up in the Kreiss matrix theorem can be replaced by the trace norm.
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    A New Approach to Backward Error Analysis of Lu Factorization (1999)
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    BIT 39 (1999), S. 385-402 
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    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; backward error analysis ; growth factor
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    Topics: Mathematics
    Notes: Abstract A new backward error analysis of LU factorization is presented. It allows to obtain a sharper upper bound for the forward error and a new definition of the growth factor that we compare with the well known Wilkinson growth factor for some classes of matrices. Numerical experiments show that the new growth factor is often of order approximately log2 n whereas Wilkinson's growth factor is of order n or $$\sqrt n$$ .
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    A note on unconditionally stable linear multistep methods (1967)
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    BIT 7 (1967), S. 65-70 
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    ISSN: 1572-9125
    Keywords: Differential equations ; multistep methods ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It has been shown by Dahlquist [3] that the trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. It is the purpose of this note to show that a slightly different stability requirement permits methods of higher accuracy.
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    Multiwavelet approximation methods for pseudodifferential equations on curves. Stability and convergence analysis (1998)
    Springer
    Advances in computational mathematics 9 (1998), S. 145-171 
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    ISSN: 1572-9044
    Keywords: periodic pseudodifferential equations ; multiwavelets ; splines with multiple knots ; generalized Galerkin–Petrov schemes ; boundary element methods ; error analysis ; stability ; Strang–Fix condition ; 65J10 ; 65N30 ; 65N35 ; 65R20 ; 47G30 ; 45P05 ; 41A25 ; 41A30 ; 41A15
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    Notes: Abstract We develop a stability and convergence analysis of Galerkin–Petrov schemes based on a general setting of multiresolution generated by several refinable functions for the numerical solution of pseudodifferential equations on smooth closed curves. Particular realizations of such a multiresolution analysis are trial spaces generated by biorthogonal wavelets or by splines with multiple knots. The main result presents necessary and sufficient conditions for the stability of the numerical method in terms of the principal symbol of the pseudodifferential operator and the Fourier transforms of the generating multiscaling functions as well as of the test functionals. Moreover, optimal convergence rates for the approximate solutions in a range of Sobolev spaces are established.
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    Diagonally implicit Runge–Kutta methods for 3D shallow water applications (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 229-250 
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    ISSN: 1572-9044
    Keywords: numerical analysis ; shallow water problems ; DIRK methods ; stability ; 65L06 ; 65L20 ; 65M12 ; 65M20
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    Topics: Mathematics
    Notes: Abstract We construct A‐stable and L‐stable diagonally implicit Runge–Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge–Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge–Kutta methods are suitable methods for integrating shallow water problems in the sense that the stability boundary is relatively large and that the usually quite fine vertical resolution of the discretized spatial domain is not involved in the stability condition.
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    Numerical stability of biorthogonal wavelet transforms (1995)
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    Advances in computational mathematics 4 (1995), S. 1-26 
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    ISSN: 1572-9044
    Keywords: Wavelets ; biorthogonal wavelets ; stability ; primary 15A12 ; 65F35 ; secondary 42C15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL → ∞. These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.
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    Some remarks on the second variation formula for the area (1993)
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    Annals of global analysis and geometry 11 (1993), S. 221-235 
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    ISSN: 1572-9060
    Keywords: Second variation formula ; Morse index ; stability ; 53C
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    Topics: Mathematics
    Notes: Abstract Iff is a minimal, isometric immersion of the Riemannian manifoldM of dimensionn in a Riemannian manifold $$\overline M$$ of dimensionm and ifI N is the „differential Jacobi operator” acting on the cross sections of the normal bundleN(M), we obtain some information on the Morse index and on the stability ofM through a detailed geometric analysis of the immersionf obtained when considering the higher fundamental forms off.
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    On stable surfaces of constant gauss curvature in space forms (1995)
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    Annals of global analysis and geometry 13 (1995), S. 141-148 
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    ISSN: 1572-9060
    Keywords: Gauss curvature ; stability ; 53
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    Topics: Mathematics
    Notes: Abstract We prove that a domain on a surface of constant curvature is stable provided the integral of the mean curvature is small enough.
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    Stability of Hypersurfaces with Constant $$r$$ -Mean Curvature (1997)
    Springer
    Annals of global analysis and geometry 15 (1997), S. 277-297 
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    ISSN: 1572-9060
    Keywords: mean curvature ; $$r$$ -mean curvature ; sphere ; stability ; stable
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    Topics: Mathematics
    Notes: Abstract We deal with compact hypersurfaces immersed in space forms with constant $$r$$ -mean curvature. They are critical points for a variational problem. We show they are stable if and only if they are geodesic spheres, generalizing results on constant curvature hypersurfaces.
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    The maximal accuracy of stable difference schemes for the wave equation (1995)
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    BIT 35 (1995), S. 83-115 
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    ISSN: 1572-9125
    Keywords: finite difference methods ; wave equation ; accuracy ; stability ; Padé approximants ; order stars ; Riemann surface
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    Topics: Mathematics
    Notes: Abstract We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation,u tt =c 2 u xx , given by $$\sum\limits_{j = - S}^S {b_j U_{n + 1,m + j} + } \sum\limits_{j = - S}^S {a_j U_{n,m + j} + } \sum\limits_{j = - S}^S {b_j U_{n - 1,m + j} } = 0.$$ It has already been proved that the maximal order of accuracyp of such schemes is given byp ≤ 2(s + S). In this paper we show that the requirement of stability does not reduce this maximal order for any choice of the pair (s, S). The result is proved by introducing an order star on the Riemann surface of the algebraic function associated with the scheme. Furthermore, Padé schemes, withS = 0,s 〉 0, ands = 0,S 〉 0, are proved to be stable for 0 〈 μ 〈 1, where μ is the Courant number. These schemes can be implemented with high-order absorbing boundary conditions without reducing the range of μ for which stable solutions are obtained.
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    Derivative free multipoint iterative methods for simple and multiple roots (1986)
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    BIT 26 (1986), S. 93-99 
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    ISSN: 1572-9125
    Keywords: Primary 65HO5 ; nonlinear equation ; multiple roots ; multipoint iterative methods ; error constant ; stability ; efficiency
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    Topics: Mathematics
    Notes: Abstract A one-parameter family of derivative free multipoint iterative methods of orders three and four are derived for finding the simple and multiple roots off(x)=0. For simple roots, the third order methods require three function evaluations while the fourth order methods require four function evaluations. For multiple roots, the third order methods require six function evaluations while the fourth order methods require eight function evaluations. Numerical results show the robustness of these methods.
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    A note on contractivity in the numerical solution of initial value problems (1987)
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    BIT 27 (1987), S. 424-437 
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    ISSN: 1572-9125
    Keywords: 65 L 05 ; 65 L 20 ; stability ; contractivity ; numerical solution of stiff initial value problems in ordinary differential equations ; Runge-Kutta methods ; Rosenbrock methods ; rational Runge-Kutta methods
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    Topics: Mathematics
    Notes: Abstract This paper concerns the stability analysis of numerical methods for approximating the solutions to (stiff) initial value problems. Our analysis includes the case of (nonlinear) systems of differential equations that are essentially more general than the classical test equationU′=λU, with λ a complex constant. We explore the relation between two stability concepts, viz. the concepts of contractivity and weak contractivity. General Runge-Kutta methods, one-stage Rosenbrock methods and a notable rational Runge-Kutta method are analysed in some detail.
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    Netwon interpolation at Leja points (1990)
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    BIT 30 (1990), S. 332-346 
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    ISSN: 1572-9125
    Keywords: 65D05 ; polynomial interpolaton ; Newton form ; stability ; Leja points ; ordering of interpolation points
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    Topics: Mathematics
    Notes: Abstract The Newton form is a convenient representation for interpolation polynomials. Its sensitivity to perturbations depends on the distribution and ordering of the interpolation points. The present paper bounds the growth of the condition number of the Newton form when the interpolation points are Leja points for fairly general compact sets K in the complex plane. Because the Leja points are defined recursively, they are attractive to use with the Newton form. If K is an interval, then the Leja points are distributed roughly like Chebyshev points. Our investigation of the Newton form defined by interpolation at Leja points suggests an ordering scheme for arbitrary interpolation points.
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    Stability Concepts in Topological Dynamics by Nonstandard Methods (1997)
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    Acta applicandae mathematicae 49 (1997), S. 35-54 
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    ISSN: 1572-9036
    Keywords: dynamical systems ; stability ; pseudo orbit tracing property ; nonstandard analysis
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    Topics: Mathematics
    Notes: Abstract It is known that it is not possible to introduce C0 -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rn. Classically these amount to considering the space of all systems on a given subset of Rn as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.
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    A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations (1992)
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    BIT 32 (1992), S. 634-649 
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    ISSN: 1572-9125
    Keywords: AMS(MOS): 65L20 ; CR: 5.17 ; delay differential equations ; numerical solution ; Runge-Kutta methods ; interpolation procedures ; stability
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    Topics: Mathematics
    Notes: Abstract This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU′(t)=λU(t)+μU(t−τ) with λ, μ ε C, Re(λ)〈−|μ|, and τ〉0. Ifc i denotes theith abscissa of a given Runge-Kutta method, then in thenth stept n−1→t n :=t n−1+h of the numerical process our interpolation procedure computes an approximation toU(t n−1+c i h−τ) from approximations that have already been generated by the process at pointst j−1+c i h(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem.
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    On the Robustness of Gaussian Elimination with Partial Pivoting (2000)
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    BIT 40 (2000), S. 62-73 
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    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; pivoting
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    Topics: Mathematics
    Notes: Abstract It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.
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    Runge-Kutta Methods for the Numerical Solution of Stiff Semilinear Systems (2000)
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    BIT 40 (2000), S. 611-639 
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    ISSN: 1572-9125
    Keywords: Runge-Kutta methods ; stability ; convergence ; stiff problems
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    Topics: Mathematics
    Notes: Abstract This paper studies the stability and convergence properties of general Runge-Kutta methods when they are applied to stiff semilinear systems y′(t) = J(t)y(t) + g(t, y(t)) with the stiffness contained in the variable coefficient linear part. We consider two assumptions on the relative variation of the matrix J(t) and show that for each of them there is a family of implicit Runge-Kutta methods that is suitable for the numerical integration of the corresponding stiff semilinear systems, i.e. the methods of the family are stable, convergent and the stage equations possess a unique solution. The conditions on the coefficients of a method to belong to these families turn out to be essentially weaker than the usual algebraic stability condition which appears in connection with the B-stability and convergence for stiff nonlinear systems. Thus there are important RK methods which are not algebraically stable but, according to our theory, they are suitable for the numerical integration of semilinear problems. This paper also extends previous results of Burrage, Hundsdorfer and Verwer on the optimal convergence of implicit Runge-Kutta methods for stiff semilinear systems with a constant coefficients linear part.
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    Quasi-geodesic segments and Gromov hyperbolic spaces (1996)
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    Geometriae dedicata 62 (1996), S. 281-298 
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    ISSN: 1572-9168
    Keywords: 53C23 ; Hyperbolicity ; stability ; quasi-geodesics
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    Topics: Mathematics
    Notes: Abstract It is known that for a geodesic metric space hyperbolicity in the sense of Gromov implies geodesic stability. In this paper it is shown that the converse is also true. So Gromov hyperbolicity and geodesic stability are equialent for geodesic metric spaces.
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    Uniform stability at permanently acting disturbances of solutions of Navier-Stokes equations for compressible isothermic fluids (1994)
    Springer
    Acta applicandae mathematicae 37 (1994), S. 129-136 
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    ISSN: 1572-9036
    Keywords: 35B35 ; 35Q30 ; 76N10 ; stability ; Navier-Stokes equations ; compressible fluids
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    Topics: Mathematics
    Notes: Abstract We prove that the uniform stability at permanently acting disturbances of a given solution of the Navier-Stokes equations for viscous compressible isothermic fluid is a consequence of the uniform exponential stability of the zero solution of so-called linearized equations.
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    Growth and long-run stability (1987)
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    Acta applicandae mathematicae 9 (1987), S. 219-237 
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    ISSN: 1572-9036
    Keywords: 34A34 ; 34D99 ; 90A16 ; Nonlinear differential equations ; stability ; growth ; economic dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00047540
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  • 98
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    Electronic Resource
    Runge–Kutta–Nyström‐type parallel block predictor–corrector methods (1999)
    Springer
    Advances in computational mathematics 10 (1999), S. 115-133 
    Details
    ISSN: 1572-9044
    Keywords: Runge–Kutta–Nyström methods ; predictor–corrector methods ; stability ; parallelism ; 65M12 ; 65M20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018930732643
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  • 99
    Electronic Resource
    Electronic Resource
    q-Difference intertwining operators and q-conformal invariant equations (1996)
    Springer
    Acta applicandae mathematicae 44 (1996), S. 81-116 
    Details
    ISSN: 1572-9036
    Keywords: 17B37 ; 81R50 ; 22E47 ; quantum groups ; intertwining differential operators ; conformal invariance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We first recall a canonical procedure for the construction of the invariant differential operators and equations for arbitrary complex or real noncompact semisimple Lie groups. Then we present the application of this procedure to the case of quantum groups. In detail is given the construction of representations of the quantum algebra U q (sl(n)) labelled by n−1 complex numbers and acting in the spaces of functions of n(n−1)/2 noncommuting variables, which generate a q-deformed SL(4) flag manifold. The conditions for reducibility of these representations and the procedure for the construction of the q-difference intertwining operators are given. Using these results for the case n=4 we propose infinite hierarchies of q-difference equations which are q-conformal invariant. The lowest member of one of these hierarchies are new q-Maxwell equations. We propose also new q-Minkowski spacetime which is part of a q-deformed SU(2,2) flag manifold.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00116517
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  • 100
    Electronic Resource
    Electronic Resource
    The stability of rational approximations of analytic semigroups (1993)
    Springer
    BIT 33 (1993), S. 74-84 
    Details
    ISSN: 1572-9125
    Keywords: 65J10 ; 65M12 ; Analytic semigroup ; Banach space ; rational approximation ; A-acceptable ; A(θ)-acceptable ; stability ; Crank-Nicolson method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown thatA-acceptable and, more generally,A(θ)-arational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01990345
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