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  • stability  (680)
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  • 1
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    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
    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].
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  • 2
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    Circuits, systems and signal processing 19 (2000), S. 423-435 
    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.
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  • 3
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    Circuits, systems and signal processing 19 (2000), S. 13-25 
    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.
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  • 4
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    Computing 24 (1980), S. 341-347 
    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.
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  • 5
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    Computing 51 (1993), S. 271-292 
    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.
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  • 6
    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.
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  • 7
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    European journal of nutrition 29 (1990), S. 219-228 
    ISSN: 1436-6215
    Keywords: Vitamin K ; Menadion ; Menadiol ; Bioverfügbarkeit ; Stabilität ; Geflügel ; vitamin K ; menadione ; menadiol ; bioavailability ; stability ; poultry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Medicine
    Description / Table of Contents: Summary A bioassay of vitamin K is described, based on the prothrombin clotting time of 3-week-old, vitamin-K-depleted, and cumatetralyl-sensitized male broiler chicks, using a homologous thrombokinase preparation. With this test it could be shown that the diacetate and dibutyrate esters of menadiol are vitamin-K-active. The bioactivity of menadione from these menadiolesters amounted to about 70 % of the standard menadione from a coated menadione sodium bisulfite (Dohyfral). Menadiol seems to be temperature-resistant under such conditions, whereby two uncoated MSB preparations lost about 60 % of their activity.
    Notes: Zusammenfassung In einem biologischen Testverfahren an Cumatetralyl sensibilisierten Küken konnte in 3 Versuchen anhand des Parameters Thromboplastinzeit mit homologer Thrombokinase gezeigt werden, da\ Menadioldiacetat und Menadioldibutyrat Vitamin-K-wirksam sind. Die biologische Wirksamkeit von Menadion aus diesen Menadiolestern betrug ca. 70 % der Menadionaktivität aus gecoatetem Menadionbisulfit (Dohyfral®). Im Gegensatz zu 2 ungeschützten MSB-Präparationen, welche bei Wärmebelastung ca. 60 % ihrer ursprünglichen Wirkung verloren, waren die Menadiolester temperaturstabil.
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  • 8
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    OR spectrum 20 (1998), S. 101-107 
    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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  • 9
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    OR spectrum 20 (1998), S. 101-107 
    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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  • 10
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    OR spectrum 16 (1994), S. 47-52 
    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.
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  • 11
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    OR spectrum 18 (1996), S. 231-239 
    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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  • 12
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    Empirical economics 23 (1998), S. 387-400 
    ISSN: 1435-8921
    Keywords: Key words: Money demand ; cointegration ; stability ; regime shift ; JEL classification: E41 ; C22
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract. Using several tests for structural stability in regressions with I(1) variables and for the existence of cointegration in models with regime shifts, the empirical evidence on the existence of a structural break in the Spanish long-run demand for broad money (ALP2) is analysed.  The results indicate that shifts affecting the demand for ALP2 in recent years have substantially altered its long-run properties. As to the cause of this structural break, emphasis is placed on the role played by the increasing openness of the Spanish financial system to international markets as obstacles to free capital movements have progressively disappeared.
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  • 13
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    Stochastic environmental research and risk assessment 12 (1998), S. 191-204 
    ISSN: 1436-3259
    Keywords: Keywords: groundwater flow ; inverse problems ; stability ; geostatistical interpolation ; kriging.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The Differential System Method (DSM) permits identification of the physical parameters of finite-difference groundwater flow models in a confined aquifer when piezometric head and source terms are known at each point of the finite-difference lattice for at least two independent flow situations for which the hydraulic gradients are not parallel. Since piezometric head data are usually few and sparse, interpolation of the measured data onto a regular grid can be performed with geostatistical techniques. We apply kriging to the sparse data of a synthetic aquifer to evaluate the stability of the DSM with respect to uncorrelated measurement errors and interpolation errors. The numerical results show that the DSM is stable.
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    Mathematical programming 47 (1990), S. 117-141 
    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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    Mathematical programming 54 (1992), S. 57-67 
    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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    Mathematical programming 61 (1993), S. 197-214 
    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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  • 17
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    Computing 44 (1990), S. 187-196 
    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.
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  • 18
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    Computing 35 (1985), S. 85-91 
    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.
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  • 19
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    Computing 35 (1985), S. 325-344 
    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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  • 20
    ISSN: 1435-1536
    Keywords: Emulsions ; stability ; interfacial properties of emulsions ; soybean protein ; glycerides ; stabilised O/W emulsions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The influence of chemically modified 7S fraction of soybean protein (7MSPF), and its partial replacement by mono- and di-glycerides in various ratios, on the rate of drop coalescence in concentrated corn oil-in-water emulsions has been investigated. A total emulsifier concentration of 2.0 % (wt/wt) was used. The minimum drop coalescence rate was achieved when using 1.0% (wt/wt) 7MSPF in conjunction with 0.5% (wt/wt) monoglyceride and 0.5 % (wt/wt) di-glyceride at pH 5.5. At other mono-/di-glycerides and protein/glycerides ratios, and at other pHs, the rate of drop coalescence was higher than when 2.0% (wt/wt) 7MSPF was used. The reduction in drop coalescence rate under these conditions is attributed to association of 7MSPF with the glycerides at the oil-water interface. The influence of protein/glycerides ratio on the viscoelastic properties of mixed interfacial films supports this view.
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    Rheologica acta 22 (1983), S. 284-290 
    ISSN: 1435-1528
    Keywords: Viscometric flow ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract This paper examines three-dimensional disturbances of a plane steady shear flow of simple fluids with short memory. Under the assumption of nearly-viscometric flow, constitutive equations are derived and then a general form of the Reynolds-Orr energy equation is obtained. With the aid of this derived energy formula, sufficient conditions are generated for the stability of three-dimensional disturbances of the planar viscometric flow. These conditions are analysed and a comparison is made with the corresponding two-dimensional stability problem. There is a strong indication that the basic flow is less stable against three-dimensional disturbances than against two-dimensional ones.
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    Rheologica acta 26 (1987), S. 119-126 
    ISSN: 1435-1528
    Keywords: Maxwell fluid ; planeCouette flow ; stability ; criticalWeissenberg number
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Abstract The stability behaviour of a Maxwell fluid in a simple plane shear flow for a class of special perturbations is investigated. Necessary and sufficient stability criteria, especially a critical Weissenberg number for the stability (We k ≈ 4) are given. The results of the analysis are in qualitative agreement with experimental observations.
    Notes: Zusammenfassung Es wird das Stabilitätsverhalten eines Maxwell-Fluids in einer einfachen ebenen Scherströmung für eine spezielle Störungsklasse untersucht. Notwendige und hinreichende Stabilitätskriterien sowie eine kritische Weissenbergzahl (We k ≈ 4) werden angegeben. Die Ergebnisse der Analyse stehen mit experimentellen Befunden in qualitativer Übereinstimmung.
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    Fire technology 23 (1987), S. 175-185 
    ISSN: 1572-8099
    Keywords: Fire evaluation ; expert ; consensus ; stability ; reliability ; validity ; scaling measurement
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract In this article some of the methodological problems associated with using the Delphi technique for the development of a Firesafety Evaluation (Points) Scheme are examined. These problems relate to: questionnaire design, the merits and demerits of Delphi groups versus panel groups, the definition of key terms (such as expert, consensus and stability), the reliability, validity and level of measurement achieved by Likert-type scaling techniques, and the differences in the decisionmaking processes of expert and nonexpert groups.
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  • 24
    ISSN: 1572-8358
    Keywords: Epidemiology ; sleeping sickness ; vector controls ; differential equations ; spacialization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract A compartmental model is described for the spread of Gambian sleeping sickness in a spatially heterogeneous environment in which vector and human populations migrate between two "patches": the village and the plantations. The number of equilibrium points depends on two "summary parameters": gr the proportion removed among human infectives, and R0, the basic reproduction number. The origin is stable for R0 〈1 and unstable for R0 〉1. Control strategies are assessed by studying the mix of vector control between the two patches that bring R0 below 1. The results demonstrate the importance of vector control in the plantations. For example if 20 percent of flies are in the village and the blood meal rate in the village is 10 percent, then a 20 percent added vector mortality in the village must be combined with a 9 percent added mortality in the plantations in order to bring R0 below 1. The results are quite insentive to the blood meal rate in the village. Optimal strategies (that minimize the total number of flies trapped in both patches) are briefly discussed.
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    Acta biotheoretica 39 (1991), S. 1-14 
    ISSN: 1572-8358
    Keywords: Hematological diseases ; first order partial differential equations ; stability
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    Topics: Biology
    Notes: Abstract To address the possibility that proliferative disorders may originate from interactions between multiple populations of proliferating and maturing cells, we formulate a model for this process as a set of coupled nonlinear first order partial differential equations. Using recent results for the asymptotic behaviour of the solutions to this model, we demonstrate that there exists a region of coupling coefficients, maturation rates, and proliferation rates that will guarantee the stable coexistence of coupled cellular populations. The analysis shows that increases in the coupling between populations may ultimately lead to a loss of stability. Furthermore, the analysis indicates that increases (decreases) in the maturation and/or proliferation rates above (below) critical levels will lead either to instability in the populations or the destruction of one population and the persistence of the other.
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    Acta biotheoretica 48 (2000), S. 207-218 
    ISSN: 1572-8358
    Keywords: Dynamical population ; fishing efforts ; metapopulation ; time scales ; aggregation method ; equilibrium ; stability
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    Topics: Biology
    Notes: Abstract This work presents a specific stock-effort dynamical model. The stocks correspond to two populations of fish moving and growing between two fishery zones. They are harvested by two different fleets. The effort represents the number of fishing boats of the two fleets that operate in the two fishing zones. The bioeconomical model is a set of four ODE's governing the fishing efforts and the stocks in the two fishing areas. Furthermore, the migration of the fish between the two patches is assumed to be faster than the growth of the harvested stock. The displacement of the fleets is also faster than the variation in the number of fishing boats resulting from the investment of the fishing income. So, there are two time scales: a fast one corresponding to the migration between the two patches, and a slow time scale corresponding to growth. We use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model for the total fishing effort and fish stock of the two fishing zones. The mathematical analysis of the model is shown. Under some conditions, we obtain a stable equilibrium, which is a desired situation, as it leads to a sustainable harvesting equilibrium, keeping the stock at exploitable densities.
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    Journal of intelligent manufacturing 4 (1993), S. 183-198 
    ISSN: 1572-8145
    Keywords: Assembly planning ; subassembly ; liaison graph ; geometric reasoning ; assembly cost ; stability ; partial-order graph
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The distribution of assembly workstations enables assembly operations to be done in parallel, while the multiple routing of parts in flexible assembly systems allows the opportunistic scheduling of assembly operations. This paper presents an assembly planning system, called the Assembly Coplanner, which automatically constructs an assembly partial order and generates a set of assembly instructions from a liaison graph representation of an assembly based on the extraction of preferred subassemblies. Assembly planning in Coplanner is carried out by the co-operation of multiple planning agents, such as the geometric reasoner, the physical reasoner, the resource manager and the plan coordinator, under the constraints of finding a cost-effective assembly plan in a flexible assembly system. The Coplanner identifies spatial parallelism in assembly as a means of constructing temporal parallelism among assembly operations. This is achieved in the following way: (1) the selection of a set of tentative subassemblies by decomposing a liaison graph into a set of subgraphs based on feasibility and difficulty of disassembly; (2) the evaluation of each of the tentative subassemblies in terms of assembly cost represented by subassembly selection indices; and (3) the construction of a hierarchical partial order graph (HPOG) as an assembly plan. A case study applying the Coplanner to a mechanical assembly is illustrated in this paper.
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  • 28
    ISSN: 1572-8900
    Keywords: Chemiluminescence ; oxidation ; stability ; acrylonitrile-butadiene-styrene (ABS) ; ABS/polycarbonate blend
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    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The thermal oxidative stability of various ABS/PC compounds was studied by means of the chemiluminescence technique. Similarly to pure ABS, Irganox 1076 and Irganox MD 1024 perform as moderate antioxidants in ABS/PC and (ABS/PC + lubricant) blends. Neither Tinuvin 144, Irgaphos 168, nor their mixture affects the durability of the ABS/PC blend. At the same time, (Irgaphos 168 + Tinuvin 144) in combination with Irganoxes was found to provide a noticeable enhancement in durability to the (ABS/PC + lubricant) system. Titanium dioxide pigments by themselves have only a slight influence on the oxidative stability of the ABS/PC blend. Durability of the (ABS/PC + pigment) and (ABS/PC + lubricant) systems was found to be the same and the overall protective effect of Irganox 1076 was similar in both the (ABS/PC + lubricant) and the (ABS/PC + lubricant + pigment) systems. Certain modifiers significantly improve the durability of the ABS/PC compounds, although their function may differ in the systems with and without pigments.
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  • 29
    ISSN: 1572-8900
    Keywords: Chemiluminescence ; oxidation ; stability ; acrylonitrile-butadiene-styrene (ABS)
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    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The influence of lubricants, UV stabilizers, antioxidants, and metal deactivators on the resistance of ABS to thermal oxidation was studied by means of the chemiluminescence technique. Neither of the additives seems to affect significantly the induction period of oxidation. At the same time, the influence of various additives on the oxidation rate constant is remarkably different: the introduction of lubricants and UV stabilizers increases its value, while antioxidants and metal deactivators have the opposite effect. For the particular systems studied durability is decreased in samples containing the lubricant and UV stabilizers and increased in samples stabilized with the antioxidant and metal deactivator.
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  • 30
    ISSN: 1572-8900
    Keywords: Capillary zone electrophoresis ; oligomers ; lactic acid ; glycolic acid ; 3-hydroxybutyric acid ; water solubility ; stability ; degradation
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    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In an attempt to increase the range of analytical techniques able to monitor ultimate degradation stages of degradable, biodegradable, and bioresorbable polymers, capillary zone electrophoresis (CZE) was used to analyze tentatively oligomers formed during thermal condensation of lactic, glycolic, anddl-3-hydroxybutyric acids. The influence of the buffer and of capillary coating are discussed in terms of electroosmotic flow. Typical analyses were first performed using a 0.1M borate buffer (pH 8.9) with anodic injection. In the case of lactic acid, seven peaks were well separated, while only three peaks were observed for glycolic acid. A more complex situation was found fordl-3-hydroxybutyric acid oligomers. The first five peaks were split. The major component of each doublet was attributed to hydroxy-terminated oligomers, whereas the satellite peaks were assigned to oligomers bearing a C=C double bond at the noncarboxylic terminus. CZE of pH-sensitive lactic acid oligomers was also performed in 0.05M phosphate buffer (pH 6.8) with cathodic injection after physical coating of the fused-silica capillary with DEAE-Dextran. The buffer-soluble fraction present in lactic acid oligomers was extracted from a dichloromethane solution. Extracts issued from different batches of lactic acid condensates gave a constant water-solubility pattern whose cutoff was at the level of the decamer. CZE was also used to monitor thein vitro aging of aqueous solutions of these water-soluble oligomers. The lactyllactic acid dimer appeared more stable than higher oligomers, thus showing that ultimate stages of the degradation did not proceed at random. These physicochemical characteristics were used to complement the degradation pathway based on diffusion of oligomers duringin vitro aging of large size lactic acid plates made by compression molding. CZE data showed that lactic acid was the only component which was released in the aqueous medium during degradation.
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    Journal of inorganic and organometallic polymers and materials 2 (1992), S. 79-85 
    ISSN: 1572-8870
    Keywords: Phthalocyanines ; polymers ; siloxanes ; conductivity ; stability
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The author's work on the incorporation of phthalocyanines into inorganic polymers is reviewed. The synthesis of poly(siloxane phthalocyanines) and the synthesis and characterization of fluoro(phthalocyanine) Group III compounds and their conducting derivatives are described.
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    Journal of polymers and the environment 3 (1995), S. 199-203 
    ISSN: 1572-8900
    Keywords: Chemiluminescence ; oxidation ; stability ; acrylonitrile-butadiene-styrene
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    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The thermal oxidative stability of various formulations based on emulsion-grade ABS was studied by the chemiluminescence technique. Emulsion products were found to be essentially less stable than ionic mass polymerization resins. Among the antioxidants studied, Santonox R is clearly more efficient than Irganox 1076 and Irganox 3114, and its superiority is reflected primarily in improved induction period values. The introduction of Tinuvin 770 and Tinuvin 328 UV stabilizers into emulsion resins does not change the durability of the products. In mixtures where both Irganox 1076 and UV stabilizers are present, a certain antagonistic effect was noted at high UV stabilizer concentrations.
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  • 33
    ISSN: 1572-8927
    Keywords: Chromium(III) ; β-diketones ; β-diketonates ; chelation ; complexation ; correlation ; stability ; equilibrium
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    Topics: Chemistry and Pharmacology
    Notes: Abstract It has been demonstrated that the logarithm of the stability constant of some monochelated chromium(III) compounds, with structurally similar 1,3-dicarbonylic species, is linearly related to the negative logarithm of the acid ionization constant of the ligand. Graphical and analytical correlations which could be useful in predicting equilibrium constants of chromium(III)-β-diketonates, as well as other first-row transition metal derivatives, have been developed. A quantitative evaluation of the complexes stability has been carried out, providing information about the effects of ligand substituents on the equilibrium constants.
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    Catalysis letters 10 (1991), S. 225-232 
    ISSN: 1572-879X
    Keywords: VPI-5 ; stability ; molecular sieve ; post-synthesis treatments
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Thorough washing of a VPI-5 synthesized with n-dipropylamine as template improves greatly its thermal stability while no major change is observed in the template content. A detailed study of the influence of the pretreatment conditions shows that in order to obtain a high thermal stability (up to at least 960 °C) two parameters are of importance. The removal of both the template and the adsorbed water requires either a low heating rate at atmospheric pressure or a low pressure (less than 3 Torr) when the heating rate is 300 ° per hour.
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    ISSN: 1572-879X
    Keywords: metal-oxygen cluster compounds ; heteropoly acids ; stability ; pH ; aqueous solutions
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The stabilities of the solid superacids H3Mo12O40, H3PW12O40, H4SiMo12O40 and H4SiW12O40 in aqueous solution have been measured at various values of pH by use of ion chromatographic analyses. The aforementioned acids are completely decomposed at values of pH, 4.0, 5.2, 7.0 and 11.0, respectively. The stabilities in aqueous solution with respect to pH follow the order H4SiW12O40 〉 H3PW12O40 〉 H4SiMo12O40 〉 H3PMo12O40.
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    Journal of dynamics and differential equations 1 (1989), S. 269-298 
    ISSN: 1572-9222
    Keywords: Geometric mechanics ; reduction ; stability ; chaos ; rigid body dynamics ; periodic orbits ; 58F
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    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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    Journal of dynamics and differential equations 10 (1998), S. 151-188 
    ISSN: 1572-9222
    Keywords: Fourth-order solitary waves ; stability ; instability
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    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.
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    Journal of dynamics and differential equations 6 (1994), S. 37-51 
    ISSN: 1572-9222
    Keywords: Celestial mechanics ; relative equilibria ; stability
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    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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    Order 1 (1984), S. 21-28 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05A05 ; Partially ordered sets ; Sperner's Theorem ; LYM property ; product of chains
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    Notes: Abstract Let P be the poset k 1 × ... × k n , which is a product of chains, where n≥1 and k 1≥ ... ≥k n ≥2. Let $$M = k_1 - \sum\nolimits_{i = 2}^n {(k_i - 1)} $$ . P is known to have the Sperner property, which means that its maximum ranks are maximum antichains. Here we prove that its maximum ranks are its only maximum antichains if and only if either n=1 or M≤1. This is a generalization of a classical result, Sperner's Theorem, which is the case k 1= ... =k n =2. We also determine the number and location of the maximum ranks of P.
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    Order 12 (1995), S. 213-220 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C25 ; Parallel computation ; m-machine problem ; tree
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    Topics: Mathematics
    Notes: Abstract LetP={v 1,...,v n } be a set ofn jobs to be executed on a set ofm identical machines. In many instances of scheduling problems, if a jobv i has to be executed before the jobv j and both jobs are to be executed on different machines, some sort of information exchange has to take place between the machines executing them. The time it takes for this exchange of information is called a communication delay. In this paper we give anO(n) algorithm to find an optimal scheduling with communication delays when the number of machines is not limited and the precedence constraints on the jobs form a tree.
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    Order 12 (1995), S. 327-349 
    ISSN: 1572-9273
    Keywords: 06A07 ; 06A10 ; Partially ordered set ; linear extension ; balancing pairs ; cross-product conjecture ; Ahlswede-Daykin inequality ; sorting
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    Topics: Mathematics
    Notes: Abstract In a finite partially ordered set, Prob (x〉y) denotes the proportion of linear extensions in which elementx appears above elementy. In 1969, S. S. Kislitsyn conjectured that in every finite poset which is not a chain, there exists a pair (x,y) for which 1/3⩽Prob(x〉y)⩽2/3. In 1984, J. Kahn and M. Saks showed that there exists a pair (x,y) with 3/11〈Prob(x〉y)〈8/11, but the full 1/3–2/3 conjecture remains open and has been listed among ORDER's featured unsolved problems for more than 10 years. In this paper, we show that there exists a pair (x,y) for which (5−√5)/10⩽Prob(x〉y)⩽(5+√5)/10. The proof depends on an application of the Ahlswede-Daykin inequality to prove a special case of a conjecture which we call the Cross Product Conjecture. Our proof also requires the full force of the Kahn-Saks approach — in particular, it requires the Alexandrov-Fenchel inequalities for mixed volumes. We extend our result on balancing pairs to a class of countably infinite partially ordered sets where the 1/3–2/3 conjecture isfalse, and our bound is best possible. Finally, we obtain improved bounds for the time required to sort using comparisons in the presence of partial information.
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    Order 13 (1996), S. 101-117 
    ISSN: 1572-9273
    Keywords: 06A10 ; (Partially) ordered set ; maximal chain ; maximal antichain ; cutset ; fibre
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    Topics: Mathematics
    Notes: Abstract There is a product of two linear orders of size $$2^{\aleph _0 } $$ with the property that every subset or complement thereof contains a maximal chain. Furthermore, for regular ℵα, there is a product of two linear orders of size ℵα+2 that when colored with fewer than ℵα colors always has a monochromatic maximal chain. As a corollary, for every uncountable strong limit cardinal κ, there is an ordered set of cardinality κ that must be colored with at least κ colors before no monochromatic maximal chains are present. Duals of these results show that at least as much is true for maximal antichains.
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    Order 2 (1985), S. 193-198 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06D99 ; 52A25 ; Finite distributive lattices ; finite posets ; valuations ; convex polytopes ; extreme points
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    Topics: Mathematics
    Notes: Abstract Let L be a finite distributive lattice and V(L) the real vector space of all valuations on L. We verify the conjecture of Geissinger that the extreme points of the convex polytope M(L)={v ∈ L : 0 ≤ v ≤ 1} are precisely the 0–1 valuations.
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    Order 2 (1985), S. 257-264 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68E05 ; Sorting ; merging ; linear extension
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    Topics: Mathematics
    Notes: Abstract For a finite poset P and x, yεP let pr(x〉y) be the fraction of linear extensions which put x above y. N. Linial has shown that for posets of width 2 there is always a pair x, y with 1/3 ⩽ pr(x〉y)⩽2/3. The disjoint union C 1∪C 2 of a 1-element chain with a 2-element chain shows that the bound 1/3 cannot be further increased. In this paper the extreme case is characterized: If P is a poset of width 2 then the bound 1/3 is exact iff P is an ordinal sum of C 1∪C 2's and C 1's.
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    Order 3 (1986), S. 283-286 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06A12 ; 06B99 ; Partially ordered set ; semilattice ; lattice ; cofinality
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    Topics: Mathematics
    Notes: Abstract A partial ordering on a set P can be weakened to an upper or lower semilattice ordering, respectively a lattice ordering, if and only if P is filtered in the appropriate direction(s).
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    Order 3 (1987), S. 355-357 
    ISSN: 1572-9273
    Keywords: 05App ; 06A10 ; Factor poset ; antichain ; depth
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    Topics: Mathematics
    Notes: Abstract Denote g(m, n) the minimum of min A, where A is a subset of {1, 2, ..., m} of size n and there do not exist two distinct x and y in A such that x divides y. We use a method of poset to prove that g(m, n)=2 i for positive integer i≤log3 m and 1+s(m, i−1)〈n≤1+s(m, i), where s(m, i) is the number of odd integers x such that m/3 i 〈x≤m.
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    Order 4 (1987), S. 127-142 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68-XX ; Poset ; closures ; Hasse diagram
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    Topics: Mathematics
    Notes: Abstract The combinatorial properties of the poset of closures are studied, especially the degrees in the Hasse diagram.
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    Order 3 (1986), S. 1-2 
    ISSN: 1572-9273
    Keywords: 06A10 ; Jump number
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    Topics: Mathematics
    Notes: Abstract The following result is proved in this note: For any positive integers w and t, if an ordered set P has jump number at least (t+1) w−1, then either the width of P is more than w, or P has a tower, i.e., a linear sum of pairs of noncomparable elements, of height more than t.
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    Order 4 (1987), S. 155-164 
    ISSN: 1572-9273
    Keywords: 05C55 ; 06A10 ; 62J ; Regressions ; Ramsey theory
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    Topics: Mathematics
    Notes: Abstract A regressive function (also called a regression or contractive mapping) on a partial order P is a function σ mapping P to itself such that σ(x)≤x. A monotone k-chain for σ is a k-chain on which σ is order-preserving; i.e., a chain x 1〈...〈xksuch that σ(x 1)≤...≤σ(xk). Let P nbe the poset of integer intervals {i, i+1, ..., m} contained in {1, 2, ..., n}, ordered by inclusion. Let f(k) be the least value of n such that every regression on P nhas a monotone k+1-chain, let t(x,j) be defined by t(x, 0)=1 and t(x,j)=x t(x,j−1). Then f(k) exists for all k (originally proved by D. White), and t(2,k) 〈 f(K) 〈t(е + εk, k) , where εk → 0 as k→∞. Alternatively, the largest k such that every regression on P nis guaranteed to have a monotone k-chain lies between lg*(n) and lg*(n)−2, inclusive, where lg*(n) is the number of appliations of logarithm base 2 required to reduce n to a negative number. Analogous results hold for choice functions, which are regressions in which every element is mapped to a minimal element.
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    Order 4 (1987), S. 269-272 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05A15 ; Interval order ; enumeration
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    Topics: Mathematics
    Notes: Abstract An algorithm is obtained for enumerating the interval orders of a given cardinality.
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    Order 3 (1987), S. 345-353 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06A23 ; Order-dimension ; Ferrers relation ; partition lattice ; linear lattice
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    Topics: Mathematics
    Notes: Abstract The aim of this paper is to study the order-dimension of partition lattices and linear lattices. Our investigations were motivated by a question due to Bill Sands: For a lattice L, does dim L=n always imply |L|≥2 n ? We will answer this question in the negative since both classes of lattices mentioned above form counterexamples. In the case of the partition lattices, we will determine the dimension up to an absolute constant. For the linear lattice over GF(2), L n , we determine the dimension up to a factor C/n for an absolute constant C.
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    Order 3 (1987), S. 369-382 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partial order ; tree ; chain decomposition ; width
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    Topics: Mathematics
    Notes: Abstract We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval [a,b] contains at most λ maximal chains, if some antichain has cardinality v, and if there are χ1 chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ⩽χ1λv (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).
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    Order 4 (1987), S. 37-42 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partially ordered sets ; Van der Waerden's arithmetic sequence
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    Topics: Mathematics
    Notes: Abstract Van der Waerden's arithmetic sequence theorem—in particular, the ‘density version’ of Szemerédi—is generalized to partially ordered sets in the following manner. Let w and t be fixed positive integers and ε〉0. Then for every sufficiently large partially ordered set P of width at most w, every subset S of P satisfying |S|≥ε|P| contains a chain a 1, a 2,..., a 1 such that the cardinality of the interval [a i, a i+1] in P is the same for each i.
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    Order 5 (1988), S. 163-171 
    ISSN: 1572-9273
    Keywords: 05C45 ; 05C70 ; 06A10 ; Boolean lattice ; Hamiltonian cycle ; matching
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    Topics: Mathematics
    Notes: Abstract New classes of explicit matchings for the bipartite graph ℬ(k) consisting of the middle two levels of the Boolean lattice on 2k+1 elements are constructed and counted. This research is part of an ongoing effort to show that ℬ(k) is Hamiltonian.
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    Order 6 (1989), S. 59-68 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; minimal cutset ; chain complete ; special points ; regular posets ; Menger's theorem
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    Topics: Mathematics
    Notes: Abstract If P is a poset, the associated PT-order is the quasi order ⊴ in which a ⊴ b holds if every maximal chain of P which passes through a also passes through b. P is special if whenever A is a chain in P and a=sup A or inf A, then there is b ∈ A such that b ⊴ a. It is proved that if P is chain complete and special then the set of ⊴-maximal elements is ⊴-dominating and contains a minimal cutset. As corollaries of this, we give partial answers to (i) a question of Rival and Zaguia by showing that if P is regular and special every element is in a minimal cutset and (ii) a question of Brochet and Pouzet by showing that if P is chain complete and special then it has the Menger property.
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    Order 7 (1990), S. 145-167 
    ISSN: 1572-9273
    Keywords: 06A10 ; 08A40 ; 08B10 ; 08C05 ; 08C15 ; Order-primal ; clone ; congruence-distributive ; duality ; category equivalence ; near-unanimity function
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    Topics: Mathematics
    Notes: Abstract A finite, nontrivial algebra is order-primal if its term functions are precisely the monotone functions for some order on the underlying set. We show that the prevariety generated by an order-primal algebra P is relatively congruence-distributive and that the variety generated by P is congruence-distributive if and only if it contains at most two non-ismorphic subdirectly irreducible algebras. We also prove that if the prevarieties generated by order-primal algebras P and Q are equivalent as categories, then the corresponding orders or their duals generate the same order variety. A large class of order-primal algebras is described each member of which generates a variety equivalent as a category to the variety determined by the six-element, bounded ordered set which is not a lattice. These results are proved by considering topological dualities with particular emphasis on the case where there is a monotone near-unanimity function.
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    Order 7 (1990), S. 249-266 
    ISSN: 1572-9273
    Keywords: 05C99 ; 06A10 ; Covering graph ; partially ordered set
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    Topics: Mathematics
    Notes: Abstract We give a construction of lattices whose covering graphs can be oriented as a graded order with bottom v for any vertex v in the lattice.
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    Order 7 (1990), S. 329-339 
    ISSN: 1572-9273
    Keywords: 06A10 ; 60C05 ; Partially ordered set ; random order ; dimension
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    Topics: Mathematics
    Notes: Abstract A relationship is established between (partially) ordered sets of dimension 2 chosen randomly on a labelled set, chosen randomly by isomorphism type, or generated by pairs of random linear orderings. As a consequence we are able to determine the limiting probability (in each of the above sample spaces) that a two-dimensional order is rigid, is uniquely realizable, or has uniquely orientable comparability graph; all these probabilities lie strictly between 0 and 1. Finally, we show that the number of 2-dimensional (partial) orderings of a labelled n-element set is $$(1 + o(1))n!^2 /(2\sqrt e ).$$ .
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    Order 7 (1990), S. 353-359 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C15 ; Linear extension ; jump number
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    Topics: Mathematics
    Notes: Abstract An ordered set P is called K-free if it does not contain a four-element subset {a, b, c, d} such that a 〈 b is the only comparability among these elements. In this paper we present a polynomial algorithm to find the jump number of K-free ordered sets.
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    Order 6 (1990), S. 313-318 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partial order ; linear extension ; majority cycle
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    Topics: Mathematics
    Notes: Abstract For points x and y in a poset (X, 〉) let x〉 p y mean that more linear extensions of the poset have x above y than y above x. It has been known for some time that 〉 p can have cycles when the height of the poset is two or more. Moreover, the smallest posets with a 〉 p cycle have nine points and heights of 2, 3 and 4. We show here that height-1 posets can also have 〉 p cycles. Our smallest example for this phenomenon has 15 points.
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    Order 6 (1990), S. 351-366 
    ISSN: 1572-9273
    Keywords: 05A17 ; 06A10 ; Young's lattice ; matching ; partially ordered set
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    Topics: Mathematics
    Notes: Abstract If the level sets of a ranked partially ordered set are totally ordered, the greedy match between adjacent levels is defined by successively matching each vertex on one level to the first available unmatched vertex, if any, on the next level. Aigner showed that the greedy match produces symmetric chains in the Boolean algebra. We extend that result to partially ordered sets which are products of chains. It is widely thought that for Young's lattices corresponding to rectangles, the greedy match is complete. We show here that the greedy match is, in fact, complete for n×2, n×3 and n×4 rectangles but not for n×k rectangles if k≥5 and n is sufficiently large.
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    Order 7 (1990), S. 5-9 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05C25 ; 20B25 ; 20B27 ; Automorphism group ; comparability graph ; covering graph
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    Topics: Mathematics
    Notes: Abstract Let G be a group and H a subgroup of G. It is shown that there exists a partially ordered set (X, ⩽) such that G is isomorphic to the group of all automorphisms of the comparability graph of (X, ⩽) and such that under this isomorphism H is mapped onto the group of all order-automorphisms of (X, ⩽). There also exists a partially ordered set (Y, ⩽) such that G is isomorphic to the group of all automorphisms of the covering graph of (Y, ⩽) and such that under this isomorphism H is mapped onto the group of all order-automorphisms of (Y, ⩽). In this representation X and Y can be taken to be finite if G is finite and of the same cardinality as G if G is infinite.
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    Order 7 (1990), S. 267-273 
    ISSN: 1572-9273
    Keywords: 06A10 ; Linear extension ; realization
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    Notes: Abstract A k-realization of an ordered set P is a sequence of k linear orderings of the underlying set of P, whose intersection is (the order relation of) P. We determine the status of the number of k-realizations with respect to comparability invariance, and we show that among all orders on the set {1, 2, ..., n}, the antichain has the most k-realizations, for any k〉1. The latter intuitively reasonable result rests ultimately on an observation related to comparability invariance for numbers of linear extensions.
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    Order 7 (1990), S. 349-352 
    ISSN: 1572-9273
    Keywords: 68C15 ; 06A10 ; Posets ; preemptive ; scheduling
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    Topics: Mathematics
    Notes: Abstract Optimal preemptive schedules of jobs with unit completion times and given precedence constraints may require arbitrarily many short intervals of work on a single task.
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    Order 8 (1991), S. 63-75 
    ISSN: 1572-9273
    Keywords: 06A10 ; Infinite ordered set ; spanned ; maximal chain ; disjoint family ; cutset-number
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    Topics: Mathematics
    Notes: Abstract We say that an ordered set P is spanned by a family C of chains if P=(P, ⩽) is the transitive closure of ∪{(C, ≤ | C) C ∈ C. It is shown that there is a function h: ω→ω such that if P is spanned by k〈ω chains, then P has a finite cutset-number ⩽h(k) (i.e. for any x∈P, there is a finite set F of size |F|⩽h(k)−1, such that the elements of F are incomparable with x and {x}∪F meets every maximal chain of P). The function h is exponentially bounded but eventually dominates any polynomial function, even if it is only required that there are at most h(k) pairwise disjoint maximal chains in P, whenever P is spanned by k〈ω chains.
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    Order 9 (1992), S. 367-396 
    ISSN: 1572-9273
    Keywords: 06A05 ; 06A10 ; 06A99 ; Ordering ; axiomatization ; closure properties ; transitivity
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    Topics: Mathematics
    Notes: Abstract A set of six axioms for sets of relations is introduced. All well-known sets of specific orderings, such as linear and weak orderings, satisfy these axioms. These axioms impose criteria of closedness with respect to several operations, such as concatenation, substitution and restriction. For operational reasons and in order to link our results with the literature, it is shown that specific generalizations of the transitivity condition give rise to sets of relations which satisfy these axioms. Next we study minimal extensions of a given set of relations which satisfy the axioms. By this study we come to the fundamentals of orderings: They appear to be special arrangements of several types of disorder. Finally we notice that in this framework many new sets of relations have to be regarded as a set of orderings and that it is not evident how to minimize the number of these new sets of orderings.
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    Order 9 (1992), S. 163-175 
    ISSN: 1572-9273
    Keywords: Primary 06A07 ; secondary 05C70 ; Partial order ; interval ; stability ; covering ; Sperner property ; symmetric chains ; NP-completeness
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    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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    Positivity 1 (1997), S. 319-330 
    ISSN: 1572-9281
    Keywords: delay equations ; stability ; positive solutions ; spectral growth condition
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    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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    ISSN: 1572-9281
    Keywords: asymptotic stability ; dichotomic maps ; retarded functional differential equation ; stability
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    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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    Queueing systems 12 (1992), S. 369-389 
    ISSN: 1572-9443
    Keywords: Perturbation analysis ; stability ; stochastic difference equations ; simulation
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    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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    Queueing systems 13 (1993), S. 87-110 
    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
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    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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    Queueing systems 15 (1994), S. 279-288 
    ISSN: 1572-9443
    Keywords: Sample-path ; point processes ; workload ; stability
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    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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    Queueing systems 21 (1995), S. 67-95 
    ISSN: 1572-9443
    Keywords: Polling systems ; stability ; stationary regime
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    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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    Queueing systems 22 (1996), S. 47-63 
    ISSN: 1572-9443
    Keywords: Sample-path analysis ; stability ; rate stability ; ω-rate stability ; input-output process ; queueing ; infinite-server queues
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    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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    Queueing systems 22 (1996), S. 345-366 
    ISSN: 1572-9443
    Keywords: State-dependent service and interarrival times ; Lindley equation ; recursive stochastic equations ; stability ; normal approximations
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    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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    Queueing systems 29 (1998), S. 55-73 
    ISSN: 1572-9443
    Keywords: multi‐server queue ; customer class ; state‐dependent routing ; stability ; Markov chain ; fluid limit
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    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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    Queueing systems 32 (1999), S. 131-168 
    ISSN: 1572-9443
    Keywords: stability ; positive recurrence ; fluid limit ; polling system ; exhaustive service policy
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    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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    Queueing systems 34 (2000), S. 1-35 
    ISSN: 1572-9443
    Keywords: multiple access ; CDMA ; rates of convergence ; stability ; functional limit theorems ; transient analysis ; Markov-modulated capture channel
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    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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    Queueing systems 16 (1994), S. 115-137 
    ISSN: 1572-9443
    Keywords: Polling systems ; stability ; stochastic continuity ; general arrival process ; functional limit theorems.
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    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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    Celestial mechanics and dynamical astronomy 56 (1993), S. 45-50 
    ISSN: 1572-9478
    Keywords: Restricted problem ; stability ; planets of double stars
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    Topics: Physics
    Notes: Abstract Numerical simulations are made within the framework of the plane restricted three-body problem, in order to find out if stable orbits for planets around one of the two components in double stars can exist. For any given set of initial parameters (the mass ratio of the two stars and the eccentricity of their orbit around each other), the phase-space of initial positions and velocities is systematically explored. In previous works, systematic exploration of the circular model as well as studies of more realistic (elliptic) cases such as Sun-Jupiter and the nearby α Centauri and Sirius systems, large stable planetary orbits were found to exist around both components of the binary, up to distances from each star of the order or more than half the binary's periastron separation. The first results presented here for the η Coronae Borealis system confirm the previous studies.
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    Celestial mechanics and dynamical astronomy 58 (1994), S. 203-213 
    ISSN: 1572-9478
    Keywords: libration points ; resonances ; stability
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    Topics: Physics
    Notes: Abstract The stability of the triangular libration points in the case when the first and the second order resonances appear was investigated. It was proved that the first order resonances do not cause instability. The second order resonances may lead to instability. Domains of the instability in the two-dimensional parameter space were determined.
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    Celestial mechanics and dynamical astronomy 74 (1999), S. 19-57 
    ISSN: 1572-9478
    Keywords: stability ; Hamiltonian ; two centers ; oblate planet ; galactic disks ; dipole
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    Topics: Physics
    Notes: Abstract Relative equilibria occur in a wide variety of physical applications, including celestial mechanics, particle accelerators, plasma physics, and atomic physics. We derive sufficient conditions for Lyapunov stability of circular orbits in arbitrary axisymmetric gravitational (electrostatic) and magnetic fields, including the effects of local mass (charge) and current density. Particularly simple stability conditions are derived for source‐free regions, where the gravitational field is harmonic (∇2U = 0) or the magnetic field irrotational (∇ × B = 0). In either case the resulting stability conditions can be expressed geometrically (coordinate‐free) in terms of dimensionless stability indices. Stability bounds are calculated for several examples, including the problem of two fixed centers, the J2 planetary model, galactic disks, and a toroidal quadrupole magnetic field.
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    Celestial mechanics and dynamical astronomy 75 (1999), S. 251-285 
    ISSN: 1572-9478
    Keywords: unrestricted problem ; rotational motion ; rigid body dynamics ; libration points ; stability ; resonances
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    Topics: Physics
    Notes: Abstract We present an analysis of the model introduced by Kokoriev and Kirpichnikov (1988) for the study of unrestricted planar motion of a point mass and a symmetric rigid body whose gravity field is approximated by two point masses (a dumb-bell model). To show possible generalization of the model, we give a systematic derivation of equations of motion for a more general unrestricted problem of a point and a rigid body possessing a plane of dynamical symmetry. We give a simple description of bifurcation of triangular libration points, and we perform an analysis of their linear stability. We propose to extend the model of Kokoriev and Kirpichnikov (1988) to a case when the symmetric body is oblate. In the proposed model the gravity field of moving and rotating body is approximated by two complex masses at complex distance (a complex dumb-bell model). An analysis of bifurcation of the triangular libration points in this model is also presented.
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    Celestial mechanics and dynamical astronomy 78 (2000), S. 227-241 
    ISSN: 1572-9478
    Keywords: stability ; normal form ; spin-orbit resonance
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    Topics: Physics
    Notes: Abstract We consider a model of spin-orbit interaction, describing the motion of an oblate satellite rotating about an internal spin-axis and orbiting about a central planet. The resulting second order differential equation depends upon the parameters provided by the equatorial oblateness of the satellite and its orbital eccentricity. Normal form transformations around the main spin-orbit resonances are carried out explicitly. As an outcome, one can compute some invariants; the fact that these quantities are not identically zero is a necessary condition to prove the existence of nearby periodic orbits (Birkhoff fixed point theorem). Moreover, the nonvanishing of the invariants provides also the stability of the spin-orbit resonances, since it guarantees the existence of invariant curves surrounding the periodic orbit.
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    Journal of computational analysis and applications 2 (2000), S. 293-308 
    ISSN: 1572-9206
    Keywords: parabolic equations ; ADI scheme ; stability
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    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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    Journal of dynamics and differential equations 5 (1993), S. 625-671 
    ISSN: 1572-9222
    Keywords: Scalar reaction-diffusion equation ; singular perturbation methods ; internal layer ; Neumann layer ; stability ; 35K57 ; 35B25 ; 35B35
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    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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    Journal of dynamics and differential equations 6 (1994), S. 639-658 
    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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    Order 1 (1985), S. 235-247 
    ISSN: 1572-9273
    Keywords: 06A10 ; Chain ; antichain ; cutset
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    Topics: Mathematics
    Notes: Abstract A subset A of an ordered set P is a cutset if each maximal chain of P meets A; if, in addition, A is an antichain call it an antichain cutset. Our principal result is a characterization, by means of a ‘forbidden configuration’, of those finite ordered sets, which can be expressed as the union of antichain cutsets.
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    Order 1 (1985), S. 317-331 
    ISSN: 1572-9273
    Keywords: 06A10 ; 60C05 ; Partially ordered set ; probabilistic methods ; dimension
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    Topics: Mathematics
    Notes: Abstract Letk andn be positive integers and fix a setS of cardinalityn; letP k (n) be the (partial) order onS given by the intersection ofk randomly and independently chosen linear orders onS. We begin study of the basic parameters ofP k (n) (e.g., height, width, number of extremal elements) for fixedk and largen. Our object is to illustrate some techniques for dealing with these ‘random orders’ and to lay the groundwork for future research, hoping that they will be found to have useful properties not obtainable by known constructions.
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    Order 1 (1985), S. 371-375 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; chain ; antichain ; cutset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown that ifP is a poset containing noN, then every minimal cutset inP is an antichain, that the converse also holds whenP is finite, and that this converse fails in general.
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    Order 1 (1984), S. 35-46 
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered set ; chain ; antichains ; width ; cutset
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An ordered set (P,≤) has the m cutset property if for each x there is a set Fx with cardinality less than m, such that each element of Fx is incomparable to x and {x} ∪ Fx meets every maximal chain of (P,≤). Let n be least, such that each element x of any P having the m cutset property belongs to some maximal antichain of cardinality less than n. We specify n for m 〈 w. Indeed, n-1=m= width P for m=1,2,n=5 if m=3 and n⩾ℵ1 if m ≥4. With the added hypothesis that every bounded chain has a supremum and infimum in P, it is shown that for 4⩽m⩽ℵ0, n=ℵ0. That is, if each element x has a finite cutset Fx, each element belongs to a finite maximal antichain.
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    Order 1 (1984), S. 7-19 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05C20 ; 68C25 ; Partial order ; linear extension ; jump number ; line digraph ; cyclomatic number ; spanning branching ; Eulerian digraph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is to present a graph-theoretic approach to the jump number problem for N-free posets which is based on the observation that the Hasse diagram of an N-free poset is a line digraph. Therefore, to every N-free poset P we can assign another digraph which is the root digraph of the Hasse diagram of P. Using this representation we show that the jump number of an N-free poset is equal to the cyclomatic number of its root digraph and can be found (without producing any linear extension) by an algorithm which tests if a given poset is N-free. Moreover, we demonstrate that there exists a correspondence between optimal linear extensions of an N-free poset and spanning branchings of its root digraph. We provide also another proof of the fact that optimal linear extensions of N-free posets are exactly greedy linear extensions. In conclusion, we discuss some possible generalizations of these results to arbitrary posets.
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    Order 1 (1984), S. 83-92 
    ISSN: 1572-9273
    Keywords: 06A10 ; Ordered sets ; exponentiation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently there has been significant progress in the study of powers of ordered sets. Much of this work has concerned cancellation laws for powers and uses these two steps. First, logarithmic operators are introduced to transform cancellation problems for powers into questions involving direct product decompositions. Second, refinement theorems for direct product decompositions are brought to bear. Here we present two results with the aim of highlighting these steps.
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  • 94
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    Order 11 (1994), S. 197-210 
    ISSN: 1572-9273
    Keywords: 06A10 ; 68C25 ; On-line algorithm ; lattice of maximal antichains
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the on-line computation of the lattice of maximal antichains of a finite poset $$\tilde P$$ . This on-line computation satisfies what we call the “linear extension hypothesis”: the new incoming vertex is always maximal in the current subposet of $$\tilde P$$ . In addition to its theoretical interest, this abstraction of the lattice of antichains of a poset has structural properties which give it interesting practical behavior. In particular, the lattice of maximal antichains may be useful for testing distributed computations, for which purpose the lattice of antichains is already widely used. Our on-line algorithm has a run time complexity of $$\mathcal{O}((\left| P \right| + \omega ^2 (P))\omega (P)\left| {MA(P)} \right|),$$ , where |P| is the number of elements of the poset, $$\tilde P$$ , |MA(P)| is the number of maximal antichains of $$\tilde P$$ and ω(P) is the width of $$\tilde P$$ . This is more efficient than the best off-line algorithms known so far.
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    Order 11 (1994), S. 309-316 
    ISSN: 1572-9273
    Keywords: 90B35 ; 06A10 ; Scheduling ; communication delays ; parallel processors ; precedence constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that a greedy algorithm for scheduling unit time jobs on two machines with unit communication delays produces an optimal schedule when the precedence constraints are given by a rooted forest. We also give a min/max relationship for the length of such a schedule. The min/max result (for forests and two machines) shows that the addition of unit communication delays increases the optimal schedule length by at most one.
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    Order 2 (1985), S. 25-40 
    ISSN: 1572-9273
    Keywords: 06A10 ; 05C20 ; 05C38 ; Order ; diagram ; graph ; orientation ; cycle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study some equivalent and necessary conditions for a finite graph to be the covering graph of a (partially) ordered set. For each κ≥1, M. Aigner and G. Prins have introduced a notion of a vertex colouring, here called κ-good colouring, such that a 1-good colouring is the usual concept and graphs that have a 2-good colouring are precisely covering graphs. We present some inequalities for the corresponding chromatic numbers χκ, especially for x 2. There exist graphs that satisfy these inequalities for κ=2 but are not covering graphs. We show also that x 2 cannot be bounded by a function of x=x 1. A construction of Nešetřil and Rödl is used to show that x 2 is not bounded by a function of the girth.
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    Order 2 (1985), S. 387-402 
    ISSN: 1572-9273
    Keywords: 06A10 ; Poset ; linear extension ; correlation ; universal correlation ; Graham, Yao, and Yao inequality ; xyz inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Posets $$A,{\text{ }}B \subseteq X{\text{ x }}X$$ are said to be correlated with respect to another poset R on X (we write A↑ R B) if P(R∪A) P(R∪B)≤P(R∪A∪B) P(R). Here P(S) is the probability that a randomly chosen bijection from X to the totally ordered set with |X| elements is a linear extension of S. We study triples (A, B, R) such that A ↑ R B holds for all extensions S of R (we write A $$\begin{array}{*{20}c} \uparrow \\ \uparrow \\ \end{array}$$ R B). Two well-known correlation inequalities, the xyz inequality and an inequality of Graham, Yao, and Yao, can be considered as giving cases when this relation holds. We show when the Graham, Yao, and Yao inequality holds strictly. Our main result is a classification of all R such that (a, b) $$\begin{array}{*{20}c} \uparrow \\ \uparrow \\ \end{array}$$ R (c, d) holds, where a, b, c, d are elements of X.
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    Order 3 (1986), S. 15-20 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partially ordered set
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let P be a partially ordered set. Define k = k (P) = max p∈ |{x ∈ P : p 〈 x or p = x}|, i.e., every element is comparable with at most k others. Here it is proven that there exists a constant c (c 〈 50) such that dim P 〈 ck(log k)2. This improves an earlier result of Rödl and Trotter (dim P ≤2 k 2+2). Our proof is nonconstructive, depending in part on Lovász' local lemma.
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    Order 2 (1985), S. 269-274 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partial order ; fixed point ; comparability graph
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We show that the fixed point property is comparability invariant for finite ordered sets; that is, if P and Q are finite ordered sets with isomorphic comparability graphs, then P has the fixed point property if and only if Q does. In the process we give a characterization of comparability invariants which can also be used to give shorter proofs of some known results.
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    Order 5 (1988), S. 21-22 
    ISSN: 1572-9273
    Keywords: 06A10 ; Dimension ; width ; chain-covering number
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A partially ordered set with no infinite antichains may have arbitrarily large dimension.
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