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  • stability
  • Springer  (12)
  • American Institute of Physics (AIP)
  • Cell Press
  • Institute of Electrical and Electronics Engineers (IEEE)
  • 1985-1989  (12)
  • 1985  (12)
Collection
Publisher
  • Springer  (12)
  • American Institute of Physics (AIP)
  • Cell Press
  • Institute of Electrical and Electronics Engineers (IEEE)
Years
  • 1985-1989  (12)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    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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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Acta applicandae mathematicae 4 (1985), S. 225-258 
    ISSN: 1572-9036
    Keywords: 92A15 ; Prey ; predator ; competition ; dynamical system ; ordinary differential equation ; phase diagram ; equilibrium ; trajectory ; stability ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a problem of the dynamics of prey-predator populations suggested by the content of a letter of the biologist Umberto D'Ancona to Vito Volterra. The main feature of the problem is the special type of competition between predators of the same species as well as of different species. Two classes of cases are investigated: a first class in which the behaviour of the predator is ‘blind’ and the second one in which the behaviour is ‘intelligent’. A qualitative analysis of the dynamical systems under consideration is followed by a numerical analysis of the most significant cases.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 21 (1985), S. 285-298 
    ISSN: 1432-1416
    Keywords: Population dynamics ; coexistence ; mutualism ; persistence ; predator-mediated coexistence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations x i = X i f i (i = 1, 2, 3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the f i , in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 22 (1985), S. 81-104 
    ISSN: 1432-1416
    Keywords: FitzHugh-Nagumo equation ; pulse solution ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The FitzHugh-Nagumo equation u t =u xx +f(u)-w, u t =b(u-dw), is a simplified mathematical description of a nerve axon. If the parameters b〉0 and d⩾0 are taken suitably, this equation has two travelling pulse solutions with different propagation speeds. We study the stability of the fast pulse solution when b〉0 is sufficiently small. It is proved analytically by eigenvalue analysis that the fast pulse solution is “exponentially stable” if d〉0, and is “marginally stable” but not exponentially stable if d=0.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 24 (1985), S. 551-555 
    ISSN: 1435-1528
    Keywords: Torsional flow ; Oldroyd-B fluid ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract It is shown that the exact solution of the torsional flow of a class of Oldroyd-type fluids is kinematically similar to that for a Newtonian fluid. Furthermore, it is shown by a linearized stability analysis and by numerical integration, that the basic flow is unstable at high Weissenberg numbers. An Oldroyd fluid which has a negative second-normal stress coefficient is found to be more stable than one with zero (or positive) second-normal stress coefficient in this flow.
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 24 (1985), S. 321-322 
    ISSN: 1435-1528
    Keywords: Viscometric flow ; stability ; short memory approximation ; change of type ; upper convected Maxwell model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Rheologica acta 24 (1985), S. 469-473 
    ISSN: 1435-1528
    Keywords: Liquid crystal ; nematic ; semigroup ; stability ; tumbled state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract In shear flow of a nematic liquid crystal withα 3 ≧ 0 flow alignment cannot occur. The stability of the stationary in-plane solution, “the tumbled state”, is investigated using abstract techniques. Employing the existence of an elastic energy a sufficient criterion for stability is formulated. This criterion depends on the in-plane solution which is obtainable as a quadrature that is non-elementary except in special cases. It is shown that the tumbled state is stable and asymptotically stable for some physical configurations. The criterion presented is not a necessary condition for stability and thus only gives a lower bound.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical methods of operations research 29 (1985), S. 65-104 
    ISSN: 1432-5217
    Keywords: Additive cost criterion ; analytic behaviour of strategies ; ES strategy ; list schedule ; MES strategy ; priority rule ; quasi-stability ; regular measure of performance ; scheduling problems ; set strategy ; shift property ; stability ; stochastic scheduling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The paper introduces the finite class of set strategies for stochastic scheduling problems. It is shown that the knownstable classes of strategies such as ES and MES strategies are of this type, as arelist-scheduling strategies such as LEPT and SEPT and other, more complicatedpriority-type strategies. Roughly speaking, set strategies are characterized by the fact that the decision as to which jobs should be started at timet depends only on the knowledge of the two sets of jobs finished up to timet and being processed at timet. Contrary to list scheduling strategies, set strategies may involve deliberate idleness of machines, i.e. may not be greedy and can therefore not generally be induced by priority rules. It is demonstrated that set strategies have useful properties. They are e.g.λ n -almost everywhere continuous and therefore show satisfactorystability behaviour w.r.t. weak convergence of the joint distribution of job durations. Furthermore, the optimum w.r.t.all strategies is already attained on this class if job durations are independent and exponentially distributed and the performance measure fulfills a certainshift condition. This shift property is a quite natural concept and generalizes aspects of the notion ofadditivity in semi-Markov decision theory and stochastic dynamic optimization. Its complete analytical characterization is a major object of this paper. Typical additive cost criteria such as makespan and flowtime are of course covered, which yields simultaneously a first step towards generalization of optimality of LEPT and SEPT rules, as known for special cases. In fact, in view of the obtained optimality result, the question of when deliberate idleness of machines can be avoided, gains considerable interest, as it characterizes stochastic environments in whichpriority strategies are optimal. This provides a major link with current research on the analysis of networks of queues in the context of computer systems.
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  • 10
    ISSN: 1573-0646
    Keywords: 2,5-diaziridinyl-3,6-bis(2-hydroxyethylamino)-1,4-benzoquinone ; BZQ ; light-sensitive ; solution ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Medicine
    Notes: Summary The stability of the potential antitumour agent 2,5-diaziridinyl-3,6-bis(2-hydroxyethylamino)-1,4-benzoquinone (BZQ; NSC 224070) has been investgated by high-performance liquid chromatography. At 22°C in 0.05M buffer, BZQ was most stable at pH 9 with an apparent first-order rate constant (k) of about 0.014 h−11. There was reduced stability at pH values above and below 9.0. At a pH of 3 and 12 the values of k were 38 and 0.3 h−1, respectively. Stability of BZQ was adversely affected by increased temperatures (above 0°C), increased buffer concentration and light. Solutions of BZQ could not be frozen for any length of time, as the drug precipitated out in a form that would not redissolve (possibly a polymer). For parenteral administration to patients, it is suggested that BZQ would be most stable in 1.26% sodium bicarbonate solution when at room temperature, under normal laboratory lighting, 5% of the drug degraded (t0.95) in 5.5 h. Increased stability is obtainable in this medium by refrigeration and vigorous exclusion of light. Long term (24 h) infusions of BZQ could be considered in hypotonic sodium bicarbonate (30 mM) with careful exclusion of light as long as the volume of the infusion was small, e.g. 1 ml/h. Under these conditions to.95 was 42 h at 21.5°C.
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  • 11
    Electronic Resource
    Electronic Resource
    Springer
    Periodica mathematica Hungarica 16 (1985), S. 1-5 
    ISSN: 1588-2829
    Keywords: Primary 34A50, 65L05 ; Secondary 41A15 ; Differential equations ; initial value problem ; spline function ; linear multistep method ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we continue the study [4] of the stability question of the quasidouble step spline function approximations,s(x) ∈ C m−2 , to the initial value problemy (n) = f(x, y, ⋯, y (n−1) ). It will be shown that the method is unstable and hence divergent form ≥ n + 4.
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  • 12
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 47 (1985), S. 235-252 
    ISSN: 1573-2878
    Keywords: Uncertain dynamical systems ; robotic tracking ; stability ; deterministic feedback control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The tracking problem for a robotic manipulator withn controlled degrees of freedom and uncertain dynamics is considered. Based on the deterministic theory of Refs. 1–15 and requiring only knowledge of bounds on the system uncertainty, a classC of continuous feedback controls (adapted from Ref. 11) is proposed with respect to which the uncertain tracking system is practically stabilizable in the sense that, given a feasible path to be tracked and an arbitrarily small neighborhood σ of the origin in the appropriate error space, there exists a control inC such that the tracking error for the feedback controlled uncertain system is ultimately bounded with respect to σ. The theory is illustrated in a numerical example of a robot with two degrees of freedom.
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