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  • Articles  (293)
  • stability  (293)
  • Springer  (293)
  • Mathematics  (222)
  • Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics  (102)
  • 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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    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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  • 3
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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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  • 4
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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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  • 5
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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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  • 6
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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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  • 7
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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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  • 8
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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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  • 9
    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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  • 10
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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
    Source: Springer Online Journal Archives 1860-2000
    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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  • 11
    ISSN: 1572-8900
    Keywords: Chemiluminescence ; oxidation ; stability ; acrylonitrile-butadiene-styrene (ABS) ; ABS/polycarbonate blend
    Source: Springer Online Journal Archives 1860-2000
    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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  • 12
    ISSN: 1572-8900
    Keywords: Chemiluminescence ; oxidation ; stability ; acrylonitrile-butadiene-styrene (ABS)
    Source: Springer Online Journal Archives 1860-2000
    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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  • 13
    ISSN: 1572-8900
    Keywords: Capillary zone electrophoresis ; oligomers ; lactic acid ; glycolic acid ; 3-hydroxybutyric acid ; water solubility ; stability ; degradation
    Source: Springer Online Journal Archives 1860-2000
    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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  • 14
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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
    Source: Springer Online Journal Archives 1860-2000
    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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  • 15
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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
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.
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    Journal of dynamics and differential equations 10 (1998), S. 151-188 
    ISSN: 1572-9222
    Keywords: Fourth-order solitary waves ; stability ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study ground-state traveling wave solutions of a fourth-order wave equation. We find conditions on the speed of the waves which imply stability and instability of the solitary waves. The analysis depends on the variational characterization of the ground states rather than information about the linearized operator.
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    Journal of dynamics and differential equations 6 (1994), S. 37-51 
    ISSN: 1572-9222
    Keywords: Celestial mechanics ; relative equilibria ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A criterion for the linear stability of relative equilibria of the Newtoniann-body problem is found in the case whenn−1 of the masses are small. Several stable periodic orbits of the problem are presented as examples.
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  • 18
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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
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a finite ranked posetP, let α(P) be the maximum size of a subset ofP such that no two elements of it belong simultaneously to some interval ofP and let ϱ(P) be the minimum number of intervals covering all elements ofP. We say thatP has the strong interval stability property (resp. the strong interval covering property) if for each subposetP′ induced by consecutive levels ofP, i.e.,P′=P (l)∪...∪P (u), one has α(P′)=max{|P (l)|, |P (u)|} (resp. ϱ(P′)=max{|P (l)|, |P (u)|}). We prove these properties for several classes of posets and discuss some general facts concerning the numbers α(P) and ϱ(P), e.g., NP-completeness and min-max relations.
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    Positivity 1 (1997), S. 319-330 
    ISSN: 1572-9281
    Keywords: delay equations ; stability ; positive solutions ; spectral growth condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove stability for a semilinear delay equation, whose nonlinearity is majorized by a linear positive operator. The key ingredients are a spectral condition, positivity of solutions to the linear problem, and lattice properties of the Banach space.
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  • 20
    ISSN: 1572-9281
    Keywords: asymptotic stability ; dichotomic maps ; retarded functional differential equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation $$x'(t) = - b(t)x(t - r)$$ and of itsnonlinear generalization $$x'(t) = b(t)f(x(t - r))$$ are established.
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    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
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The multiple existences and their stability properties of stationary solutions with a single transition layer in some scalar reaction-diffusion equation are shown. Each solution is constructed by using classical singular perturbation methods and its stability property is determined by a simple algebraic quantity, say index, appearing in the construction of a solution.
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    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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    Set-valued analysis 5 (1997), S. 73-88 
    ISSN: 1572-932X
    Keywords: differential inclusion ; invariance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The properties of invariance, stability, asymptotic stability and attainability of a given compact set $$K \subset \mathbb{R}^n $$ with respect to a differential inclusion, have weak and strong versions: the weak version requires existence of a trajectory with the corresponding property, while the strong one requires this property for all trajectories. The following statement is proven in the paper (under slight restrictions) for each of the above-mentioned properties: if K has the weak property with respect to $$\dot x \in F(x) $$ , then there is a (regulation) mapping G such that G(x) ⊂ F(x) ∀ x and G has the strong property with respect to $${\dot x}$$ ε G(x). In addition, certain regularity of the set of solutions of the last inclusion is claimed.
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    Set-valued analysis 5 (1997), S. 365-375 
    ISSN: 1572-932X
    Keywords: set-valued mappings ; vector optimization ; stability
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    Topics: Mathematics
    Notes: Abstract We establish optimization results for set-valued mappings, with the image space given by a topological vector space partially ordered by a cone. Moreover, we obtain stability results relative to parametrized optimization problems. We use a weak semicontinuity concept related to the order structure of the image space and show how compactness assumptions used in previous papers can be lightened.
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    Annals of operations research 27 (1990), S. 343-369 
    ISSN: 1572-9338
    Keywords: Bifurcation ; singularities ; continuation ; parametric nonlinear programming ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Bifurcation and continuation techniques are introduced as a class of methods for investigating the parametric nonlinear programming problem. Motivated by the Fritz John first-order necessary conditions, the parametric programming problem is first reformulated as a closed system of nonlinear equations which contains all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points. Since changes in the structure of the solution set and critical point type can occur only at singularities, necessary and sufficient conditions for the existence of a singularity are developed in terms of the loss of a complementarity condition, the linear dependence constraint qualification, and the singularity of the Hessian of the Lagrangian on a tangent space. After a brief introduction to elementary bifurcation theory, some simple singularities in this parametric problem are analyzed for both branching and persistence of local minima. Finally, a brief introduction to numerical continuation and bifurcation procedures is given to indicate how these facts can be used in a numerical investigation of the problem.
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    Annals of operations research 56 (1995), S. 79-93 
    ISSN: 1572-9338
    Keywords: Multistage stochastic programs ; optimization in Banach spaces ; stability ; approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Multistage stochastic programs are regarded as mathematical programs in a Banach spaceX of summable functions. Relying on a result for parametric programs in Banach spaces, the paper presents conditions under which linearly constrained convex multistage problems behave stably when the (input) data process is subjected to (small) perturbations. In particular, we show the persistence of optimal solutions, the local Lipschitz continuity of the optimal value and the upper semicontinuity of optimal sets with respect to the weak topology inX. The linear case with deterministic first-stage decisions is studied in more detail.
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    Computational & mathematical organization theory 5 (1999), S. 5-30 
    ISSN: 1572-9346
    Keywords: network models ; organization theory ; rule following ; self organized ; stability ; work teams ; work routine
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    Topics: Mathematics
    Notes: Abstract Self-organized rule-following systems are increasingly relevant objects of study in organization theory due to such systems&2018; capacity to maintain control while enabling decentralization of authority. This paper proposes a network model for such systems and examines the stability of the networks&2018; repetitive behavior. The networks examined are Ashby nets, a fundamental class of binary systems: connected aggregates of nodes that individually compute an interaction rule, a binary function of their three inputs. The nodes, which we interpret as workers in a work team, have two network inputs and one self-input. All workers in a given team follow the same interaction rule. We operationalize the notion of stability of the team&2018;s work routine and determine stability under small perturbations for all possible rules these teams can follow. To study the organizational concomitants of stability, we characterize the rules by their memory, fluency, homogeneity, and autonomy. We relate these measures to work routine stability, and find that stability in ten member teams is enhanced by rules that have low memory, high homogeneity, and low autonomy.
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    Journal of dynamics and differential equations 12 (2000), S. 117-167 
    ISSN: 1572-9222
    Keywords: singular perturbation ; standing pulses ; stability ; Hopf bifurcation ; reaction-diffusion system
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    Topics: Mathematics
    Notes: Abstract Bifurcation phenomena from standing pulse solutions of the problem $$\varepsilon \tau u_t = \varepsilon ^2 u_{xx} + f(u,v),{\text{ }}v_t = v_{xx} + g(u,v)$$ is considered. ε(〉0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g.
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    Journal of dynamics and differential equations 5 (1993), S. 189-218 
    ISSN: 1572-9222
    Keywords: Equivariant bifurcation ; symmetry ; singularity ; equivariant jets and transversality ; normal forms ; universal unfolding ; stability ; structural stability ; 58F14 ; 58E07 ; 58C27
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    Topics: Mathematics
    Notes: Abstract The theoretical machinery from singularity theory introduced by Golubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problems, is completed and expanded while generalized to the multiple parameter context. In this setting the finite determinacy theorems or normal forms, the stability of equivariant bifurcation problems, and the structural stability of the universal unfolding are discussed.
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    Journal of dynamics and differential equations 6 (1994), S. 447-486 
    ISSN: 1572-9222
    Keywords: Free boundary problems ; gasless combustion ; stability ; Hopf bifurcation ; 35R35 ; 35B40 ; 80A25
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    Topics: Mathematics
    Notes: Abstract In this paper, we analyze a simple free boundary model associated with solid combustion and some phase transition processes. There is strong evidence that this “one-phase” model captures all major features of dynamical behavior of more realistic (and complicated) combustion and phase transition models. The principal results concern the dynamical behavior of the model as a bifurcation parameter (which is related to the activation energy in the case of combustion) varies. We prove that the basic uniform front propagation is asymptotically stable against perturbations for the bifurcation parameter above the instability threshold and that a Hopf bifurcation takes place at the threshold value. Results of numerical simulations are presented which confirm that both supercritical and subcritical Hofp bifurcation may occur for physically reasonable nonlinear kinetic functions.
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    Journal of dynamics and differential equations 9 (1997), S. 463-505 
    ISSN: 1572-9222
    Keywords: Difference equations ; random perturbation ; averaging ; diffusion approximation ; randomly perturbed iterations ; stability ; 3SR60 ; 60H15 ; 60J99
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    Topics: Mathematics
    Notes: Abstract Let (X, ℬ) and (Y,C) be two measurable spaces withX being a linear space. A system is determined by two functionsf(X): X→ X andϕ:X×Y→X, a (small) positive parameterε and a homogeneous Markov chain {y n } in (Y,C) which describes random perturbations. States of the system, say {x n ɛ ∈X, n=0, 1,⋯}, are determined by the iteration relations:x n+1 ɛ =f(x n ɛ )+ɛϕ(x n ɛ ,Yn+1) forn≥0, wherex 0 ɛ =x 0 is given. Here we study the asymptotic behavior of the solutionx n ɛ asε → 0 andn → ∞ under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.
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    Set-valued analysis 5 (1997), S. 377-390 
    ISSN: 1572-932X
    Keywords: differential inclusions ; stability ; boundedness of solutions ; Lyapunov functions
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    Topics: Mathematics
    Notes: Abstract For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions.
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    Set-valued analysis 4 (1996), S. 361-374 
    ISSN: 1572-932X
    Keywords: 34A60 ; 34E15 ; 34C29 ; differential inclusion ; singular perturbation ; averaging method ; controlability ; stability
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    Notes: Abstract We consider nonlinear, singularly perturbed differential inclusions and apply the averaging method in order to construct a limit differential inclusion for slow motion. The main approximation result states that the existence and regularity of the limit differential inclusion suffice to describe the limit behavior of the slow motion. We give explicit approximation rates for the uniform convergence on compact time intervals. The approach works under controllability or stability properties of fast motion.
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    Set-valued analysis 7 (1999), S. 209-238 
    ISSN: 1572-932X
    Keywords: nonsmooth analysis ; subdifferentials ; coderivatives ; implicit function theorem ; solvability ; stability ; open mapping theorem ; metric regularity ; multidirectional mean value inequality
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    Topics: Mathematics
    Notes: Abstract We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.
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    Set-valued analysis 1 (1993), S. 393-402 
    ISSN: 1572-932X
    Keywords: Primary: 49J40, 65K10, 47A55, 47H05, 65L20 ; Variational inequality ; perturbation ; unbounded and nonsmooth operators ; convex sets ; Hausdorff distance ; regularization ; monotonicity ; convergence ; stability
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    Notes: Abstract The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains Ω are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.
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    Journal of dynamics and differential equations 1 (1989), S. 299-325 
    ISSN: 1572-9222
    Keywords: Commodity markets ; time delays ; stability ; Hopf bifurcation ; 34K15 ; 45J05 ; 90A16
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    Topics: Mathematics
    Notes: Abstract A model for the dynamics of price adjustment in a single commodity market is developed. Nonlinearities in both supply and demand functions are considered explicitly, as are delays due to production lags and storage policies, to yield a nonlinear integrodifferential equation. Conditions for the local stability of the equilibrium price are derived in terms of the elasticities of supply and demand, the supply and demand relaxation times, and the equilibrium production-storage delay. The destabilizing effect of consumer memory on the equilibrium price is analyzed, and the ensuing Hopf bifurcations are described.
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    Journal of dynamics and differential equations 4 (1992), S. 161-190 
    ISSN: 1572-9222
    Keywords: Delay differential equations ; equilibrium ; stability ; limiting equations ; population dynamics ; 34K20 ; 34K25 ; 92A15
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    Topics: Mathematics
    Notes: Abstract Applying an analytical method and several limiting equations arguments, some sufficient conditions are provided for the existence of a unique positive equilibriumK for the delay differential equationx=−γx+D(x t ), which is the general form of many population models. The results are concerned with the global attractivity, uniform stability, and uniform asymptotic stability ofK. Application of the results to some known population models, which shows the effectiveness of the methods applied here, is also presented.
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    Journal of dynamics and differential equations 5 (1993), S. 105-128 
    ISSN: 1572-9222
    Keywords: Delay system ; stability ; relative variance ; dynamical disease
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    Notes: Abstract A new approach to the study of delay systems, applicable to physiological control systems and other systems where little information about the time delays is available, is examined. The method is based on the fact that stability information can be deduced from the statistical properties of the probability distribution that encodes the structure of the time delay. The main statistical variables used are the usual expectation parameter,E, and a modified variance, calledrelative variance and denotedR, that is invariant under time scale changes. Recent work of the author has shown that stability often improves asR increases whileE remains fixed. A four-parameter family of delay models is analysed in this paper, and the (E, R) pair is found to be a reliable indicator of stability over the global parameter domain of the family.
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    Journal of dynamics and differential equations 6 (1994), S. 325-334 
    ISSN: 1572-9222
    Keywords: Nonlinear Schrödinger equations ; anisotropic standing waves ; stability ; concentration compactness principle ; Davey-Stewartson system ; 35Q35 ; 35B35
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    Topics: Mathematics
    Notes: Abstract We study the stability of standing waves for a nonlinear Schrödinger equation, which derives from the generalized Davey-Stewartson system in the elliptic-elliptic case. We prove the existence of stable standing waves under certain conditions.
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    Journal of dynamics and differential equations 6 (1994), S. 631-637 
    ISSN: 1572-9222
    Keywords: stability ; fixed point index ; periodic solutions
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    Notes: Abstract In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR 2 has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.
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    Set-valued analysis 8 (2000), S. 253-266 
    ISSN: 1572-932X
    Keywords: Hausdorff metric ; linear inequality systems ; stability
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    Notes: Abstract In this paper, we propose a Hausdorff metric to measure the “distance” between two linear inequality systems on a real normed space X. For this topology, which comes through a pseudo-metric in the set Σ of linear inequality systems, the closedness of the feasible set mapping is studied, and at the same time a characterization of the stability of the subset Σ c of consistent sytems is given.
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    Annals of operations research 99 (2000), S. 251-265 
    ISSN: 1572-9338
    Keywords: stochastic programming ; bond portfolio management ; interest ratescenarios ; stability ; sensitivity
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    Topics: Mathematics , Economics
    Notes: Abstract The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients – the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.
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    Acta applicandae mathematicae 28 (1992), S. 1-42 
    ISSN: 1572-9036
    Keywords: 35R30 ; Inverse scattering ; stability ; noisy data
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    Notes: Abstract An algorithm is given for calculating the solution to the 3D inverse scattering problem with noisy discrete fixed energy data. The error estimates for the calculated solution are derived. The methods developed are of a general nature and can be used in many applications: in nondestructive evaluation and remote sensing, in geophysical exploration, medical diagnostics, and technology.
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    Advances in computational mathematics 10 (1999), S. 271-289 
    ISSN: 1572-9044
    Keywords: delay differential equations ; steady state solutions ; stability ; 34K20 ; 65J10
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    Notes: Abstract The characteristic equation of a system of delay differential equations (DDEs) is a nonlinear equation with infinitely many zeros. The stability of a steady state solution of such a DDE system is determined by the number of zeros of this equation with positive real part. We present a numerical algorithm to compute the rightmost, i.e., stability determining, zeros of the characteristic equation. The algorithm is based on the application of subspace iteration on the time integration operator of the system or its variational equations. The computed zeros provide insight into the system’s behaviour, can be used for robust bifurcation detection and for efficient indirect calculation of bifurcation points.
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    Annals of global analysis and geometry 11 (1993), S. 387-395 
    ISSN: 1572-9060
    Keywords: Curvatures of hypersurfaces ; Reilly's inequality ; stability ; 53 A 10 ; 53 C 42
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    Notes: Abstract We generalize Reilly's inequality for the first eigenvalue of immersed submanifolds ofIR m +1 and the total (squared) mean curvature, to hypersurfaces ofIR m +1 and the first eigenvalue of the higher order curvatures. We apply this to stability problems. We also consider hypersurfaces in hyperbolic space.
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    Applications of mathematics 45 (2000), S. 161-176 
    ISSN: 1572-9109
    Keywords: reaction-diffusion system ; unilateral conditions ; quasivariational inequality ; Leray-Schauder degree ; eigenvalue ; stability
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    Notes: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
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    BIT 17 (1977), S. 321-328 
    ISSN: 1572-9125
    Keywords: 5.15 ; nonlinear equation ; root finding ; multiple root ; secant method ; Steffensen procedure ; order of convergence ; efficiency ; stability
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    Notes: Abstract A superlinear procedure for finding a multiple root is presented. In it the secant method is applied to the given function divided by a divided difference whose increment shrinks toward zero as the root is approached. Two function evaluations per step are required, but no derivatives need be calculated.
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    BIT 33 (1993), S. 332-350 
    ISSN: 1572-9125
    Keywords: AMS(MOS): 65L06 ; Multistep collocation method ; continuous solution ; stability
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    Notes: Abstract This paper describes an implementation of multistep collocation methods, which are applicable to stiff differential problems, singular perturbation problems, and D.A.E.s of index 1 and 2. These methods generalize one-step implicit Runge-Kutta methods as well as multistep one-stage BDF methods. We give numerical comparisons of our code with two representative codes for these methods, RADAU5 and LSODE.
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    BIT 36 (1996), S. 531-541 
    ISSN: 1572-9125
    Keywords: Meromorphic resolvent ; stability ; power bounded
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    Topics: Mathematics
    Notes: Abstract Tools to estimate resolvents are developed and a model result is given for power bounded operators: the dimension showing up in the Kreiss matrix theorem can be replaced by the trace norm.
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    BIT 39 (1999), S. 385-402 
    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; backward error analysis ; growth factor
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    Notes: Abstract A new backward error analysis of LU factorization is presented. It allows to obtain a sharper upper bound for the forward error and a new definition of the growth factor that we compare with the well known Wilkinson growth factor for some classes of matrices. Numerical experiments show that the new growth factor is often of order approximately log2 n whereas Wilkinson's growth factor is of order n or $$\sqrt n$$ .
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    BIT 7 (1967), S. 65-70 
    ISSN: 1572-9125
    Keywords: Differential equations ; multistep methods ; stability
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    Notes: Abstract It has been shown by Dahlquist [3] that the trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. It is the purpose of this note to show that a slightly different stability requirement permits methods of higher accuracy.
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    Advances in computational mathematics 9 (1998), S. 145-171 
    ISSN: 1572-9044
    Keywords: periodic pseudodifferential equations ; multiwavelets ; splines with multiple knots ; generalized Galerkin–Petrov schemes ; boundary element methods ; error analysis ; stability ; Strang–Fix condition ; 65J10 ; 65N30 ; 65N35 ; 65R20 ; 47G30 ; 45P05 ; 41A25 ; 41A30 ; 41A15
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    Notes: Abstract We develop a stability and convergence analysis of Galerkin–Petrov schemes based on a general setting of multiresolution generated by several refinable functions for the numerical solution of pseudodifferential equations on smooth closed curves. Particular realizations of such a multiresolution analysis are trial spaces generated by biorthogonal wavelets or by splines with multiple knots. The main result presents necessary and sufficient conditions for the stability of the numerical method in terms of the principal symbol of the pseudodifferential operator and the Fourier transforms of the generating multiscaling functions as well as of the test functionals. Moreover, optimal convergence rates for the approximate solutions in a range of Sobolev spaces are established.
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    Advances in computational mathematics 12 (2000), S. 229-250 
    ISSN: 1572-9044
    Keywords: numerical analysis ; shallow water problems ; DIRK methods ; stability ; 65L06 ; 65L20 ; 65M12 ; 65M20
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    Notes: Abstract We construct A‐stable and L‐stable diagonally implicit Runge–Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge–Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge–Kutta methods are suitable methods for integrating shallow water problems in the sense that the stability boundary is relatively large and that the usually quite fine vertical resolution of the discretized spatial domain is not involved in the stability condition.
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    Advances in computational mathematics 4 (1995), S. 1-26 
    ISSN: 1572-9044
    Keywords: Wavelets ; biorthogonal wavelets ; stability ; primary 15A12 ; 65F35 ; secondary 42C15
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    Topics: Mathematics
    Notes: Abstract For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL → ∞. These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.
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    Annals of global analysis and geometry 11 (1993), S. 221-235 
    ISSN: 1572-9060
    Keywords: Second variation formula ; Morse index ; stability ; 53C
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    Topics: Mathematics
    Notes: Abstract Iff is a minimal, isometric immersion of the Riemannian manifoldM of dimensionn in a Riemannian manifold $$\overline M$$ of dimensionm and ifI N is the „differential Jacobi operator” acting on the cross sections of the normal bundleN(M), we obtain some information on the Morse index and on the stability ofM through a detailed geometric analysis of the immersionf obtained when considering the higher fundamental forms off.
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    Annals of global analysis and geometry 13 (1995), S. 141-148 
    ISSN: 1572-9060
    Keywords: Gauss curvature ; stability ; 53
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    Topics: Mathematics
    Notes: Abstract We prove that a domain on a surface of constant curvature is stable provided the integral of the mean curvature is small enough.
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    Annals of global analysis and geometry 15 (1997), S. 277-297 
    ISSN: 1572-9060
    Keywords: mean curvature ; $$r$$ -mean curvature ; sphere ; stability ; stable
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    Topics: Mathematics
    Notes: Abstract We deal with compact hypersurfaces immersed in space forms with constant $$r$$ -mean curvature. They are critical points for a variational problem. We show they are stable if and only if they are geodesic spheres, generalizing results on constant curvature hypersurfaces.
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  • 59
    ISSN: 1572-9125
    Keywords: finite difference methods ; wave equation ; accuracy ; stability ; Padé approximants ; order stars ; Riemann surface
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    Notes: Abstract We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation,u tt =c 2 u xx , given by $$\sum\limits_{j = - S}^S {b_j U_{n + 1,m + j} + } \sum\limits_{j = - S}^S {a_j U_{n,m + j} + } \sum\limits_{j = - S}^S {b_j U_{n - 1,m + j} } = 0.$$ It has already been proved that the maximal order of accuracyp of such schemes is given byp ≤ 2(s + S). In this paper we show that the requirement of stability does not reduce this maximal order for any choice of the pair (s, S). The result is proved by introducing an order star on the Riemann surface of the algebraic function associated with the scheme. Furthermore, Padé schemes, withS = 0,s 〉 0, ands = 0,S 〉 0, are proved to be stable for 0 〈 μ 〈 1, where μ is the Courant number. These schemes can be implemented with high-order absorbing boundary conditions without reducing the range of μ for which stable solutions are obtained.
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    BIT 26 (1986), S. 93-99 
    ISSN: 1572-9125
    Keywords: Primary 65HO5 ; nonlinear equation ; multiple roots ; multipoint iterative methods ; error constant ; stability ; efficiency
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    Topics: Mathematics
    Notes: Abstract A one-parameter family of derivative free multipoint iterative methods of orders three and four are derived for finding the simple and multiple roots off(x)=0. For simple roots, the third order methods require three function evaluations while the fourth order methods require four function evaluations. For multiple roots, the third order methods require six function evaluations while the fourth order methods require eight function evaluations. Numerical results show the robustness of these methods.
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    BIT 27 (1987), S. 424-437 
    ISSN: 1572-9125
    Keywords: 65 L 05 ; 65 L 20 ; stability ; contractivity ; numerical solution of stiff initial value problems in ordinary differential equations ; Runge-Kutta methods ; Rosenbrock methods ; rational Runge-Kutta methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper concerns the stability analysis of numerical methods for approximating the solutions to (stiff) initial value problems. Our analysis includes the case of (nonlinear) systems of differential equations that are essentially more general than the classical test equationU′=λU, with λ a complex constant. We explore the relation between two stability concepts, viz. the concepts of contractivity and weak contractivity. General Runge-Kutta methods, one-stage Rosenbrock methods and a notable rational Runge-Kutta method are analysed in some detail.
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    BIT 30 (1990), S. 332-346 
    ISSN: 1572-9125
    Keywords: 65D05 ; polynomial interpolaton ; Newton form ; stability ; Leja points ; ordering of interpolation points
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    Topics: Mathematics
    Notes: Abstract The Newton form is a convenient representation for interpolation polynomials. Its sensitivity to perturbations depends on the distribution and ordering of the interpolation points. The present paper bounds the growth of the condition number of the Newton form when the interpolation points are Leja points for fairly general compact sets K in the complex plane. Because the Leja points are defined recursively, they are attractive to use with the Newton form. If K is an interval, then the Leja points are distributed roughly like Chebyshev points. Our investigation of the Newton form defined by interpolation at Leja points suggests an ordering scheme for arbitrary interpolation points.
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    Acta applicandae mathematicae 49 (1997), S. 35-54 
    ISSN: 1572-9036
    Keywords: dynamical systems ; stability ; pseudo orbit tracing property ; nonstandard analysis
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    Topics: Mathematics
    Notes: Abstract It is known that it is not possible to introduce C0 -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rn. Classically these amount to considering the space of all systems on a given subset of Rn as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.
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    BIT 32 (1992), S. 634-649 
    ISSN: 1572-9125
    Keywords: AMS(MOS): 65L20 ; CR: 5.17 ; delay differential equations ; numerical solution ; Runge-Kutta methods ; interpolation procedures ; stability
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    Topics: Mathematics
    Notes: Abstract This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU′(t)=λU(t)+μU(t−τ) with λ, μ ε C, Re(λ)〈−|μ|, and τ〉0. Ifc i denotes theith abscissa of a given Runge-Kutta method, then in thenth stept n−1→t n :=t n−1+h of the numerical process our interpolation procedure computes an approximation toU(t n−1+c i h−τ) from approximations that have already been generated by the process at pointst j−1+c i h(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem.
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    BIT 40 (2000), S. 62-73 
    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; pivoting
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    Topics: Mathematics
    Notes: Abstract It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.
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    BIT 40 (2000), S. 611-639 
    ISSN: 1572-9125
    Keywords: Runge-Kutta methods ; stability ; convergence ; stiff problems
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    Topics: Mathematics
    Notes: Abstract This paper studies the stability and convergence properties of general Runge-Kutta methods when they are applied to stiff semilinear systems y′(t) = J(t)y(t) + g(t, y(t)) with the stiffness contained in the variable coefficient linear part. We consider two assumptions on the relative variation of the matrix J(t) and show that for each of them there is a family of implicit Runge-Kutta methods that is suitable for the numerical integration of the corresponding stiff semilinear systems, i.e. the methods of the family are stable, convergent and the stage equations possess a unique solution. The conditions on the coefficients of a method to belong to these families turn out to be essentially weaker than the usual algebraic stability condition which appears in connection with the B-stability and convergence for stiff nonlinear systems. Thus there are important RK methods which are not algebraically stable but, according to our theory, they are suitable for the numerical integration of semilinear problems. This paper also extends previous results of Burrage, Hundsdorfer and Verwer on the optimal convergence of implicit Runge-Kutta methods for stiff semilinear systems with a constant coefficients linear part.
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    Geometriae dedicata 62 (1996), S. 281-298 
    ISSN: 1572-9168
    Keywords: 53C23 ; Hyperbolicity ; stability ; quasi-geodesics
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    Topics: Mathematics
    Notes: Abstract It is known that for a geodesic metric space hyperbolicity in the sense of Gromov implies geodesic stability. In this paper it is shown that the converse is also true. So Gromov hyperbolicity and geodesic stability are equialent for geodesic metric spaces.
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    Acta applicandae mathematicae 37 (1994), S. 129-136 
    ISSN: 1572-9036
    Keywords: 35B35 ; 35Q30 ; 76N10 ; stability ; Navier-Stokes equations ; compressible fluids
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    Topics: Mathematics
    Notes: Abstract We prove that the uniform stability at permanently acting disturbances of a given solution of the Navier-Stokes equations for viscous compressible isothermic fluid is a consequence of the uniform exponential stability of the zero solution of so-called linearized equations.
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    Acta applicandae mathematicae 9 (1987), S. 219-237 
    ISSN: 1572-9036
    Keywords: 34A34 ; 34D99 ; 90A16 ; Nonlinear differential equations ; stability ; growth ; economic dynamics
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    Topics: Mathematics
    Notes: Abstract This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.
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    Advances in computational mathematics 10 (1999), S. 115-133 
    ISSN: 1572-9044
    Keywords: Runge–Kutta–Nyström methods ; predictor–corrector methods ; stability ; parallelism ; 65M12 ; 65M20
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    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
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    BIT 33 (1993), S. 74-84 
    ISSN: 1572-9125
    Keywords: 65J10 ; 65M12 ; Analytic semigroup ; Banach space ; rational approximation ; A-acceptable ; A(θ)-acceptable ; stability ; Crank-Nicolson method
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    Topics: Mathematics
    Notes: Abstract It is shown thatA-acceptable and, more generally,A(θ)-arational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method.
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    BIT 33 (1993), S. 285-303 
    ISSN: 1572-9125
    Keywords: 65L05 ; stiffness ; stability ; pseudospectra
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    Topics: Mathematics
    Notes: Abstract It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pseudospectra instead of spectra. Numerical experiments with an adaptive ODE solver illustrate these findings.
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    BIT 39 (1999), S. 620-645 
    ISSN: 1572-9125
    Keywords: Numerical integrator ; oscillatory solutions ; Schrödinger equation ; quantum-classical coupling ; error bounds ; stability
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    Topics: Mathematics
    Notes: Abstract We study time integration methods for equations of mixed quantum-classical molecular dynamics in which Newtonian equations of motion and Schrödinger equations are nonlinearly coupled. Such systems exhibit different time scales in the classical and the quantum evolution, and the solutions are typically highly oscillatory. The numerical methods use the exponential of the quantum Hamiltonian whose product with a state vector is approximated using Lanczos' method. This allows time steps that are much larger than the inverse of the highest frequencies. We describe various integration schemes and analyze their error behaviour, without assuming smoothness of the solution. As preparation and as a problem of independent interest, we study also integration methods for Schrödinger equations with time-dependent Hamiltonian.
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    BIT 40 (2000), S. 226-240 
    ISSN: 1572-9125
    Keywords: Stochastic differential equations ; regularisation ; stability
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    Topics: Mathematics
    Notes: Abstract This paper is devoted to the numerical analysis of ill-posed problems of evolution equations in Banach spaces using certain classes of stochastic one-step methods. The linear stability properties of these methods are studied. Regularisation is given by the choice of the regularisation parameter as α = $$\sqrt {\tau _n }$$ , where τ n is the stepsize and provides the convergence on smooth initial data. The case of the approximation of well-posed problems is also considered.
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    BIT 34 (1994), S. 62-79 
    ISSN: 1572-9125
    Keywords: AMS(MOS) 65D30 ; 65B05 ; adaptive ; cubature ; singularity ; extrapolation ; stability
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    Topics: Mathematics
    Notes: Abstract A new approach to the integration of vertex singularities is described. This approach is based on a non-uniform subdivision of the region of integration and the technique fits well to the subdivision strategy used in many adaptive algorithms. A nice feature with this approach is that it can be used in any dimension and on any region of integration which can be subdivided into subregions of the same form. The strategy can be applied both to vertex singularities and internal point singularities. In the latter case this can be done without an initial subdivision of the region in order to put the singular point in a vertex. It turns out that the technique has excellent numerical stability properties.
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    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 809-816 
    ISSN: 1420-9039
    Keywords: 34D20 ; 34D35 ; 35Q72 ; 73H10 ; 73K03 ; Elastic string ; stability ; energy-momentum ; axial motion
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    Topics: Mathematics , Physics
    Notes: Abstract We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish “orbitai” stability (modulo this collection of relative equilibria). For a well-defined class of “soft” materials, there is an upper bound on the axial speed sufficient for stability; “stiff” materials are shown to be orbitally stable at any axial speed.
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    Monatshefte für Mathematik 126 (1998), S. 117-124 
    ISSN: 1436-5081
    Keywords: 52A20 ; 52A22 ; star bodies ; spherical integral transformations ; convex bodies ; stability
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    Topics: Mathematics
    Notes: Abstract LetK be ad-dimensional star body (with respect to the origino). It is known that the (d−1)-dimensional volume of the intersections ofK with the hyperplanes througho does not uniquely determineK. Uniqueness can only be achieved under additional assumptions, such as central symmetry. Here it is pointed out that if one uses, instead of intersections by hyperplanes, intersections by half-planes that containo on the boundary, then, without any additional assumptions, the volume of these intersections determinesK uniquely. This assertion, and more general results of this kind, together with stability estimates, are obtained from uniqueness results and estimates concerning a particular spherical integral transformation.
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    Archive for rational mechanics and analysis 72 (1980), S. 203-218 
    ISSN: 1432-0673
    Keywords: simple fluid ; viscoelastic ; fading memory ; stability ; Liapunov function ; dynamical system
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    Topics: Mathematics , Physics
    Notes: Abstract The nonlinear equations of motion for an incompressible simple fluid, occupying a fixed bounded container, are formulated on the basis of the “finitelinear” viscoelasticity theory for materials with fading memory; this formal boundary-initial value problem is then viewed as a nonlinear abstract evolution equation on a certain Hilbert space. It is shown that a linearized version of this evolution equation is associated with a linear dynamical system on this Hilbert space, and several results for stability and asymptotic behavior for this linearized problem are proved through the use of Liapunov stability methods. On the assumption that the original nonlinear evolution equation also is associated with some dynamical system on the same space, it is shown that the rest condition of the fluid is stable and all motions are bounded. The Liapunov function employed for this purpose can be interpreted as a mechanical energy function for the fluid.
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    Archive of applied mechanics 67 (1997), S. 447-456 
    ISSN: 1432-0681
    Keywords: Key words rotation ; stability ; energy criterion ; variational analysis ; functional analysis ; eigenvalue problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Stability of a heavy rotating rod with a variable cross section is studied by energy method. Bifurcation points for the system of equilibrium equations are analyzed. It is shown that for the case when the rotation speed exceeds the critical one, the trivial solution ceases to be the minimizer of the potential energy, so that rod loses stability, according to the energy criteria. Also, a new estimate of the maximal rod deflection in the post-critical state is obtained.
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    Archive of applied mechanics 65 (1995), S. 507-521 
    ISSN: 1432-0681
    Keywords: rod vibrations ; stability ; tip mass ; non-conservative forces ; non-selfadjoint problems
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Separable and non-selfadjoint boundary-value problems representing the vibration of linearly elastic unidimensional systems are considered. The elastic system is modelled as a continuous distributed-parameter system where singularities in the mass distribution function can be neatly taken into account. Specifically, extending Green's function approach, the free vibration, stability and forced vibration of fixed-free rods with a tip mass and under the action of uniformly distributed non-conservative loads have been investigated analytically.
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    Archive of applied mechanics 65 (1995), S. 99-109 
    ISSN: 1432-0681
    Keywords: Key words Bars ; voids ; viscoelasticity ; stability ; critical load
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  Dynamic stability of an elastic bar with voids is considered. Using the Lyapunov approach some new sufficient stability conditions are obtained and explicit expressions for the critical load are derived.
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    Archive of applied mechanics 65 (1995), S. 133-141 
    ISSN: 1432-0681
    Keywords: Shear deformation ; elastically supported beams ; axial compression ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary The influence of shear deformation on the buckling behavior of a beam supported laterally by a Winkler elastic foundation is studied. A full investigation of the bifurcation points at which, under axial load, the beam becomes critical with respect to one or two simultaneous buckling modes is made. The configurations and stabilities of the equilibrium paths that bifurcate from the critical points are derived. From the results of theoretical analysis, it becomes evident that shear deformation has a considerable effect upon the equilibriums and stabilities of the post-buckling of the beam. The results for the Bernoulli-Euler beam can be obtained as a limiting case for those of the present beam by letting the shear stiffness tend to infinity.
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    Archive of applied mechanics 65 (1995), S. 178-193 
    ISSN: 1432-0681
    Keywords: Periodic motion ; modal treatment ; itrations ; time variance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Übersicht Lineare, periodisch zeitvariante Bewegungsgleichungen treten im Hubschrauber- und Windturbinenbau auf. Der Getriebebau und die Rotordynamik liefern weitere Beispiele. In diesem Bericht wird ein systematischer Weg zu ihrer Lösung dargestellt. Mit dem Ansatz von Hill wird die homogene Lösung über die Lösung eines Eigenwertproblems gewonnen. Nach Anpassung an die Anfangsbedingungen liefert sie die Fundamentalmatrix des Systems. Ähnlich wie bei zeitinvarianten Systemen, existieren auch bei zeitvarianten Systemen Orthogonalitätsbedingungen, die die Eigenvektoren erfüllen. Die Eigenvektoren selbst sind allerdings zeitabhängig. Benutzt man die Eigenvektoren als Ansatzvektor zur Berechnung der erzwungenen Schwingungen (Transformation mit der zeitvarianten Modalmatrix des Systems), so gelingt es, die Bewegungsgleichungen des Systems in entkoppelte, zeitinvariante zu überführen. Sie lassen sich in bekannter Weise lösen. Dieses Vorgehen wird auf eine moderne Windkraftanlage angewandt. Sie wurde zunächst mit 372 Freiheitsgraden modelliert, die aber auf 18 vor der numerischen Weiterbehandlung kondensiert wurden. Das Stabilitätsverhalten und die Antwortspektren auf stochastische Anregung durch den Wind wurden auf dem oben beschriebenen Weg ermittelt.
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    Archive of applied mechanics 65 (1995), S. 178-193 
    ISSN: 1432-0681
    Keywords: Key words Periodic motion ; modal treatment ; itrations ; time variance ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Übersicht  Lineare, periodisch zeitvariante Bewegungsgleichungen treten im Hubschrauber- und Windturbinenbau auf. Der Getriebebau und die Rotordynamik liefern weitere Beispiele. In diesem Bericht wird ein systematischer Weg zu ihrer Lösung dargestellt. Mit dem Ansatz von Hill wird die homogene Lösung über die Lösung eines Eigenwertproblems gewonnen. Nach Anpassung an die Anfangsbedingungen liefert sie die Fundamentalmatrix des Systems. Ähnlich wie bei zeitinvarianten Systemen, existieren auch bei zeitvarianten Systemen Orthogonalitätsbedingungen, die die Eigenvektoren erfüllen. Die Eigenvektoren selbst sind allerdings zeitabhängig. Benutzt man die Eigenvektoren als Ansatzvektor zur Berechnung der erzwungenen Schwingungen (Transformation mit der zeitvarianten Modalmatrix des Systems), so gelingt es, die Bewegungsgleichungen des Systems in entkoppelte, zeitinvariante zu überführen. Sie lassen sich in bekannter Weise lösen. Dieses Vorgehen wird auf eine moderne Windkraftanlage angewandt. Sie wurde zunächst mit 372 Freiheitsgraden modelliert, die aber auf 18 vor der numerischen Weiterbehandlung kondensiert wurden. Das Stabilitätsverhalten und die Antwortspektren auf stochastische Anregung durch den Wind wurden auf dem oben beschriebenen Weg ermittelt.
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    Archive of applied mechanics 66 (1996), S. 291-299 
    ISSN: 1432-0681
    Keywords: stability ; elasticity ; singularities ; bifurcation ; material instabilities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Branching analysis for the homogeneous deformations of a compressible elastic unit cube under dead loading is performed. Critical conditions for branching of the equilibrium paths are derived and the post-critical equilibrium paths are described. Special attention is given to the compound branching.
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    Archive of applied mechanics 65 (1995), S. 133-141 
    ISSN: 1432-0681
    Keywords: Key words Shear deformation ; elastically supported beams ; axial compression ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  The influence of shear deformation on the buckling behavior of a beam supported laterally by a Winkler elastic foundation is studied. A full investigation of the bifurcation points at which, under axial load, the beam becomes critical with respect to one or two simultaneous buckling modes is made. The configurations and stabilities of the equilibrium paths that bifurcate from the critical points are derived. From the results of theoretical analysis, it becomes evident that shear deformation has a considerable effect upon the equilibriums and stabilities of the post-buckling of the beam. The results for the Bernoulli-Euler beam can be obtained as a limiting case for those of the present beam by letting the shear stiffness tend to infinity.
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    Archive of applied mechanics 70 (2000), S. 17-29 
    ISSN: 1432-0681
    Keywords: Key words free-surface flow ; solidification ; strip casting ; steady state ; nonuniqueness ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary The paper is concerned with a one-dimensional analysis of plane open-channel flow with continuous solidification. The process is of relevance for recent developments in the casting of steel and other metals. The bottom of the channel consists of a rotating casting roll and a horizontal cooling table, where the solidified material is withdrawn with given velocity. The study is restricted to the region downstream of the top of the casting roll. Surface tension is neglected. In the main part of the analysis inviscid fluid flow is considered since the Reynolds number is very large in the applications. It is found that the steady-state solutions are nonunique in a certain parameter range. In addition to a continuous solution, there are two solutions including hydraulic jumps, with one hydraulic jump being located on the casting roll, the other one on the cooling table. Regarding the stability of the non unique solutions, the evolution of disturbances is investigated numerically as an initial-value problem. It is concluded that the hydraulic jump on the cooling table is unstable, while the other discontinuous solution as well as the continuous solution are stable for sufficiently small disturbances. Which stable solution is attained in the steady state, depends on the history of the process. Friction at the liquid/solid interface is taken into account in the last part of the analysis. A constant friction coefficient is assumed. It is found that the history of the process determines the steady-state solution if, and only if, the friction coefficient is sufficiently small. For larger values of the friction coefficient, the steady-state solution is unique and independent of the history of the transient process. Furthermore, for sufficiently large friction coefficients, stable hydraulic jumps are found, in contrast to the inviscid case, also on the cooling table.
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    Archive of applied mechanics 65 (1995), S. 507-521 
    ISSN: 1432-0681
    Keywords: Key words rod vibrations ; stability ; tip mass ; non-conservative forces ; non-selfadjoint problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  Separable and non-selfadjoint boundary-value problems representing the vibration of linearly elastic unidimensional systems are considered. The elastic system is modelled as a continuous distributed-parameter system where singularities in the mass distribution function can be neatly taken into account. Specifically, extending Green’s function approach, the free vibration, stability and forced vibration of fixed-free rods with a tip mass and under the action of uniformly distributed non-conservative loads have been investigated analytically.
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    Archive of applied mechanics 66 (1996), S. 264-272 
    ISSN: 1432-0681
    Keywords: asymptotic expansion ; stability ; boundary layer ; laminar flow ; heat transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary By means of a combined method it is demonstrated for regular perturbation problems how the higher order terms of an asymptotic expansion may be determined from numerical solutions of the non-expanded basic equations. The method is applied to heat transfer effects in a laminar boundary layer and to the analysis of its stability. All first- and second-order coefficients of the problem are determined from numerical solutions of the basic set of equations.
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    Archive of applied mechanics 66 (1996), S. 264-272 
    ISSN: 1432-0681
    Keywords: Key words asymptotic expansion ; stability ; boundary layer ; laminar flow ; heat transfer
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  By means of a combined method it is demonstrated for regular perturbation problems how the higher order terms of an asymptotic expansion may be determined from numerical solutions of the non-expanded basic equations. The method is applied to heat transfer effects in a laminar boundary layer and to the analysis of its stability. All first- and second-order coefficients of the problem are determined from numerical solutions of the basic set of equations.
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    Archive of applied mechanics 69 (1999), S. 47-54 
    ISSN: 1432-0681
    Keywords: Key words Bifurcation ; stability ; multibody system dynamics ; singularity theory ; Liapunov's direct method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary In this paper, the global behavior of relative equilibrium states of a three-body satellite with flexible connection under the action of the gravitational torque is studied. With geometric method, the conditions of existence of nontrivial solutions to the relative equilibrium equations are determined. By using reduction method and singularity theory, the conditions of occurrence of bifurcation from trivial solutions are derived, which agree with the existence conditions of nontrivial solutions, and the bifurcation is proved to be pitchfork-bifurcation. The Liapunov stability of each equilibrium state is considered, and a stability diagram in terms of system parameters is presented.
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    Archive of applied mechanics 65 (1995), S. 99-109 
    ISSN: 1432-0681
    Keywords: Bars ; voids ; viscoelasticity ; stability ; critical load
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Dynamic stability of an elastic bar with voids is considered. Using the Lyapunov approach some new sufficient stability conditions are obtained and explicit expressions for the critical load are derived.
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  • 93
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    OR spectrum 15 (1994), S. 197-203 
    ISSN: 1436-6304
    Keywords: Inventory ; dynamic programming ; stability ; Lagerhaltung ; Dynamische Optimierung ; Stabilität
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Die Menge der Kostenparameter, für die eine optimale Lösung des dynamischen Losgrößenmodells optimal bleibt wird hier Stabilitätsregion genannt. Die Größe einer solchen Menge kann als Maß der Robustheit einer Lösung angesehen werden. Es ist zu erwarten, daß die Stabilitätsregionen mit wachsendem Zeithorizont schrumpfen und daß sie in diesem Sinne monoton sind. In der vorliegenden Arbeit werden verschiedene hinreichende Bedingungen für diese Monotonie untersucht. Die Bedingungen setzen unter anderem die Existenz von Planungs- und Vorhersage-Horizonten voraus und verallgemeinern so Ergebnisse einer früheren Arbeit, in der Aussagen für gewöhnliche Planungs-Horizonte vorgestellt wurden.
    Notes: Abstract The set of cost inputs for which an optimal solution of the dynamic lot size model remains valid is called stability region. The size of this region may be viewed as a measure of robustness of a solution. It is an expectation that the stability regions shrink with growing time horizons and that they are monotonous in this sense. In the present paper several sufficient conditions implying monotonicity will be studied. The conditions cover the existence of planning and forecast horizons and generalize the results of a previous paper in wich monotonicity results were presented for the case of ordinary planning horizons.
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  • 94
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    Meccanica 29 (1994), S. 195-210 
    ISSN: 1572-9648
    Keywords: Chetaev functional ; pendulum ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si considera il problema di stabilità di punti di equilibrio di un pendolo fisico con un filo inestensibile appeso ad esso dal punto di vista del teorema di Lagrange sulla stabilità e sulla sua inversione. Difficoltà specifiche relative allo studio di un sistema meccanico di dimensione infinita sono discusse. Si suggerisce un nuovo metodo per lo studio della stabilità rispetto a due metriche. L'influenza di fenomeni di risonanza sul moto del sistema ridotto (linearizzato) è considerata.
    Notes: Abstract The problem of stability of equilibria of a physical pendulum with a nonstretchable thread attached to it is considered from the standpoint of the Lagrange theorem on stability and its inversion. Specific difficulties which one faces when studying an infinite dimensional mechanical system are discussed. A new approach to the study of stability with respect to two metrics is suggested. The influence of resonant phenomena on the motion of the shortened (linearized) system is considered.
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  • 95
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    Journal of intelligent and robotic systems 27 (2000), S. 195-209 
    ISSN: 1573-0409
    Keywords: wall-climbing robot ; electromagnetic grippers ; stability ; additional support element ; sliding and turning over conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Legged-climbing robot is considered. Each foot of the robot has an electromagnet system for robot"s holding on a metal surface. This surface can be both vertical and inclined, including negative slope. Analytical calculation of robot stability under turn over or sliding conditions has been made. Critical slopes have been determined. One of these slopes corresponds to minimal reserve of robot stability towards sliding and another to minimal reserve of robot stability towards turning-over. As total reserve of stability of a robot is always equal to the minimal one of these reserves. Additional support elements of elastic material with high coefficient of friction, along with electromagnet, allows to increase minimal reserve of robot stability towards sliding. The use of such support elements leads to redistributing force of normal support reaction between electromagnet (which surface has low coefficient of friction) and additional support element (which surface has high coefficient of friction). It is just what leads to increasing the total friction force and as a consequence to increasing of minimal reserve of robot stability towards sliding.
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  • 96
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    Journal of intelligent and robotic systems 3 (1990), S. 259-289 
    ISSN: 1573-0409
    Keywords: Nonlinear decoupling ; feedback linearization ; functional analysis ; elastic robots ; robustness ; stability ; pole assignment ; nonlinear systems ; robot control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A robustness analysis and synthesis for incomplete nonlinear decoupling for a class of nonlinear systems is discussed. Rigid and elastic-joint robot models belong to this class. For the elastic case, a transformation facilitates the robustness analysis under a weak assumption. Charts with H 1- and H ∞- norms of closed-loop disturbance transfer functions of the nonlinear-decoupled system are presented for a robust pole assignment.
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  • 97
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    Journal of intelligent and robotic systems 6 (1992), S. 51-63 
    ISSN: 1573-0409
    Keywords: Scheduling ; flexible manufacturing systems ; stability ; feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A genetic manufacturing environment is considered. The emphasis is on small-lot, discrete, and asynchronous type of manufacturing systems rather than high volume and continuous type. Two classes of scheduling policies are proposed to render the machine stable. The policies are of feedback type. The decision is made in real-time and on-line.
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  • 98
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    Journal of intelligent and robotic systems 6 (1992), S. 219-240 
    ISSN: 1573-0409
    Keywords: Force control ; slip-stick friction ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper explores two practical issues related to the force control of manipulators. The first issue examined is how system stability is effected by commonly occurring manipulator nonlinearities, such as sampled-data, control signal saturation and slip-stick friction. It is shown that discretely implemented force control algorithms can drive the feedback force controlled manipulator into a limit cycle, even for a very small sampling period that by far satisfies Shannon's sampling theorem. The bounds of stability are enhanced by the presence of control signal saturation and slip stick friction. The second issue investigated is the inclusion of a high gain inner position loop as a means to minimize the unpredictability in the steady state error due to slip-stick friction. In order to support the theoretical conclusions, experiments were performed with the PUMP 560 industrial robot testbed facility developed at Colorado State University.
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  • 99
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    K-Theory 1 (1987), S. 185-196 
    ISSN: 1573-0514
    Keywords: Quadratic space ; patching diagram ; projective module ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that every quadratic space of sufficiently large index contains a hyperbolic orthogonal summand.
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  • 100
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    K-Theory 10 (1996), S. 491-516 
    ISSN: 1573-0514
    Keywords: 57M60 ; 57N13 ; 57R91 ; 19G38 ; topological 4-manifold ; pseudofree action ; equivariant intersection form ; stability ; topological rigidity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the algebraic aspects of the classification of pseudofree, locally linear group actions on a simply connected 4-manifold, particularly with the splitting and stability properties of the associated Hermitian intersection module and its isometry group. Our main result is the proof of stability of the equivariant intersection form for a large class of pseudofree actions. We also prove a topological rigidity theorem stating that two locally linear, pseudofree actions on a closed, oriented, simply connected 4-manifold, with the equivariant intersection forms indefinite and of rank at least 3 at each irreducible character, are topologically conjugate by an orientation preserving homeomorphism if and only if their oriented local representations at the corresponding fixed points are linearly equivalent.
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