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  • 1
    Electronic Resource
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    Springer
    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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    Computing 24 (1980), S. 341-347 
    ISSN: 1436-5057
    Keywords: Numerical analysis ; Volterra integral equations of the second kind ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Ziel dieser Arbeit ist es, die Stabilitätseigenschaften einer Klasse Volterrascher Integralgleichungen zweiter Art zu untersuchen. Unsere Behandlung ist der üblichen Stabilitätsanalyse ähnlich, in der die Kernfunktionen zu einer im voraus beschränkten Klasse von Testfunktionen gehören. Wir haben die Klasse der “endlich zerlegbaren” Kerne betrachtet. Stabilitätsbedingungen werden abgeleitet und verglichen mit den Bedingungen für die einfache Testgleichung. Es zeigt sich, daß die neuen Kriteria einschränkender sind als die konventionellen Bedingungen. Der praktische Wert wird getestet durch numerische Experimente mit der Trapezregel.
    Notes: Abstract The purpose of this paper is to analyse the stability properties of a class of multistep methods for second kind Volterra integral equations. Our approach follows the usual analysis in which the kernel function is a priori restricted to a special class of test functions. We consider the class of finitely decomposable kernels. Stability conditions will be derived and compared with those obtained with the simple test equation. It turns out that the new criteria are more severe than the conventional conditions. The practical value is tested by numerical experiments with the trapezoidal rule.
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  • 3
    ISSN: 1436-5057
    Keywords: 65 L 05 ; Rosenbrock-type methods ; quasilinear-implicit differential equations ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Bei der Lösung quasilinear-impliziter ODEs mittels Rosenbrock-Typ-Methoden können trotz guter Stabilitätseigenschaften (A- bzw. L-Stabilität) des Grundverfahrens Stabilitätsprobleme auftreten. Diese Schwierigkeiten sind auf Ungenauigkeiten bei der Berechnung künstlich eingeführter Komponenten (Überführung in DAEs) zurückzuführen. Die Arbeit untersucht die Ursachen für diese Effekte und zeigt Möglichkeiten, diese zu überwinden.
    Notes: Abstract The solution of quasilinear-implicit ODEs using Rosenbrock type methods may suffer from stability problems despite stability properties such as A-stability or L-stability, respectively. These problems are caused by inexact computation of artificial introduced components (transformation to DAE system). The paper investigates the source of the numerical difficulties and shows modifications to overcome them.
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  • 4
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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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  • 5
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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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  • 6
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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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  • 7
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    Lasers in medical science 10 (1995), S. 93-104 
    ISSN: 1435-604X
    Keywords: Copper vapour laser ; Electron microscopy ; Illumination time ; Numerical modelling ; Optimal treatment ; Port-wine stain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Physics , Technology
    Notes: Abstract This paper reports the electron microscopy results obtained from two patients who were treated with 5 W of yellow (578 nm) light from a copper vapour laser with an illumination time of 3.6 ms and a 0.3 mm spot diameter. The endpoint of treatment was transient blanching. Following treatment, erythema was observed. There was minimal damage to the epidermis and non-vascular tissue such as the nerve fibres. There was severe damage to the endothelial cells of the ectatic vessels. Twenty-four hours after treatment, platelet activation and collagen were present, indicating that these vessels were no longer viable. Theoretical calculations are used to determine the flow of heat within and away from a 50μm diameter vessel. From this, heating of the entire vessel is shown to occur with illumination times of 4 ms, with minimal heating of the non-vascular tissue. Shorter illuminations do not heat the entire vessel, while the use of longer illumination times will cause excessive damage to the surrounding non-vascular tissue. Illumination times close to 4 ms must be regarded as optimal.
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  • 8
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    Empirical economics 23 (1998), S. 387-400 
    ISSN: 1435-8921
    Keywords: Key words: Money demand ; cointegration ; stability ; regime shift ; JEL classification: E41 ; C22
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract. Using several tests for structural stability in regressions with I(1) variables and for the existence of cointegration in models with regime shifts, the empirical evidence on the existence of a structural break in the Spanish long-run demand for broad money (ALP2) is analysed.  The results indicate that shifts affecting the demand for ALP2 in recent years have substantially altered its long-run properties. As to the cause of this structural break, emphasis is placed on the role played by the increasing openness of the Spanish financial system to international markets as obstacles to free capital movements have progressively disappeared.
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  • 9
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    Stochastic environmental research and risk assessment 12 (1998), S. 191-204 
    ISSN: 1436-3259
    Keywords: Keywords: groundwater flow ; inverse problems ; stability ; geostatistical interpolation ; kriging.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The Differential System Method (DSM) permits identification of the physical parameters of finite-difference groundwater flow models in a confined aquifer when piezometric head and source terms are known at each point of the finite-difference lattice for at least two independent flow situations for which the hydraulic gradients are not parallel. Since piezometric head data are usually few and sparse, interpolation of the measured data onto a regular grid can be performed with geostatistical techniques. We apply kriging to the sparse data of a synthetic aquifer to evaluate the stability of the DSM with respect to uncorrelated measurement errors and interpolation errors. The numerical results show that the DSM is stable.
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  • 10
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    Colloid & polymer science 261 (1983), S. 373-374 
    ISSN: 1435-1536
    Keywords: Electron microscopy ; short-time staining ; nodular structure ; crystallization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 11
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    Colloid & polymer science 260 (1982), S. 564-569 
    ISSN: 1435-1536
    Keywords: lin. Polyethylene ; Single crystals ; Heat of Fusion ; DSC ; Electron microscopy
    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 Recently published results for solution crystallized PE single crystals have shown, that the experimental heat of fusionΔH * is higher, if the solvent is exchanged to silicon oil (oil suspension samples) as compared with dried mats. This has been interpreted by the collapse of the original hollow pyramids during drying, inducing lateral defects within the lamellae. The present investigation does not confirm this unexpected result.ΔH * of dried mats (T c 66 to 91 °C) and of the corresponding oil suspension samples agree within the rather small limits of experimental error. The crystallinities as derived fromΔH *, density or WAXS are in excellent agreement. SEM micrographs of cold fractured dried mats show their spongy macromorphology, but TEM micrographs of stained ultra-thin sections reveal the lamellar morphology of the walls, consisting of curved lamellae and stacked hollow pyramides. If a dried mat is sintered at room temperature, a dense transparent film is obtained with a rather regular stacked morphology of large flat lamellae.ΔH * of these films agrees with that of the original mat.
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  • 12
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    Rheologica acta 22 (1983), S. 284-290 
    ISSN: 1435-1528
    Keywords: Viscometric flow ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract This paper examines three-dimensional disturbances of a plane steady shear flow of simple fluids with short memory. Under the assumption of nearly-viscometric flow, constitutive equations are derived and then a general form of the Reynolds-Orr energy equation is obtained. With the aid of this derived energy formula, sufficient conditions are generated for the stability of three-dimensional disturbances of the planar viscometric flow. These conditions are analysed and a comparison is made with the corresponding two-dimensional stability problem. There is a strong indication that the basic flow is less stable against three-dimensional disturbances than against two-dimensional ones.
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  • 13
    ISSN: 1572-8358
    Keywords: Epidemiology ; sleeping sickness ; vector controls ; differential equations ; spacialization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract A compartmental model is described for the spread of Gambian sleeping sickness in a spatially heterogeneous environment in which vector and human populations migrate between two "patches": the village and the plantations. The number of equilibrium points depends on two "summary parameters": gr the proportion removed among human infectives, and R0, the basic reproduction number. The origin is stable for R0 〈1 and unstable for R0 〉1. Control strategies are assessed by studying the mix of vector control between the two patches that bring R0 below 1. The results demonstrate the importance of vector control in the plantations. For example if 20 percent of flies are in the village and the blood meal rate in the village is 10 percent, then a 20 percent added vector mortality in the village must be combined with a 9 percent added mortality in the plantations in order to bring R0 below 1. The results are quite insentive to the blood meal rate in the village. Optimal strategies (that minimize the total number of flies trapped in both patches) are briefly discussed.
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  • 14
    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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  • 15
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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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  • 16
    ISSN: 1572-879X
    Keywords: metal-oxygen cluster compounds ; heteropoly acids ; stability ; pH ; aqueous solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The stabilities of the solid superacids H3Mo12O40, H3PW12O40, H4SiMo12O40 and H4SiW12O40 in aqueous solution have been measured at various values of pH by use of ion chromatographic analyses. The aforementioned acids are completely decomposed at values of pH, 4.0, 5.2, 7.0 and 11.0, respectively. The stabilities in aqueous solution with respect to pH follow the order H4SiW12O40 〉 H3PW12O40 〉 H4SiMo12O40 〉 H3PMo12O40.
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    Journal of dynamics and differential equations 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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    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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  • 19
    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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    Queueing systems 21 (1995), S. 67-95 
    ISSN: 1572-9443
    Keywords: Polling systems ; stability ; stationary regime
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A stationary regime for polling systems with general ergodic (G/G) arrival processes at each station is constructed. Mutual independence of the arrival processes is not required. It is shown that the stationary workload so constructed is minimal in the stochastic ordering sense. In the model considered the server switches from station to station in a Markovian fashion, and a specific service policy is applied to each queue. Our hypotheses cover the purely gated, thea-limited, the binomial-gated and other policies. As a by-product we obtain sufficient conditions for the stationary regime of aG/G/1/∞ queue with multiple server vacations (see Doshi [11]) to be ergodic.
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    Queueing systems 22 (1996), S. 47-63 
    ISSN: 1572-9443
    Keywords: Sample-path analysis ; stability ; rate stability ; ω-rate stability ; input-output process ; queueing ; infinite-server queues
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract An input-output processZ = {Z(t), t ⩾ 0} is said to beω-rate stable ifZ(t) = o(ω(t)) for some non-negative functionω(t). We prove that the processZ is ω-rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions forω-rate-stability can be verified from input data. For example, using input information, we establishω-rate stability of the workload for multiserver queues, an ATM multiplexer, andω-rate stability of queue-length processes for infinite server queues.
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    Queueing systems 22 (1996), S. 345-366 
    ISSN: 1572-9443
    Keywords: State-dependent service and interarrival times ; Lindley equation ; recursive stochastic equations ; stability ; normal approximations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a modification of the standardG/G/1 queueing system with infinite waiting space and the first-in-first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. When the waiting-time distributions converge to a proper limit, Whitt [10] proposed a normal approximation for this steady-state limit. In this paper we prove a limit theorem for the steady-state limit of the system. Thus, our result provides a solid foundation for Whitt's normal approximation of the steady-state distribution of the system.
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    Queueing systems 29 (1998), S. 55-73 
    ISSN: 1572-9443
    Keywords: multi‐server queue ; customer class ; state‐dependent routing ; stability ; Markov chain ; fluid limit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a multi‐station queue with a multi‐class input process when any station is available for the service of only some (not all) customer classes. Upon arrival, any customer may choose one of its accessible stations according to some state‐dependent policy. We obtain simple stability criteria for this model in two particular cases when service rates are either station‐ or class‐independent. Then, we study a two‐station queue under general assumptions on service rates. Our proofs are based on the fluid approximation approach.
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    Queueing systems 32 (1999), S. 131-168 
    ISSN: 1572-9443
    Keywords: stability ; positive recurrence ; fluid limit ; polling system ; exhaustive service policy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We introduce a generalized criterion for the stability of Markovian queueing systems in terms of stochastic fluid limits. We consider an example in which this criterion may be applied: a polling system with two stations and two heterogeneous servers.
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    Celestial mechanics and dynamical astronomy 74 (1999), S. 19-57 
    ISSN: 1572-9478
    Keywords: stability ; Hamiltonian ; two centers ; oblate planet ; galactic disks ; dipole
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Relative equilibria occur in a wide variety of physical applications, including celestial mechanics, particle accelerators, plasma physics, and atomic physics. We derive sufficient conditions for Lyapunov stability of circular orbits in arbitrary axisymmetric gravitational (electrostatic) and magnetic fields, including the effects of local mass (charge) and current density. Particularly simple stability conditions are derived for source‐free regions, where the gravitational field is harmonic (∇2U = 0) or the magnetic field irrotational (∇ × B = 0). In either case the resulting stability conditions can be expressed geometrically (coordinate‐free) in terms of dimensionless stability indices. Stability bounds are calculated for several examples, including the problem of two fixed centers, the J2 planetary model, galactic disks, and a toroidal quadrupole magnetic field.
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    Celestial mechanics and dynamical astronomy 75 (1999), S. 251-285 
    ISSN: 1572-9478
    Keywords: unrestricted problem ; rotational motion ; rigid body dynamics ; libration points ; stability ; resonances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present an analysis of the model introduced by Kokoriev and Kirpichnikov (1988) for the study of unrestricted planar motion of a point mass and a symmetric rigid body whose gravity field is approximated by two point masses (a dumb-bell model). To show possible generalization of the model, we give a systematic derivation of equations of motion for a more general unrestricted problem of a point and a rigid body possessing a plane of dynamical symmetry. We give a simple description of bifurcation of triangular libration points, and we perform an analysis of their linear stability. We propose to extend the model of Kokoriev and Kirpichnikov (1988) to a case when the symmetric body is oblate. In the proposed model the gravity field of moving and rotating body is approximated by two complex masses at complex distance (a complex dumb-bell model). An analysis of bifurcation of the triangular libration points in this model is also presented.
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    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 56 (1995), S. 79-93 
    ISSN: 1572-9338
    Keywords: Multistage stochastic programs ; optimization in Banach spaces ; stability ; approximation
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    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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    Queueing systems 27 (1997), S. 205-226 
    ISSN: 1572-9443
    Keywords: multiclass queueing networks ; ergodicity ; stability ; performance analysis
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    Topics: Computer Science
    Notes: Abstract We develop the use of piecewise linear test functions for the analysis of stability of multiclass queueing networks and their associated fluid limit models. It is found that if an associated LP admits a positive solution, then a Lyapunov function exists. This implies that the fluid limit model is stable and hence that the network model is positive Harris recurrent with a finite polynomial moment. Also, it is found that if a particular LP admits a solution, then the network model is transient.
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    Queueing systems 28 (1998), S. 33-54 
    ISSN: 1572-9443
    Keywords: queueing networks ; throughput ; closed networks ; efficiency ; stability
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    Topics: Computer Science
    Notes: Abstract A closed network is said to be “guaranteed efficient” if the throughput converges under all non-idling policies to the capacity of the bottlenecks in the network, as the number of trapped customers increases to infinity. We obtain a necessary condition for guaranteed efficiency of closed re-entrant lines. For balanced two-station systems, this necessary condition is almost sufficient, differing from it only by the strictness of an inequality. This near characterization is obtained by studying a special type of virtual station called “alternating visit virtual station”. These special virtual stations allow us to relate the necessary condition to certain indices arising in heavy traffic studies using a Brownian network approximation, as well as to certain policies proposed as being extremal with respect to the asymptotic loss in the throughput. Using the near characterization of guaranteed efficiency we also answer the often pondered question of whether an open network or its closed counterpart has greater throughput - the answer is that neither can assure a greater guaranteed throughput.
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    Queueing systems 33 (1999), S. 293-325 
    ISSN: 1572-9443
    Keywords: stability ; fluid models ; multiclass queueing networks ; piecewise linear Lyapunov functions ; linear Lyapunov functions ; monotone global stability ; static buffer priority disciplines
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    Topics: Computer Science
    Notes: Abstract This paper studies the stability of a three‐station fluid network. We show that, unlike the two‐station networks in Dai and Vande Vate [18], the global stability region of our three‐station network is not the intersection of its stability regions under static buffer priority disciplines. Thus, the “worst” or extremal disciplines are not static buffer priority disciplines. We also prove that the global stability region of our three‐station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three‐station network. We also show that the LP proposed by Bertsimas et al. [1] does not characterize either the global stability region or even the monotone global stability region of our three‐station network. Further, we demonstrate that the LP related to the linear Lyapunov function proposed by Chen and Zhang [11] does not characterize the stability region of our three‐station network under a static buffer priority discipline.
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    Celestial mechanics and dynamical astronomy 63 (1995), S. 205-225 
    ISSN: 1572-9478
    Keywords: Restricted three body problem ; Lagrangian points ; resonances ; stability
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    Topics: Physics
    Notes: Abstract The problem of stability of the Lagrangian pointL 4 in the circular restricted problem of three bodies is investigated close to the 1 : 2 commensurability of the long and short period libration. By stability we define boundedness of the solution for a given initial finite displacement from the equilibrium point as function of the mass parameter μ close to the commensurability. A rigorous treatment close to the resonance condition is possible using a transformation that diagonalizes the matrix related to the linear part of the equations of motion. The so obtained equations are further transformed to action angle type variables. Then using an isolated resonance approach, only the slowly varying terms are kept in the equations and two independent isolating first integrals can be found. These integrals finally enable us to solve the stability problem in an exact way. The so obtained results are compared to numeric integration of the equations of motion and are found to be in perfect agreement.
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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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    Topics: Mathematics
    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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    Queueing systems 29 (1998), S. 129-159 
    ISSN: 1572-9443
    Keywords: rate-based feedback control ; ATM networks ; stability ; optimal algorithms
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    Topics: Computer Science
    Notes: Abstract Motivated by ABR class of service in ATM networks, we study a continuous time queueing system with a feedback control of the arrival rate of some of the sources. The feedback about the queue length or the total workload is provided at regular intervals (variations on it, especially the traffic management specification TM 4.0, are also considered). The propagation delays can be nonnegligible. For a general class of feedback algorithms, we obtain the stability of the system in the presence of one or more bottleneck nodes in the virtual circuit. Our system is general enough that it can be useful to study feedback control in other network protocols. We also obtain rates of convergence to the stationary distributions and finiteness of moments. For the single botterneck case, we provide algorithms to compute the stationary distributions and the moments of the sojourn times in different sets of states. We also show analytically (by showing continuity of stationary distributions and moments) that for small propagation delays, we can provide feedback algorithms which have higher mean throughput, lower probability of overflow and lower delay jitter than any open loop policy. Finally these results are supplemented by some computational results.
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    Queueing systems 31 (1999), S. 171-206 
    ISSN: 1572-9443
    Keywords: scheduling ; open multiclass queueing networks ; discrete-review policies ; fluid models ; stability
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    Topics: Computer Science
    Notes: Abstract This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value r k (q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable. In such a policy, system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed. Stability is proved by combining elementary large deviations theory with an analysis of an associated fluid control problem. These results are extended to systems with class dependent setup times as well as systems with alternate routing and admission control capabilities.
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    ISSN: 1572-9443
    Keywords: dam ; storage process ; saturation rule ; intermittent production ; state dependent rates ; state dependent jumps ; stability ; positive Harris recurrence
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    Notes: Abstract We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.
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    Queueing systems 26 (1997), S. 343-363 
    ISSN: 1572-9443
    Keywords: retrial queues ; stability ; ergodicity ; renovation
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    Topics: Computer Science
    Notes: Abstract We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ 〉 λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers.
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    Queueing systems 32 (1999), S. 99-130 
    ISSN: 1572-9443
    Keywords: neural network ; inhibition ; stability ; Markov process ; fluid limit ; Harris-recurrence ; transience
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    Topics: Computer Science
    Notes: Abstract The subject of the paper is the stability analysis of some neural networks consisting of a finite number of interacting neurons. Following the approach of Dai [5] we use the fluid limit model of the network to derive a sufficient condition for positive Harris-recurrence of the associated Markov process. This improves the main result in Karpelevich et al. [11] and, at the same time, sheds some new light on it. We further derive two different conditions that are sufficient for transience of the state process and illustrate our results by classifying some examples according to positive recurrence or transience.
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    Queueing systems 32 (1999), S. 195-231 
    ISSN: 1572-9443
    Keywords: window flow control ; TCP ; stability ; multiclass networks ; stationary ergodic point processes ; (max,+)-linear system
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    Topics: Computer Science
    Notes: Abstract We focus on window flow control as used in packet-switched communication networks. The approach consists in studying the stability of a system where each node on the path followed by the packets of the controlled connection is modeled by a FIFO (First-In-First-Out) queue of infinite capacity which receives in addition some cross traffic represented by an exogenous flow. Under general stochastic assumptions, namely for stationary and ergodic input processes, we show the existence of a maximum throughput allowed by the flow control. Then we establish bounds on the value of this maximum throughput. These bounds, which do not coincide in general, are reached by time-space scalings of the exogenous flows. Therefore, the performance of the window flow control depends not only on the traffic intensity of the cross flows, but also on fine statistical characteristics such as the burstiness of these flows. These results are illustrated by several examples, including the case of a nonmonotone, nonconvex and fractal stability region.
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    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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    Topics: Mathematics
    Notes: Abstract The characteristic equation of a system of delay differential equations (DDEs) is a nonlinear equation with infinitely many zeros. The stability of a steady state solution of such a DDE system is determined by the number of zeros of this equation with positive real part. We present a numerical algorithm to compute the rightmost, i.e., stability determining, zeros of the characteristic equation. The algorithm is based on the application of subspace iteration on the time integration operator of the system or its variational equations. The computed zeros provide insight into the system’s behaviour, can be used for robust bifurcation detection and for efficient indirect calculation of bifurcation points.
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    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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    Topics: Mathematics
    Notes: Abstract A new backward error analysis of LU factorization is presented. It allows to obtain a sharper upper bound for the forward error and a new definition of the growth factor that we compare with the well known Wilkinson growth factor for some classes of matrices. Numerical experiments show that the new growth factor is often of order approximately log2 n whereas Wilkinson's growth factor is of order n or $$\sqrt n$$ .
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    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 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 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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    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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    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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    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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    Celestial mechanics and dynamical astronomy 61 (1995), S. 181-196 
    ISSN: 1572-9478
    Keywords: Periodic solutions ; stability ; restricted three-body problem
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    Topics: Physics
    Notes: Abstract The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.
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    Celestial mechanics and dynamical astronomy 67 (1997), S. 181-204 
    ISSN: 1572-9478
    Keywords: Hamiltonian systems ; symplectic mappings ; normal forms ; resonances ; stability ; three degrees of freedom
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    Topics: Physics
    Notes: Abstract We analyze four-dimensional symplectic mappings in the neighbourhood of an elliptic fixed point whose eigenvalues are close to satisfy a third-order resonance. Using the perturbative tools of resonant normal forms, the geometry of the orbits and the existence of elliptic or hyperbolic one-dimensional tori (fixed lines) is worked out. This allows one to give an analytical estimate of the stability domain when the resonance is unstable. A comparison with numerical results for the four-dimensional Hénon mapping is given.
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    Celestial mechanics and dynamical astronomy 61 (1995), S. 1-19 
    ISSN: 1572-9478
    Keywords: Three body problem ; stability ; surface of section ; commensurability
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    Topics: Physics
    Notes: Abstract The model of the circular restricted problem of three bodies is used to investigate the sensitivity of the third body motion when it is given a positional or velocity deviation away from the L4 triangular libration point. The x-axis is used as a criteria for defining the stability of the third body motion. Poincaré's surfaces of section are used to compare the regions of periodic, quasi-periodic and stochastic motion to the trajectories found using the definition of stability (not crossing the x-axis) defined in this study. Values of the primary/secondary mass ratios (μ) ranging from 0 to the linear critical value 0.038521... are investigated. Using this new form of stability measure, it is determined that certain values of μ are more stable than others. The results of this study are compared, and found, to give agreeable results to other studies which investigate commensurabilities of the long and short period terms of periodic orbits.
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    Celestial mechanics and dynamical astronomy 61 (1995), S. 261-285 
    ISSN: 1572-9478
    Keywords: galactic dynamics ; periodic orbits ; stability
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    Topics: Physics
    Notes: Abstract We study the stability of axial orbits in analytical galactic potentials as a function of the energy of the orbit and the ellipticity of the potential. The problem is solved by an analytical method, the validity of which is not limited to small amplitudes. The lines of neutral stability divide the parameter space in regions corresponding to different organizations of the main families of orbits in the symmetry planes.
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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
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
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  • 60
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    Celestial mechanics and dynamical astronomy 66 (1996), S. 191-202 
    ISSN: 1572-9478
    Keywords: resonance ; restricted problem ; stability
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    Topics: Physics
    Notes: Abstract The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases ω1 = 2ω2 and ω1 = 3ω2. The motion is unstable for all the values of parameters q and A when ω1 = 2ω2 and the motion is unstable and stable depending upon the values of the parameters q and A when ω1 = 3ω2. Here q is the radiation parameter and A is the oblateness parameter.
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    Celestial mechanics and dynamical astronomy 69 (1997), S. 271-281 
    ISSN: 1572-9478
    Keywords: restricted three-body problem ; libration points ; stability
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    Topics: Physics
    Notes: Abstract The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied. It is found that L4,5 are unstable in the whole range 0 ≤ µ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable for 0 〈 µ 〈 µ0, where µ is the mass parameter and µ0 = 0.03852....
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    Celestial mechanics and dynamical astronomy 69 (1997), S. 317-330 
    ISSN: 1572-9478
    Keywords: artificial satellite ; Nekhoroshev's theory ; normal form ; stability
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    Topics: Physics
    Notes: Abstract We investigate the significance of long time stabilty predictions in the light of Nekhoroshev's theory by studying the orbits of artificial satellites. As a simplified model problem we consider the so-called J2problem for an earth's satellite, neglecting luni-solar perturbations and nonconservative effects. We consider a wide range of orbits, excluding those which are too close to the critical inclination. Most of the orbits turn out to be stable for times larger than the estimated age of the solar system, thus proving that, as far as dissipation can be neglected, stability in Nekhoroshev's sense may be effective for physically realistic systems.
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    Celestial mechanics and dynamical astronomy 70 (1998), S. 41-58 
    ISSN: 1572-9478
    Keywords: three-body problem ; libration points ; stability ; normal forms.
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    Topics: Physics
    Notes: Abstract In this paper we consider the problem of motion of an infinitesimal point mass in the gravity field of an uniformly rotating dumb-bell. The aim of our study is to investigate Liapunov stability of Lagrangian libration points of this problem. We analyze the stability of libration points in the whole range of parameters ω, μ of the problem. In particular, we consider all resonance cases when the order of resonance is not greater than five.
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  • 64
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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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  • 65
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    Optical review 6 (1999), S. 28-36 
    ISSN: 1349-9432
    Keywords: optical propagation equation ; stability ; picosecond pulse ; 3-dimensional computation ; Fresnel’s distribution ; fast Fourier transform
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    Topics: Physics
    Notes: Abstract We present a new simulation code able to simulate the entire propagation of laser pulse, from the amplifiers level up to the focusing stage. This algorithm has some new characteristics that we intend to present. It computes the three-dimensional optical propagation equation using no approximation other than its picosecond expression. The stability has been carefully studied so that it can be applied to any geometry. This is a great improvement since, up to now only cylindrical geometry was accessible for accuracy. In this paper we also present a method using Fast Fourier Transform able to evaluate with a high accuracy, Fresnel’s distribution of a focused laser pulse. The advantages provided by our algorithm are its rapidity and its high physical understanding of the focusing phenomena.
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  • 66
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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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    Catalysis letters 40 (1996), S. 261-264 
    ISSN: 1572-879X
    Keywords: Ti-substituted MCM-41 ; stability ; dehydrogenation of ethanol ; hydroxylation of phenol ; XRD ; XANES
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The thermal and chemical stability of a titanium-substituted MCM-41 (TiMCM-41) with Si/Ti mole ratio of 39 and pore diameter of 2.4 nm was studied with the small-angle X-ray diffraction and X-ray absorption near-edge structure techniques. The TiMCM-41 was stable in helium flow below 1273 K and under gas-phase reaction conditions of ethanol dehydrogenation (ethanol/ O2 = 1 mol/mol, 373–723 K). Under liquid-phase reaction conditions of phenol hydroxylation (phenol/35% H2O2 /acetone in moles=3∶1∶7,333K), however, it lost the MCM-41structure and titanium was leached out of the silicalite framework.
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    Catalysis letters 53 (1998), S. 97-101 
    ISSN: 1572-879X
    Keywords: ethene hydroformylation ; heterogeneous catalysts ; cobalt catalysts ; gas‐phase deposition ; dispersion ; stability
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The results from ethene hydroformylation at 173°C showed that a Co(acac)3/SiO2 catalyst prepared from Co(acac)3 precursor by gas‐phase deposition was three times as active as a catalyst prepared by impregnation from cobalt nitrate, but oxo‐selectivities were similar. The high propanal selectivities on the Co(acac)3/SiO2 seem to be related to the presence of highly dispersed active sites favouring CO insertion. As dispersion is decreased from 23 to 8% due to increasing metal content (from 5 to 16 wt%), oxo‐selectivity decreased from 39 to 25%. The activity of Co(acac)3/SiO2 remained unchanged during 68 h on stream. The gas‐phase deposition technique described here is a promising method for the preparation of active, selective and stable heterogeneous hydroformylation catalysts.
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  • 70
    ISSN: 1572-879X
    Keywords: nanolithography ; model catalyst ; palladium ; copper ; stability ; spin-coating ; SEM ; AFM ; XPS
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Metal clusters arranged on nanostructured oxidized silicon wafers are presented as new model catalyst systems. A photoresist layer spun on top of a wafer was patterned by laser interference exposure. The grid obtained after removing the exposed parts of the resist is used as an etching mask. Hollows with diameters of 300 nm and depths between 50 and 60 nm were etched into the oxide layer using wet chemical methods. Two methods were applied to deposit metal clusters (Pd or Cu) in a defined way within the hollows. The particles ranged from 10 to 50 nm in height and from 80 to 200 nm in diameter. The model catalyst systems were characterized by atomic force microscopy and X-ray photoelectron spectroscopy. The method presented here allows us to produce 4 inch wafers that are covered completely by nanometer-sized structures in a reasonable period of time.
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    Applied physics 33 (1984), S. 115-131 
    ISSN: 1432-0649
    Keywords: 02.20 ; 42.55 ; 42.60D
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    Topics: Physics
    Notes: Abstract This study puts forward the concept of helical distributed feedback (DFB) lasers. The basic features of this new type of laser are derived by group theoretical considerations on cylindrical, circular linear periodic, and helical waveguide and laser structures. It is demonstrated that not only linear periodic structures but also helical structures show Bragg and DFB effects. Microwave and far-infrared experiments on passive helical metal waveguides reveal Bragg resonances in transmission. These results initiated the first experimental realization of a helical DFB gas laser, i.e. an optically pumped 496μm CH3F laser with a helical metal waveguide of a pitch close to 250μm. This helical DFB laser shows higher-mode selectivity than the corresponding linear DFB laser. Finally, we show that the concept of helical DFB also applies to dye lasers with internal DFB incorporated by a mixture of the dye with a cholesteric liquid crystal.
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    Applied physics 34 (1984), S. 17-21 
    ISSN: 1432-0649
    Keywords: 42.55
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    Topics: Physics
    Notes: Abstract Twenty-four new optically pumped submillimetre laser lines have been observed when CH3OH is excited using a13C18O2 pump laser. Four of these lines have been assigned to transitions involving the CO stretching band. In addition to these lines, a further six new lines have been observed when pumping with12C18O2 and13C16O2 lasers. One of these lines has been assigned to a transition involving the CO stretching band. The observation of infrared-infrared double resonance signals in CH3OH has allowed the prediction of a further six laser lines which should be excited using a13C18O2 pump laser.
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    Applied physics 34 (1984), S. 221-228 
    ISSN: 1432-0649
    Keywords: 42.55 ; 41
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    Topics: Physics
    Notes: Abstract The conditions under which a cooperative emission from different friges occurs in the scattering between a relativistic electron beam and two interfering laser beams are discussed. In particular, the conditions to have an electron grating are discussed.
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    Applied physics 35 (1984), S. 77-82 
    ISSN: 1432-0649
    Keywords: 42.55 ; 42.65
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    Notes: Abstract The coexistence of bistability and repetitive passive Q-switching of a CO2 laser with a gaseous saturable absorber has been investigated experimentally. With CH3F as the saturable absorber bistability has been observed simultaneously with passive Q-switching, whereas with CH3OH either one of these phenomena can only exist, as demonstrated for the first time. The measured features of both systems can be explained qualitatively by rate-equation theory.
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    Applied physics 35 (1984), S. 127-129 
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    Keywords: 42.55
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    Topics: Physics
    Notes: Abstract Strong submillimetre laser action has been obtained on five lines of a new laser gas, formaldoxime. Several new emission lines have also been produced by isotopic CO2 laser pumping of14NH3 and15NH3. One of these lines at 102.9 μm is a rotation-inversion transition in the 2v 2 state, and is the first example of cw laser action in such a highly excited state.
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  • 76
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    Keywords: 33 ; 82.50 ; 42.55
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    Notes: Abstract We measured the photoionization cross-sections of anthracene, 1,2-benzanthracene,p-terphenyl, and 2,5-diphenylfuran molecules excited to the singlet and triplet electronic states intermediate in the stepwise two-photon ionization process at 266 nm (all compounds) and at 355, 391 and 417 nm (anthracene).
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    Applied physics 28 (1982), S. 373-381 
    ISSN: 1432-0649
    Keywords: 42.55 ; 42.80 ; 52
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    Notes: Abstract We investigated noise and fluctuations of the output power of cataphoretic HeSe+ lasers in positive column plasma. Direct coupling of laser output power noise and fluctuations of the local population inversion was found. An investigation of the positive column plasma showed moving striations being responsible for the gain fluctuations. Whereas the local plasma properties are dominated by high frequency striations in the 100 kHz range, integrated quantities such as laser gain per pass are most strongly influenced by low-frequency waves with a continuous noise spectrum below 200 kHz. External modulation of the discharge voltage or current at a frequency near thehf striations reduces laser noise and increases laser output power.
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  • 78
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    Keywords: 32 ; 42.55
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    Notes: Abstract Optical absorption,S 1 lifetime, and photostability are investigated for a series of heptamethine ir dyes and related to chemical structure. The high photostability of several dyes and the large range ofS 1 lifetimes make these dyes very interesting for ir dye lasers and for ir mode-locked laser systems.
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    Applied physics 29 (1982), S. 13-14 
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    Keywords: 42.55
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    Notes: Abstract Intense far-infrared laser action is reported for carbonyl fluoride and vinyl fluoride. Eleven new lines with wavelengths between 339 μm≦λ≦538 μm were obtained by optically pumping carbonyl fluoride with numerous lines of the 10.4 μm band of a cw CO2 laser. Twenty-three lines with wavelengths in the range 172 μm≦λ≦783 μm were detected when pumping the recently discovered efficient FIR laser molecule vinyl fluoride. In addition, three very weak new lines were found using 1.1-difluoroethylen.
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    Applied physics 29 (1982), S. 263-267 
    ISSN: 1432-0649
    Keywords: 42.55 ; 42.65 ; 42.80
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    Notes: Abstract The duration, shape, and background intensity level of pulses of a passively modelocked Nd-glass laser are determined by noncollinear phase-matched four-photon frequency mixing of time-separated fundamental and second-harmonic pulses in a KI crystal. The pulse shape is found to be slightly asymmetric with slower trailing than rising parts. The background intensity level before and behind the main pulse is about 5¢10−6 the peak pulse intensity.
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    Applied physics 30 (1983), S. 1-4 
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    Keywords: 33 ; 42.55
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    Topics: Physics
    Notes: Abstract Twenty FIR laser lines with wavelengths between 146 and 2000 μm have been observed from deuterated formyl fluoride (DCOF) optically pumped with isotopic CO2 lasers. Tunable diode laser measurements on thev 4 band of DCOF were combined with earlier high precision spectroscopic data on thev 3 andv 4 bands, and enabled identification of the transitions responsible for 9 of the new FIR lines.
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    Applied physics 30 (1983), S. 135-142 
    ISSN: 1432-0649
    Keywords: 42.55 ; 42.60 ; 42.80
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    Topics: Physics
    Notes: Abstract An analysis of cw synchronously pumped dye lasers is presented. Under the assumption that the cavity (tuning element) bandwidth is much wider than the bandwidth of the transform limited pulses generated, the pulse forming dynamics is rigorously treated. It is shown that for a finite mismatch between the lengths of the dye and the pump lasers, a steady-state pulse develops in the dye laser cavity with a conserved pulseshape. The characteristics (energy, shape, peak power, duration) of these pulses of ultimate width are quantitatively determined as a function of cavity mismatch. An analytical solution for the pulse envelope is determined, which yieldsI(t)∝Sech2(t/t p ) to a good approximation.
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    Applied physics 32 (1983), S. 75-78 
    ISSN: 1432-0649
    Keywords: 33 ; 34 ; 42.55
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    Topics: Physics
    Notes: Abstract Multiphoton absorption (MPA) of the CO2 laser 9 μmR(30) line (pulse width 60 ns, FWHM) by NH3 and NH3/N2 mixtures was studied as a function of gas composition, pressure and laser fluence (Φ). MPA occurs for Φ smaller than those that have been used for optically pumped NH3/N2 lasers; consequently a simple two-level absorption model will not adequately describe laser action in these systems. The photon energy deposited in NH3/N2 mixtures can be calculated from the MPA cross-section and the fluence dependence of the illumination geometry. An examination of the efficiency of conversion of this absorbed energy to the reported radiant energy of optically pumped NH3/N2 lasers shows an optimum value which depends on pressure, and gas composition.
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    Applied physics 32 (1983), S. 105-111 
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    Keywords: 42.55
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    Notes: Abstract The effects of H2, He, and N2 buffer gases on the efficiency of the cw 12.08 μm NH3 Raman laser are studied experimentally. The laser output power is increased by nearly 60% with the addition of H2 or He, which we essentially attribute to the high thermal conductivity of these buffer gases. In the optimum conditions (NH3/H2:1/1 mixture with 0.35 Torr partial pressure of NH3) 3.3 W output power at 12.08 μm is obtained which corresponds to 11% power conversion efficiency.
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    Applied physics 32 (1983), S. 127-135 
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    Keywords: 42.55 ; 42.60
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    Notes: Abstract A cw uv copper hollow cathode laser is described, which could be operated for a longer time duration with an output power of 7 mW in the 260 nm region. A double-cathode configuration with a protection for the mirrors from metal-vapour deposition is presented. Characteristics of the laser output power, the spontaneous emission, and the ion densities in the negative glow were measured as depending on the discharge current, the neon gas pressure, and the size of the cathode slit. The observed saturation of the laser output power at high discharge current (1 A/cm2) and the optimum slot size are discussed.
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    Applied physics 33 (1984), S. 23-27 
    ISSN: 1432-0649
    Keywords: 42.55 ; 42.60
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    Notes: Abstract For the first time stable cw output of a FIR-CO2 hybrid laser has been achieved at wavelengths shorter than 300 μm. Due to the saturable absorber characteristic of the FIR laser gas, cw or pulsed emission is observed on both, the CO2 and the FIR laser output, depending on the operating conditions. Results are reported on different resonant lines in CH3OH and the 67 μm Raman line in NH3. The good efficiency of this laser is also demonstrated by the excitation of two new emission lines in CH3OH, namely 49 and 56 μm, pumped by 9R(22) and 9R(24), respectively.
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    Applied physics 34 (1984), S. 83-86 
    ISSN: 1432-0649
    Keywords: 33.50 ; 34.50 ; 42.55
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    Notes: Abstract An XeF pumped vapor phase POPOP dye laser with a pulse duration of 300 ns was obtained when trans-stilbene was used as triplet quencher. An energy conversion efficiency of 7,5% with a peak power efficiency of 12% was measured.
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    Applied physics 34 (1984), S. 175-177 
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    Notes: Abstract 47 new cw far-infrared laser lines with wavelenths between 453 and 2356 μm have been obtained by optically pumping vinyl bromide (C2H3Br) by a CO2 laser. A significant portion of these lines has wavelengths longer than 750 μm.
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    Applied physics 35 (1984), S. 163-166 
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    Keywords: 42.50 ; 42.55 ; 42.60
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    Notes: Abstract We present an analytical expression for the small-signal gain of a Free Electron Laser (FEL) in the presence of a Gaussian mode. To describe the electron beam evolution we use the one-dimensional (1-d) Vlasov equation. Our perturbation result, valid for small values of the parameterq (length of the undulatorL divided by the Rayleigh rangeZ R), can be extrapolated to values ofq≈4÷5.
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  • 90
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    Notes: Abstract A radiofrequency excited atomic Xe slab laser with an active volume of 2 × 10 × 300 mm3 using a quartz envelope containing the laser-gas mixture shows a stable cw performance with an output power of almost 1 W. The free-running system oscillates, depending on gas composition and density, on several lines between 1.73 and 3.51 μm. Line competition phenomena are observed. Single-line oscillation yields more than 500 mW.
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  • 91
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    Notes: Abstract The kinetics of cavitation and associated photo-mechanical effects induced by underwater pulsed-laser irradiation of solid targets has been studied experimentally and analyzed with theoretical methods. A xenon-chloride excimer laser of 150 ns pulse duration has been utilized to produce ablation and local photofragmentation of artificial samples of hard tissues at fluences of 12–24 J/cm2. The evolution of pressure wave and cavitation formations developing in the liquid from the target surface after laser irradiation has been observed with a time-resolved imaging technique employing a pump-probe laser arrangement. The analysis of experimental results has been performed by using the theoretical model of “point explosion” that has been successfully applied to fit the cavitation kinetics, providing also quantitative information on the energy transfer during photo-acoustic interactions.
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  • 92
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    Notes: Abstract We systematically investigate the difference between both actively and passively mode-locked lasers with Gain-at-the-End (GE) and Gain-in-the-Middle (GM) at the example of Nd:YLF lasers. The GE laser generates pulse widths approximately three times shorter than a comparable GM cavity. This is due to enhanced Spatial Hole Burning (SHB) which effectively flattens the saturated gain and allows for a larger lasing bandwidth compared to a GM cavity. We first investigate enhanced SHB by measuring the cw mode spectrum, where we have observed that the mode spacing in GE cavities depends primarily on the crystal length. This was also confirmed for a Nd:LSB crystal, where the pump absorption length was significantly shorter than the crystal length. In mode-locked operation, pulse widths of 4 ps for passive mode locking and 5 ps for active mode locking are demonstrated with GE cavities, compared to 11 ps for passive and 17 ps for active mode locking with GM cavities. Additionally, the time-bandwidth product for the GE cavity is approximately twice the ideal product for a sech2 pulse shape and cannot be improved by dispersion compensation alone, while the GM cavity has nearly ideal time-bandwidth-limited performance. The results for the GM cavity compare well to existing theories taking into account the added effect of pump-power-dependent gain bandwidth which increases the bandwidth of Nd: YLF from 360 to 〉 500 GHz. In a following paper [1] (called Part II) a rigorous theoretical treatment of the effects due to SHB will be presented.
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    Applied physics 62 (1996), S. 357-365 
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    Keywords: 42.55 ; 42.60
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The plasma electrode design concept is applied for the first time to an HF laser. The discharge along the surface of a dielectric (sliding discharge) is used as a plasma cathode for the main laser discharge. The laser operates at atmospheric pressure with a gas mixture of He/SF6/C3H8. Details are presented on the efficiency of energy transfer, the dependence of laser performance on circuit parameters, gas mixture, relative energy loading and time delay between the plasma electrode and main discharges. The F atom production rate is estimated from the linear dependence of the output energy on the electric charge passed through the discharge. Output energies of 600 mJ were obtained at 1.6% efficiency from a small active discharge of 108 cm3 volume and 38 cm length, while the maximum specific input and output energies were 370 J/1 and 5.7 J/1, respectively. These values compare favourably with those reported in the literature for non-chain-reaction-type gas mixtures at 1 atm pressure and demonstrate that the plasma electrode design is a powerful scheme for developing gas-discharge lasers.
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  • 94
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    Applied physics 26 (1981), S. 161-167 
    ISSN: 1432-0649
    Keywords: 52.80 ; 42.55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new magnetic discharge stabilization technique for coaxial laser systems is described. The approach utilizes crosses electric and magnetic fields to create and maintain a large and rapidly rotating plasma volume which does not experience glow-to-arc transitions. Very high cw specific discharge power loadings have been achieved even without the benefit of external gas cooling or circulation. Performance is insensitive to gas composition and pressure such that high power coaxial discharges have been run in CO2 laser gas mixtures up to several hundred torr. Stable cw discharges have also been obtained in mixtures containing several torr of SF6. The technique appears to be readily scalable to give very large excited volumes in systems with comparatively small overall physical dimensions.
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  • 95
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    Applied physics 32 (1983), S. 83-84 
    ISSN: 1432-0649
    Keywords: 42.55 ; 33.80
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A population inversion between the 62 P 3/2 and 62 P 1/2 state of thallium has been achieved for the first time by incoherent photodissociation of TII. This is accomplished by using wall-ablating flashlamps of short risetime and appropriate light filtering. The inversion lasts about 4 μs and is terminated by quenching collisions.
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  • 96
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    Applied physics 32 (1983), S. 193-198 
    ISSN: 1432-0649
    Keywords: 42.55 ; 33 ; 82.50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The vibrational relaxation time constant for theB v=0 vibrational level of XeCl* has been investigated by observing the coupling between theB v=1 andB v=0 vibrational levels under saturated lasing conditions. Based on this observation, estimates of the expected extraction efficiency from theB-state have been made.
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  • 97
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    Applied physics 33 (1984), S. 9-16 
    ISSN: 1432-0649
    Keywords: 42.60 ; 42.20 ; 42.55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We derive the most general equations of motion for the electrons and the electromagnetic field in a free-electron laser including the effects of diffraction and pulse propagation. The field evolution is expressed in terms of the amplitudes and phases of a complete set of transverse modes. The analytic solution is given in the small-signal regime, where the theory is shown to be in excellent agreement with a recent experiment at Orsay.
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  • 98
    ISSN: 1432-0649
    Keywords: 42.55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Experiments on pressure dependence of a CF4 laser have been carried out to elucidate dynamic characteristics of CF4 molecules pumped by CO2 lasers. The results are followed by a model calculation which characterizes collisional quenching of the energy levels related to the stimulated emission. The enhancement of the laser output induced by buffer-gas addition, which was found under specific conditions, is discussed in relation to the competition between laser and superfluorescent emissions.
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  • 99
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    Applied physics 26 (1981), S. 73-76 
    ISSN: 1432-0649
    Keywords: 07 ; 42.55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A liquid nitrogen cooled cw CO-Laser is described, with which laser action up to 8.18 μm (v=36→35) has been achieved.
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  • 100
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    Applied physics 26 (1981), S. 141-146 
    ISSN: 1432-0649
    Keywords: 42.55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We have designed and tested a pulsed single-mode dye laser for spectroscopy experiments. The dye laser is pumped by a 6 kHz copper vapor laser to produce up to 230 mW average power at over 5% efficiency in a nearly diffraction limited beam. The dye laser pulse closely resembles the 30 ns pump pulse. Using an electronic servo loop, the 60 MHz wide line can be scanned, without mode hopping, through the 16 GHz permitted by the travel on the piezo driven mirror mount.
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