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  • kinetics  (355)
  • stability  (333)
  • Springer  (687)
  • Cambridge University Press
  • 1995-1999  (586)
  • 1980-1984  (101)
  • 1955-1959
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  • 1
    Electronic Resource
    Electronic Resource
    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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    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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  • 8
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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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  • 9
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    Colloid & polymer science 261 (1983), S. 188-189 
    ISSN: 1435-1536
    Keywords: Polymerization ; kinetics ; redox polymerization ; acrylamide
    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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  • 10
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    Colloid & polymer science 262 (1984), S. 366-373 
    ISSN: 1435-1536
    Keywords: kinetics ; isothermal crystallization ; polymer ; spherulite ; differential scanning calorimetry
    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 In the DSC technique, isothermal crystallization experiments are usually performed on thin flat specimens, but their interpretation generally uses theories developed for an unbounded volume. In this paper, isothermal crystallization of spherical entities in the volume limited by two parallel infinite planes is considered. Our model, derived from Avrami's theory, gives an analytical expression for the transformed volume fraction as a function of time. It is shown that the influence of thickness becomes important when thickness becomes of the order of or smaller than the average spherulite radius. The main effects of a decreasing thickness are a slower crystallization kinetics and a decrease in the Avrami exponent. These results can be used to interpret experimental data obtained in isothermal polymer crystallization.
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  • 11
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    Colloid & polymer science 261 (1983), S. 621-625 
    ISSN: 1435-1536
    Keywords: Polyamide 6 ; crystallisation ; kinetics ; titania
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The kinetics of isothermal and nonisothermal crystallization of polyamide-6 (PA6) containing titania was studied by means of DSC. It was found thatTiO 2 causes an acceleration in the crystallization of polyamide-6 and lowers the value of the Avrami exponent,n. The presence of TiO2 does not affect equilibrium melting pointT m 0 , glass temperatureT g, or surface free energiesσ e andσ of the basal and lateral surfaces.
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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
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    Fire technology 20 (1984), S. 47-63 
    ISSN: 1572-8099
    Keywords: Extinguishment ; fire modeling ; mass loss ; heat release ; char ; reflash ; sprinklers ; radiant flux ; kinetics ; reaction rate ; heat loss ; ash ; latent heat ; spray density ; extinguishing agents
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying
    Notes: Abstract The Ad Hoc Mathematical Fire Modeling Working Group was organized about seven years ago to facilitate voluntary cooperation and coordination in developing mathematical fire modeling capability. The group has a steering committee of representatives of agencies that support fire modeling and related research. These include the National Bureau of Standards' Center for Fire Research, Factory Mutual Research Corp., the Naval Research Laboratory, NASA, and the Federal Aviation Agency. The Group holds plenary meetings when it seems desirable to do so (about once each 1 1/2 years), and workshops on topical subjects. Three workshops were held in 1983. Normally, Group meetings are held before or after other meetings at which a number of interested personnel would likely be present. Minutes are mailed to those who attended and to others (including European and Japanese personnel) who have indicated interest. This workshop was arranged by Ron Alpert of Factory Mutual Research Corp. and held at their facilities at Norwood, MA, in November 1983.
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  • 14
    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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  • 15
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    Journal of solution chemistry 11 (1982), S. 339-346 
    ISSN: 1572-8927
    Keywords: Carbon dioxide ; hydrolysis ; aqueous solution ; kinetics ; activation volume
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The pressure dependence of the dehydration reaction of H2CO3 was measured in acidic aqueous solution for pressures up to 1 kbar using a high-pressure stopped-flow instrument. The corresponding volume of activation was found to be 6.4±0.4 cm3-mol−1 at 25°C and 0.5 ionic strength. Volume equation calculations result in a value of −9.9±1.9cm3-mol−1 for the volume of activation for the hydrolysis of CO2 under the same conditions. For the first time, the reaction mechanism can be interpreted in terms of dissociative and associative modes, respectively. These data are used to construct an overall reaction volume profile.
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  • 16
    ISSN: 1572-8927
    Keywords: Temperature jump ; kinetics ; thermodynamics ; TRIS ; iminodiacetic acid ; magnesium ion ; phenol red
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Equations describing the temperature jump amplitudes associated with a system of two coupled reactions (TRIS-phenol red) as well as the ternary system (Mg2+-iminodiacetic acid-phenol red) are presented. The termodynamic parameters calculated from experimentally measured temperature perturbation amplitudes using a multiparametric curve fitting procedure are found to be in good agreement with those determined from pH- and costant rate thermometric titrations. For phenol red, pK I =7.55, ΔH I =3.45 kcal, and for Mg2+ iminodiacetic acid, log K M =2.84, ΔH M =3.25 kcal, were obtained. It is shown that this method can be used to determine accurate thermodynamic enthalpy changes over a narrow temperature interval of less than 1.0°C from a single experiment requiring about 50 μl of sample solution.
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  • 17
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    Journal of solution chemistry 12 (1983), S. 771-781 
    ISSN: 1572-8927
    Keywords: Ultrasonics ; kinetics ; aqueous solution ; iso-butyl cellosolve
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Ultrasonic absorption and velocity measurements in aqueous solution of iso-butyl cellosolve (ethylene glycol iso-butyl ether) as a function of the concentration are reported. The two relaxational absorptions have been attributed to the perturbation of the equilibria expressed by AB⇌A+B and Aα(1/n)An where A is the solute, B is the solvent, AB is the complex and A n is the solute aggregate. The rate constants for each step have been determined. From the concentration dependence of the maximum excess absorption per wave length, the enthalpy change and the volume change for the reaction between the solute and the solvent have been determined for aqueous solutions of butyl cellosolve (ethylene glycol n-butyl ether), iso-butyl cellosolve and propyl cellosolve (ethylene glycol n-propyl ether). The results are consistent with a hydrogen bonding reaction. The effect of the ethers on water structure are considered and it is clear that the fraction of water molecules which can hydrogen bond to the solute decreases with the increasing hydrophobicity of the solute.
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  • 18
    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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  • 19
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    Journal of applied electrochemistry 29 (1999), S. 191-200 
    ISSN: 1572-8838
    Keywords: cyclic redox reaction ; dissolution ; kinetics ; manganese dioxide ; mechanism ; pyrite
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper describes a study of the kinetics and mechanism of MnO2 dissolution in H2SO4 in the presence of pyrite through leaching and electrochemical parameters. Manganese(iv) was found to dissolve mainly through reduction by the ferrous ion generated during oxidation of pyrite by the ferric ion. The oxidation which is slower and rate controlling may proceed through two different reactions, one producing S0 and the other SO42−. Manganese dissolution runs at the same rate as that of pyrite oxidation by maintaining ferrous ion concentration at a much lower level than that of ferric. Kinetic equations based on corrosion coupling principles are developed to explain the observed leaching behaviour.
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  • 20
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    Journal of chemical crystallography 28 (1998), S. 69-72 
    ISSN: 1572-8854
    Keywords: Co(III) complex ; crystal structure ; kinetics ; steric effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The title compound crystallizes in the orthorhombic space group Pnma, with a = 7.9209(5), b = 9.818(1), c = 16.867(2) Å, and Z = 4. The structure was solved employing 1864 independent x-ray reflections with I〉2σ(I) by Patterson and difference Fourier techniques and refined by full-matrix least-squares to R = 0.036. The trans-[CO(NH3)4(NH2CH3)Cl](ClO4)2 molecule is on a crystallographic mirror plane. The cobalt ion is in an elongated octahedral coordination with four equatorial ammonia ligands [average Co–N distance equal to 1.966(2) Å], an axial methylamine [Co–N=1.965(3)Å], and an axial chlorine ion [Co–Cl=2.2771(9)Å]. Kinetic steric effects of the complex are interpreted in terms of structural results.
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  • 21
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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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  • 22
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    Adsorption 1 (1995), S. 133-151 
    ISSN: 1572-8757
    Keywords: PSA process ; sensitivity ; equilibria ; kinetics ; heats
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract Mathematical models for pressure swing adsorption (PSA) processes essentially require the simultaneous solutions of mass, heat and momentum balance equations for each step of the process using appropriate boundary conditions for the steps. The key model input variables needed for estimating the separation performance of the process are the multicomponent adsorption equilibria, kinetics and heats of adsorption for the system of interest. A very detailed model of an adiabatic Skarstrom PSA cycle for production of high purity methane from a ethylene-methane bulk mixture is developed to study the sensitivity of the process performance to the input variables. The adsorption equilibria are described by the heterogeneous Toth model which accounts for variations of isosteric heats of adsorption of the components with adsorbate loading. A linear driving force model is used to describe the kinetics. The study shows that small errors in the heats of adsorption of the components can severely alter the overall performance of the process (methane recovery and productivity). The adsorptive mass transfer coefficients of the components also must be known fairly accurately in order to obtain precise separation performance.
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  • 23
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    Adsorption 2 (1996), S. 265-277 
    ISSN: 1572-8757
    Keywords: frequency response ; diffusion cell ; kinetics ; diffusion ; heat effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract This paper deals with frequency response (FR) analysis of a closed diffusion cell system with two resonators, that is both the LHS and RHS volumes are modulated. The analysis is made for a homogeneous particle described by a single effective diffusivity as well as a biporous pellet described by macropore and micropore diffusions. It is shown that if the perturbation of the volume of the reservoir #2 is lagged behind that of the reservoir #1 by 3π/2, the pressure response in reservoir #1 is significantly enhanced with larger amplitude as well as phase angle. When the perturbations of the two reservoirs are out of phase, the heat effect is reduced and can become insignificant when the two perturbations are completely out of phase (ψ = π). Under such a condition, the pressure difference between the two reservoirs could be doubled. In the case of biporous pellets, it is shown that the FR behaviours obtained for micropore diffusion control and macropore diffusion control are well distinguished. In the former case, the FR system reduces to a traditional batch adsorber one while in the latter case, the FR behaviour is the same as for a two resonator system with homogeneous particles. This difference can be used for the discrimination of micropore and macropore diffusion processes.
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  • 24
    ISSN: 1572-8757
    Keywords: characterisation ; equilibria ; kinetics ; micropore size distribution ; n-butane ; nutshell
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract Adsorption equilibria and dynamics ofn-butane on two activated carbon samples prepared from the physical activation of nutshell are studied in this paper. The micropore size distribution (MPSD) is considered as the main source of solid heterogeneity. Lennard-Jones' potential theory and Dubinin's theory (TVFM) are used in the equilibria data to derive the MPSD, which is well fitted by a Gamma distribution function. The adsorption energy distribution derived from the MPSD is very asymmetric for both the samples studied, and this energy distribution used in the HMSD/HMSMD kinetics models for the study of adsorption dynamics ofn-butane.
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  • 25
    ISSN: 1572-8773
    Keywords: acidophilic ; strain ; oxidation ; kinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Abstract Recovery of metal values from sulfide ores by use of acidophilic microorganisms is gaining importance. A number of commercial/pilot plants are setup to find out the techno-economic feasibility of the overall process. The main drawback in the process is the slow kinetics of dissolution of metal values from the sulfide ores. To make the technology e attractive the kinetics should be improved considerably. There are various factors which determine the overall kinetics such as bacterial activity and concentration, iron and sulfur oxidation, oxygen consumption, reactor design and nature of ore. A brief review has been made dealing with the above parameters
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  • 26
    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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    Catalysis letters 37 (1996), S. 167-172 
    ISSN: 1572-879X
    Keywords: dissociation ; kinetics ; Co-Mo sulphide ; H2S
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    Topics: Chemistry and Pharmacology
    Notes: Abstract In this study, a high surface area 4Co∶6Mo∶100γ-Al2O3 sulphide prepared using precipitation from homogeneous solution (PFHS) has been used for the catalytic splitting of hydrogen sulphide into H2 and elemental sulphur. The activity of this new formulation was significantly better than previously reported recipes. Kinetic data collected over a wide range of H2S partial pressures between 883 and 983 K revealed that, although the decomposition followed a first-order law, a mechanism involving H2S adsorption on co-ordinative unsaturation sites of the Co-Mo sulphide catalyst gave a Langmuir-Hinshelwood rate expression that yielded satisfactory model parameters. In particular, the scission of the surface H-S bond appeared to be the rate determining step.
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    Catalysis letters 37 (1996), S. 173-179 
    ISSN: 1572-879X
    Keywords: ammonia synthesis ; iron catalysts ; potassium promotion ; kinetics
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Measurements were performed of reaction rate in the process of ammonia synthesis (T=370–470°C) on doubly promoted (DP) (Al2O3, CaO) and triply promoted (TP) (K2O, Al2O3, CaO) iron catalysts. The latter were obtained by impregnation of the reduced and subsequently passivated DP precursors with alcoholic solution of KOH. The studies were carried out under high total pressure (10 MPa) in a wide range of ammonia partial pressure in the gas phase: from 0.25 to about 7 bar. The results are shown to be authoritative for the so-called kinetic regime. The effect of the presence of K+ cations in the catalyst was the stronger, as the temperature of the reaction was the lower and, in particular, the ammonia pressure in the gas phase the higher. The obtained results are in good accordance with the results of Somorjai's studies on activity of iron single crystal surfaces both clean and covered with (K+O) adlayer.
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    ISSN: 1572-882X
    Keywords: accelerated tests ; aging tests ; cellulose degradation ; durability ; kinetics
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    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract Accelerated aging tests are credible and useful to predict paper permanence only if such tests can be shown to correlate with natural aging. In the first part of this study, a kinetic model was developed based on the accelerated aging results. In this report, we have shown that this kinetic model can indeed predict the natural aging results of lignin-free sheets with a statistical confidence. This is the first quantitative comparison of accelerated aging with natural aging.
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    Journal of dynamics and differential equations 10 (1998), S. 151-188 
    ISSN: 1572-9222
    Keywords: Fourth-order solitary waves ; stability ; instability
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    Topics: Mathematics
    Notes: Abstract We study ground-state traveling wave solutions of a fourth-order wave equation. We find conditions on the speed of the waves which imply stability and instability of the solitary waves. The analysis depends on the variational characterization of the ground states rather than information about the linearized operator.
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    Positivity 1 (1997), S. 319-330 
    ISSN: 1572-9281
    Keywords: delay equations ; stability ; positive solutions ; spectral growth condition
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    Topics: Mathematics
    Notes: Abstract We prove stability for a semilinear delay equation, whose nonlinearity is majorized by a linear positive operator. The key ingredients are a spectral condition, positivity of solutions to the linear problem, and lattice properties of the Banach space.
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    ISSN: 1572-9281
    Keywords: asymptotic stability ; dichotomic maps ; retarded functional differential equation ; stability
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    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
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    Topics: Computer Science
    Notes: Abstract A stationary regime for polling systems with general ergodic (G/G) arrival processes at each station is constructed. Mutual independence of the arrival processes is not required. It is shown that the stationary workload so constructed is minimal in the stochastic ordering sense. In the model considered the server switches from station to station in a Markovian fashion, and a specific service policy is applied to each queue. Our hypotheses cover the purely gated, thea-limited, the binomial-gated and other policies. As a by-product we obtain sufficient conditions for the stationary regime of aG/G/1/∞ queue with multiple server vacations (see Doshi [11]) to be ergodic.
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    Queueing systems 22 (1996), S. 47-63 
    ISSN: 1572-9443
    Keywords: Sample-path analysis ; stability ; rate stability ; ω-rate stability ; input-output process ; queueing ; infinite-server queues
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    Topics: Computer Science
    Notes: Abstract An input-output processZ = {Z(t), t ⩾ 0} is said to beω-rate stable ifZ(t) = o(ω(t)) for some non-negative functionω(t). We prove that the processZ is ω-rate stable under weak conditions that include the assumption that input satisfies a linear burstiness condition and Z is asymptotically average stable. In many cases of interest, the conditions forω-rate-stability can be verified from input data. For example, using input information, we establishω-rate stability of the workload for multiserver queues, an ATM multiplexer, andω-rate stability of queue-length processes for infinite server queues.
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    Queueing systems 22 (1996), S. 345-366 
    ISSN: 1572-9443
    Keywords: State-dependent service and interarrival times ; Lindley equation ; recursive stochastic equations ; stability ; normal approximations
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    Topics: Computer Science
    Notes: Abstract We consider a modification of the standardG/G/1 queueing system with infinite waiting space and the first-in-first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. When the waiting-time distributions converge to a proper limit, Whitt [10] proposed a normal approximation for this steady-state limit. In this paper we prove a limit theorem for the steady-state limit of the system. Thus, our result provides a solid foundation for Whitt's normal approximation of the steady-state distribution of the system.
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    Queueing systems 29 (1998), S. 55-73 
    ISSN: 1572-9443
    Keywords: multi‐server queue ; customer class ; state‐dependent routing ; stability ; Markov chain ; fluid limit
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    Topics: Computer Science
    Notes: Abstract We consider a multi‐station queue with a multi‐class input process when any station is available for the service of only some (not all) customer classes. Upon arrival, any customer may choose one of its accessible stations according to some state‐dependent policy. We obtain simple stability criteria for this model in two particular cases when service rates are either station‐ or class‐independent. Then, we study a two‐station queue under general assumptions on service rates. Our proofs are based on the fluid approximation approach.
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    Queueing systems 32 (1999), S. 131-168 
    ISSN: 1572-9443
    Keywords: stability ; positive recurrence ; fluid limit ; polling system ; exhaustive service policy
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    Topics: Computer Science
    Notes: Abstract We introduce a generalized criterion for the stability of Markovian queueing systems in terms of stochastic fluid limits. We consider an example in which this criterion may be applied: a polling system with two stations and two heterogeneous servers.
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    Celestial mechanics and dynamical astronomy 74 (1999), S. 19-57 
    ISSN: 1572-9478
    Keywords: stability ; Hamiltonian ; two centers ; oblate planet ; galactic disks ; dipole
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    Topics: Physics
    Notes: Abstract Relative equilibria occur in a wide variety of physical applications, including celestial mechanics, particle accelerators, plasma physics, and atomic physics. We derive sufficient conditions for Lyapunov stability of circular orbits in arbitrary axisymmetric gravitational (electrostatic) and magnetic fields, including the effects of local mass (charge) and current density. Particularly simple stability conditions are derived for source‐free regions, where the gravitational field is harmonic (∇2U = 0) or the magnetic field irrotational (∇ × B = 0). In either case the resulting stability conditions can be expressed geometrically (coordinate‐free) in terms of dimensionless stability indices. Stability bounds are calculated for several examples, including the problem of two fixed centers, the J2 planetary model, galactic disks, and a toroidal quadrupole magnetic field.
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    Celestial mechanics and dynamical astronomy 75 (1999), S. 251-285 
    ISSN: 1572-9478
    Keywords: unrestricted problem ; rotational motion ; rigid body dynamics ; libration points ; stability ; resonances
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    Topics: Physics
    Notes: Abstract We present an analysis of the model introduced by Kokoriev and Kirpichnikov (1988) for the study of unrestricted planar motion of a point mass and a symmetric rigid body whose gravity field is approximated by two point masses (a dumb-bell model). To show possible generalization of the model, we give a systematic derivation of equations of motion for a more general unrestricted problem of a point and a rigid body possessing a plane of dynamical symmetry. We give a simple description of bifurcation of triangular libration points, and we perform an analysis of their linear stability. We propose to extend the model of Kokoriev and Kirpichnikov (1988) to a case when the symmetric body is oblate. In the proposed model the gravity field of moving and rotating body is approximated by two complex masses at complex distance (a complex dumb-bell model). An analysis of bifurcation of the triangular libration points in this model is also presented.
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    Set-valued analysis 5 (1997), S. 73-88 
    ISSN: 1572-932X
    Keywords: differential inclusion ; invariance ; stability
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    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
    Source: Springer Online Journal Archives 1860-2000
    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
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.
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    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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    Journal of solution chemistry 27 (1998), S. 1123-1138 
    ISSN: 1572-8927
    Keywords: Sol–gel processing ; hydrolysis ; condensation ; kinetics ; methoxydimethyloctylsilane ; copper nitrate hydrate ; phase diagram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The reaction rate was determined for copper nitrate hydrate with methoxydimethyloctylsilane (MDOS) in methanol. The rate constants of hydrolysis and condensation were established by quantitative measurement of the product and Karl Fischer water determination. The reaction with the hydrated copper salt resulted in the phase separation of an insoluble product from the reaction mixture. The structure of the product was determined, by Fourier Transform Infrared Spectrometry (FTIR) and Nuclear Magnetic Resonance (NMR) to be a dimer of the MDOS. The results showed the alcohol, producing condensation reaction was negligible in the formation of the dimer. contrary to the case for the well-known reaction by trialkoxysilanes and tetraalkoxysilanes.
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    ISSN: 1572-8927
    Keywords: Enthalpies of reaction ; heats of reaction ; kinetics ; ester hydrolysis ; microcalorimetry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The conditions under which the Picker flow microcalorimeter can be used to measure enthalpies and rates of reactions were investigated. For this purpose, systematic studies were made of the enthalpies of neutralization of HCl, HBr, HNO 3 , acetic, proprionic, and butyric acids with NaOH, enthalpies of hydrolysis of methyl and ethyl acetate with NaOH, and the reaction rates of the ester hydrolysis with NaOH. The general procedure and various sources of error are discussed and it is concluded that enthalpies of slow reactions can be measured to about 1% when the calorimeter is operated in the quasi-isothermal mode and the reaction rates to about 3% when operated in the quasi-adiabatic mode.
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    Cellulose 4 (1997), S. 1-5 
    ISSN: 1572-882X
    Keywords: paper ; degradation ; ageing ; kinetics ; modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Process Engineering, Biotechnology, Nutrition Technology
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    Cellulose 3 (1996), S. 243-267 
    ISSN: 1572-882X
    Keywords: aging tests ; cellulose degradation ; durability ; kinetics ; paper properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The validity of accelerated aging tests to predict and rank papers on their permanence has been under question, preventing the development of performance-based standards for permanent paper. We conducted a general kinetic analysis to investigate the aging process of paper. A general kinetic model is proposed to describe the depolymerization of cellulose. Experimentally it was shown that in the case of aging, cellulose degradation follows classic first-order kinetics as a special case of our general kinetic model. The Arrhenius equation was critically re-examined for the case of a multiple reaction system. It was shown analytically that the Arrhenius equation is still applicable when certain conditions are met. This was convincingly supported by experimental results. We also analysed the dependence of the degradation rate on the moisture content and hydrogen ion concentration. By conducting systematic experiments on these two factors, a general and quantitative relationship was established to explain the contribution of each factor and their interactions. Finally, based on this kinetic analysis, the effects of storage conditions on the life expectancy of paper were estimated.
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  • 58
    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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    Topics: Computer Science
    Notes: Abstract We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.
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    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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    Journal of inorganic and organometallic polymers and materials 8 (1998), S. 111-117 
    ISSN: 1572-8870
    Keywords: Organosiloxane ; kinetics ; poly(phenylmethylsiloxane) ; catalyst ; anionic ; ring-opening
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    Topics: Chemistry and Pharmacology
    Notes: Abstract It is well known that the rate of polymerization for an anionic mechanism is dependent on the ability of the bulk material or solvent system to disassociate the ion pair at the propagating chain end. In the anionic ring-opening polymerization of cyclic organosiloxanes in particular, the larger and softer the counter ion, the more rapidly the reaction proceeds. A recently developed phosphazene initiator system provides a large, soft counter ion relative to other traditional initiators used for the polymerization of poly(dimethylsiloxane) (PDMS). This novel initiator system was used in this investigation for the ring-opening polymerization of tetraphenyltetramethylcyclotetrasiloxane (P4) and the reaction kinetics under bulk and solution conditions were investigated. The new initiator system showed a dramatic increase in the rate of polymerization over the conventional potassium hydroxide-catalyzed system. Furthermore, this initiator was sufficiently reactive to be useful for the ring-opening polymerization of P4 at 293 K.
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  • 63
    ISSN: 1572-8900
    Keywords: Cellulose ; alkaline degradation ; peeling off ; degree of polymerization ; kinetics ; (gluco)isosaccharinic acid
    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 degradation of cellulosic materials, differing mainly in the degree of polymerization and the number of reducing end groups, was studied under the alkaline conditions similar to those existing in a cementitious repository for low- and intermediate-level radioactive waste (pH 13.3, T = 25°C). The kinetics of alkaline degradation (peeling-off reaction) were studied and the data analyzed by the model of Haas et al. [13]. The observed kinetic parameters for the propagation reaction and overall stopping reaction were compared with literature data. Although measured under different experimental conditions, literature data and data from this study show a consistent picture. Differences in the extent of degradation observed for the different cellulosic materials could be satisfactorily explained by differences in reducing end group content and, consequently, by differences in the degrees of polymerization. Besides the number of reducing end groups, the degree of amorphousness also plays an important role. The main degradation products formed under the experimental conditions used are α- and β-(gluco)isosaccharinic acid. This is in agreement with many other studies on alkaline degradation of cellulose. The two isomers are formed in roughly equal amounts.
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    Topics in catalysis 5 (1998), S. 133-147 
    ISSN: 1572-9028
    Keywords: NMR ; catalysis ; high pressure ; dynamic equilibria ; magnetization transfer ; sapphire tube ; gas phase ; kinetics
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    Topics: Chemistry and Pharmacology
    Notes: Abstract High resolution NMR techniques are applicable to a variety of aspects of catalysis. Methods for studying homogeneously-catalyzed systems under high gas pressure are described along with approaches for obtaining mechanistic and dynamic information. Many of the same techniques may be applied to heterogeneous catalysis by following the reaction chemistry by gas phase NMR.
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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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  • 69
    ISSN: 1572-9028
    Keywords: nonlinear temperature behavior ; Eyring plot ; modified Eyring plot ; selectivity ; selection process ; enantioselectivity ; selection level ; isoinversion principle ; isoinversion temperature ; inversion temperature ; kinetics ; catalysis ; asymmetric hydrogenation ; dihydroxylation ; cocyclization
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The influence of the temperature on selectivity is described under special consideration of nonlinearities in the corresponding modified Eyring plots. Reasons for the experimentally well-known behavior are discussed. Furthermore, the conditions for nonlinear temperature behavior are quantified and a concept is described which allows the determination of the temperature dependence of a single reaction pathway in a selection process.
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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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  • 73
    ISSN: 1572-9125
    Keywords: finite difference methods ; wave equation ; accuracy ; stability ; Padé approximants ; order stars ; Riemann surface
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    Topics: Mathematics
    Notes: Abstract We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation,u tt =c 2 u xx , given by $$\sum\limits_{j = - S}^S {b_j U_{n + 1,m + j} + } \sum\limits_{j = - S}^S {a_j U_{n,m + j} + } \sum\limits_{j = - S}^S {b_j U_{n - 1,m + j} } = 0.$$ It has already been proved that the maximal order of accuracyp of such schemes is given byp ≤ 2(s + S). In this paper we show that the requirement of stability does not reduce this maximal order for any choice of the pair (s, S). The result is proved by introducing an order star on the Riemann surface of the algebraic function associated with the scheme. Furthermore, Padé schemes, withS = 0,s 〉 0, ands = 0,S 〉 0, are proved to be stable for 0 〈 μ 〈 1, where μ is the Courant number. These schemes can be implemented with high-order absorbing boundary conditions without reducing the range of μ for which stable solutions are obtained.
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    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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    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
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    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
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    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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    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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    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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    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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    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
    Source: Springer Online Journal Archives 1860-2000
    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
    Source: Springer Online Journal Archives 1860-2000
    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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  • 89
    ISSN: 1572-8757
    Keywords: micropore size distribution ; activated carbon ; adsorption ; desorption ; equilibrium ; kinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract This paper deals with the prediction of adsorption equilibrium and kinetics of hydrocarbons onto activated carbon samples having different micropore size distribution (MPSD). The microporous structure of activated carbon is characterised by the distribution of slit-shaped micropores, which is assumed to be the sole source of surface heterogeneity. The interaction between adsorbate molecule and pore walls is described by the Lennard-Jones potential theory. Different adsorbates have access to different pore size range of activated carbon due to the size exclusion, a phenomenon could have a significant influence on both multicomponent equilibria and kinetics. Activated carbons with three different MPSDs are studied with ethane and propane as the two model adsorbates. The Heterogeneous Macropore Surface Diffusion model (HMSD) is employed to simulate adsorption kinetics. The simulation results show that the MPSD is an important factor affecting both the multicomponent equilibria and kinetics.
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  • 90
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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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  • 91
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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
    Source: Springer Online Journal Archives 1860-2000
    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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  • 92
    ISSN: 1572-879X
    Keywords: nanolithography ; model catalyst ; palladium ; copper ; stability ; spin-coating ; SEM ; AFM ; XPS
    Source: Springer Online Journal Archives 1860-2000
    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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  • 93
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    Catalysis letters 60 (1999), S. 51-57 
    ISSN: 1572-879X
    Keywords: furfural hydrogenation ; Cu/carbon catalysts ; kinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Furfural hydrogenation over copper dispersed on three forms of carbon – activated carbon, diamond and graphitized fibers – were studied. Only hydrogenation of the C=O bond to form either furfuryl alcohol or 2‐methyl furan occurred at temperatures from 473 to 573 K. Reduction at 573 K gave the most active catalysts, all three catalysts had activation energies of 16 kcal/mol, and turnover frequencies were 0.018–0.032 s-1 based on the number of Cu0 + Cu+ sites, which were counted by N2O adsorption at 363 K and CO adsorption at 300 K, respectively. The Cu/activated carbon catalyst showed no deactivation during 10 h on stream, in contrast to the other two catalysts. A simple Langmuir–Hinshelwood model invoking two types of sites was able to fit all kinetic data quite satisfactorily, thus it was consistent with the presence of both Cu0 and Cu+ sites.
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  • 94
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    Catalysis letters 60 (1999), S. 167-171 
    ISSN: 1572-879X
    Keywords: ammonia decomposition ; iron catalyst ; kinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The decomposition of ammonia is a reaction associated with the process of the nitriding of metals. The kinetics of the ammonia decomposition on iron catalysts has been studied using a differential reactor with internal mixing. The balance between the inlet and outlet ammonia quantity has been used to determine the degree of conversion. The rate of ammonia decomposition could be described by the following expression: r = k0 exp (Ea/RT)pNH3. The activation energy of the ammonia decomposition process has been found for samples with potassium as E a= 96 kJ/mol, for samples without potassium as E a= 87 kJ/mol.
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  • 95
    ISSN: 1572-8757
    Keywords: kinetics ; isotope-exchange ; nitrogen ; adsorption ; methane ; zeolite ; equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The Isotope Exchange Technique (IET) was used to simultaneously measure pure and binary gas adsorption equilibria and kinetics (self-diffusivities) of CH4 and N2 on pelletized 4A zeolite. The experiment was carried out isothermally without disturbing the adsorbed phase. CH4 was selectively adsorbed over N2 by the zeolite because of its higher polarizability. The multi-site Langmuir model described the pure gas and binary adsorption equilibria fairly well at three different temperatures. The selectivity of adsorption of CH4 over N2 increased with increasing pressure at constant gas phase composition and temperature. This curious behavior was caused by the differences in the sizes of the adsorbates. The diffusion of CH4 and N2 into the zeolite was an activated process and the Fickian diffusion model described the uptake of both pure gases and their mixtures. The self-diffusivity of N2 was an order of magnitude larger than that for CH4. The pure gas self-diffusivities for both components were constants over a large range of surface coverages (0 〈 θ 〈 0.5). The self-diffusivities of CH4 and N2 from their binary mixtures were not affected by the presence of each other, compared to their pure gas self-diffusivities at identical surface coverages.
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  • 96
    ISSN: 1572-8773
    Keywords: aromatic donor molecules ; horseradish peroxidase ; kinetics ; lactoperoxidase
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Abstract Based on kinetic evidence, it has been shown for the first time that the mode of binding of aromatic donor molecules is similar in horseradish peroxidase and lactoperoxidase; also that the nature of the heme plays an important role in the reaction with hydrogen peroxide, and has no effect on the reaction of the intermediate compound II with aromatic substrates.
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  • 97
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    Catalysis letters 31 (1995), S. 431-438 
    ISSN: 1572-879X
    Keywords: partial hydrogenation of benzene ; production of cyclohexene ; kinetics ; reaction mechanism ; ruthenium catalyst
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A method has been developed for direct measurement of reaction rates in a continuously operated slurry (CST-) reactor. In contrast to the usual procedure in a two-liquid-phase system the reactor contains only one liquid phase, an aqueous zinc chloride solution in which a ruthenium lanthanoxide catalyst is suspended. The selectivity of benzene hydrogenation with respect to cyclohexene is higher when the new one-liquid-phase procedure is applied. With decreasing degree of benzene conversion the selectivity with respect to cyclohexene approaches 100%. The conclusion is that cyclohexane is formed only by consecutive hydrogenation of cyclohexene.
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  • 98
    ISSN: 1572-879X
    Keywords: non-uniform surface ; kinetics ; ethanol ; oxidation ; molybdenum oxide
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Temkin's theory of rates of catalytic reactions on non-uniform surfaces is extended to the MoO3-catalyzed oxidation of ethanol to acetaldehyde. Two types of sites are assumed to be present, an oxygen atom site that can be modeled with uniform properties and a metal atom site characterized by non-uniform properties both for ethanol chemisorption to an ethoxide intermediate and the conversion of this intermediate to acetaldehyde. The rate-limiting step is the cleavage of a C-H bond in the absorbed ethoxide intermediate. Non-uniform surface kinetics leads to a kinetic rate expression of the form $$v = kP_{C_2 H_5 OH}^{1 - m} P_{O_2 }^{(1 - m)/4} P_{H_2 O}^{ - (1 - m)/2} $$ . Such a rate expression, withm=0.14, is shown to provide a good fit to kinetic data for the selective oxidation of ethanol on a silica supported molybdenum oxide catalyst.
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  • 99
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    Catalysis letters 36 (1996), S. 31-36 
    ISSN: 1572-879X
    Keywords: ethanol ; kinetics ; oxidation ; oxydehydrogenation ; platinum ; structure sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The effect of the platinum particle size was investigated for the catalytic oxidative dehydrogenation of aqueous ethanol to ethanal at a temperature of 303 K, an ethanol concentration of 260 mol m−3, a partial oxygen pressure 60 kPa, a pH of 9, and an ethanal and ethanoate concentration of 20 mol m−3. A particle size effect on the turnover frequency was observed but only for particle sizes smaller than 2 nm. Hence, the reaction shows a limited structure sensitivity.
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  • 100
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    Catalysis letters 55 (1998), S. 73-77 
    ISSN: 1572-879X
    Keywords: enantioselectivity ; hydrogenation of ethyl pyruvate ; Pt/alumina catalyst ; solvent effects ; kinetics ; solvent polarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The influence of solvent on the kinetics of enantioselective hydrogenation of ethyl pyruvate by Pt/Al2O3/dihydrocinchonidine is reported. In a non‐polar solvent, toluene, the reaction is approximately zero order in substrate at constant hydrogen pressure, while under the same conditions and at the same substrate concentration, in the polar solvents ethanol and propylene carbonate the reaction shows a first‐order substrate concentration dependence. Fits to a Michaelis–Menten rate expression show that these differences are the expression of the relative magnitudes of the adsorption term in the rate expression, which in turn reflects the influence of the solvent on the adsorption–desorption processes which take place at the catalyst surface.
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