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  • Articles  (1,063)
  • kinetics  (534)
  • stability  (376)
  • optimal control
  • Springer  (1,063)
  • Chemistry and Pharmacology  (686)
  • Mathematics  (378)
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  • Articles  (1,063)
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  • 1
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    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
    ISSN: 1531-5851
    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
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  • 2
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    Mathematical programming 52 (1991), S. 11-17 
    ISSN: 1436-4646
    Keywords: Modeling ; cancer ; optimization ; optimal control ; drug delivery
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we consider the problems of modeling the tumor growth and optimize the chemotherapy treatment. A biologically based model is used with the goal of solving an optimization problem involving discrete delivery of antineoplastic drugs. Our model is formulated via compartmental analysis in order to take into account the cell cycle. The cost functional measures not only the final size of the tumor but also the total amount of drug delivered. We propose an algorithm based on the discrete maximum principle to solve the optimal drug schedule problem. Our numerical results show nice interpretations from the medical point of view.
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  • 3
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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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  • 4
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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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  • 5
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    OR spectrum 16 (1994), S. 47-52 
    ISSN: 1436-6304
    Keywords: Vector optimization ; approximately efficient solutions ; stability ; Vektoroptimierung ; Näherungslösungen ; Stabilität
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir führen ein Konzept für Näherungslösungen in der Vektoroptimierung ein und vergleichen dieses mit einem neuen Konzept aus [8]. Weiterhin untersuchen wir Beziehungen zwischen der Menge der Näherungslösungen eines Vektoroptimierungsproblems und den Näherungslösungen eines entsprechenden parametrischen Ersatzproblems. Schließlich beweisen wir Stabilitätseigenschaften des skalaren Ersatzproblems.
    Notes: Abstract We introduce a concept for approximately efficient solutions in vector optimization and compare it with another recent concept given in [8]. Further, we study relations between the set of approximately efficient solutions of a vector optimization problem and the approximate solutions of a corresponding parametric surrogate optimization problem. Finally, we prove stability properties for the scalar surrogate problem.
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  • 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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    Mathematical programming 47 (1990), S. 117-141 
    ISSN: 1436-4646
    Keywords: Bifurcation ; singularity ; parametric programming ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The structure of solutions to the nonlinear parametric programming problem with a one dimensional parameter is analyzed in terms of the bifurcation behavior of the curves of critical points and the persistence of minima along these curves. Changes in the structure of the solution occur at singularities of a nonlinear system of equations motivated by the Fritz John first-order necessary conditions. It has been shown that these singularities may be completely partitioned into seven distinct classes based upon the violation of one or more of the following: a complementarity condition, a constraint qualification, and the nonsingularity of the Hessian of the Lagrangian on a tangent space. To apply classical bifurcation techniques to these singularities, a further subdivision of each case is necessary. The structure of curves of critical points near singularities of lowest (zero) codimension within each case is analyzed, as well as the persistence of minima along curves emanating from these singularities. Bifurcation behavior is also investigated or discussed for many of the subcases giving rise to a codimension one singularity.
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  • 8
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    Mathematical programming 54 (1992), S. 57-67 
    ISSN: 1436-4646
    Keywords: Matchings ; stability ; extreme points ; polytope
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The purpose of this paper is to extend a modified version of a recent result of Vande Vate (1989) which characterizes stable matchings as the extreme points of a certain polytope. Our proofs are simpler and more transparent than those of Vande Vate.
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  • 9
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    Mathematical programming 61 (1993), S. 197-214 
    ISSN: 1436-4646
    Keywords: Epi-convergence ; epi-distance ; stability ; convex optimization ; approximate solutions ; subgradients ; level sets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We prove that theε-optimal solutions of convex optimization problems are Lipschitz continuous with respect to data perturbations when these are measured in terms of the epi-distance. A similar property is obtained for the distance between the level sets of extended real valued functions. We also show that these properties imply that theε-subgradient mapping is Lipschitz continuous.
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  • 10
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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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  • 11
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    Colloid & polymer science 266 (1988), S. 958-964 
    ISSN: 1435-1536
    Keywords: a-Se colloids ; photoadsorption ; kinetics ; activation energy ; compensation effect
    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 this study, a model is developed to explain in microscopic terms the results obtained from thermally activated photoadsorption experiments in a-Se colloids. The observed compensation effect can be described for two different cases. At low efficiency adsorption, the process is controlled by the potential at the boundary layer. In the high efficiency adsorption case, the process is controlled by diffusion transport.
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  • 12
    ISSN: 1435-1536
    Keywords: Emulsions ; stability ; interfacial properties of emulsions ; soybean protein ; glycerides ; stabilised O/W emulsions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The influence of chemically modified 7S fraction of soybean protein (7MSPF), and its partial replacement by mono- and di-glycerides in various ratios, on the rate of drop coalescence in concentrated corn oil-in-water emulsions has been investigated. A total emulsifier concentration of 2.0 % (wt/wt) was used. The minimum drop coalescence rate was achieved when using 1.0% (wt/wt) 7MSPF in conjunction with 0.5% (wt/wt) monoglyceride and 0.5 % (wt/wt) di-glyceride at pH 5.5. At other mono-/di-glycerides and protein/glycerides ratios, and at other pHs, the rate of drop coalescence was higher than when 2.0% (wt/wt) 7MSPF was used. The reduction in drop coalescence rate under these conditions is attributed to association of 7MSPF with the glycerides at the oil-water interface. The influence of protein/glycerides ratio on the viscoelastic properties of mixed interfacial films supports this view.
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  • 13
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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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  • 14
    ISSN: 1435-1536
    Keywords: Phospholipid bilayer ; kinetics ; laser temperature jump ; phase transition
    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 iodine-laser temperature-jump technique has been used to investigate the main phase transition in single shell vesicles of dimyristoylphosphatidylcholine. The probe molecules DPH and TMA-DPH were incorporated into the lipid bilayer and laserT-jump experiments with turbidity and flourescence polarization detection were performed. We found three well separated relaxation processes between 5 μs and 10 ms. The relaxation signals showed strong cooperativity in the relaxation times as well as in their corresponding amplituedes. We attributed the relaxation to the formation and dissolution of clusters of different order inside the bilayer.
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  • 15
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    Colloid & polymer science 265 (1987), S. 58-64 
    ISSN: 1435-1536
    Keywords: Polymerisation ; emulsion ; styrene ; methylmethacrylate ; kinetics
    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 dependence of emulsion polymerisation rates on a number of important parameters is considered. Attention is paid to the use of seeded emulsion systems for the evaluation of radical desorption coefficients (k o). Experimental conditions are shown to be important. When the average number of radicals per particle is low, large changes in the rate coefficient for chain termination do not have a large effect on the kinetics. With styrene and methylmethacrylate, radical re-absorption by the polymer particles is shown to be important and radical capture efficiences can be high. Consistency is established between the results of a number of workers and values fork o are shown to be lower than those calculated from chain transfer rates.
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  • 16
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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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  • 17
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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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  • 18
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    Rheologica acta 26 (1987), S. 119-126 
    ISSN: 1435-1528
    Keywords: Maxwell fluid ; planeCouette flow ; stability ; criticalWeissenberg number
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Abstract The stability behaviour of a Maxwell fluid in a simple plane shear flow for a class of special perturbations is investigated. Necessary and sufficient stability criteria, especially a critical Weissenberg number for the stability (We k ≈ 4) are given. The results of the analysis are in qualitative agreement with experimental observations.
    Notes: Zusammenfassung Es wird das Stabilitätsverhalten eines Maxwell-Fluids in einer einfachen ebenen Scherströmung für eine spezielle Störungsklasse untersucht. Notwendige und hinreichende Stabilitätskriterien sowie eine kritische Weissenbergzahl (We k ≈ 4) werden angegeben. Die Ergebnisse der Analyse stehen mit experimentellen Befunden in qualitativer Übereinstimmung.
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  • 19
    ISSN: 1572-8900
    Keywords: Chemiluminescence ; oxidation ; stability ; acrylonitrile-butadiene-styrene (ABS) ; ABS/polycarbonate blend
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The thermal oxidative stability of various ABS/PC compounds was studied by means of the chemiluminescence technique. Similarly to pure ABS, Irganox 1076 and Irganox MD 1024 perform as moderate antioxidants in ABS/PC and (ABS/PC + lubricant) blends. Neither Tinuvin 144, Irgaphos 168, nor their mixture affects the durability of the ABS/PC blend. At the same time, (Irgaphos 168 + Tinuvin 144) in combination with Irganoxes was found to provide a noticeable enhancement in durability to the (ABS/PC + lubricant) system. Titanium dioxide pigments by themselves have only a slight influence on the oxidative stability of the ABS/PC blend. Durability of the (ABS/PC + pigment) and (ABS/PC + lubricant) systems was found to be the same and the overall protective effect of Irganox 1076 was similar in both the (ABS/PC + lubricant) and the (ABS/PC + lubricant + pigment) systems. Certain modifiers significantly improve the durability of the ABS/PC compounds, although their function may differ in the systems with and without pigments.
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  • 20
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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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  • 21
    ISSN: 1572-8900
    Keywords: Chemiluminescence ; oxidation ; stability ; acrylonitrile-butadiene-styrene (ABS)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The influence of lubricants, UV stabilizers, antioxidants, and metal deactivators on the resistance of ABS to thermal oxidation was studied by means of the chemiluminescence technique. Neither of the additives seems to affect significantly the induction period of oxidation. At the same time, the influence of various additives on the oxidation rate constant is remarkably different: the introduction of lubricants and UV stabilizers increases its value, while antioxidants and metal deactivators have the opposite effect. For the particular systems studied durability is decreased in samples containing the lubricant and UV stabilizers and increased in samples stabilized with the antioxidant and metal deactivator.
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  • 22
    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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  • 23
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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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  • 24
    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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  • 25
    ISSN: 1572-8927
    Keywords: Solvolysis ; kinetics ; aqueous solvent mixtures ; Co(III) complexes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The kinetics of the solvolysis of [Co(CN)5Cl]3− have been investigated in water +2-methoxyethanol and water + diethylene glycol mixtures. Although the addition of these linear hydrophilic cosolvent molecules to water produces curvature in the variation of log(rate constant) with the reciprocal of the dielectric constant, their effect on the enthalpy and entropy of activation is minimal, unlike the effect of hydrophobic cosolvents. The application of a Gibbs energy cycle to the solvolysis in water and in the mixtures using either solvent-sorting or TATB values for the Gibbs energy of transfer of the chloride ion between water and the mixture shows that the relative stability of the emergent solvated Co(III) ion in the transition state compared to that of Co(CN)5Cl3− in the initial state increases with increasing content of cosolvent in the mixture. By comparing the effects of other cosolvents on the solvolysis, this differential increase in the relative stabilities of the two species increases with the degree of hydrophobicity of the cosolvent.
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  • 26
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    Journal of solution chemistry 6 (1977), S. 203-216 
    ISSN: 1572-8927
    Keywords: Glucose ; kinetics ; mixed solvent ; kinetic isotope effect ; enthalpy of activation ; entropy of activation ; tetrahydrofuran ; tert-butanol ; mutarotation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The mutarotation rates of glucose in aqueous mixtures of tetrahydrofuran andtert-butanol in the mole fraction (xi) range 0〈xi〈0.2 have been measured at 5° intervals in the range 5–35°C. The kinetic deuterium isotope effects have been determined for the same solvent compositions at 25 and 35°C. A statistical analysis of the Arrhenius plots indicates that the experimental errors, although small, are too large for the establishment of any compensation behavior between ΔH
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  • 27
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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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    Journal of inorganic and organometallic polymers and materials 2 (1992), S. 79-85 
    ISSN: 1572-8870
    Keywords: Phthalocyanines ; polymers ; siloxanes ; conductivity ; stability
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The author's work on the incorporation of phthalocyanines into inorganic polymers is reviewed. The synthesis of poly(siloxane phthalocyanines) and the synthesis and characterization of fluoro(phthalocyanine) Group III compounds and their conducting derivatives are described.
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  • 29
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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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    Journal of solution chemistry 19 (1990), S. 1073-1084 
    ISSN: 1572-8927
    Keywords: Solvolysis ; kinetics ; mixtures of water+cosolvent
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Rates of solvolysis of the complex cation [Co(4tBupy)4Cl2]+ have been determined in mixtures of water with the hydrophobic solvent, t-butyl alcohol. The solvent composition at which the extremum is found in the variation of the enthalpy ΔH* and the entropy ΔS* of activation correlates well with the extremum in the variation of the relative partial molar volume of t-butyl alcohol in the mixture and the straight line found for the variation of ΔH* with ΔS* is coincident with the same plot for water + 2-propanol mixtures. A free energy cycle is applied to the process initial state (C n+) going to the transition state [M(n+1)+...Cl−] in water and in the mixture using free energies of transfer of the individual ionic species, ΔG t o (i), from water into the mixture. Values for ΔG t o (i) are derived from the solvent sorting method and from the TATB/TPTB method: using data from either method, changes in solvent structure on going from water into the mixture are found to stabilize the cation in the transition state, M(n+1)+, more than in the initial state, C n+. This is compared with the application of the free energy cycle to the solvolysis of complexes [Co(Rpy)4Cl2]+ and [Coen2LCl]+ in mixtures of water with methanol, 2-propanol or t-butyl alcohol: the above conclusion regarding the relative stabilization of the cations holds for all these complexes in their solvolyses in water+alcohol mixtures using values of ΔG t o (Cl−) from either source.
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    Journal of solution chemistry 2 (1973), S. 217-238 
    ISSN: 1572-8927
    Keywords: Cation ; energies ; H. S. Frank ; M. Eigen ; R. G. Wilkins ; kinetics ; ligand substitution ; mechanism ; mixed solvents ; nonaqueous ; solvation ; solvent ; solvent structure ; solvent exchange ; transition metal
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The role of the solvent in reactions involving ions is considered in relation to the structure of liquids. The rate constants and activation parameters for ligand substitutions at divalent transition metal cations in various solvents are compared with those for solvent exchanges. The differences are related to structural properties of the solvents, represented by their heats of evaporation and fluidities, and interpreted with the aid of a model developed from that of Frank and Wen. Water is not a typical solvent.
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  • 32
    ISSN: 1572-8927
    Keywords: Chromium(III) ; β-diketones ; β-diketonates ; chelation ; complexation ; correlation ; stability ; equilibrium
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    Topics: Chemistry and Pharmacology
    Notes: Abstract It has been demonstrated that the logarithm of the stability constant of some monochelated chromium(III) compounds, with structurally similar 1,3-dicarbonylic species, is linearly related to the negative logarithm of the acid ionization constant of the ligand. Graphical and analytical correlations which could be useful in predicting equilibrium constants of chromium(III)-β-diketonates, as well as other first-row transition metal derivatives, have been developed. A quantitative evaluation of the complexes stability has been carried out, providing information about the effects of ligand substituents on the equilibrium constants.
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  • 33
    ISSN: 1572-8927
    Keywords: Cu(II) ; kinetics ; reduction ; temperature dependence ; H2O2, NaCl, NaBr, NaClO4
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The rates of reduction of Cu(II) with H2O2 have been measured in NaCl and NaBr solutions and mixtures with NaClO4 as a function of pH (6 to 9), temperature (5 to 45°C) and ionic composition (0.1 to 6M). The effect of pH on the rates was found to be independent of temperature and ionic composition. The rates increased as a function of [H+] raised to the power of 1.3 to 1.6. Speciation calculations indicate that this pH dependence can be attributed to Cu(OH)2 being the reactive species. The rate constants in NaCl and NaBr and mixtures with NaClO4 were independent of ionic strength, but proportional to the halide concentration raised to the power of 2.0 (0.2 to 2.6M). These results can be attributed to Cu(OH)2Cl 2 2− being the reactive species to reduction with H2O2. The Cu(I) halide complexes formed from the reduction are not easily oxidized with O2 or H2O2. The faster rates in Br− solutions, which form stronger complexes with Cu+, support this contention. Measurements made in NaCl with added NaHCO3, NaB(OH)4 EDTA, NTA and glycine were also made. These measurements indicate that the CuL complexes (L=B(OH) 4 − , CO 3 2− , EDTA, NTA, and glycine) are not very reactive to reduction with H2O2. The addition of Mg2+ or Ca2+ caused the rates to increase due to the formation of MgL or CaL complexes and the resultant release of reactive Cu2+.
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    Journal of solution chemistry 23 (1994), S. 483-500 
    ISSN: 1572-8927
    Keywords: Thermodynamics ; kinetics ; chemical relaxation ; temperature-jump ; amplitudes
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Amplitudes of chemical relaxation signals can provide useful information as to the thermodynamics of coupled chemical reactions. The temperature-jump technique has been used to investigate the thermodynamic behavior of the Nickel(II)-3,5-dinitrosalicylate system in buffer solution, where complex formation steps are coupled to proton transfer steps. The analysis of the relaxation curves is based on the transformation of a set of coupled elementary reactions into a set of uncoupled ‘normal reactions.’ By analogy with classical titrations, the experiments have been performed by changing the metal ion concentration at constant ligand concentration and pH. Each measured amplitude is associated in this way to a point of a ‘dynamic titration’ and a procedure is formulated by which the values of the equilibrium constants and enthalpies of the normal reactions are simultaneously obtained by simple linear plots. From the dependence of these parameters on suitable functions of the concentrations of the reactants the values of ΔG° and ΔH° of the individual steps are derived. It is shown that the addition of a buffer (instead of an indicator) influences the stoichiometric coefficients of the normal reaction in such a way that measurable amplitudes are produced in systems that, as the presently investigated, in unbuffered solution would remain insensitive to the external perturbation. The circumstances under which the dynamic method offers advantages over the classical techniques are discussed.
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    Journal of solution chemistry 5 (1976), S. 163-169 
    ISSN: 1572-8927
    Keywords: Solvent effects ; tetramethylurea ; hydrolysis ; hydrogen bonding ; kinetics
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Tetramethylurea was hydrolyzed in aqueous hydrochloric acid at temperatures of 80, 90, and 100°C. All reactions were carried out in an excess of both tetramethylurea and water, with first-order dependence on acid concentration being observed. As the concentration of water was increased, the rate of hydrolysis decreased until equimolar amounts of water and tetramethylurea were present. Subsequent addition of water had no effect on the observed rate.
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    Adsorption 1 (1995), S. 133-151 
    ISSN: 1572-8757
    Keywords: PSA process ; sensitivity ; equilibria ; kinetics ; heats
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    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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    Adsorption 2 (1996), S. 265-277 
    ISSN: 1572-8757
    Keywords: frequency response ; diffusion cell ; kinetics ; diffusion ; heat effects
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    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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  • 38
    ISSN: 1572-8757
    Keywords: characterisation ; equilibria ; kinetics ; micropore size distribution ; n-butane ; nutshell
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    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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    Catalysis letters 10 (1991), S. 225-232 
    ISSN: 1572-879X
    Keywords: VPI-5 ; stability ; molecular sieve ; post-synthesis treatments
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Thorough washing of a VPI-5 synthesized with n-dipropylamine as template improves greatly its thermal stability while no major change is observed in the template content. A detailed study of the influence of the pretreatment conditions shows that in order to obtain a high thermal stability (up to at least 960 °C) two parameters are of importance. The removal of both the template and the adsorbed water requires either a low heating rate at atmospheric pressure or a low pressure (less than 3 Torr) when the heating rate is 300 ° per hour.
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  • 40
    ISSN: 1572-8773
    Keywords: acidophilic ; strain ; oxidation ; kinetics
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    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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  • 41
    ISSN: 1572-879X
    Keywords: Fischer-Tropsch synthesis ; reaction activation barrier ; carbon chain growth and termination ; kinetics
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    Topics: Chemistry and Pharmacology
    Notes: Abstract A method is established, by which the difference of the reaction activation barriers of carbon chain growth and termination in Fischer-Tropsch (FT) synthesis can be determined from experiments. A FT synthesis is carried out on Fe/Zn catalyst. We apply the method to analyze the experimental result and obtain the difference of reaction activation barriers of carbon chain growth and termination of α-olefins on the catalyst.
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  • 42
    ISSN: 1572-879X
    Keywords: metal-oxygen cluster compounds ; heteropoly acids ; stability ; pH ; aqueous solutions
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The stabilities of the solid superacids H3Mo12O40, H3PW12O40, H4SiMo12O40 and H4SiW12O40 in aqueous solution have been measured at various values of pH by use of ion chromatographic analyses. The aforementioned acids are completely decomposed at values of pH, 4.0, 5.2, 7.0 and 11.0, respectively. The stabilities in aqueous solution with respect to pH follow the order H4SiW12O40 〉 H3PW12O40 〉 H4SiMo12O40 〉 H3PMo12O40.
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    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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    Adsorption 6 (2000), S. 137-147 
    ISSN: 1572-8757
    Keywords: adsorption ; kinetics ; linear driving force model ; process design
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    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The Linear Driving Force (LDF) model for gas adsorption kinetics is frequently and successfully used for analysis of adsorption column dynamic data and for adsorptive process designs because it is simple, analytic, and physically consistent. Yet, there is a substantial difference in the characteristics of isothermal batch uptake curves on adsorbent particles by the LDF and the more rigorous Fickian Diffusion (FD) model. It is demonstrated by using simple model systems that the characteristics of the adsorption kinetics at the single pore or the adsorbent particle level are lost in (a) evaluating overall uptake on a heterogeneous porous solid, (b) calculating breakthrough curves from a packed adsorbent column, and (c) establishing the efficiency of separation by an adsorptive process due to repeated averaging of the base kinetic property. That is why the LDF model works in practice.
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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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    Catalysis letters 27 (1994), S. 79-90 
    ISSN: 1572-879X
    Keywords: kinetics ; carbon ; oxygen ; recombination ; rhodium ; surface characterisation ; XPS ; AES
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Different mechanisms of atomic carbon and oxygen recombination on a rhodium surface are studied with Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). The kinetics of adsorbed carbidic carbon oxidation (carbon coverageθ c ≈ 0.1–0.3 ML) by gas-phase oxygen that proceeds by a Langmuir-Hinshelwood reaction mechanism, provides the value of the activation energy for recombination (E rec ⇂t ≈ 170±20 kJ/mol).E rec ⇂t depends slightly on the carbon coverage. An Eley-Rideal type of reaction was observed for adsorbed oxygen and atomic gas-phase carbon recombination which occurs in a dynamic regime. The low value found for the activation energy (near zero) is consistent with the mechanism that this exothermic reaction is too fast for energy dissipation into the substrate; the energy is mainly transferred into translational, vibrational and rotational energy of CO.
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  • 47
    ISSN: 1572-879X
    Keywords: ammonia synthesis ; kinetics ; ruthenium catalysts ; promotional effect
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The kinetics of NH3 synthesis over carbon-based ruthenium catalysts promoted with barium or alkali was studied. Both the ammonia partial pressure dependencies of the reaction rates (T = 400°C, p = 63 bar, H2 : N2 = 3 : 1) and the pressure variations of the activity (T = 370°C, p= 4–63 bar, H2 : NN2 = 3 : 1) were found to be different for Ba and for the alkali (K, Cs). Ba–Ru/C proved to be more sensitive to the NH3 content and to the total pressure. The rate of synthesis over the alkali-promoted catalysts is, in turn, much stronger influenced by the ruthenium dispersion. TOFs of NH3 synthesis for the promoted samples at 370°C and 4 bar (Ba 0.085 1/s, Cs 0.05 1/s, K 0.035 1/s) are significantly higher than that for the Ru(0001) basal plane (0.0085 1/s results from the literature data at 370°C, 2 bar). The most active Ru/C samples (Ba or Cs) exceed significantly the fused iron catalyst, especially at high conversions.
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    Journal of dynamics and differential equations 1 (1989), S. 269-298 
    ISSN: 1572-9222
    Keywords: Geometric mechanics ; reduction ; stability ; chaos ; rigid body dynamics ; periodic orbits ; 58F
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    Topics: Mathematics
    Notes: Abstract We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.
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    Journal of dynamics and differential equations 10 (1998), S. 151-188 
    ISSN: 1572-9222
    Keywords: Fourth-order solitary waves ; stability ; instability
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    Topics: Mathematics
    Notes: Abstract We study ground-state traveling wave solutions of a fourth-order wave equation. We find conditions on the speed of the waves which imply stability and instability of the solitary waves. The analysis depends on the variational characterization of the ground states rather than information about the linearized operator.
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    Journal of dynamics and differential equations 6 (1994), S. 37-51 
    ISSN: 1572-9222
    Keywords: Celestial mechanics ; relative equilibria ; stability
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    Topics: Mathematics
    Notes: Abstract A criterion for the linear stability of relative equilibria of the Newtoniann-body problem is found in the case whenn−1 of the masses are small. Several stable periodic orbits of the problem are presented as examples.
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    Order 9 (1992), S. 163-175 
    ISSN: 1572-9273
    Keywords: Primary 06A07 ; secondary 05C70 ; Partial order ; interval ; stability ; covering ; Sperner property ; symmetric chains ; NP-completeness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Given a finite ranked posetP, let α(P) be the maximum size of a subset ofP such that no two elements of it belong simultaneously to some interval ofP and let ϱ(P) be the minimum number of intervals covering all elements ofP. We say thatP has the strong interval stability property (resp. the strong interval covering property) if for each subposetP′ induced by consecutive levels ofP, i.e.,P′=P (l)∪...∪P (u), one has α(P′)=max{|P (l)|, |P (u)|} (resp. ϱ(P′)=max{|P (l)|, |P (u)|}). We prove these properties for several classes of posets and discuss some general facts concerning the numbers α(P) and ϱ(P), e.g., NP-completeness and min-max relations.
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    Positivity 1 (1997), S. 319-330 
    ISSN: 1572-9281
    Keywords: delay equations ; stability ; positive solutions ; spectral growth condition
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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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  • 53
    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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    Annals of operations research 98 (2000), S. 45-64 
    ISSN: 1572-9338
    Keywords: optimal control ; partial differential equations ; numerical methods ; transdermal systems ; acetylene reactors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We present an approach to compute optimal control functions in dynamic models based on one-dimensional partial differential algebraic equations (PDAE). By using the method of lines, the PDAE is transformed into a large system of usually stiff ordinary differential algebraic equations and integrated by standard methods. The resulting nonlinear programming problem is solved by the sequential quadratic programming code NLPQL. Optimal control functions are approximated by piecewise constant, piecewise linear or bang-bang functions. Three different types of cost functions can be formulated. The underlying model structure is quite flexible. We allow break points for model changes, disjoint integration areas with respect to spatial variable, arbitrary boundary and transition conditions, coupled ordinary and algebraic differential equations, algebraic equations in time and space variables, and dynamic constraints for control and state variables. The PDAE is discretized by difference formulae, polynomial approximations with arbitrary degrees, and by special update formulae in case of hyperbolic equations. Two application problems are outlined in detail. We present a model for optimal control of transdermal diffusion of drugs, where the diffusion speed is controlled by an electric field, and a model for the optimal control of the input feed of an acetylene reactor given in form of a distributed parameter system.
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    Annals of operations research 98 (2000), S. 65-87 
    ISSN: 1572-9338
    Keywords: train control ; optimal control ; discrete control ; optimal switching times
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider the problem of determining an optimal driving strategy in a train control problem with a generalised equation of motion. We assume that the journey must be completed within a given time and seek a strategy that minimises fuel consumption. On the one hand we consider the case where continuous control can be used and on the other hand we consider the case where only discrete control is available. We pay particular attention to a unified development of the two cases. For the continuous control problem we use the Pontryagin principle to find necessary conditions on an optimal strategy and show that these conditions yield key equations that determine the optimal switching points. In the discrete control problem, which is the typical situation with diesel-electric locomotives, we show that for each fixed control sequence the cost of fuel can be minimised by finding the optimal switching times. The corresponding strategies are called strategies of optimal type and in this case we use the Kuhn–Tucker equations to find key equations that determine the optimal switching times. We note that the strategies of optimal type can be used to approximate as closely as we please the optimal strategy obtained using continuous control and we present two new derivations of the key equations. We illustrate our general remarks by reference to a typical train control problem.
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    Annals of operations research 98 (2000), S. 333-351 
    ISSN: 1572-9338
    Keywords: production planning ; stochastic dynamic programming ; optimal control ; long-run average cost
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    Topics: Mathematics , Economics
    Notes: Abstract We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.
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    Journal of computational analysis and applications 2 (2000), S. 293-308 
    ISSN: 1572-9206
    Keywords: parabolic equations ; ADI scheme ; stability
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    Topics: Mathematics
    Notes: Abstract An ADI scheme for solving three-dimensional parabolic equations withfirst-order derivatives and variable coefficients has been developed basedon our previous papers and the idea of the modified upwind differencescheme. This ADI scheme is second-order accurate and unconditionallystable. Further, a small parameter can be chosen which makes it suitablefor simulating fast-transient phenomena or for computations on fine spatialmeshes. The method is illustrated with numerical examples.
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    Journal of dynamics and differential equations 5 (1993), S. 625-671 
    ISSN: 1572-9222
    Keywords: Scalar reaction-diffusion equation ; singular perturbation methods ; internal layer ; Neumann layer ; stability ; 35K57 ; 35B25 ; 35B35
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    Topics: Mathematics
    Notes: Abstract The multiple existences and their stability properties of stationary solutions with a single transition layer in some scalar reaction-diffusion equation are shown. Each solution is constructed by using classical singular perturbation methods and its stability property is determined by a simple algebraic quantity, say index, appearing in the construction of a solution.
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    Journal of dynamics and differential equations 6 (1994), S. 639-658 
    ISSN: 1572-9222
    Keywords: Symmetry ; parabolic equations ; positive solutions ; stability
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    Topics: Mathematics
    Notes: Abstract Symmetry properties of positive solutions of a Dirichlet problem for a strongly nonlinear parabolic partial differential equation in a symmetric domainD ⊂ R n are considered. It is assumed that the domainD and the equation are invariant with respect to a group {Q} of transformations ofD. In examples {Q} consists of reflections or rotations. The main result of the paper is the theorem which states that any compact inC(D) negatively invariant set which consists of positive functions consists ofQ-symmetric functions. Examples of negatively invariant sets are (in autonomous case) equilibrium points, omega-limit sets, alpha-limit sets, unstable sets of invariant sets, and global attractors. Application of the main theorem to equilibrium points gives the Gidas-Ni-Nirenberg theorem. Applying the theorem to omega-limit sets, we obtain the asymptotical symmetrization property. That means that a bounded solutionu(t) asr→∞ approaches subspace of symmetric functions. One more result concerns properties of eigenfunctions of linearizations of the equations at positive equilibrium points. It is proved that all unstable eigenfunctions are symmetric.
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    Set-valued analysis 5 (1997), S. 73-88 
    ISSN: 1572-932X
    Keywords: differential inclusion ; invariance ; stability
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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 27 (1990), S. 343-369 
    ISSN: 1572-9338
    Keywords: Bifurcation ; singularities ; continuation ; parametric nonlinear programming ; stability
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    Topics: Mathematics , Economics
    Notes: Abstract Bifurcation and continuation techniques are introduced as a class of methods for investigating the parametric nonlinear programming problem. Motivated by the Fritz John first-order necessary conditions, the parametric programming problem is first reformulated as a closed system of nonlinear equations which contains all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points. Since changes in the structure of the solution set and critical point type can occur only at singularities, necessary and sufficient conditions for the existence of a singularity are developed in terms of the loss of a complementarity condition, the linear dependence constraint qualification, and the singularity of the Hessian of the Lagrangian on a tangent space. After a brief introduction to elementary bifurcation theory, some simple singularities in this parametric problem are analyzed for both branching and persistence of local minima. Finally, a brief introduction to numerical continuation and bifurcation procedures is given to indicate how these facts can be used in a numerical investigation of the problem.
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    Annals of operations research 56 (1995), S. 79-93 
    ISSN: 1572-9338
    Keywords: Multistage stochastic programs ; optimization in Banach spaces ; stability ; approximation
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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
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Self-organized rule-following systems are increasingly relevant objects of study in organization theory due to such systems&2018; capacity to maintain control while enabling decentralization of authority. This paper proposes a network model for such systems and examines the stability of the networks&2018; repetitive behavior. The networks examined are Ashby nets, a fundamental class of binary systems: connected aggregates of nodes that individually compute an interaction rule, a binary function of their three inputs. The nodes, which we interpret as workers in a work team, have two network inputs and one self-input. All workers in a given team follow the same interaction rule. We operationalize the notion of stability of the team&2018;s work routine and determine stability under small perturbations for all possible rules these teams can follow. To study the organizational concomitants of stability, we characterize the rules by their memory, fluency, homogeneity, and autonomy. We relate these measures to work routine stability, and find that stability in ten member teams is enhanced by rules that have low memory, high homogeneity, and low autonomy.
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    Journal of dynamics and differential equations 12 (2000), S. 117-167 
    ISSN: 1572-9222
    Keywords: singular perturbation ; standing pulses ; stability ; Hopf bifurcation ; reaction-diffusion system
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    Topics: Mathematics
    Notes: Abstract Bifurcation phenomena from standing pulse solutions of the problem $$\varepsilon \tau u_t = \varepsilon ^2 u_{xx} + f(u,v),{\text{ }}v_t = v_{xx} + g(u,v)$$ is considered. ε(〉0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g.
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    Journal of dynamics and differential equations 5 (1993), S. 189-218 
    ISSN: 1572-9222
    Keywords: Equivariant bifurcation ; symmetry ; singularity ; equivariant jets and transversality ; normal forms ; universal unfolding ; stability ; structural stability ; 58F14 ; 58E07 ; 58C27
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    Topics: Mathematics
    Notes: Abstract The theoretical machinery from singularity theory introduced by Golubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problems, is completed and expanded while generalized to the multiple parameter context. In this setting the finite determinacy theorems or normal forms, the stability of equivariant bifurcation problems, and the structural stability of the universal unfolding are discussed.
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    Journal of dynamics and differential equations 6 (1994), S. 447-486 
    ISSN: 1572-9222
    Keywords: Free boundary problems ; gasless combustion ; stability ; Hopf bifurcation ; 35R35 ; 35B40 ; 80A25
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    Topics: Mathematics
    Notes: Abstract In this paper, we analyze a simple free boundary model associated with solid combustion and some phase transition processes. There is strong evidence that this “one-phase” model captures all major features of dynamical behavior of more realistic (and complicated) combustion and phase transition models. The principal results concern the dynamical behavior of the model as a bifurcation parameter (which is related to the activation energy in the case of combustion) varies. We prove that the basic uniform front propagation is asymptotically stable against perturbations for the bifurcation parameter above the instability threshold and that a Hopf bifurcation takes place at the threshold value. Results of numerical simulations are presented which confirm that both supercritical and subcritical Hofp bifurcation may occur for physically reasonable nonlinear kinetic functions.
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    Journal of dynamics and differential equations 9 (1997), S. 463-505 
    ISSN: 1572-9222
    Keywords: Difference equations ; random perturbation ; averaging ; diffusion approximation ; randomly perturbed iterations ; stability ; 3SR60 ; 60H15 ; 60J99
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    Topics: Mathematics
    Notes: Abstract Let (X, ℬ) and (Y,C) be two measurable spaces withX being a linear space. A system is determined by two functionsf(X): X→ X andϕ:X×Y→X, a (small) positive parameterε and a homogeneous Markov chain {y n } in (Y,C) which describes random perturbations. States of the system, say {x n ɛ ∈X, n=0, 1,⋯}, are determined by the iteration relations:x n+1 ɛ =f(x n ɛ )+ɛϕ(x n ɛ ,Yn+1) forn≥0, wherex 0 ɛ =x 0 is given. Here we study the asymptotic behavior of the solutionx n ɛ asε → 0 andn → ∞ under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.
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    Set-valued analysis 5 (1997), S. 377-390 
    ISSN: 1572-932X
    Keywords: differential inclusions ; stability ; boundedness of solutions ; Lyapunov functions
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    Topics: Mathematics
    Notes: Abstract For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions.
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    Set-valued analysis 4 (1996), S. 361-374 
    ISSN: 1572-932X
    Keywords: 34A60 ; 34E15 ; 34C29 ; differential inclusion ; singular perturbation ; averaging method ; controlability ; stability
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    Topics: Mathematics
    Notes: Abstract We consider nonlinear, singularly perturbed differential inclusions and apply the averaging method in order to construct a limit differential inclusion for slow motion. The main approximation result states that the existence and regularity of the limit differential inclusion suffice to describe the limit behavior of the slow motion. We give explicit approximation rates for the uniform convergence on compact time intervals. The approach works under controllability or stability properties of fast motion.
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    Set-valued analysis 7 (1999), S. 209-238 
    ISSN: 1572-932X
    Keywords: nonsmooth analysis ; subdifferentials ; coderivatives ; implicit function theorem ; solvability ; stability ; open mapping theorem ; metric regularity ; multidirectional mean value inequality
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    Topics: Mathematics
    Notes: Abstract We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.
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    Set-valued analysis 1 (1993), S. 393-402 
    ISSN: 1572-932X
    Keywords: Primary: 49J40, 65K10, 47A55, 47H05, 65L20 ; Variational inequality ; perturbation ; unbounded and nonsmooth operators ; convex sets ; Hausdorff distance ; regularization ; monotonicity ; convergence ; stability
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    Topics: Mathematics
    Notes: Abstract The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains Ω are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.
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    Annals of operations research 37 (1992), S. 403-413 
    ISSN: 1572-9338
    Keywords: Lagrange multiplier rule ; Pontryagin's maximum principle ; optimal control
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    Topics: Mathematics , Economics
    Notes: Abstract In this paper a modified form of Pontryagin's maximum principle is developed, which also holds for problems of optimal control with respect to functions of several independent variables.
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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
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    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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    Catalysis letters 68 (2000), S. 55-58 
    ISSN: 1572-879X
    Keywords: promoting effect ; B2O3 ; Cu/ZnO/Al2O3 catalyst ; methanol synthesis ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The addition of B2O3 to a Cu/ZnO/Al2O3 catalyst increased the activity of the catalyst for methanol synthesis after an induction period during the reaction. The stability of the B2O3-containing Cu/ZnO/Al2O3 catalyst was greatly improved by the addition of a small amount of colloidal silica to the catalyst.
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    ISSN: 1572-879X
    Keywords: potassium desorption ; stability ; excitation ; iron catalyst ; Rydberg atoms
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Well‐characterized catalyst model compounds of KAlO2 and KFeO2 are investigated by thermal desorption of potassium from the material. The desorbing fluxes of ions, atoms and highly excited states (field ionizable Rydberg states) were studied with surface and field ionization detectors in a vacuum apparatus. From the Arrhenius plots the activation energies for desorption of K and K+ were determined. The chemical state of potassium at the surfaces is concluded to be: ionic on KAlO2 (with the K desorption barrier of 1.76 eV) and covalent on KFeO2 (barrier of 2.73 eV). These results agree with the data obtained earlier for industrial catalysts for ammonia and styrene production. They are interpreted in terms of the Schottky cycle, which is completed for KAlO2 and fails for KFeO2. This failure indicates a non‐equilibrium desorption process. K Rydberg states are only found to desorb from KFeO2, in agreement with the suggestion that such states in some way are responsible for the catalytic activity.
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    Journal of solution chemistry 3 (1974), S. 881-887 
    ISSN: 1572-8927
    Keywords: Binary aqueous mixtures ; solubilities ; kinetics
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    Topics: Chemistry and Pharmacology
    Notes: Abstract A treatment which predicts the solubilities of gases in solvent mixtures is examined in the context of the analysis of kinetic data for reactions in aqueous mixtures. The treatment is qualitatively successful to some extent in resolving the effects of changes in the initial state of the reacting substrate in the activation parameters.
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    Journal of dynamics and differential equations 1 (1989), S. 299-325 
    ISSN: 1572-9222
    Keywords: Commodity markets ; time delays ; stability ; Hopf bifurcation ; 34K15 ; 45J05 ; 90A16
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    Topics: Mathematics
    Notes: Abstract A model for the dynamics of price adjustment in a single commodity market is developed. Nonlinearities in both supply and demand functions are considered explicitly, as are delays due to production lags and storage policies, to yield a nonlinear integrodifferential equation. Conditions for the local stability of the equilibrium price are derived in terms of the elasticities of supply and demand, the supply and demand relaxation times, and the equilibrium production-storage delay. The destabilizing effect of consumer memory on the equilibrium price is analyzed, and the ensuing Hopf bifurcations are described.
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    Journal of dynamics and differential equations 4 (1992), S. 161-190 
    ISSN: 1572-9222
    Keywords: Delay differential equations ; equilibrium ; stability ; limiting equations ; population dynamics ; 34K20 ; 34K25 ; 92A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Applying an analytical method and several limiting equations arguments, some sufficient conditions are provided for the existence of a unique positive equilibriumK for the delay differential equationx=−γx+D(x t ), which is the general form of many population models. The results are concerned with the global attractivity, uniform stability, and uniform asymptotic stability ofK. Application of the results to some known population models, which shows the effectiveness of the methods applied here, is also presented.
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    Journal of dynamics and differential equations 5 (1993), S. 105-128 
    ISSN: 1572-9222
    Keywords: Delay system ; stability ; relative variance ; dynamical disease
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    Topics: Mathematics
    Notes: Abstract A new approach to the study of delay systems, applicable to physiological control systems and other systems where little information about the time delays is available, is examined. The method is based on the fact that stability information can be deduced from the statistical properties of the probability distribution that encodes the structure of the time delay. The main statistical variables used are the usual expectation parameter,E, and a modified variance, calledrelative variance and denotedR, that is invariant under time scale changes. Recent work of the author has shown that stability often improves asR increases whileE remains fixed. A four-parameter family of delay models is analysed in this paper, and the (E, R) pair is found to be a reliable indicator of stability over the global parameter domain of the family.
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    Journal of dynamics and differential equations 6 (1994), S. 325-334 
    ISSN: 1572-9222
    Keywords: Nonlinear Schrödinger equations ; anisotropic standing waves ; stability ; concentration compactness principle ; Davey-Stewartson system ; 35Q35 ; 35B35
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    Topics: Mathematics
    Notes: Abstract We study the stability of standing waves for a nonlinear Schrödinger equation, which derives from the generalized Davey-Stewartson system in the elliptic-elliptic case. We prove the existence of stable standing waves under certain conditions.
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    Journal of dynamics and differential equations 6 (1994), S. 631-637 
    ISSN: 1572-9222
    Keywords: stability ; fixed point index ; periodic solutions
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    Topics: Mathematics
    Notes: Abstract In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR 2 has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.
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    Set-valued analysis 8 (2000), S. 31-50 
    ISSN: 1572-932X
    Keywords: stability in optimization ; generalized equations ; Lipschitz continuity ; mathematical programming ; optimal control
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    Topics: Mathematics
    Notes: Abstract We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the stability with respect to canonical perturbations of a mathematical program in a Hilbert space and an optimal control problem with inequality control constraints. For stationary points of these problems, Aubin continuity and Lipschitzian localization coincide; moreover, both properties are equivalent to surjectivity of the map of the gradients of the active constraints combined with a strong second-order sufficient optimality condition.
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    Set-valued analysis 8 (2000), S. 111-126 
    ISSN: 1572-932X
    Keywords: viability ; optimal control ; value function
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    Topics: Mathematics
    Notes: Abstract In this paper we explain that various (possibly discontinuous) value functions for optimal control problem under state-constraints can be approached by a sequence of value functions for suitable discretized systems. The key-point of this approach is the characterization of epigraphs of the value functions as suitable viability kernels. We provide new results for estimation of the convergence rate of numerical schemes and discuss conditions for the convergence of discrete optimal controls to the optimal control for the initial problem.
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    Set-valued analysis 8 (2000), S. 253-266 
    ISSN: 1572-932X
    Keywords: Hausdorff metric ; linear inequality systems ; stability
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    Topics: Mathematics
    Notes: Abstract In this paper, we propose a Hausdorff metric to measure the “distance” between two linear inequality systems on a real normed space X. For this topology, which comes through a pseudo-metric in the set Σ of linear inequality systems, the closedness of the feasible set mapping is studied, and at the same time a characterization of the stability of the subset Σ c of consistent sytems is given.
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    Annals of operations research 15 (1988), S. 289-311 
    ISSN: 1572-9338
    Keywords: Flexible manufacturing system ; dynamic routing ; material handling ; robotics ; semi-Markovian decision process ; optimal control ; stochastic optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract An optimal routing policy is obtained for Flexible Manufacturing Systems (FMSs) with limited buffers at the work stations. This policy is used to effectively drive a robotic material handling system. The routing decisions are made by a supervising computer on a real-time basis in order to avoid any work station running out of inputs and to control the blocking of the material handling system. Using our model, general material handling times can be assumed. The optimal policy and several key performance measures are computed, following the problem formulation as a continuous-time, semi-Markovian decision process. Fast convergence and computational stability are ensured by the ergodic solution algorithm augmented to solve the functional equations of the renewal process. The solution algorithm was implemented, tested on an extensive range of problems regarding the structure and the performance of the optimal policy. Complex environments involving diverse processing times, as well as very limited buffer storage, were examined. The interaction between the allocation of buffer spaces to work stations, the structural properties of the optimal monotone (threshold-type) policy and the system performance are also investigated.
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    Annals of operations research 98 (2000), S. 19-44 
    ISSN: 1572-9338
    Keywords: optimal control ; nonlinear systems ; parabolic systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider first nonlinear systems of the form x=A(x)x+B(x)u together with a standard quadratic cost functional and replace the system by a sequence of time-varying approximations for which the optimal control problem can be solved explicitly. We then show that the sequence converges. Although it may not converge to a global optimal control of the nonlinear system, we also consider a similar approximation sequence for the equation given by the necessary conditions of the maximum principle and we shall see that the first method gives solutions very close to the optimal solution in many cases. We shall also extend the results to parabolic PDEs which can be written in the above form on some Hilbert space.
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    Annals of operations research 99 (2000), S. 251-265 
    ISSN: 1572-9338
    Keywords: stochastic programming ; bond portfolio management ; interest ratescenarios ; stability ; sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients – the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.
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  • 90
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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
    Source: Springer Online Journal Archives 1860-2000
    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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  • 91
    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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  • 92
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    Journal of solution chemistry 15 (1986), S. 221-229 
    ISSN: 1572-8927
    Keywords: Ultrasonics ; kinetics ; aqueous solution ; triethylene glycol monobutyl ether
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The ultrasonic absorption from 6.5 to 220 MHz and velocities at 2.5 MHz have been measured in aqueous solution of triethylene glycol monobutyl ether as a function of concentration at 25°C. A single relaxational excess absorption, observed from 0.60 to 2.5 mol-dm−3, is attributed to a perturbation of an equilibrium associated with solute-solvent interaction. Rate constants for the forward and reverse processes have been determined from the concentration dependence of the relaxation frequency, and the influence on the water structure by an addition of the solute has been considered. Solution densities were also measured in order to obtain the expansivity of the solution. The standard volume and enthalpy changes of the reaction have been estimated from the concentration dependence of the maximum excess absorption per wave length. A linear relationship between the number of oxyethylene groups and the free energy change between bonded water and nonbonded water is established.
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  • 93
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    Journal of solution chemistry 22 (1993), S. 1151-1158 
    ISSN: 1572-8927
    Keywords: Molecular complexes ; solvent effect ; stability ; solid CT complexes ; nicotine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Interaction of nicotine with tetracyanoethylene and iodine was investigated spectrophotometrically and found to form strong CT complexes (n−π and n-σ*, respectively). The donor site involved in CT interaction is the pyrrolidine nitrogen. The nicotine-I2 complex exists as the ionic structure (nicotine) I+-I 3 − . Formation constants of the CT complexes in various solvents were determined from 10 to 25°C and are discussed in terms of the nature of the electron acceptor and solvent polarity. Solid CT complexes were synthesized and were characterized by microchemical analysis and infrared spectra techniques.
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  • 94
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    Acta applicandae mathematicae 28 (1992), S. 1-42 
    ISSN: 1572-9036
    Keywords: 35R30 ; Inverse scattering ; stability ; noisy data
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An algorithm is given for calculating the solution to the 3D inverse scattering problem with noisy discrete fixed energy data. The error estimates for the calculated solution are derived. The methods developed are of a general nature and can be used in many applications: in nondestructive evaluation and remote sensing, in geophysical exploration, medical diagnostics, and technology.
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  • 95
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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
    Source: Springer Online Journal Archives 1860-2000
    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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  • 96
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    Acta applicandae mathematicae 57 (1999), S. 287-338 
    ISSN: 1572-9036
    Keywords: sub-Riemannian geometry ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is a continuation of a series of papers, dealing with contact sub-Riemannian metrics on R3. We study the special case of contact metrics that correspond to isoperimetric problems on the plane. The purpose is to understand the nature of the corresponding optimal synthesis, at least locally. It is equivalent to studying the associated sub-Riemannian spheres of small radius. It appears that the case of generic isoperimetric problems falls down in the category of generic sub-Riemannian metrics that we studied in our previous papers (although, there is a certain symmetry). Thanks to the classification of spheres, conjugate-loci and cut-loci, done in those papers, we conclude immediately. On the contrary, for the Dido problem on a 2-d Riemannian manifold (i.e. the problem of minimizing length, for a prescribed area), these results do not apply. Therefore, we study in details this special case, for which we solve the problem generically (again, for generic cases, we compute the conjugate loci, cut loci, and the shape of small sub-Riemannian spheres, with their singularities). In an addendum, we say a few words about: (1) the singularities that can appear in general for the Dido problem, and (2) the motion of particles in a nonvanishing constant magnetic field.
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  • 97
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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
    Source: Springer Online Journal Archives 1860-2000
    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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  • 98
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    Annals of global analysis and geometry 11 (1993), S. 387-395 
    ISSN: 1572-9060
    Keywords: Curvatures of hypersurfaces ; Reilly's inequality ; stability ; 53 A 10 ; 53 C 42
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We generalize Reilly's inequality for the first eigenvalue of immersed submanifolds ofIR m +1 and the total (squared) mean curvature, to hypersurfaces ofIR m +1 and the first eigenvalue of the higher order curvatures. We apply this to stability problems. We also consider hypersurfaces in hyperbolic space.
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  • 99
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    Applications of mathematics 45 (2000), S. 161-176 
    ISSN: 1572-9109
    Keywords: reaction-diffusion system ; unilateral conditions ; quasivariational inequality ; Leray-Schauder degree ; eigenvalue ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
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  • 100
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    BIT 17 (1977), S. 321-328 
    ISSN: 1572-9125
    Keywords: 5.15 ; nonlinear equation ; root finding ; multiple root ; secant method ; Steffensen procedure ; order of convergence ; efficiency ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A superlinear procedure for finding a multiple root is presented. In it the secant method is applied to the given function divided by a divided difference whose increment shrinks toward zero as the root is approached. Two function evaluations per step are required, but no derivatives need be calculated.
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