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  • Articles  (206)
  • stability  (159)
  • optimal control
  • Springer  (206)
  • 1995-1999  (206)
  • Mathematics  (137)
  • Chemistry and Pharmacology  (69)
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  • Articles  (206)
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  • 1
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    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
    ISSN: 1531-5851
    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
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  • 2
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    OR spectrum 20 (1998), S. 101-107 
    ISSN: 1436-6304
    Keywords: Competitive location model ; Nash equilibria ; stability ; reachability ; Wettbewerbsmodelle in der Standorttheorie ; Nash Gleichgewicht ; Stabilität ; Erreichbarkeit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In der Arbeit werden die Standorte von Duopolisten in einem Baum untersucht. Unter der Annahme festgesetzter Preise werden notwendige und hinreichende Bedingungen für Nash Gleichgewichte für Standorte auf Bäumen hergeleitet. Unter Verwendung dieser Bedingungen wird dann gezeigt, daß — angenommen Nash Gleichgewichte existieren — diese in einem wiederholt angewandten sequentiellen Standortfindungsprozeß, in dem beide Duopolisten als Zielfunktion kurzfristige Gewinnmaximierung haben, auch erreicht werden.
    Notes: Abstract This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.
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  • 3
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    OR spectrum 20 (1998), S. 101-107 
    ISSN: 1436-6304
    Keywords: Key words: Competitive location model ; Nash equilibria ; stability ; reachability ; Schlüsselwörter: Wettbewerbsmodelle in der Standorttheorie ; Nash Gleichgewicht ; Stabilität ; Erreichbarkeit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. In der Arbeit werden die Standorte von Duopolisten in einem Baum untersucht. Unter der Annahme festgesetzter Preise werden notwendige und hinreichende Bedingungen für Nash Gleichgewichte für Standorte auf Bäumen hergeleitet. Unter Verwendung dieser Bedingungen wird dann gezeigt, daß– angenommen Nash Gleichgewichte existieren – diese in einem wiederholt angewandten sequentiellen Standortfindungsprozeß, in dem beide Duopolisten als Zielfunktion kurzfristige Gewinnmaximierung haben, auch erreicht werden. “Equilibrium is a place in heaven, but how do we get there from here?”
    Notes: Abstract. This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.
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  • 4
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    OR spectrum 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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  • 5
    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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  • 6
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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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  • 7
    ISSN: 1572-879X
    Keywords: metal-oxygen cluster compounds ; heteropoly acids ; stability ; pH ; aqueous solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The stabilities of the solid superacids H3Mo12O40, H3PW12O40, H4SiMo12O40 and H4SiW12O40 in aqueous solution have been measured at various values of pH by use of ion chromatographic analyses. The aforementioned acids are completely decomposed at values of pH, 4.0, 5.2, 7.0 and 11.0, respectively. The stabilities in aqueous solution with respect to pH follow the order H4SiW12O40 〉 H3PW12O40 〉 H4SiMo12O40 〉 H3PMo12O40.
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  • 8
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    Journal of dynamics and differential equations 10 (1998), S. 151-188 
    ISSN: 1572-9222
    Keywords: Fourth-order solitary waves ; stability ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study ground-state traveling wave solutions of a fourth-order wave equation. We find conditions on the speed of the waves which imply stability and instability of the solitary waves. The analysis depends on the variational characterization of the ground states rather than information about the linearized operator.
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  • 9
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    Positivity 1 (1997), S. 319-330 
    ISSN: 1572-9281
    Keywords: delay equations ; stability ; positive solutions ; spectral growth condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove stability for a semilinear delay equation, whose nonlinearity is majorized by a linear positive operator. The key ingredients are a spectral condition, positivity of solutions to the linear problem, and lattice properties of the Banach space.
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  • 10
    ISSN: 1572-9281
    Keywords: asymptotic stability ; dichotomic maps ; retarded functional differential equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation $$x'(t) = - b(t)x(t - r)$$ and of itsnonlinear generalization $$x'(t) = b(t)f(x(t - r))$$ are established.
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  • 11
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    Set-valued analysis 5 (1997), S. 73-88 
    ISSN: 1572-932X
    Keywords: differential inclusion ; invariance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The properties of invariance, stability, asymptotic stability and attainability of a given compact set $$K \subset \mathbb{R}^n $$ with respect to a differential inclusion, have weak and strong versions: the weak version requires existence of a trajectory with the corresponding property, while the strong one requires this property for all trajectories. The following statement is proven in the paper (under slight restrictions) for each of the above-mentioned properties: if K has the weak property with respect to $$\dot x \in F(x) $$ , then there is a (regulation) mapping G such that G(x) ⊂ F(x) ∀ x and G has the strong property with respect to $${\dot x}$$ ε G(x). In addition, certain regularity of the set of solutions of the last inclusion is claimed.
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  • 12
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    Set-valued analysis 5 (1997), S. 365-375 
    ISSN: 1572-932X
    Keywords: set-valued mappings ; vector optimization ; stability
    Source: Springer Online Journal Archives 1860-2000
    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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  • 13
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    Annals of operations research 56 (1995), S. 79-93 
    ISSN: 1572-9338
    Keywords: Multistage stochastic programs ; optimization in Banach spaces ; stability ; approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Multistage stochastic programs are regarded as mathematical programs in a Banach spaceX of summable functions. Relying on a result for parametric programs in Banach spaces, the paper presents conditions under which linearly constrained convex multistage problems behave stably when the (input) data process is subjected to (small) perturbations. In particular, we show the persistence of optimal solutions, the local Lipschitz continuity of the optimal value and the upper semicontinuity of optimal sets with respect to the weak topology inX. The linear case with deterministic first-stage decisions is studied in more detail.
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  • 14
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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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  • 15
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    Journal of dynamics and differential equations 9 (1997), S. 463-505 
    ISSN: 1572-9222
    Keywords: Difference equations ; random perturbation ; averaging ; diffusion approximation ; randomly perturbed iterations ; stability ; 3SR60 ; 60H15 ; 60J99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let (X, ℬ) and (Y,C) be two measurable spaces withX being a linear space. A system is determined by two functionsf(X): X→ X andϕ:X×Y→X, a (small) positive parameterε and a homogeneous Markov chain {y n } in (Y,C) which describes random perturbations. States of the system, say {x n ɛ ∈X, n=0, 1,⋯}, are determined by the iteration relations:x n+1 ɛ =f(x n ɛ )+ɛϕ(x n ɛ ,Yn+1) forn≥0, wherex 0 ɛ =x 0 is given. Here we study the asymptotic behavior of the solutionx n ɛ asε → 0 andn → ∞ under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.
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  • 16
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    Set-valued analysis 5 (1997), S. 377-390 
    ISSN: 1572-932X
    Keywords: differential inclusions ; stability ; boundedness of solutions ; Lyapunov functions
    Source: Springer Online Journal Archives 1860-2000
    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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  • 17
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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
    Source: Springer Online Journal Archives 1860-2000
    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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  • 18
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    Set-valued analysis 7 (1999), S. 209-238 
    ISSN: 1572-932X
    Keywords: nonsmooth analysis ; subdifferentials ; coderivatives ; implicit function theorem ; solvability ; stability ; open mapping theorem ; metric regularity ; multidirectional mean value inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.
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  • 19
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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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  • 20
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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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  • 21
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    BIT 36 (1996), S. 531-541 
    ISSN: 1572-9125
    Keywords: Meromorphic resolvent ; stability ; power bounded
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Tools to estimate resolvents are developed and a model result is given for power bounded operators: the dimension showing up in the Kreiss matrix theorem can be replaced by the trace norm.
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  • 22
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    BIT 39 (1999), S. 385-402 
    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; backward error analysis ; growth factor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new backward error analysis of LU factorization is presented. It allows to obtain a sharper upper bound for the forward error and a new definition of the growth factor that we compare with the well known Wilkinson growth factor for some classes of matrices. Numerical experiments show that the new growth factor is often of order approximately log2 n whereas Wilkinson's growth factor is of order n or $$\sqrt n$$ .
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  • 23
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    Advances in computational mathematics 9 (1998), S. 145-171 
    ISSN: 1572-9044
    Keywords: periodic pseudodifferential equations ; multiwavelets ; splines with multiple knots ; generalized Galerkin–Petrov schemes ; boundary element methods ; error analysis ; stability ; Strang–Fix condition ; 65J10 ; 65N30 ; 65N35 ; 65R20 ; 47G30 ; 45P05 ; 41A25 ; 41A30 ; 41A15
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    Notes: Abstract We develop a stability and convergence analysis of Galerkin–Petrov schemes based on a general setting of multiresolution generated by several refinable functions for the numerical solution of pseudodifferential equations on smooth closed curves. Particular realizations of such a multiresolution analysis are trial spaces generated by biorthogonal wavelets or by splines with multiple knots. The main result presents necessary and sufficient conditions for the stability of the numerical method in terms of the principal symbol of the pseudodifferential operator and the Fourier transforms of the generating multiscaling functions as well as of the test functionals. Moreover, optimal convergence rates for the approximate solutions in a range of Sobolev spaces are established.
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  • 24
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    Advances in computational mathematics 4 (1995), S. 1-26 
    ISSN: 1572-9044
    Keywords: Wavelets ; biorthogonal wavelets ; stability ; primary 15A12 ; 65F35 ; secondary 42C15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL → ∞. These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.
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    Annals of global analysis and geometry 13 (1995), S. 141-148 
    ISSN: 1572-9060
    Keywords: Gauss curvature ; stability ; 53
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    Topics: Mathematics
    Notes: Abstract We prove that a domain on a surface of constant curvature is stable provided the integral of the mean curvature is small enough.
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    Annals of global analysis and geometry 15 (1997), S. 277-297 
    ISSN: 1572-9060
    Keywords: mean curvature ; $$r$$ -mean curvature ; sphere ; stability ; stable
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    Topics: Mathematics
    Notes: Abstract We deal with compact hypersurfaces immersed in space forms with constant $$r$$ -mean curvature. They are critical points for a variational problem. We show they are stable if and only if they are geodesic spheres, generalizing results on constant curvature hypersurfaces.
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  • 27
    ISSN: 1572-9125
    Keywords: finite difference methods ; wave equation ; accuracy ; stability ; Padé approximants ; order stars ; Riemann surface
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation,u tt =c 2 u xx , given by $$\sum\limits_{j = - S}^S {b_j U_{n + 1,m + j} + } \sum\limits_{j = - S}^S {a_j U_{n,m + j} + } \sum\limits_{j = - S}^S {b_j U_{n - 1,m + j} } = 0.$$ It has already been proved that the maximal order of accuracyp of such schemes is given byp ≤ 2(s + S). In this paper we show that the requirement of stability does not reduce this maximal order for any choice of the pair (s, S). The result is proved by introducing an order star on the Riemann surface of the algebraic function associated with the scheme. Furthermore, Padé schemes, withS = 0,s 〉 0, ands = 0,S 〉 0, are proved to be stable for 0 〈 μ 〈 1, where μ is the Courant number. These schemes can be implemented with high-order absorbing boundary conditions without reducing the range of μ for which stable solutions are obtained.
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    Acta applicandae mathematicae 49 (1997), S. 35-54 
    ISSN: 1572-9036
    Keywords: dynamical systems ; stability ; pseudo orbit tracing property ; nonstandard analysis
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    Topics: Mathematics
    Notes: Abstract It is known that it is not possible to introduce C0 -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rn. Classically these amount to considering the space of all systems on a given subset of Rn as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.
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    Geometriae dedicata 62 (1996), S. 281-298 
    ISSN: 1572-9168
    Keywords: 53C23 ; Hyperbolicity ; stability ; quasi-geodesics
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    Topics: Mathematics
    Notes: Abstract It is known that for a geodesic metric space hyperbolicity in the sense of Gromov implies geodesic stability. In this paper it is shown that the converse is also true. So Gromov hyperbolicity and geodesic stability are equialent for geodesic metric spaces.
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  • 30
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    Advances in computational mathematics 10 (1999), S. 115-133 
    ISSN: 1572-9044
    Keywords: Runge–Kutta–Nyström methods ; predictor–corrector methods ; stability ; parallelism ; 65M12 ; 65M20
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    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
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    Acta applicandae mathematicae 46 (1997), S. 29-48 
    ISSN: 1572-9036
    Keywords: Hamilton–Jacobi–Bellman equations ; nonlinear potentials ; nonlinear PDE ; viscosity solutions ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A formal method of constructing the viscosity solutions for abstract nonlinear equations of Hamilton–Jacobi–Bellman (HJB) type was developed in the previous work of the author. A new advantage of this method (which was called an ‘nonlinear potentials’ method) is that it gives a possibility to choose at the first step an expected regularity of the solution and then – to construct this solution. This makes the whole procedure more simple because an analysis of regularity of viscosity solutions is usually the most complicated step. Nonlinear potentials method is a generalization of Krylov's approach to study HJB equations. In this article nonlinear potentials method is applied to elliptic degenerate HJB equations in Rd with variable coefficients.
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  • 32
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    BIT 39 (1999), S. 620-645 
    ISSN: 1572-9125
    Keywords: Numerical integrator ; oscillatory solutions ; Schrödinger equation ; quantum-classical coupling ; error bounds ; stability
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    Topics: Mathematics
    Notes: Abstract We study time integration methods for equations of mixed quantum-classical molecular dynamics in which Newtonian equations of motion and Schrödinger equations are nonlinearly coupled. Such systems exhibit different time scales in the classical and the quantum evolution, and the solutions are typically highly oscillatory. The numerical methods use the exponential of the quantum Hamiltonian whose product with a state vector is approximated using Lanczos' method. This allows time steps that are much larger than the inverse of the highest frequencies. We describe various integration schemes and analyze their error behaviour, without assuming smoothness of the solution. As preparation and as a problem of independent interest, we study also integration methods for Schrödinger equations with time-dependent Hamiltonian.
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    Czechoslovak mathematical journal 47 (1997), S. 409-424 
    ISSN: 1572-9141
    Keywords: R δ-set ; homotopic ; contractible ; evolution triple ; evolution inclusion ; compact embedding ; optimal control
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    Topics: Mathematics
    Notes: Abstract In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field F(t, x), we are able to show that the solution set is in fact an R δ-set. Finally some applications to infinite dimensional control systems are also presented.
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    Czechoslovak mathematical journal 48 (1998), S. 291-312 
    ISSN: 1572-9141
    Keywords: evolution triple ; optimal control ; monotone operator ; hemicontinuous operator ; parabolic system ; property (Q)
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    Topics: Mathematics
    Notes: Abstract We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
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    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 809-816 
    ISSN: 1420-9039
    Keywords: 34D20 ; 34D35 ; 35Q72 ; 73H10 ; 73K03 ; Elastic string ; stability ; energy-momentum ; axial motion
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    Topics: Mathematics , Physics
    Notes: Abstract We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish “orbitai” stability (modulo this collection of relative equilibria). For a well-defined class of “soft” materials, there is an upper bound on the axial speed sufficient for stability; “stiff” materials are shown to be orbitally stable at any axial speed.
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    Monatshefte für Mathematik 126 (1998), S. 117-124 
    ISSN: 1436-5081
    Keywords: 52A20 ; 52A22 ; star bodies ; spherical integral transformations ; convex bodies ; stability
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    Topics: Mathematics
    Notes: Abstract LetK be ad-dimensional star body (with respect to the origino). It is known that the (d−1)-dimensional volume of the intersections ofK with the hyperplanes througho does not uniquely determineK. Uniqueness can only be achieved under additional assumptions, such as central symmetry. Here it is pointed out that if one uses, instead of intersections by hyperplanes, intersections by half-planes that containo on the boundary, then, without any additional assumptions, the volume of these intersections determinesK uniquely. This assertion, and more general results of this kind, together with stability estimates, are obtained from uniqueness results and estimates concerning a particular spherical integral transformation.
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    Catalysis letters 40 (1996), S. 261-264 
    ISSN: 1572-879X
    Keywords: Ti-substituted MCM-41 ; stability ; dehydrogenation of ethanol ; hydroxylation of phenol ; XRD ; XANES
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The thermal and chemical stability of a titanium-substituted MCM-41 (TiMCM-41) with Si/Ti mole ratio of 39 and pore diameter of 2.4 nm was studied with the small-angle X-ray diffraction and X-ray absorption near-edge structure techniques. The TiMCM-41 was stable in helium flow below 1273 K and under gas-phase reaction conditions of ethanol dehydrogenation (ethanol/ O2 = 1 mol/mol, 373–723 K). Under liquid-phase reaction conditions of phenol hydroxylation (phenol/35% H2O2 /acetone in moles=3∶1∶7,333K), however, it lost the MCM-41structure and titanium was leached out of the silicalite framework.
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    Catalysis letters 53 (1998), S. 97-101 
    ISSN: 1572-879X
    Keywords: ethene hydroformylation ; heterogeneous catalysts ; cobalt catalysts ; gas‐phase deposition ; dispersion ; stability
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The results from ethene hydroformylation at 173°C showed that a Co(acac)3/SiO2 catalyst prepared from Co(acac)3 precursor by gas‐phase deposition was three times as active as a catalyst prepared by impregnation from cobalt nitrate, but oxo‐selectivities were similar. The high propanal selectivities on the Co(acac)3/SiO2 seem to be related to the presence of highly dispersed active sites favouring CO insertion. As dispersion is decreased from 23 to 8% due to increasing metal content (from 5 to 16 wt%), oxo‐selectivity decreased from 39 to 25%. The activity of Co(acac)3/SiO2 remained unchanged during 68 h on stream. The gas‐phase deposition technique described here is a promising method for the preparation of active, selective and stable heterogeneous hydroformylation catalysts.
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  • 39
    ISSN: 1572-879X
    Keywords: nanolithography ; model catalyst ; palladium ; copper ; stability ; spin-coating ; SEM ; AFM ; XPS
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Metal clusters arranged on nanostructured oxidized silicon wafers are presented as new model catalyst systems. A photoresist layer spun on top of a wafer was patterned by laser interference exposure. The grid obtained after removing the exposed parts of the resist is used as an etching mask. Hollows with diameters of 300 nm and depths between 50 and 60 nm were etched into the oxide layer using wet chemical methods. Two methods were applied to deposit metal clusters (Pd or Cu) in a defined way within the hollows. The particles ranged from 10 to 50 nm in height and from 80 to 200 nm in diameter. The model catalyst systems were characterized by atomic force microscopy and X-ray photoelectron spectroscopy. The method presented here allows us to produce 4 inch wafers that are covered completely by nanometer-sized structures in a reasonable period of time.
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  • 40
    ISSN: 1436-5073
    Keywords: stability ; chemical species ; solutions ; calibration ; interlaboratory studies ; measurement and testing programme
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The stability of chemical species in solution during storage is one of the critical aspect that has to be carefully studied e.g. for calibration purposes or prior to the organization of interlaboratory studies using synthetic solutions. The Measurements and Testing Programme (formerly BCR) is currently undertaking projects to improve the quality of speciation analysis for a variety of species (e.g. As, Hg, Sn, Pb, Cr). In all the cases the stability of these species was carefully studied in the solutions provided to the participants. This paper gives an overview of some of the results obtained in different BCR-projects on speciation analysis.
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    K-Theory 10 (1996), S. 491-516 
    ISSN: 1573-0514
    Keywords: 57M60 ; 57N13 ; 57R91 ; 19G38 ; topological 4-manifold ; pseudofree action ; equivariant intersection form ; stability ; topological rigidity
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    Topics: Mathematics
    Notes: Abstract This paper is concerned with the algebraic aspects of the classification of pseudofree, locally linear group actions on a simply connected 4-manifold, particularly with the splitting and stability properties of the associated Hermitian intersection module and its isometry group. Our main result is the proof of stability of the equivariant intersection form for a large class of pseudofree actions. We also prove a topological rigidity theorem stating that two locally linear, pseudofree actions on a closed, oriented, simply connected 4-manifold, with the equivariant intersection forms indefinite and of rank at least 3 at each irreducible character, are topologically conjugate by an orientation preserving homeomorphism if and only if their oriented local representations at the corresponding fixed points are linearly equivalent.
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    Journal of nonlinear science 5 (1995), S. 373-418 
    ISSN: 1432-1467
    Keywords: Hamiltonian system with symmetry ; relative equilibria ; perturbation ; linearization ; stability
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    Topics: Mathematics , Physics
    Notes: Summary A relative equilibrium of a Hamiltonian system with symmetry is a point of phase space giving an evolution which is a one-parameter orbit of the action of the symmetry group of the system. The evolutions of sufficiently small perturbations of a formally stable relative equilibrium are arbitrarily confined to that relative equilibrium's orbit under the isotropy subgroup of its momentum. However, interesting evolution along that orbit, here called drift, does occur. In this article, linearizations of relative equilibria are used to construct a first order perturbation theory explaining drift, and also to determine when the set of relative equilibria near a given relative equilibrium is a smooth symplectic submanifold of phase space.
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    International journal of game theory 25 (1996), S. 1-12 
    ISSN: 1432-1270
    Keywords: Bimatrix game ; ɛ-equilibrium ; optimal strategies ; vertical linear complementarity problem ; degree ; stability
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    Topics: Mathematics , Economics
    Notes: Abstract In this article, we consider a two-person game in which the first player picks a row representative matrixM from a nonempty set $$A$$ ofm ×n matrices and a probability distributionx on {1,2,...,m} while the second player picks a column representative matrixN from a nonempty set ℬ ofm ×n matrices and a probability distribution y on 1,2,...,n. This leads to the respective costs ofx t My andx t Ny for these players. We establish the existence of an ɛ-equilibrium for this game under the assumption that $$A$$ and ℬ are bounded. When the sets $$A$$ and ℬ are compact in ℝmxn, the result yields an equilibrium state at which stage no player can decrease his cost by unilaterally changing his row/column selection and probability distribution. The result, when further specialized to singleton sets, reduces to the famous theorem of Nash on bimatrix games.
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    Journal of thermal analysis and calorimetry 49 (1997), S. 1501-1507 
    ISSN: 1572-8943
    Keywords: calcium sulphide ; gypsum ; oxidation ; phosphogypsum ; reduction ; stability ; thermogravimetry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Using a heating rate of 2°C min−1, CaS reacts with oxygen in air from 700°C to form CaSO4, with a complete conversion at 1100°C. Synthesis of CaS from the reaction between CaSO4 containing compounds and carbon compounds in air would not be possible, as the carbon reacts from 600°C with oxygen in the air to give CO2. Heating stoichiometric amounts of carbon and pure CaSO4, synthetic gypsum or phosphogypsum in a nitrogen atmosphere, results in the formation of CaS from 850°C. Using a heating rate of 10°C min−1, the formation of CaS is completed at 1080°C. Addition of 5% Fe2O3 as a catalyst lowers the starting temperature of the reaction to 750°C. Activation energy values at different fraction reaction values (α) differ between 340 and 400 kJ mol−1. The relationship between the activation energy values and conversion (α) indicates that the reaction proceeds via multiple steps.
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    Journal of thermal analysis and calorimetry 50 (1997), S. 625-632 
    ISSN: 1572-8943
    Keywords: DSC ; NMR ; 8-quinolinol compounds ; TG-DTG ; stability ; thermal decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Solid M-Ox compounds, whereM represents Mg(II), Zn(II), Pb(II) and NbO(III), and Ox is 8-quinolinol, have been prepared. Thermogravimetry, derivative thermogravimetry (TG, DTG), differential scanning calorimetry (DSC), nuclear magnetic resonance (NMR) and infrared absorption spectra (IR) have been used to characterize and to study the thermal stability and thermal decomposition of these compounds.
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    Journal of thermal analysis and calorimetry 56 (1999), S. 1285-1304 
    ISSN: 1572-8943
    Keywords: amorphous state ; combined techniques ; drug design ; drug product development ; drug substance ; drug technology ; DSC ; excipients ; failure investigations ; hydrates ; MDSC ; microcalorimetry ; pharmaceuticals ; polymorphism ; polymers ; preformulation ; process optimization ; purity ; quality control ; solvates ; stability ; sub-ambient DSC ; TG ; temperature resolved X-ray diffraction ; water interactions ; thermal microscopy ; water sorption-desorption
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Modern thermal analysis, microcalorimetry and new emerging combined techniques which deliver calorimetric, microscopic and spectroscopic data offer a powerful analytical battery for the study of pharmaceuticals. These techniques are very useful in all steps of development of new drug products as well as methods for quality control in production. The characterization of raw materials enables to understand the relationships between polymorphs, solvates and hydrates and to choose the proper development of new drug products with very small amount of material in a very short time. Information on stability, purity is valuable for new entities as well as for marketed drug substances from different suppliers. Excipients which vary from single organic or inorganic entity to complexes matrixes or polymers need to be characterized and properly controlled. The thermodynamic phase-diagrams are the basis of the studies of drug-excipients interactions. They are very useful for the development of new delivery systems. A great number of new formulations need proper knowledge of the behaviour of the glass transition temperature of the components. Semi-liquid systems, interactions in aqueous media are also successfully studied by these techniques.
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    Journal of thermal analysis and calorimetry 50 (1997), S. 807-814 
    ISSN: 1572-8943
    Keywords: DTA ; stability ; substituted InF3 glasses
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The thermal properties and devitrification behaviour of substituted InF3 glasses were studied by means of differential thermal analysis. A comparison of various simple quantitative methods to assess the level of stability of multicomponent fluoride glass systems was also made. Most of these methods are based on critical temperatures. In this paper, a new parameter,k d(T), is introduced to the stability criteria. The stabilities of several substituted InF3 glasses were evaluated experimentally and correlated with the activation energies of crystallization via this new kinetic criterion and compared with those evaluated by other criteria.
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  • 48
    ISSN: 1572-8951
    Keywords: Protein engineering ; thermolysin ; activity ; stability
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Thermolysin mutants having a variety of amino acid at the 119th position are designed by considering electrostatic field effect upon the active area. The most activated mutant has five times higher hydrolytic activity than the wild type. Negative correlation between the activity and the thermal stability is observed. A combined effect of the flexibility of the substrate binding site and the negative electrostatic field around the site is suggested as a key to enhance the activity.
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    Journal of thermal analysis and calorimetry 55 (1999), S. 727-739 
    ISSN: 1572-8943
    Keywords: ignition ; polymer combustion modelling ; stability ; steady state
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    Topics: Chemistry and Pharmacology
    Notes: Abstract A mathematical model of ignition and burning of organic polymers was used for evaluation and quantification of the tendency of polymers to ignition. The model permits investigation of the influence of one parameter of the polymer on the others. It was found that the model could be used for the verification of the ignitability method developed by Miller et al. [1]. Different steady states of combustion were found when using the model proposed. There is a characteristic steady state for normal flaming combustion, another for non-flaming combustion, and there are also unstable steady states that have no real physical meaning.
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    Journal of thermal analysis and calorimetry 56 (1999), S. 1177-1184 
    ISSN: 1572-8943
    Keywords: differential scanning calorimetry ; DNA triple helix ; oligonucleotides ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract In this work we report a thermodynamic characterization of stability and melting behaviour of two 24-mer DNA triplexes. The third strand, that binds the Watson-Crick double helix with Hoogsteen hydrogen bonds, contains 3′-3′ phosphodiester junction that determines the polarity inversion. The target double helix is composed of adjacent and alternate fragments of oligopurine-oligopyrimidine tracts. The two helices differ from the substitution of the cytosine, involved in the junction, with the thymine. Calorimetric data reported here provide a quantitative measure of the influence of pH and base modification on the stability of a DNA triplex.
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    Journal of nondestructive evaluation 14 (1995), S. 127-136 
    ISSN: 1573-4862
    Keywords: Nondestructive evaluation ; corrosion monitoring ; electrical impedance tomography ; stability ; numerical methods
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    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract We investigate the problem of detecting and assessing, by means of static electrical measurements, damage due to corrosion in a structure. Corrosion damage, which is assumed to occur in an inaccessible part of a specimen, is modelled as material loss. The detection device consists of electrodes which inject DC current and measure voltage potentials in the accessible part of the specimen. The topography of the damaged surface is estimated from the measured data. This research is meant to evaluate if a method based on static electrical measurements has the potential to be developed into a useful nondestructive evaluation tool. We propose computational methods that take the measured data and estimate the unknown damaged surface. The methods are studied in order to understand their properties. Several example calculations from synthetic data are presented. Our findings indicate that such a device has limited resolution. However, it offers several advantages that make it worthwhile to pursue further research.
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  • 52
    ISSN: 1573-4919
    Keywords: heart mitochondria ; lability ; muscle mitochondria ; oxidative phosphorylation ; stability ; taurine
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    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract We modified the isolation procedure of muscle and heart mitochondria. In human muscle, this resulted in a 3.4 fold higher yield of better coupled mitochondria in half the isolation time. In a preparation from rat muscle we studied factors that affected the stability of oxidative phosphorylation (oxphos) and found that it decreased by shaking the preparation on a Vortex machine, by exposure to light and by an increase in storage temperature. The decay was found to be different for each substrate tested. The oxidation of ascorbate was most stable and less sensitive to the treatments. When mitochondria were stored in the dark and the cold, the decrease in oxidative phosphorylation followed first order kinetics. In individual preparations of muscle and heart mitochondria, protection of oxidative phosphorylation was found by adding candidate stabilizers, such as desferrioxamine, lazaroids, taurine, carnitine, phosphocreatine, N-acetylcysteine, Trolox-C and ruthenium red, implying a role for reactive oxygen species and calcium-ions in the in vitro damage at low temperature to oxidative phosphorylation. In heart mitochondria oxphos with pyruvate and palmitoylcarnitine was most labile followed by glutamate, succinate and ascorbate.We studied the effect of taurine, hypotaurine, carnitine, and desferrioxamine on the decay of oxphos with these substrates. 1 mM taurine (n = 6) caused a significant protection of oxphos with pyruvate, glutamate and palmitoylcarnitine, but not with the other substrates. 5 mM L-carnitine (n = 6), 1 mM hypotaurine (n = 3) and 0.1 mM desferrioxamine (n = 3) did not protect oxphos with any of the substrates at a significant level. These experiments were undertaken in the hope that the in vitro stabilizers can be used in future treatment of patients with defects in oxidative phosphorylation. (Mol Cell Biochem 174: 61–66, 1997)
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  • 53
    ISSN: 1572-9036
    Keywords: (discrete-time) Markov control processes ; expected total cost ; value iteration ; policy iteration ; stability ; transient control models
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    Topics: Mathematics
    Notes: Abstract This paper studies the expected total cost (ETC) criterion for discrete-time Markov control processes on Borel spaces, and possibly unbounded cost-per-stage functions. It presents optimality results which include conditions for a control policy to be ETC-optimal and for the ETC-value function to be a solution of the dynamic programming equation. Conditions are also given for the ETC-value function to be the limit of the α-discounted cost value function as α ↑ 1, and for the Markov control process to be `stable" in the sense of Lagrange and almost surely. In addition, transient control models are fully analized. The paper thus provides a fairly complete, up-dated, survey-like presentation of the ETC criterion for Markov control processes on Borel spaces.
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    Interface science 3 (1996), S. 303-316 
    ISSN: 1573-2746
    Keywords: epitaxy ; Krudjumov-Sachs ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract In this paper we address the problems related to critical misfit and thickness in epilayer-substrate combinations of comparable bond strengths; specifically the case in which a pseudomorphic monolayer (ML) is stable and the critical thickness is about three MLs or less. Of particular interest are the average energies related to misfit strain f KS and misfit dislocations (MDs)—in the latter case the individual contributions of the oscillatory strains 〈V〉 and the epilayer-substrate disregistry 〈V〉MD. The individual energies are of interest because they may play different roles in the realization of specific growth modes. The analytical approach involves the following assumptions: (a) a rigid substrate as source of a periodic epilayer atom-substrate interaction potential which we model in terms of a low order truncated Fourier series; and (b) an epilayer which (i) deforms harmonically with zero strain gradient normal to the film plane, (ii) grows in Kurdjumov-Sachs (KS) orientation due to small misfit. f KS and in the layer-by-layer growth mode. Arguments are presented claiming that this interfacial situation may be approximated by a one-dimensional problem in which epilayer stiffness constants and equilibrium structure, as well as epilayer-substrate interaction depend on epilayer thickness; which poses a complex problem. An approximate solution could be obtained by assuming these quantities to be independent of thickness and proximities of the vacuum and the substrate. The most prominent conclusions are that the equilibrium density of MDs and hence the transition from misfit accommodation by MS to one containing MDs is a catastrophic process and that sustained minimum energy may require the overcoming of an energy barrier. While elementary implementation of the results to equilibrium growth mode theory suggests—independently of the catastrophic nature—that energetically favored misfit strain relief by misfit dislocations may, or may not, effect a transition to Stranski-Krastanov growth, a crude numerical calculation favors the transition. A proper implementation of the results require extensive numerical calculations and is planned for the near future.
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    Journal of sol gel science and technology 8 (1997), S. 523-527 
    ISSN: 1573-4846
    Keywords: UF membranes ; alumina ; zirconia coating ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract For improving chemical and thermal stability of γ -Al2O3 membranes boehmite (AlOOH) sol-particles are coated with Zr4+-species with two techniques. These techniques are heterogeneous precipitation (HP-method) and “surface-reaction-followed-by-polycondensation” (SRPC-method). A continuous coating layer is formed at relative low Zr4+-concentration, about one monolayer coverage of boehmite particles, and with the HP-method. For larger concentrations and for the SRPC-method small particles (order 1 nm) of Zr4+-species are formed on the surface of the boehmite particles. After drying and calcination up to 1000°C no continuous layer of a zirconia phase could be detected for all samples. However the thermal stability of the porous structure is improved. Phase transitions of alumina occur at temperatures of 1100°C and the porous structure of the membrane material is then destabilized.
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    Journal of sol gel science and technology 8 (1997), S. 523-527 
    ISSN: 1573-4846
    Keywords: UF membranes ; alumina ; zirconia coating ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract For improving chemical and thermal stability of γ-Al2O3 membranes boehmite (AlOOH) sol-particles are coated with Zr4+-species with two techniques. These techniques are heterogeneous precipitation (HP-method) and “surface-reaction-followed-by-polycondensation” (SRPC-method). A continuous coating layer is formed at relative low Zr4+-concentration, about one monolayer coverage of boehmite particles, and with the HP-method. For large concentrations and for the SRPC-method small particles (order 1 nm) of Zr4+-species are formed on the surface of the boehmite particles. After drying and calcination up to 1000°C no continuous layer of a zirconia phase could be detected for all samples. However the thermal stability of the porous structure is improved. Phase transitions of alumina occur at temperatures of 1100°C and the porous structure of the membrane material is then destabilized.
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    Journal of biomolecular NMR 13 (1999), S. 187-191 
    ISSN: 1573-5001
    Keywords: alignment ; bicelle ; dipolar coupling ; liquid crystal ; pH ; stability ; ubiquitin
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Abstract It is demonstrated that mixtures of ditetradecyl- phosphatidylcholine or didodecyl-phoshatidylcholine and dihexyl- phosphatidylcholine in water form lyotropic liquid crystalline phases under similar conditions as previously reported for bicelles consisting of dimyristoyl-phosphatidylcholine (DMPC) and dihexanoyl- phosphatidylcholine (DHPC). The carboxy-ester bonds present in DMPC and DHPC are replaced by ether linkages in their alkyl analogs, which prevents acid- or base-catalyzed hydrolysis of these compounds. 15N-1H dipolar couplings measured for ubiquitin over the 2.3–10.4pH range indicate that this protein retains a backbone conformation which is very similar to its structure at pH 6.5 over this entire range.
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  • 58
    ISSN: 1573-4943
    Keywords: Mannuronate lyase ; amino acid sequence ; stability ; disulfide bond ; C-terminal residue
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The complete amino acid sequences of two isoforms, SP1 and SP2, of mannuronate lyase from a wreath shell,Turbo cornutus, were determined to elucidate amino acid residues responsible for causing the more stable protein conformation of SP2. The sequences of the two isoforms were identical except for two hydrophobic C-terminal amino acid residues of SP2, Ile and Leu, which were additionally attached to Thr of the C-terminal residue of SP1 (253 residues in total). The molecular weight of SP2 was calculated to be 28,912 from the amino acid sequence data. Two disulfide bond cross-linkages were found to be between 106 and 115 and between 145 and 150, and a partially buried single SH group was located at 236. A carbohydrate chain that consisted of 3 GlcNAc, 3 Fuc, and 1 Man was anchored on Asn-105 in a typical carbohydrate-binding motif of Asn-X-Ser. This is the first evidence of the primary structure of mannuronate lyase, and no significant homology of the amino acid sequence among other proteins was found. The C-terminal truncated SP2, which was produced by digestion with carboxypeptidase Y and corresponded structurally to SP1, showed a thermal stability identical to that of SP1. These results indicate that the higher stability of SP2 than SP1 arises from the presence of the C-terminal two hydrophobic amino acid residues.
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  • 59
    ISSN: 1573-9171
    Keywords: stability ; structural thermodynamic parameters ; salvation ; ligand ; aqueous-organic media
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    Topics: Chemistry and Pharmacology
    Notes: Abstract The effect of a substituent inm-,o-, andp-aminobenzoic and isonicotinic acids and 4-amiopyridine on the stability of their complexes with Dy3+ in H2O and H2O-DMSO(DMF) has been studied by pH-metric and magnetoopticrl titration. An increase in the efficiency of the salvation of a ligand decreases the effect of a substituent on the stability of the complex.
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    Acta mathematicae applicatae sinica 12 (1996), S. 216-224 
    ISSN: 1618-3932
    Keywords: Dynamics of populations ; enemy-pest system ; persistence ; stability
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    Topics: Mathematics
    Notes: Abstract The model of a kind of predator-parasite-pest system is built in this paper in which the parasite population is controlled by predator in such a way that it preys upon the pest individuals parasitized. A disgusty of predator for preying upon the pest individuals parasitized is introduced in the model to measure the intensity that the parasite population was controlled by the predator. The persistence and the stability are studied for this system mathematically. And the influence of the disgusty on the persistence of the system is also noticed in biology.
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    Acta mathematicae applicatae sinica 13 (1997), S. 176-187 
    ISSN: 1618-3932
    Keywords: Spherical surface ; pseudospectral method ; vorticity equations ; stability ; convergence
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    Topics: Mathematics
    Notes: Abstract The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual ones, is proposed. Based on such an interpolation, the pseudospectral scheme is constructed. Its generalized stability and convergence are analyzed rigorously. The theoretical analysis and computational skills can also be applied to other nonlinear partial differential equations defined on spherical surface.
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    Numerical algorithms 10 (1995), S. 225-244 
    ISSN: 1572-9265
    Keywords: Cholesky factorization error analysis ; Hankel matrix ; least squares ; normal equations ; orthogonal factorization ; QR factorization ; semi-normal equations ; stability ; Toeplitz matrix ; weak stability ; Primary 65F25 ; Secondary 47B35 ; 65F05 ; 65F30 ; 65Y05 ; 65Y10
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    Topics: Computer Science , Mathematics
    Notes: Abstract We show that a fast algorithm for theQR factorization of a Toeplitz or Hankel matrixA is weakly stable in the sense thatR T R is close toA T A. Thus, when the algorithm is used to solve the semi-normal equationsR TRx=AT b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear systemAx=b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem min ||Ax-b||2.
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    Numerical algorithms 14 (1997), S. 343-359 
    ISSN: 1572-9265
    Keywords: progressive interpolation ; stability ; spline ; shape parameters ; geometric continuity ; 41A05 ; 41A15 ; 65D05 ; 65D07
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we study several interpolating and smoothing methods for data which are known “progressively”. The algorithms proposed are governed by recurrence relations and our principal goal is to study their stability. A recurrence relation will be said stable if the spectral radius of the associated matrix is less than one. The iteration matrices depend on shape parameters which come either from the connection at the knots, or from the nature of the interpolant between two knots. We obtain various stability domains. Moving the parameters inside these domains leads to interesting shape effects.
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    Numerical algorithms 10 (1995), S. 245-260 
    ISSN: 1572-9265
    Keywords: Multistep methods ; differential-algebraic equations ; stability ; existence and uniqueness ; convergence of iterative method ; 65L06 ; 65L20 ; 65N22
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    Topics: Computer Science , Mathematics
    Notes: Abstract Multistep methods for the differential/algebraic equations (DAEs) in the form of $$F_1 (x) = 0, F_2 (x,x',z) = 0$$ are presented, whereF 1 maps from ℝ n to ℝ ′ ,F 2 from ℝ n x ℝ n x ℝ m to ℝ s andr〈n≤r+s=n+m. By employing the deviations of the available existence theories, a new form of the multistep method for solutions of (1) is developed. Furthermore, it is shown that this method has no typical instabilities such as those that may occur in the application of multistep method to DAEs in the traditional manner. A proof of the solvability of the multistep system is provided, and an iterative method is developed for solving these nonlinear algebraic equations. Moreover, a proof of the convergence of this iterative method is presented.
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    Acta mathematicae applicatae sinica 13 (1997), S. 33-44 
    ISSN: 1618-3932
    Keywords: Inverse problem ; hyperbolic equations ; eigenvalue problem ; spectral function ; integral kernel ; stability
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    Topics: Mathematics
    Notes: Abstract In this paper, the inverse boundary value problem of the hyperbolic system of first-order differential equations is discussed. The estimate of the solution and the quantitative analysis about its stability are obtained, and some stability criteria are established.
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  • 66
    ISSN: 1573-0646
    Keywords: Antagonist G ([Arg6, D-Trp7,9,,MePhe 8 ]-Substance P {6-11}) ; analytical characterization ; parenteral formulation ; stability ; oxidative degradation products
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Medicine
    Notes: Abstract The aim of this study was to develop a stable parenteral dosage form for the investigational cytotoxic drug [Arg6, D-Trp7,9, MePhe8]-Substance P {6-11} (Substance P Antagonist G; Antagonist G). Antagonist G bulk drug was structurally and analytically characterized. The drug exhibits excellent aqueous solubility, although relatively poor aqueous stability characteristics. Lyophilization was, therefore, selected as the manufacturing process. Differential scanning calorimetry studies were conducted to determine the freeze-drying cycle parameters which resulted in a stable, lyophilized formulation of Antagonist G. The prototype, containing 50 mg Antagonist G per vial, was found to be the optimal formulation in terms of solubility, length of the freeze-drying cycle, stability, and dosage requirements in the planned phase I clinical trials. Quality control of the freeze-dried formulation showed that the manufacturing process does not change the integrity of Antagonist G. Shelf life studies demonstrated that the formulation is stable for at least 3 years, when stored at 2–8°C in a dark environment. Oxidative degradation products of Antagonist G were isolated and structurally characterized by mass spectrometry, nuclear magnetic resonance spectroscopy, and infrared spectroscopy.
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    Applied mathematics and mechanics 16 (1995), S. 195-202 
    ISSN: 1573-2754
    Keywords: nonlinear ; stability ; Lyapunov function
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In the paper Lyapumov function for a fourth order linear system is given and stability of the trivial solutions to a class of fourth order nonlinear systems is studied.
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    Applied mathematics and mechanics 16 (1995), S. 635-642 
    ISSN: 1573-2754
    Keywords: analytic mechanics ; nonholonomic system ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The stability for the equilibrium states of Chaplygin's systems is considered. The equations of motion of Chaplygin's systems and the existence conditions of their equilibrium states are given. Some criteria of stability for the equilibrium. states of Chaplygin's systems are obtained. Two examples are finally given.
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    Applied mathematics and mechanics 17 (1996), S. 869-877 
    ISSN: 1573-2754
    Keywords: thermohaline double-diffusive system ; periodic solution ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A shortout analytic method of stability in strong nonlinear autonomous system is introduced into stability analysis of the thermohaline double-diffusive system. Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions. For linear periodic solution in infinitesimal motion, the existence range of monotomic branch and oscillatory branch are outilined. The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value µ c in this case of 0〈rs-rsc≪1. The stability conclusions under different direction of vortex are drawn out.
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    Applied mathematics and mechanics 18 (1997), S. 61-68 
    ISSN: 1573-2754
    Keywords: viscoplastic dynamics ; optimal control ; variational principle ; finite element method
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper presents the optimal control variational principle for Perzyna model which is one of the main constitutive relation of viscoplasticity in dynamics. And it could also be transformed to solve the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.
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    Applied mathematics and mechanics 19 (1998), S. 163-168 
    ISSN: 1573-2754
    Keywords: nonlinear equation ; stability ; Newton's method ; auto-adjustable damping method ; the vector of damping factors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For the strongly nonlinear problems, the solution obtained in the iterative process is always difficult, even divergent due to the numerical instability. It can not fulfill the engineering requirements. Newton's method and its variants can not settle this problem. As a result, the application of numerical simulation for the strongly nonlinear problems is limited. An auto-adjustable damping method has been presented in this paper. This is a further improvement of Newton's method with damping factor. A set of vector of damping factor is introduced. This set of vector can be adjusted continuously during the iterative process in accordance with the judgement and adjustment. An effective convergence coefficient and quichening coefficient are employed to relax the restricted requirements for the initial values and to shorten the iterative process. Then, the numerical stability will be ensured for the solution of complicated strongly nonlinear equations. Using this method, some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully. It can be used for the numerical simulation of strongly nonlinear problems in engineering such as nonlinear hydrodynamics and aerodynamics, heat transfer and structural dynamic response etc.
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    Applied mathematics and mechanics 19 (1998), S. 861-867 
    ISSN: 1573-2754
    Keywords: rotating fluids ; motion of body ; small disturbances ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the disturbances to a uniformly rotating ideal fluid with a sphere moving steadily along the axis of rotation are analysed by using linearization theory, the equations of disturbance, pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method of normal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that three are three kinds of possible forms of neutral disturbances.
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    Applied mathematics and mechanics 20 (1999), S. 912-916 
    ISSN: 1573-2754
    Keywords: delay ; neural network ; stability ; TN911.23 ; O332
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, by using Liapunov functional, some sufficient conditions are obtained for the stability of the equilibrium of a neural network model with delay of the type $$u'_i \left( t \right) = - b_i u_i \left( t \right) + \sum\limits_{j = 1}^n {T_{ij} f_j } \left( {\mu _j u_j \left( {t - \tau _j } \right)} \right) + c_i ,\tau _j \geqslant 0,i = 1,2 \cdots ,n.$$
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    Applied mathematics and mechanics 16 (1995), S. 515-520 
    ISSN: 1573-2754
    Keywords: singular perturbation ; nonlinear state regulator ; optimal control ; diagonalization technique
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper will seek the optimal control and corresponding trajectories of the singularly perturbed nonlinear state regulator problem. Under appropriate hypotheses, it will be possible to complete an asymptotic solution which is uniformly valid when σ→0.
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    Applied mathematics and mechanics 19 (1998), S. 457-462 
    ISSN: 1573-2754
    Keywords: neural networks ; equilibrium ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, some sufficient conditions are obtained for the global asymptotic stability of the equilibrium of neural networks with interneuronal transmission delays of the type $$x'_i (t) = - b_i x_i (t) + \sum\limits_{j = 1}^n {\omega _{\ddot y} f_j (x_j (t - \tau _j )) + p_i (t 〉 0;i = 1,2, \cdots ,n)} $$
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    Applied mathematics and mechanics 20 (1999), S. 1384-1388 
    ISSN: 1573-2754
    Keywords: nonlinear dynamic system ; bifurcation ; stability ; TB123 ; O322
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A computation algorithm based on the Poincaré Mapping in combination with Pseudo-Arc Length Continuation Method is presented for calculating the unstable response with saddle-node bifurcation, and the singularity, which occurs using the general continuation method combined with Poincaré Mapping to follow the path, is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too. There will be two directions in which the path can be continued at each point, but only one can be used. The method of determining the direction will be presented in the paper. It can be concluded that is method is effective in analysis of nonlinear dynamic system with saddle-node bifurcations.
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    Applied mathematics and mechanics 20 (1999), S. 233-240 
    ISSN: 1573-2754
    Keywords: viscoelasticity ; cylindrical shell ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the dynamic stability of a viscoelastic circular cylindrical shell subject to an axial compressive force and a uniformly distributed radial compressive load is discussed. By using the Laplace transformation, stability conditions of viscoelastic shell under constant loads are yielded. By using synthetically the classical dynamic methods, the various dynamical properties for the dynamical system defined by the viscoelastic shell and the effect of parameters on the stability of structure are obtained.
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    Discrete event dynamic systems 5 (1995), S. 343-355 
    ISSN: 1573-7594
    Keywords: optimal control ; FMS scheduling ; maximum principle ; instant setups
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    Topics: Mathematics
    Notes: Abstract A continuous time dynamic model of discrete scheduling problems for a large class of manufacturing systems is considered in the present paper. The realistic manufacturing based on multi-level bills of materials, flexible machines, controllable buffers and deterministic demand profiles is modeled in the canonical form of optimal control. Carrying buffer costs are minimized by controlling production rates of all machines that can be set up instantly. The maximum principle for the model is studied and properties of the optimal production regimes are revealed. The solution method developed rests on the iterative approach generalizing the method of projected gradient, but takes advantage of the analytical properties of the optimal solution to reduce significantly computational efforts. Computational experiments presented demonstrate effectiveness of the approach in comparison with pure iterative method.
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    Discrete event dynamic systems 5 (1995), S. 383-403 
    ISSN: 1573-7594
    Keywords: Discrete event systems ; stability ; boundedness ; Petri nets ; manufacturing systems
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    Topics: Mathematics
    Notes: Abstract Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of “logical” discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications including manufacturing systems and computer networks (Passino et al. 1994, Burgess and Passino 1994). In this paper we extend the conventional notions and analysis of uniform boundedness, uniform ultimate boundedness, practical stability, finite time stability, and Lagrange stability so that they apply to the class of logical DES that can be defined on a metric space. Within this stability-theoretic framework we show that the standard Petri net-theoretic notions of boundedness are special cases of Lagrange stability and uniform boundedness. In addition we show that the Petri ent-theoretic approach to boundedness analysis is actually a Lyapunov approach in that the net-theoretic analysis actually produces an appropriate Lyapunov function. Moreover, via the Lyapunov approach we provide a sufficient condition for the uniform ultimate boundedness of General Petri nets. To illustrate the Petri net results, we study the boundedness properties of a rate synchronization network for manufacturing systems. In addition, we provide a detailed analysis of the Lagrange stability of a single-machine manufacturing system that uses a priority-based part servicing policy.
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    Discrete event dynamic systems 8 (1998), S. 137-173 
    ISSN: 1573-7594
    Keywords: hybrid systems ; switched systems ; timed Petri nets ; stability ; supervisory control
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    Topics: Mathematics
    Notes: Abstract In this paper, timed Petri nets are used to model and control hybrid systems. Petri nets are used instead of finite automata primarily because of the advantages they offer in dealing with concurrency and complexity issues. A brief overview of existing results on hybrid systems that are based on Petri nets is first presented. A class of timed Petri nets named programmable timed Petri nets (PTPN) is then used to model hybrid systems. Using the PTPN, the stability and supervisory control of hybrid systems are addressed and efficient algorithms are introduced. In particular, we present sufficient conditions for the uniform ultimate boundness of hybrid systems composed of multiple linear time invariant plants which are switched between using a logical rule described by a Petri net. This paper also examines the supervisory control of a hybrid system in which the continuous state is transfered to a region of the state space in a way that respects safety specifications on the plant's discrete and continuous dynamics.
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    Discrete event dynamic systems 7 (1997), S. 209-232 
    ISSN: 1573-7594
    Keywords: Stochastic recurrence equations ; performance evaluation ; ergodicity ; stability ; subadditive ergodic theory
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    Topics: Mathematics
    Notes: Abstract This paper deals with the asymptotic behavior of the stochastic dynamics of discrete event systems. In this paper we focus on a wide class of models arising in several fields and particularly in computer science. This class of models may be characterized by stochastic recurrence equations in ℝK of the form T(n+1) = φ n+1(T(n)) where φ n is a random operator monotone and 1—linear. We establish that the behaviour of the extremas of the process T(n) are linear. The results are an application of the sub-additive ergodic theorem of Kingman. We also give some stability properties of such sequences and a simple method of estimating the limit points.
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    Discrete event dynamic systems 8 (1998), S. 353-364 
    ISSN: 1573-7594
    Keywords: scheduling ; optimal control ; time-decomposition methods
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    Topics: Mathematics
    Notes: Abstract This paper discusses dynamic methods for solving a class of multi-project scheduling problems in which rates of job performances are controllable and resources such as money, energy or manpower per time unit, are renewable and continuously divisible. The objective is to complete the projects as close to the common due date as possible. Two different ways of imposing sequential precedence relations between project jobs are explored by formulating two dynamic models and studying their relationships on the optimal solution. Efficient time-decomposition algorithms for finding either globally optimal schedules or lower bound guided near-optimal solutions are suggested and computationally tested.
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    Journal of mathematical imaging and vision 7 (1997), S. 309-323 
    ISSN: 1573-7683
    Keywords: relaxation labeling processes ; consistency ; growth transformations ; Liapunov functions ; stability
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    Topics: Mathematics
    Notes: Abstract We present some new results which definitively explain thebehavior of the classical, heuristic nonlinear relaxation labelingalgorithm of Rosenfeld, Hummel, and Zucker in terms of theHummel-Zucker consistency theory and dynamical systems theory. Inparticular, it is shown that, when a certain symmetry condition is met,the algorithm possesses a Liapunov function which turns out to be (thenegative of) a well-known consistency measure. This follows almostimmediately from a powerful result of Baum and Eagon developed in thecontext of Markov chain theory. Moreover, it is seen that most of theessential dynamical properties of the algorithm are retained when thesymmetry restriction is relaxed. These properties are also shown tonaturally generalize to higher-order relaxation schemes. Someapplications and implications of the presented results are finallyoutlined.
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    Discrete event dynamic systems 8 (1998), S. 175-201 
    ISSN: 1573-7594
    Keywords: hybrid systems ; optimal control ; calculus of variations ; manufacturing systems ; queueing systems ; nonsmooth optimization ; two point boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We propose a modeling framework for a class of hybrid systems which arise in many manufacturing environments and study related optimal control problems. In this framework, discrete entities have a state characterized by a temporal component whose evolution is described by event-driven dynamics, and a physical component whose evolution is described by time-driven dynamics. As a first step towards developing an optimal control theory for such hybrid systems, we formulate a problem consisting of a single-stage manufacturing process and use calculus of variations techniques to obtain structural properties and an explicit algorithm for deriving optimal policies.
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    Discrete event dynamic systems 9 (1999), S. 45-64 
    ISSN: 1573-7594
    Keywords: hybrid dynamic systems ; event feedback ; real-time scheduling ; stability
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    Topics: Mathematics
    Notes: Abstract Based on some practical engineering problems arising from process control and space-structure control, this paper studies a class of hybrid dynamic systems in which N plants are controlled by a central controller in sharing time manner, where the plants are described by differential equations and the controller works according to the mechanism of discrete events. An event feedback strategy is suggested to be a scheduling policy such that one and only one plant among N plants is chosen to be controlled at any time. Some conditions of asymptotical and exponential stability are then given and an exponential upper bound of states norm is also estimated for the event feedback scheduling strategy. An algorithm based on event feedback strategy is presented to determine the control laws of the plants to meet the given performance. An example follows to illustrate the application and effect of the results.
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    ISSN: 1573-7594
    Keywords: Decentralized scheduling ; manufacturing systems ; corridor policies ; stability
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    Notes: Abstract Sharifnia, Caramanis, and Gershwin [1991] introduced a class of policies for manufacturing systems, called by themlinear corridor policies. They proved that their stability can be discussed by the study of a simpler subset of such policies (cone policies). This paper revisits their work presenting a different description of the dynamics of the systems under study and explores it to device a necessary and sufficient condition for stability, obtained by the strengthening of the assumptions in Sharifnia et al. (1991). This condition is shown to be simply tested (M −1≥0) and valid for various realizations.
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    Discrete event dynamic systems 8 (1998), S. 37-54 
    ISSN: 1573-7594
    Keywords: Production planning ; stochastic dynamic programming ; vanishing discount approach ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the problem of production planning in a flexible manufacturing system consisting of a single or parallel failure-prone machines producing a number of different products. The objective is to choose the rates of production of the various products over time in order to meet their demands at the minimum long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellman equation in terms of directional derivatives has a solution consisting of the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem, and in specifying an optimal control policy in terms of the potential function. The results settle a hitherto open problem as well as generalize known results.
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  • 88
    ISSN: 1573-904X
    Keywords: proteins ; aggregation ; reconstitution ; lyophilization ; additives ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Purpose. Protein stabilization during lyophilization has previously focused on optimization of the formulation as well as the freezing and dehydration process parameters. However, the effect of the reconstitution medium has been largely neglected. We have investigated its effect on aggregate formation using recombinant keratinocyte growth factor (KGF). Methods. The protein was lyophilized under suboptimal conditions to induce aggregation and precipitation upon reconstitution with water. A series of additives were examined by UV spectrophotometry and size exclusion chromatography (SEC-HPLC) for their effects on decreasing the degree of KGF aggregation and precipitation by the increase in recovery of soluble monomer. Results. Several additives resulted in a significant reduction of aggregation, including sulfated polysaccharides, surfactants, polyphosphates, and amino acids. A similar effect was achieved by adjusting the ionic strength of the reconstitution medium. SEC-HPLC indicated that the amount of soluble monomer was also increased by these additives suggesting that the recovery of the soluble protein correlates with the native, monomeric protein. Conclusions. These results suggest that optimization of reconstitution conditions will be a useful methodology for increasing the recovery of soluble, active proteins and that for KGF, the recovery of the soluble protein correlates with the native, monomeric form.
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  • 89
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    Pharmaceutical research 12 (1995), S. 599-604 
    ISSN: 1573-904X
    Keywords: famotidine ; degradation ; isothermal ; nonisothermal ; kinetics ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The kinetics of hydrolysis of famotidine in aqueous solution was studied by isothermal and nonisothermal method over the pH range of 1.71 to 10.0. Nonisothermal kinetics was studied with the purpose of determining its use in the establishment of the expiration date of pharmaceutical preparations, particularly drugs in solutions and for assessment of stability characteristics of pharmaceutical formulations during the development stage. A comparison of isothermal (55, 70 and 85°C) and nonisothermal kinetics was performed. Aqueous solutions of famotidine were buffered at pH 1.71, 2.24, 2.66, 4.0, 8.5, 9.0 and 10.0 were used. In the nonisothermal studies, the temperature rate of the reaction was continuously varied throughout the experiment. The energies of activation were found to be in close agreement for isothermal and nonisothermal studies, indicating that nonisothermal studies may save considerable amount of time in the early stages of drug development and stability testing. Logk-pH profiles were constructed for 55, 70 and 85°C from the first-order rate constants obtained from isothermal studies at pH values ranging from 1.71 to 10.00. The pH-rate profile indicated that famotidine undergoes specific acid catalysis in the acidic region and general base catalysis in the alkaline region. Hydrolysis in the acidic and alkaline media resulted in the formation of four and five degradation products, respectively. A possible degradation pathway for the acidic and alkaline hydrolysis was discussed.
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  • 90
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    Pharmaceutical research 12 (1995), S. 1371-1375 
    ISSN: 1573-904X
    Keywords: prodrug ; bispilocarpic acid diester ; hydroxypropyl-β-cyclodextrin ; inclusion complex ; solubility ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Purpose. The effects of 2-hydroxypropyl-β-cyclodextrin (HP-β-CD) on the aqueous solubility and stability of two lipophilic bispilocarpine prodrugs were investigated at pH 7.4. Methods. The solubility of prodrugs was studied by phase-solubility method (0–72.5 mM HP-β-CD). The stability of one of the prodrugs was investigated as a function of temperature (40°C–70°C) and HP-β-CD concentration (0–72.5 mM). The apparent rate constants (k 1, k 2) for degradation of prodrug in 1:1 and 1:2 inclusion complexes and apparent stability constants (K 1:1, K l:2) were calculated by the curve-fitting method. Results. The phase-solubility diagrams were classified as Ap-type and the apparent stability constants (K l:l, K l:2) for 1:1- and 1:2-inclusion complexes were calculated to be 143–815 M−l and 29–825 M−1, respectively. The stability of prodrug increased as a function of HP-β-CD concentration over the studied temperature range. The shelf-life (t 90%, calculated by the Arrhenius equation) of the prodrug in 72.5 mM HP-β-CD solution increased 5.1-fold and 6.1-fold at 25°C and 4°C, respectively. Conclusions. The solubility of the prodrugs was shown to increase markedly in phase-solubility studies. The degradation rate of prodrug in stability studies was shown to be slower in the l:2-complex than in the l:l-complex and the relative amounts of complex species were found to be dependent on CD concentration.
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  • 91
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    Pharmaceutical research 12 (1995), S. 715-719 
    ISSN: 1573-904X
    Keywords: salbutamol base drug ; oleic acid ; propellant ; metered-dose inhaler ; stability ; adsorption
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The distribution of oleic acid between Salbutamol base drug and the solvent in metered-dose inhalers (MDI's) has been investigated. The equilibrium surfactant concentration in the drug dispersions has been determined using a colorimetric method. The samples examined contained Salbutamol base drug particles and oleic acid dispersed in different propellant blends of freon 11 and 12. The maximum equilibrium concentration observed depended on the propellant blend used. The propellant blend and the distribution of the surfactant affected the dispersion stability. The effect of the surfactant is illustrated by the adsorption isotherm for oleic acid onto the Salbutamol particles. The results are correlated with zeta-potentials and particle size measurements made on similar systems in order to characterize the properties of surfactant stabilized MDI's.
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  • 92
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    Lithuanian mathematical journal 39 (1999), S. 20-32 
    ISSN: 1573-8825
    Keywords: Schrödinger equation ; explicit finite-difference schemes ; stability ; energy conservation ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider three-level explicit schemes for solving the nonlinear variable coefficient Schrödinger-type equation. Using spectral and energy methods we establish the stability and convergence of these schemes. The existence of discrete conservation laws is investigated. General results are applied for the DuFort-Frankel and leap-frog diffenrence schemes.
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  • 93
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    Mathematical notes 60 (1996), S. 383-388 
    ISSN: 1573-8876
    Keywords: optimal control ; nonlinear singular system ; state constraints ; penalty method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A control system described by a nonlinear equation of parabolic type is considered in the situation where there may be no global solution. A particular optimal control problem subject to state constraints is studied. A proof of the existence of an optimal control is presented. The penalty method is used to obtain necessary conditions for optimal control. A proof of the convergence of this method is given. The successive approximation method is used to obtain an approximate solution for the conditions derived.
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  • 94
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    Mathematical notes 63 (1998), S. 396-400 
    ISSN: 1573-8876
    Keywords: ordinary differential equations ; fast and slow time ; periodic solutions ; existence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a system of ordinary first-order differential equations. The right-hand sides of the system are proportional to a small parameter and depend almost periodically on fast time and periodically on slow time. With this system, we associate the system averaged over fast time. We assume that the averaged system has a structurally unstable periodic solution. We prove a theorem on the existence and stability of almost periodic solutions of the original system.
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  • 95
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    Mathematical notes 60 (1996), S. 269-273 
    ISSN: 1573-8876
    Keywords: abstract Cauchy problem ; uniform correctness ; perturbation theory ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The stability of the uniform correctness of the Cauchy problem $$u(t) + \frac{k}{t}u'(t) = \mathbb{A}u(t)$$ ,t〉0,u(0)=u 0,u′(0)=0 fork〉0 with respect to perturbations of the operator $$\mathbb{A}$$ is studied.
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  • 96
    ISSN: 1573-904X
    Keywords: polymer implant ; brain cancer ; carmustine ; polyanhydride ; stability ; controlled release
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
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  • 97
    ISSN: 1573-904X
    Keywords: nanoparticles ; poly(lactic acid) ; poly(lactic acid-co-ethylene oxide) ; freeze-drying ; stability ; flow cytometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Purpose. To investigate the feasibility of producing freeze-dried poly-(ethylene oxide) (PEO)-surface modified nanoparticles and to study their ability to avoid the mononuclear phagocytic system (MPS), as a function of the PEO chain length and surface density. Methods. The nanoparticles were produced by the salting-out method using blends of poly(D,L-lactic acid) (PLA) and poly(D,L-lactic acid-co-ethylene oxide) (PLA-PEO) copolymers. The nanoparticles were purified by cross-flow filtration and freeze-dried as such or with variable amounts of trehalose as a lyoprotectant. The redispersibility of the particles was determined immediately after freeze-drying and after 12 months of storage at −25° C. The uptake of the nanoparticles by human monocytes was studied in vitro by flow cytometry. Results. PLA-PEO nanoparticles could be produced from all the polymeric blends used. Particle aggregation after freeze-drying was shown to be directly related to the presence of PEO. Whereas this problem could be circumvented by use of trehalose, subsequent aggregation was shown to occur during storage. These phenomena were possibly related to the specific thermal behaviours of PEO and trehalose. In cell studies, a clear relationship between the PEO content and the decrease of uptake was demonstrated. Conclusions. The rational design of freeze-dried PEO-surface modified nanoparticles with potential MPS avoidance ability is feasible by using the polymer blends approach combined with appropriate lyoprotection and optimal storage conditions.
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  • 98
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    Pharmaceutical research 15 (1998), S. 1702-1707 
    ISSN: 1573-904X
    Keywords: stability ; isothermal ; nonisothermal ; thymopentin
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Purpose. The degradation kinetics of thymopentin (RKDVY) and its analogs (RKDVW and RPDVY) in aqueous solution was studied by isothermal and nonisothermal methods. Methods. The isothermal decomposition of thymopentin and its analogs was investigated as a function of pH (2−10), temperature (37, 57, and 80°C) and ionic strength (μ = 0.02 to 1). Nonisothermal decomposition studies were performed using a linear temperature programmer. The temperature increasing rate was set to 0.25°C per hour and the temperature interval varied from 40 to 88°C. Results. The decomposition of thymopentin and its analogs followed first order kinetics. The dependence of the rate constant on temperature followed a linear Arrhenius plot. This indicated that the degradation mechanism of thymopentin and its analogs might be the same within the temperature range studied. The energies of activation were found to be in close agreement for the isothermal and nonisothermal studies, suggesting that the nonisothermal studies may save considerable amount of time in the early stages of drug development. The logK-pH profile of thymopentin suggests that maximum stability is achieved in the pH range of 6−8. Conclusions. These results indicate that the nonisothermal methodology provides an attractive alternative to isothermal methods, as it requires a much lower amount of both material and time, to determine the peptide stability and to estimate the shelf-life for peptide pharmaceutical preparations.
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  • 99
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    Pharmaceutical research 13 (1996), S. 1008-1014 
    ISSN: 1573-904X
    Keywords: amphotericin B ; lecithin ; emulsion ; stability ; monolayer ; low-dimensional structures
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Purpose. To study the interaction of the polyene antifungal amphotericin B with phospholipid Langmuir monolayers and to correlate with stability of phospholipid-stabilized drug emulsions. Methods. Pressure—area isotherms of mixed monolayers of amphotericin B (0–20 mol%) and different phospholipid types were recorded using conventional Langmuir trough methods. Emulsion stability of amphotericin B-containing lipid emulsions was measured using dynamic light scattering. Results. Incorporation of amphotericin B into monolayers composed of saturated phospholipids (Lipoid E80-3) had a profound effect on the shape of the isotherm. This effect was directly related to the concentration of amphotericin B in the monolayer. At high drug concentrations, the shape of the isotherms became progressively similar to that of pure DPPC, thus exhibiting regions attributable to phospholipid in different phase states. This effect on isotherm shape was not observed following incorporation of the drug into monolayers composed of the equivalent unsaturated lecithin (Lipoid E80). Conclusions. These results are interpreted as indicating the formation of an amphotericin B-phospholipid complex, resulting in phase separation within the monolayer. The extent and nature of this phase separation was dependent on both the concentration of drug in the system, and the saturation state of the phospholipid component. The relevance of these observations to the stability of amphotericin B drug emulsions stabilised by saturated and unsaturated phospholipid emulsifiers is discussed. These observations may also be relevant to the toxicity of these, and other novel amphotericin B formulations.
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  • 100
    ISSN: 1573-904X
    Keywords: granulocyte-colony stimulating factor (G-CSF) ; PEG-ylation ; N-terminal ; stability ; site specific
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Purpose. The liquid stability of rhG-CSF was investigated after polyethylene glycol (PEG) with an average molecular weight of 6000 daltons was covalently attached to the N-terminal methionine residue. Methods. The conjugation methods chosen for modifying the N-terminal residue were alkylation and acylation. The N-terminally PEGylated rhG-CSF conjugates were purified by cation exchange chromatography. The physical characterization methods of SDS-PAGE, endoproteinase peptide mapping, circular dichroism and in-vivo bioassay were used to test for differences between the PEG-rhG-CSF molecules. Results. Physical characterization indicated no apparent differences in the rhG-CSF molecules that were conjugated with either method. Stability, in liquid at elevated temperatures, of these conjugated molecules indicated that the primary pathway of degradation was aggregation. Conjugation through alkylation offered the distinct advantage of decreasing, by approximately 5 times, the amount of aggregation present as compared to acylation. Conclusions. We suggest, that the increased stability observed for the molecules utilizing the alkylation conjugation method may be due to the preservation of charge on the alpha amino group of rhG-CSF.
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