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  • Articles  (1,425)
  • kinetics  (727)
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  • 01. Atmosphere::01.01. Atmosphere::01.01.07. Volcanic effects
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  • Articles  (1,425)
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  • 101
    Electronic Resource
    Electronic Resource
    On the guaranteed throughput and efficiency of closed re-entrant lines (1998)
    Springer
    Queueing systems 28 (1998), S. 33-54 
    Details
    ISSN: 1572-9443
    Keywords: queueing networks ; throughput ; closed networks ; efficiency ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A closed network is said to be “guaranteed efficient” if the throughput converges under all non-idling policies to the capacity of the bottlenecks in the network, as the number of trapped customers increases to infinity. We obtain a necessary condition for guaranteed efficiency of closed re-entrant lines. For balanced two-station systems, this necessary condition is almost sufficient, differing from it only by the strictness of an inequality. This near characterization is obtained by studying a special type of virtual station called “alternating visit virtual station”. These special virtual stations allow us to relate the necessary condition to certain indices arising in heavy traffic studies using a Brownian network approximation, as well as to certain policies proposed as being extremal with respect to the asymptotic loss in the throughput. Using the near characterization of guaranteed efficiency we also answer the often pondered question of whether an open network or its closed counterpart has greater throughput - the answer is that neither can assure a greater guaranteed throughput.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019199022922
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  • 102
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    Stability of token passing rings (1992)
    Springer
    Queueing systems 11 (1992), S. 7-33 
    Details
    ISSN: 1572-9443
    Keywords: Token passing rings ; stability ; substability ; ergodicity ; Markov chains ; Loynes' scheme ; stochastically dominant ; Little's formula ; regenerative processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract A sufficient stability condition for the standard token passing ring has been “known” since the seminal paper by Kuehn in 1979. However, this condition was derived without formal proof, and the proof seems to be of considerable interest to the research community. In fact, Watson observed that in the performance evaluation of token passing rings, “it is convenient to derive stability conditions ... (without proof)”. Our intention is to fill this gap, and to provide a formal proof of thesufficient and necessary stability condition for the token passing ring. In this paper, we present the case when the arrival process to each queue is Poisson but service times and switchover times are generally distributed. We consider in depth a gatedl-limited (l≤ ∞) service discipline for each station. We also indicate that the basic steps of our technique can be used to study the stability of some other multiqueue systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01159285
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  • 103
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    Stability of a three‐station fluid network (1999)
    Springer
    Queueing systems 33 (1999), S. 293-325 
    Details
    ISSN: 1572-9443
    Keywords: stability ; fluid models ; multiclass queueing networks ; piecewise linear Lyapunov functions ; linear Lyapunov functions ; monotone global stability ; static buffer priority disciplines
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper studies the stability of a three‐station fluid network. We show that, unlike the two‐station networks in Dai and Vande Vate [18], the global stability region of our three‐station network is not the intersection of its stability regions under static buffer priority disciplines. Thus, the “worst” or extremal disciplines are not static buffer priority disciplines. We also prove that the global stability region of our three‐station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three‐station network. We also show that the LP proposed by Bertsimas et al. [1] does not characterize either the global stability region or even the monotone global stability region of our three‐station network. Further, we demonstrate that the LP related to the linear Lyapunov function proposed by Chen and Zhang [11] does not characterize the stability region of our three‐station network under a static buffer priority discipline.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019184331042
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  • 104
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    A Multiclass Feedback Queueing Network with a Regular Skorokhod Problem (2000)
    Springer
    Queueing systems 36 (2000), S. 327-349 
    Details
    ISSN: 1572-9443
    Keywords: multiclass networks ; networks with feedback ; Skorokhod Problem ; Skorokhod Mapping ; Lipschitz continuity ; stability ; load conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a four-class two-station network with feedback, with fluid inputs and a head-of-the-line generalized processor sharing discipline at each station. We derive the Skorokhod Problem associated with the network and obtain algebraic sufficient conditions for Lipschitz continuity of the associated Skorokhod Map. This provides the first example of a multiclass network with feedback for which the associated Skorokhod Problem has been proved to be regular. As an elementary application, we show that under the conditions which guarantee Lipschitz continuity the network is stable if and only if the usual load conditions apply.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011037419624
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  • 105
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    Analytical investigation of non-linear stability of the Lagrangian pointL 4 around the commensurability 1:2 (1995)
    Springer
    Celestial mechanics and dynamical astronomy 63 (1995), S. 205-225 
    Details
    ISSN: 1572-9478
    Keywords: Restricted three body problem ; Lagrangian points ; resonances ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The problem of stability of the Lagrangian pointL 4 in the circular restricted problem of three bodies is investigated close to the 1 : 2 commensurability of the long and short period libration. By stability we define boundedness of the solution for a given initial finite displacement from the equilibrium point as function of the mass parameter μ close to the commensurability. A rigorous treatment close to the resonance condition is possible using a transformation that diagonalizes the matrix related to the linear part of the equations of motion. The so obtained equations are further transformed to action angle type variables. Then using an isolated resonance approach, only the slowly varying terms are kept in the equations and two independent isolating first integrals can be found. These integrals finally enable us to solve the stability problem in an exact way. The so obtained results are compared to numeric integration of the equations of motion and are found to be in perfect agreement.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00693415
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  • 106
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    Effect of perturbed potentials on the non-linear stability of libration pointL 4 in the restricted problem (1994)
    Springer
    Celestial mechanics and dynamical astronomy 59 (1994), S. 345-374 
    Details
    ISSN: 1572-9478
    Keywords: Lagrangian points ; stability ; oblate primary
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The non-linear stability of the libration pointL 4 in the restricted problem has been studied when there are perturbations in the potentials between the bodies. It is seen that the pointL 4 is stable for all mass ratios in the range of linear stability except for three mass ratios depending upon the perturbing functions. The theory is applied to the following four cases: (i) There are no perturbations in the potentials (classical problem). (ii) Only the bigger primary is an oblate spheroid whose axis of symmetry is perpendicular to the plane of relative motion (circular) of the primaries. (iii) Both the primaries are oblate spheroids whose axes of symmetry are perpendicular to the plane of relative motion (circular) of the primaries. (iv) The primaries are spherical in shape and the bigger is a source of radiation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00692102
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  • 107
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    Bifurcation Phenomena from Standing Pulse Solutions in Some Reaction-Diffusion Systems (2000)
    Springer
    Journal of dynamics and differential equations 12 (2000), S. 117-167 
    Details
    ISSN: 1572-9222
    Keywords: singular perturbation ; standing pulses ; stability ; Hopf bifurcation ; reaction-diffusion system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Bifurcation phenomena from standing pulse solutions of the problem $$\varepsilon \tau u_t = \varepsilon ^2 u_{xx} + f(u,v),{\text{ }}v_t = v_{xx} + g(u,v)$$ is considered. ε(〉0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009098719440
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  • 108
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    Equivariant multiparameter bifurcation via singularity theory (1993)
    Springer
    Journal of dynamics and differential equations 5 (1993), S. 189-218 
    Details
    ISSN: 1572-9222
    Keywords: Equivariant bifurcation ; symmetry ; singularity ; equivariant jets and transversality ; normal forms ; universal unfolding ; stability ; structural stability ; 58F14 ; 58E07 ; 58C27
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The theoretical machinery from singularity theory introduced by Golubitsky, Stewart, and Schaeffer, to study equivariant bifurcation problems, is completed and expanded while generalized to the multiple parameter context. In this setting the finite determinacy theorems or normal forms, the stability of equivariant bifurcation problems, and the structural stability of the universal unfolding are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01053160
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  • 109
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    A free boundary problem modeling thermal instabilities: Stability and bifurcation (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 447-486 
    Details
    ISSN: 1572-9222
    Keywords: Free boundary problems ; gasless combustion ; stability ; Hopf bifurcation ; 35R35 ; 35B40 ; 80A25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we analyze a simple free boundary model associated with solid combustion and some phase transition processes. There is strong evidence that this “one-phase” model captures all major features of dynamical behavior of more realistic (and complicated) combustion and phase transition models. The principal results concern the dynamical behavior of the model as a bifurcation parameter (which is related to the activation energy in the case of combustion) varies. We prove that the basic uniform front propagation is asymptotically stable against perturbations for the bifurcation parameter above the instability threshold and that a Hopf bifurcation takes place at the threshold value. Results of numerical simulations are presented which confirm that both supercritical and subcritical Hofp bifurcation may occur for physically reasonable nonlinear kinetic functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02218858
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  • 110
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    Discrete time semigroup transformations with random perturbations (1997)
    Springer
    Journal of dynamics and differential equations 9 (1997), S. 463-505 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02227491
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  • 111
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    On Stability and Boundedness for Lipschitzian Differential Inclusions: The Converse of Lyapunov's Theorems (1997)
    Springer
    Set-valued analysis 5 (1997), S. 377-390 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008603707291
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  • 112
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    Singularly perturbed differential inclusions: An averaging approach (1996)
    Springer
    Set-valued analysis 4 (1996), S. 361-374 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00436111
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  • 113
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    Implicit Multifunction Theorems (1999)
    Springer
    Set-valued analysis 7 (1999), S. 209-238 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008775413250
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  • 114
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    Perturbed unstable variational inequalities with unbounded operators on approximately given sets (1993)
    Springer
    Set-valued analysis 1 (1993), S. 393-402 
    Details
    ISSN: 1572-932X
    Keywords: Primary: 49J40, 65K10, 47A55, 47H05, 65L20 ; Variational inequality ; perturbation ; unbounded and nonsmooth operators ; convex sets ; Hausdorff distance ; regularization ; monotonicity ; convergence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains Ω are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01027828
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  • 115
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    Stability and performance analysis of rate-based feedback flow controlled ATM networks (1998)
    Springer
    Queueing systems 29 (1998), S. 129-159 
    Details
    ISSN: 1572-9443
    Keywords: rate-based feedback control ; ATM networks ; stability ; optimal algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Motivated by ABR class of service in ATM networks, we study a continuous time queueing system with a feedback control of the arrival rate of some of the sources. The feedback about the queue length or the total workload is provided at regular intervals (variations on it, especially the traffic management specification TM 4.0, are also considered). The propagation delays can be nonnegligible. For a general class of feedback algorithms, we obtain the stability of the system in the presence of one or more bottleneck nodes in the virtual circuit. Our system is general enough that it can be useful to study feedback control in other network protocols. We also obtain rates of convergence to the stationary distributions and finiteness of moments. For the single botterneck case, we provide algorithms to compute the stationary distributions and the moments of the sojourn times in different sets of states. We also show analytically (by showing continuity of stationary distributions and moments) that for small propagation delays, we can provide feedback algorithms which have higher mean throughput, lower probability of overflow and lower delay jitter than any open loop policy. Finally these results are supplemented by some computational results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019127929282
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  • 116
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    Dynamic scheduling in multiclass queueing networks: Stability under discrete-review policies (1999)
    Springer
    Queueing systems 31 (1999), S. 171-206 
    Details
    ISSN: 1572-9443
    Keywords: scheduling ; open multiclass queueing networks ; discrete-review policies ; fluid models ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value r k (q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable. In such a policy, system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed. Stability is proved by combining elementary large deviations theory with an analysis of an associated fluid control problem. These results are extended to systems with class dependent setup times as well as systems with alternate routing and admission control capabilities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019106213778
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  • 117
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    Queues with service times and interarrival times depending linearly and randomly upon waiting times (1990)
    Springer
    Queueing systems 6 (1990), S. 335-351 
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    ISSN: 1572-9443
    Keywords: State-dependent service and interarrival times ; Lindley equation ; recursive stochastic equations ; stability ; stochastic comparisons ; normal approximations ; scheduling arrivals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a modification of the standardG/G/1 queue with unlimited waiting space and the first-in first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. We determine when the waiting-time distributions converge to a proper limit and we develop approximations for this steady-state limit, primarily by applying previous results of Vervaat [21] and Brandt [4] for the unrestricted recursionY n+1=C n Y n +X n . Particularly appealing for applications is a normal approximation for the stationary waiting time distribution in the case when the queue only rarely becomes empty. We also consider the problem of scheduling successive interarrival times at arrival epochs, with the objective of achieving nearly maximal throughput with nearly bounded waiting times, while making the interarrival time sequence relatively smooth. We identify policies depending linearly and deterministically upon the work in the system which meet these objectives reasonably well; with these policies the waiting times are approximately contained in a specified interval a specified fraction of time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02411482
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  • 118
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    Reaction Between Copper Nitrate Hydrate and Methoxydimethyloctylsilane in Methanol (1998)
    Springer
    Journal of solution chemistry 27 (1998), S. 1123-1138 
    Details
    ISSN: 1572-8927
    Keywords: Sol–gel processing ; hydrolysis ; condensation ; kinetics ; methoxydimethyloctylsilane ; copper nitrate hydrate ; phase diagram
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The reaction rate was determined for copper nitrate hydrate with methoxydimethyloctylsilane (MDOS) in methanol. The rate constants of hydrolysis and condensation were established by quantitative measurement of the product and Karl Fischer water determination. The reaction with the hydrated copper salt resulted in the phase separation of an insoluble product from the reaction mixture. The structure of the product was determined, by Fourier Transform Infrared Spectrometry (FTIR) and Nuclear Magnetic Resonance (NMR) to be a dimer of the MDOS. The results showed the alcohol, producing condensation reaction was negligible in the formation of the dimer. contrary to the case for the well-known reaction by trialkoxysilanes and tetraalkoxysilanes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022662017881
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  • 119
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    Enthalpies of reaction and reaction rates by flow microcalorimetry: Ester hydrolysis in basic medium (1980)
    Springer
    Journal of solution chemistry 9 (1980), S. 59-73 
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    ISSN: 1572-8927
    Keywords: Enthalpies of reaction ; heats of reaction ; kinetics ; ester hydrolysis ; microcalorimetry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The conditions under which the Picker flow microcalorimeter can be used to measure enthalpies and rates of reactions were investigated. For this purpose, systematic studies were made of the enthalpies of neutralization of HCl, HBr, HNO 3 , acetic, proprionic, and butyric acids with NaOH, enthalpies of hydrolysis of methyl and ethyl acetate with NaOH, and the reaction rates of the ester hydrolysis with NaOH. The general procedure and various sources of error are discussed and it is concluded that enthalpies of slow reactions can be measured to about 1% when the calorimeter is operated in the quasi-isothermal mode and the reaction rates to about 3% when operated in the quasi-adiabatic mode.
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    URL: http://dx.doi.org/10.1007/BF00650137
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  • 120
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    Activity and stability of Cu/ZnO/Al2O3 catalyst promoted with B2O3 for methanol synthesis (2000)
    Springer
    Catalysis letters 68 (2000), S. 55-58 
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    ISSN: 1572-879X
    Keywords: promoting effect ; B2O3 ; Cu/ZnO/Al2O3 catalyst ; methanol synthesis ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The addition of B2O3 to a Cu/ZnO/Al2O3 catalyst increased the activity of the catalyst for methanol synthesis after an induction period during the reaction. The stability of the B2O3-containing Cu/ZnO/Al2O3 catalyst was greatly improved by the addition of a small amount of colloidal silica to the catalyst.
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    URL: http://dx.doi.org/10.1023/A:1019010831562
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    On the kinetics of degradation of cellulose (1997)
    Springer
    Cellulose 4 (1997), S. 1-5 
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    ISSN: 1572-882X
    Keywords: paper ; degradation ; ageing ; kinetics ; modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018408515574
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  • 122
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    Stability and excitation of potassium promoter in iron catalysts – the role of KFeO2 and KAlO2 phases (2000)
    Springer
    Catalysis letters 67 (2000), S. 129-134 
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    ISSN: 1572-879X
    Keywords: potassium desorption ; stability ; excitation ; iron catalyst ; Rydberg atoms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Well‐characterized catalyst model compounds of KAlO2 and KFeO2 are investigated by thermal desorption of potassium from the material. The desorbing fluxes of ions, atoms and highly excited states (field ionizable Rydberg states) were studied with surface and field ionization detectors in a vacuum apparatus. From the Arrhenius plots the activation energies for desorption of K and K+ were determined. The chemical state of potassium at the surfaces is concluded to be: ionic on KAlO2 (with the K desorption barrier of 1.76 eV) and covalent on KFeO2 (barrier of 2.73 eV). These results agree with the data obtained earlier for industrial catalysts for ammonia and styrene production. They are interpreted in terms of the Schottky cycle, which is completed for KAlO2 and fails for KFeO2. This failure indicates a non‐equilibrium desorption process. K Rydberg states are only found to desorb from KFeO2, in agreement with the suggestion that such states in some way are responsible for the catalytic activity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019013504729
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  • 123
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    Prediction of paper permanence by accelerated aging I. Kinetic analysis of the aging process (1996)
    Springer
    Cellulose 3 (1996), S. 243-267 
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    ISSN: 1572-882X
    Keywords: aging tests ; cellulose degradation ; durability ; kinetics ; paper properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The validity of accelerated aging tests to predict and rank papers on their permanence has been under question, preventing the development of performance-based standards for permanent paper. We conducted a general kinetic analysis to investigate the aging process of paper. A general kinetic model is proposed to describe the depolymerization of cellulose. Experimentally it was shown that in the case of aging, cellulose degradation follows classic first-order kinetics as a special case of our general kinetic model. The Arrhenius equation was critically re-examined for the case of a multiple reaction system. It was shown analytically that the Arrhenius equation is still applicable when certain conditions are met. This was convincingly supported by experimental results. We also analysed the dependence of the degradation rate on the moisture content and hydrogen ion concentration. By conducting systematic experiments on these two factors, a general and quantitative relationship was established to explain the contribution of each factor and their interactions. Finally, based on this kinetic analysis, the effects of storage conditions on the life expectancy of paper were estimated.
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    A correlation of gas solubilities and kinetics of hydrolysis in binary aqueous mixtures (1974)
    Springer
    Journal of solution chemistry 3 (1974), S. 881-887 
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    ISSN: 1572-8927
    Keywords: Binary aqueous mixtures ; solubilities ; kinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A treatment which predicts the solubilities of gases in solvent mixtures is examined in the context of the analysis of kinetic data for reactions in aqueous mixtures. The treatment is qualitatively successful to some extent in resolving the effects of changes in the initial state of the reacting substrate in the activation parameters.
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    Consumer memory and price fluctuations in commodity markets: An integrodifferential model (1989)
    Springer
    Journal of dynamics and differential equations 1 (1989), S. 299-325 
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    ISSN: 1572-9222
    Keywords: Commodity markets ; time delays ; stability ; Hopf bifurcation ; 34K15 ; 45J05 ; 90A16
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A model for the dynamics of price adjustment in a single commodity market is developed. Nonlinearities in both supply and demand functions are considered explicitly, as are delays due to production lags and storage policies, to yield a nonlinear integrodifferential equation. Conditions for the local stability of the equilibrium price are derived in terms of the elasticities of supply and demand, the supply and demand relaxation times, and the equilibrium production-storage delay. The destabilizing effect of consumer memory on the equilibrium price is analyzed, and the ensuing Hopf bifurcations are described.
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    Stable steady state of some population models (1992)
    Springer
    Journal of dynamics and differential equations 4 (1992), S. 161-190 
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    ISSN: 1572-9222
    Keywords: Delay differential equations ; equilibrium ; stability ; limiting equations ; population dynamics ; 34K20 ; 34K25 ; 92A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Applying an analytical method and several limiting equations arguments, some sufficient conditions are provided for the existence of a unique positive equilibriumK for the delay differential equationx=−γx+D(x t ), which is the general form of many population models. The results are concerned with the global attractivity, uniform stability, and uniform asymptotic stability ofK. Application of the results to some known population models, which shows the effectiveness of the methods applied here, is also presented.
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    The relative variance criterion for stability of delay systems (1993)
    Springer
    Journal of dynamics and differential equations 5 (1993), S. 105-128 
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    ISSN: 1572-9222
    Keywords: Delay system ; stability ; relative variance ; dynamical disease
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new approach to the study of delay systems, applicable to physiological control systems and other systems where little information about the time delays is available, is examined. The method is based on the fact that stability information can be deduced from the statistical properties of the probability distribution that encodes the structure of the time delay. The main statistical variables used are the usual expectation parameter,E, and a modified variance, calledrelative variance and denotedR, that is invariant under time scale changes. Recent work of the author has shown that stability often improves asR increases whileE remains fixed. A four-parameter family of delay models is analysed in this paper, and the (E, R) pair is found to be a reliable indicator of stability over the global parameter domain of the family.
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    Stability of standing waves for the generalized Davey-Stewartson system (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 325-334 
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    ISSN: 1572-9222
    Keywords: Nonlinear Schrödinger equations ; anisotropic standing waves ; stability ; concentration compactness principle ; Davey-Stewartson system ; 35Q35 ; 35B35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the stability of standing waves for a nonlinear Schrödinger equation, which derives from the generalized Davey-Stewartson system in the elliptic-elliptic case. We prove the existence of stable standing waves under certain conditions.
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    The index of lyapunov stable fixed points in two dimensions (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 631-637 
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    ISSN: 1572-9222
    Keywords: stability ; fixed point index ; periodic solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR 2 has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.
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    Stability of Linear Inequality Systems Measured by the Hausdorff Metric (2000)
    Springer
    Set-valued analysis 8 (2000), S. 253-266 
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    ISSN: 1572-932X
    Keywords: Hausdorff metric ; linear inequality systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we propose a Hausdorff metric to measure the “distance” between two linear inequality systems on a real normed space X. For this topology, which comes through a pseudo-metric in the set Σ of linear inequality systems, the closedness of the feasible set mapping is studied, and at the same time a characterization of the stability of the subset Σ c of consistent sytems is given.
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    Stability Properties of a Bond Portfolio Management Problem (2000)
    Springer
    Annals of operations research 99 (2000), S. 251-265 
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    ISSN: 1572-9338
    Keywords: stochastic programming ; bond portfolio management ; interest ratescenarios ; stability ; sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients – the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.
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    Dam processes with state dependent batch sizes and intermittent production processes with state dependent rates (1996)
    Springer
    Queueing systems 24 (1996), S. 37-57 
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    ISSN: 1572-9443
    Keywords: dam ; storage process ; saturation rule ; intermittent production ; state dependent rates ; state dependent jumps ; stability ; positive Harris recurrence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider a dam process with a general (state dependent) release rule and a pure jump input process, where the jump sizes are state dependent. We give sufficient conditions under which the process has a stationary version in the case where the jump times and sizes are governed by a marked point process which is point (Palm) stationary and ergodic. We give special attention to the Markov and Markov regenerative cases for which the main stability condition is weakened. We then study an intermittent production process with state dependent rates. We provide sufficient conditions for stability for this process and show that if these conditions are satisfied, then an interesting new relationship exists between the stationary distribution of this process and a dam process of the type we explore here.
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    On the stability of retrial queues (1997)
    Springer
    Queueing systems 26 (1997), S. 343-363 
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    ISSN: 1572-9443
    Keywords: retrial queues ; stability ; ergodicity ; renovation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ 〉 λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers.
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    Recurrence and transience properties of some neural networks: an approach via fluid limit models (1999)
    Springer
    Queueing systems 32 (1999), S. 99-130 
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    ISSN: 1572-9443
    Keywords: neural network ; inhibition ; stability ; Markov process ; fluid limit ; Harris-recurrence ; transience
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The subject of the paper is the stability analysis of some neural networks consisting of a finite number of interacting neurons. Following the approach of Dai [5] we use the fluid limit model of the network to derive a sufficient condition for positive Harris-recurrence of the associated Markov process. This improves the main result in Karpelevich et al. [11] and, at the same time, sheds some new light on it. We further derive two different conditions that are sufficient for transience of the state process and illustrate our results by classifying some examples according to positive recurrence or transience.
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    Window flow control in FIFO networks with cross traffic (1999)
    Springer
    Queueing systems 32 (1999), S. 195-231 
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    ISSN: 1572-9443
    Keywords: window flow control ; TCP ; stability ; multiclass networks ; stationary ergodic point processes ; (max,+)-linear system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We focus on window flow control as used in packet-switched communication networks. The approach consists in studying the stability of a system where each node on the path followed by the packets of the controlled connection is modeled by a FIFO (First-In-First-Out) queue of infinite capacity which receives in addition some cross traffic represented by an exogenous flow. Under general stochastic assumptions, namely for stationary and ergodic input processes, we show the existence of a maximum throughput allowed by the flow control. Then we establish bounds on the value of this maximum throughput. These bounds, which do not coincide in general, are reached by time-space scalings of the exogenous flows. Therefore, the performance of the window flow control depends not only on the traffic intensity of the cross flows, but also on fine statistical characteristics such as the burstiness of these flows. These results are illustrated by several examples, including the case of a nonmonotone, nonconvex and fractal stability region.
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    Reaction Kinetics for the Anionic Ring-Opening Polymerization of Tetraphenyltetramethylcyclotetrasiloxane Using a Fast Initiator System (1998)
    Springer
    Journal of inorganic and organometallic polymers and materials 8 (1998), S. 111-117 
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    ISSN: 1572-8870
    Keywords: Organosiloxane ; kinetics ; poly(phenylmethylsiloxane) ; catalyst ; anionic ; ring-opening
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract It is well known that the rate of polymerization for an anionic mechanism is dependent on the ability of the bulk material or solvent system to disassociate the ion pair at the propagating chain end. In the anionic ring-opening polymerization of cyclic organosiloxanes in particular, the larger and softer the counter ion, the more rapidly the reaction proceeds. A recently developed phosphazene initiator system provides a large, soft counter ion relative to other traditional initiators used for the polymerization of poly(dimethylsiloxane) (PDMS). This novel initiator system was used in this investigation for the ring-opening polymerization of tetraphenyltetramethylcyclotetrasiloxane (P4) and the reaction kinetics under bulk and solution conditions were investigated. The new initiator system showed a dramatic increase in the rate of polymerization over the conventional potassium hydroxide-catalyzed system. Furthermore, this initiator was sufficiently reactive to be useful for the ring-opening polymerization of P4 at 293 K.
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    Degradation of Cellulosic Materials Under the Alkaline Conditions of a Cementitious Repository for Low- and Intermediate-Level Radioactive Waste. II. Degradation Kinetics (1999)
    Springer
    Journal of polymers and the environment 7 (1999), S. 41-51 
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    ISSN: 1572-8900
    Keywords: Cellulose ; alkaline degradation ; peeling off ; degree of polymerization ; kinetics ; (gluco)isosaccharinic acid
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Energy, Environment Protection, Nuclear Power Engineering , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The degradation of cellulosic materials, differing mainly in the degree of polymerization and the number of reducing end groups, was studied under the alkaline conditions similar to those existing in a cementitious repository for low- and intermediate-level radioactive waste (pH 13.3, T = 25°C). The kinetics of alkaline degradation (peeling-off reaction) were studied and the data analyzed by the model of Haas et al. [13]. The observed kinetic parameters for the propagation reaction and overall stopping reaction were compared with literature data. Although measured under different experimental conditions, literature data and data from this study show a consistent picture. Differences in the extent of degradation observed for the different cellulosic materials could be satisfactorily explained by differences in reducing end group content and, consequently, by differences in the degrees of polymerization. Besides the number of reducing end groups, the degree of amorphousness also plays an important role. The main degradation products formed under the experimental conditions used are α- and β-(gluco)isosaccharinic acid. This is in agreement with many other studies on alkaline degradation of cellulose. The two isomers are formed in roughly equal amounts.
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    Ultrasonic absorption of the oxyethylene group in aqueous nonelectrolyte solutions (1986)
    Springer
    Journal of solution chemistry 15 (1986), S. 221-229 
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    ISSN: 1572-8927
    Keywords: Ultrasonics ; kinetics ; aqueous solution ; triethylene glycol monobutyl ether
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The ultrasonic absorption from 6.5 to 220 MHz and velocities at 2.5 MHz have been measured in aqueous solution of triethylene glycol monobutyl ether as a function of concentration at 25°C. A single relaxational excess absorption, observed from 0.60 to 2.5 mol-dm−3, is attributed to a perturbation of an equilibrium associated with solute-solvent interaction. Rate constants for the forward and reverse processes have been determined from the concentration dependence of the relaxation frequency, and the influence on the water structure by an addition of the solute has been considered. Solution densities were also measured in order to obtain the expansivity of the solution. The standard volume and enthalpy changes of the reaction have been estimated from the concentration dependence of the maximum excess absorption per wave length. A linear relationship between the number of oxyethylene groups and the free energy change between bonded water and nonbonded water is established.
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    Interaction of nicotine with π and σ electron acceptors (1993)
    Springer
    Journal of solution chemistry 22 (1993), S. 1151-1158 
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    ISSN: 1572-8927
    Keywords: Molecular complexes ; solvent effect ; stability ; solid CT complexes ; nicotine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Interaction of nicotine with tetracyanoethylene and iodine was investigated spectrophotometrically and found to form strong CT complexes (n−π and n-σ*, respectively). The donor site involved in CT interaction is the pyrrolidine nitrogen. The nicotine-I2 complex exists as the ionic structure (nicotine) I+-I 3 − . Formation constants of the CT complexes in various solvents were determined from 10 to 25°C and are discussed in terms of the nature of the electron acceptor and solvent polarity. Solid CT complexes were synthesized and were characterized by microchemical analysis and infrared spectra techniques.
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    Stability estimates in inverse scattering (1992)
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    Acta applicandae mathematicae 28 (1992), S. 1-42 
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    ISSN: 1572-9036
    Keywords: 35R30 ; Inverse scattering ; stability ; noisy data
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An algorithm is given for calculating the solution to the 3D inverse scattering problem with noisy discrete fixed energy data. The error estimates for the calculated solution are derived. The methods developed are of a general nature and can be used in many applications: in nondestructive evaluation and remote sensing, in geophysical exploration, medical diagnostics, and technology.
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    High resolution NMR techniques in catalysis (1998)
    Springer
    Topics in catalysis 5 (1998), S. 133-147 
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    ISSN: 1572-9028
    Keywords: NMR ; catalysis ; high pressure ; dynamic equilibria ; magnetization transfer ; sapphire tube ; gas phase ; kinetics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract High resolution NMR techniques are applicable to a variety of aspects of catalysis. Methods for studying homogeneously-catalyzed systems under high gas pressure are described along with approaches for obtaining mechanistic and dynamic information. Many of the same techniques may be applied to heterogeneous catalysis by following the reaction chemistry by gas phase NMR.
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    Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations (1999)
    Springer
    Advances in computational mathematics 10 (1999), S. 271-289 
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    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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    On the first eigenvalue of the linearized operator of ther-th mean curvature of a hypersurface (1993)
    Springer
    Annals of global analysis and geometry 11 (1993), S. 387-395 
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    ISSN: 1572-9060
    Keywords: Curvatures of hypersurfaces ; Reilly's inequality ; stability ; 53 A 10 ; 53 C 42
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We generalize Reilly's inequality for the first eigenvalue of immersed submanifolds ofIR m +1 and the total (squared) mean curvature, to hypersurfaces ofIR m +1 and the first eigenvalue of the higher order curvatures. We apply this to stability problems. We also consider hypersurfaces in hyperbolic space.
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    Destabilization for quasivariational inequalities of reaction-diffusion type (2000)
    Springer
    Applications of mathematics 45 (2000), S. 161-176 
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    ISSN: 1572-9109
    Keywords: reaction-diffusion system ; unilateral conditions ; quasivariational inequality ; Leray-Schauder degree ; eigenvalue ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
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    A secant method for multiple roots (1977)
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    BIT 17 (1977), S. 321-328 
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    ISSN: 1572-9125
    Keywords: 5.15 ; nonlinear equation ; root finding ; multiple root ; secant method ; Steffensen procedure ; order of convergence ; efficiency ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A superlinear procedure for finding a multiple root is presented. In it the secant method is applied to the given function divided by a divided difference whose increment shrinks toward zero as the root is approached. Two function evaluations per step are required, but no derivatives need be calculated.
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    Numerical experiments with a multistep Radau method (1993)
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    BIT 33 (1993), S. 332-350 
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    ISSN: 1572-9125
    Keywords: AMS(MOS): 65L06 ; Multistep collocation method ; continuous solution ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes an implementation of multistep collocation methods, which are applicable to stiff differential problems, singular perturbation problems, and D.A.E.s of index 1 and 2. These methods generalize one-step implicit Runge-Kutta methods as well as multistep one-stage BDF methods. We give numerical comparisons of our code with two representative codes for these methods, RADAU5 and LSODE.
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    Meromorphic resolvents and power bounded operators (1996)
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    BIT 36 (1996), S. 531-541 
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    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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    A New Approach to Backward Error Analysis of Lu Factorization (1999)
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    BIT 39 (1999), S. 385-402 
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    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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    A note on unconditionally stable linear multistep methods (1967)
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    BIT 7 (1967), S. 65-70 
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    ISSN: 1572-9125
    Keywords: Differential equations ; multistep methods ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It has been shown by Dahlquist [3] that the trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. It is the purpose of this note to show that a slightly different stability requirement permits methods of higher accuracy.
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    Multiwavelet approximation methods for pseudodifferential equations on curves. Stability and convergence analysis (1998)
    Springer
    Advances in computational mathematics 9 (1998), S. 145-171 
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    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
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    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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    URL: http://dx.doi.org/10.1023/A:1018977120831
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    Selectivity from a kinetic point of view: nonlinear behavior of logarithmic product ratios as a function of the reciprocal temperature (1998)
    Springer
    Topics in catalysis 5 (1998), S. 159-176 
    Details
    ISSN: 1572-9028
    Keywords: nonlinear temperature behavior ; Eyring plot ; modified Eyring plot ; selectivity ; selection process ; enantioselectivity ; selection level ; isoinversion principle ; isoinversion temperature ; inversion temperature ; kinetics ; catalysis ; asymmetric hydrogenation ; dihydroxylation ; cocyclization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The influence of the temperature on selectivity is described under special consideration of nonlinearities in the corresponding modified Eyring plots. Reasons for the experimentally well-known behavior are discussed. Furthermore, the conditions for nonlinear temperature behavior are quantified and a concept is described which allows the determination of the temperature dependence of a single reaction pathway in a selection process.
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    URL: http://dx.doi.org/10.1023/A:1019185532627
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    Diagonally implicit Runge–Kutta methods for 3D shallow water applications (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 229-250 
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    ISSN: 1572-9044
    Keywords: numerical analysis ; shallow water problems ; DIRK methods ; stability ; 65L06 ; 65L20 ; 65M12 ; 65M20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We construct A‐stable and L‐stable diagonally implicit Runge–Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge–Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge–Kutta methods are suitable methods for integrating shallow water problems in the sense that the stability boundary is relatively large and that the usually quite fine vertical resolution of the discretized spatial domain is not involved in the stability condition.
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    URL: http://dx.doi.org/10.1023/A:1018969203026
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    Numerical stability of biorthogonal wavelet transforms (1995)
    Springer
    Advances in computational mathematics 4 (1995), S. 1-26 
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    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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    Some remarks on the second variation formula for the area (1993)
    Springer
    Annals of global analysis and geometry 11 (1993), S. 221-235 
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    ISSN: 1572-9060
    Keywords: Second variation formula ; Morse index ; stability ; 53C
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Iff is a minimal, isometric immersion of the Riemannian manifoldM of dimensionn in a Riemannian manifold $$\overline M$$ of dimensionm and ifI N is the „differential Jacobi operator” acting on the cross sections of the normal bundleN(M), we obtain some information on the Morse index and on the stability ofM through a detailed geometric analysis of the immersionf obtained when considering the higher fundamental forms off.
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    On stable surfaces of constant gauss curvature in space forms (1995)
    Springer
    Annals of global analysis and geometry 13 (1995), S. 141-148 
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    ISSN: 1572-9060
    Keywords: Gauss curvature ; stability ; 53
    Source: Springer Online Journal Archives 1860-2000
    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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    Stability of Hypersurfaces with Constant $$r$$ -Mean Curvature (1997)
    Springer
    Annals of global analysis and geometry 15 (1997), S. 277-297 
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    ISSN: 1572-9060
    Keywords: mean curvature ; $$r$$ -mean curvature ; sphere ; stability ; stable
    Source: Springer Online Journal Archives 1860-2000
    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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    URL: http://dx.doi.org/10.1023/A:1006514303828
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    The maximal accuracy of stable difference schemes for the wave equation (1995)
    Springer
    BIT 35 (1995), S. 83-115 
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    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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    Derivative free multipoint iterative methods for simple and multiple roots (1986)
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    BIT 26 (1986), S. 93-99 
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    ISSN: 1572-9125
    Keywords: Primary 65HO5 ; nonlinear equation ; multiple roots ; multipoint iterative methods ; error constant ; stability ; efficiency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A one-parameter family of derivative free multipoint iterative methods of orders three and four are derived for finding the simple and multiple roots off(x)=0. For simple roots, the third order methods require three function evaluations while the fourth order methods require four function evaluations. For multiple roots, the third order methods require six function evaluations while the fourth order methods require eight function evaluations. Numerical results show the robustness of these methods.
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    A note on contractivity in the numerical solution of initial value problems (1987)
    Springer
    BIT 27 (1987), S. 424-437 
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    ISSN: 1572-9125
    Keywords: 65 L 05 ; 65 L 20 ; stability ; contractivity ; numerical solution of stiff initial value problems in ordinary differential equations ; Runge-Kutta methods ; Rosenbrock methods ; rational Runge-Kutta methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper concerns the stability analysis of numerical methods for approximating the solutions to (stiff) initial value problems. Our analysis includes the case of (nonlinear) systems of differential equations that are essentially more general than the classical test equationU′=λU, with λ a complex constant. We explore the relation between two stability concepts, viz. the concepts of contractivity and weak contractivity. General Runge-Kutta methods, one-stage Rosenbrock methods and a notable rational Runge-Kutta method are analysed in some detail.
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    Netwon interpolation at Leja points (1990)
    Springer
    BIT 30 (1990), S. 332-346 
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    ISSN: 1572-9125
    Keywords: 65D05 ; polynomial interpolaton ; Newton form ; stability ; Leja points ; ordering of interpolation points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The Newton form is a convenient representation for interpolation polynomials. Its sensitivity to perturbations depends on the distribution and ordering of the interpolation points. The present paper bounds the growth of the condition number of the Newton form when the interpolation points are Leja points for fairly general compact sets K in the complex plane. Because the Leja points are defined recursively, they are attractive to use with the Newton form. If K is an interval, then the Leja points are distributed roughly like Chebyshev points. Our investigation of the Newton form defined by interpolation at Leja points suggests an ordering scheme for arbitrary interpolation points.
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    Stability Concepts in Topological Dynamics by Nonstandard Methods (1997)
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    Acta applicandae mathematicae 49 (1997), S. 35-54 
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    ISSN: 1572-9036
    Keywords: dynamical systems ; stability ; pseudo orbit tracing property ; nonstandard analysis
    Source: Springer Online Journal Archives 1860-2000
    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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    A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations (1992)
    Springer
    BIT 32 (1992), S. 634-649 
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    ISSN: 1572-9125
    Keywords: AMS(MOS): 65L20 ; CR: 5.17 ; delay differential equations ; numerical solution ; Runge-Kutta methods ; interpolation procedures ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU′(t)=λU(t)+μU(t−τ) with λ, μ ε C, Re(λ)〈−|μ|, and τ〉0. Ifc i denotes theith abscissa of a given Runge-Kutta method, then in thenth stept n−1→t n :=t n−1+h of the numerical process our interpolation procedure computes an approximation toU(t n−1+c i h−τ) from approximations that have already been generated by the process at pointst j−1+c i h(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem.
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    On the Robustness of Gaussian Elimination with Partial Pivoting (2000)
    Springer
    BIT 40 (2000), S. 62-73 
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    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; pivoting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.
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    Runge-Kutta Methods for the Numerical Solution of Stiff Semilinear Systems (2000)
    Springer
    BIT 40 (2000), S. 611-639 
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    ISSN: 1572-9125
    Keywords: Runge-Kutta methods ; stability ; convergence ; stiff problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper studies the stability and convergence properties of general Runge-Kutta methods when they are applied to stiff semilinear systems y′(t) = J(t)y(t) + g(t, y(t)) with the stiffness contained in the variable coefficient linear part. We consider two assumptions on the relative variation of the matrix J(t) and show that for each of them there is a family of implicit Runge-Kutta methods that is suitable for the numerical integration of the corresponding stiff semilinear systems, i.e. the methods of the family are stable, convergent and the stage equations possess a unique solution. The conditions on the coefficients of a method to belong to these families turn out to be essentially weaker than the usual algebraic stability condition which appears in connection with the B-stability and convergence for stiff nonlinear systems. Thus there are important RK methods which are not algebraically stable but, according to our theory, they are suitable for the numerical integration of semilinear problems. This paper also extends previous results of Burrage, Hundsdorfer and Verwer on the optimal convergence of implicit Runge-Kutta methods for stiff semilinear systems with a constant coefficients linear part.
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    Quasi-geodesic segments and Gromov hyperbolic spaces (1996)
    Springer
    Geometriae dedicata 62 (1996), S. 281-298 
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    ISSN: 1572-9168
    Keywords: 53C23 ; Hyperbolicity ; stability ; quasi-geodesics
    Source: Springer Online Journal Archives 1860-2000
    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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    Sur l'instabilite de certaines positions d'equilibre relatif dans le probleme des n corps (1990)
    Springer
    Celestial mechanics and dynamical astronomy 49 (1990), S. 219-231 
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    ISSN: 1572-9478
    Keywords: n-body problem ; stability ; relative equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Description / Table of Contents: Abstract We prove in this paper the instability, for all n ⩾ 4, of the configurations of relative equilibrium in the n-body problem where the n bodies submitted to newtonian mutual attractions are at the vertices of a regular polypon with n sides. For this proof we show that the equations of variations projected to the n bodies plan P have at least two conjugate characteristic exponents with a strictly positive real part; while these equations projected to an orthogonal axis to P have some solutions with secular terms.
    Notes: Resumé On démontre dans cet article l'instabilité, pour tout n ⩾ 4, des configurations d'équilibre relatif dans le problème des n corps, oú les n corps soumises aux attractions newtonniennes mutuelles se trouvent aux sommets d'un polygone régulier de n cotés. La preuve consiste à montrer que les équations aux variations, projetées sur le plan P des n corps, possèdent au moins deux exposants caractéristiques complexes connugués dont la parr'e réelle est strictement positive; alors que ces equations projetées sur un axe orthogonal à P possèdent des solutions ayant des termes séculaires.
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    On a class of variational equations transformable to the Gauss hypergeometric equation (1992)
    Springer
    Celestial mechanics and dynamical astronomy 53 (1992), S. 145-150 
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    ISSN: 1572-9478
    Keywords: Monodromy matrix ; Gauss hypergeometric equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new class of linear ordinary differential equations with periodic coefficients is found which can be transformed to the Gauss hypergeometric equation, and therefore the monodromy matrices are computable explicitly. These equations appear as the variational equations around a straight-line solution in Hamiltonian systems of the form H = T(p) + V(q), where T(p) and V(q) are homogeneous functions of p and q, respectively.
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    Asteroid 522 Helga is chaotic and stable (1993)
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    Celestial mechanics and dynamical astronomy 56 (1993), S. 323-324 
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    ISSN: 1572-9478
    Keywords: chaos ; stability ; asteroids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
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    The Trojan asteroid belt: Proper elements, stability, chaos and families (1993)
    Springer
    Celestial mechanics and dynamical astronomy 57 (1993), S. 59-94 
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    ISSN: 1572-9478
    Keywords: asteroids ; libration ; proper elements ; stability ; chaos ; families
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract I have computed proper elements for 174 asteroids in the 1 : 1 resonance with Jupiter, that is for all the reliable orbits available (numbered and multi-opposition). The procedure requires numerical integration, under the perturbations by the four major planets, for 1,000,000 years; the output is digitally filtered and compressed into a “synthetic theory” (as defined within theLONGSTOP project). The proper modes of oscillation of the variables related to eccentricity, perihelion, inclination and node define proper elements. A third proper element is defined as the amplitude of the oscillation of the semimajor axis associated with the libration period; because of the strong nonlinearity of the problem, this component cannot be determined by a simple Fourier transform to the frequency domain. I therefore give another definition, which results in very good stability with time. For 87% of the computed orbits, the stability of the proper elements-at least over 1M yr-is within the following bounds: 0.001AU in semimajor axis, 0.0025 in eccentricity and sine of inclination. Half of the cases with degraded stability of the proper elements are found to be chaotic, with e-folding times between 16,000 and 660,000yr; in some other cases, chaotic behaviour does not result in a significantly decreased stability of the proper elements (stable chaos). The accuracy and stability of these proper elements is good enough to allow a search for asteroid families; however, the dynamical structure of the Trojan belt is very different from the one of the main belt, and collisional events among Trojans can result in a distribution of fragments difficult to identify. The occurrence of couples of Trojans with very close proper elements is proven not to be statistically significant in almost all cases. As the only exception, the couple 1583 Antilochus — 3801 Thrasimedes is significant; however, it is not easy to account for it by a conventional collisional theory. The Menelaus group is confirmed as a strong candidate collisional family; Teucer and Sarpedon could be considered as significant clusters. A number of other clumps are detected (by the same automated clustering method used for the main belt by Zappalà et al., 1990, 1992), but the total number of Trojans with reliable orbits is not large enough to detect many significant candidate families.
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    The dynamics of solar sails with a non-point source of radiation pressure (1990)
    Springer
    Celestial mechanics and dynamical astronomy 49 (1990), S. 249-264 
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    ISSN: 1572-9478
    Keywords: Solar sails ; radiation pressure ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The form of the solar radiation pressure on a heliocentric orbiting solar sail is obtained for a finite angular sized and limb darkened solar disk by the use of the radiation pressure tensor. It is found that the usual inverse square variation of the solar radiation pressure is modified by the finite angular size, and to a lesser extent by the solar limb darkening. The actual magnitude of the modification is in itself small, except at close heliocentric distances. However, its existence has implications for the dynamical stability of solar sails both in parked and circular orbital configurations and for the accuracy of trajectory calculations, particularly for sails in the inner solar system.
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    Bifurcations of separatrices in the averaged planar general three-body problem at first-order resonance (1994)
    Springer
    Celestial mechanics and dynamical astronomy 60 (1994), S. 307-315 
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    ISSN: 1572-9478
    Keywords: Asteroid ; libration ; resonance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is known that an abridged case of the averaged planar general three-body problem, at first-order resonance, is analytically integrated, using an expansion of the disturbing function linear in the eccentricities. There exist different methods with the help of which the integration can be performed. For the first time Sessin and Ferraz-Mello in the years 1981–88 (Sessin, 1981, 1983; Ferraz-Mello and Sessin, 1984; Ferraz-Mello, 1987, 1988) did an analytic integration for the restricted elliptic three-body problem, in terms of the variablesK andH (K=ΣD j e j cos (ψ1−π j ),H=ΣD j e j sin (ψ1−π j ),D j = const, wheree j and π j are, respectively, the eccentricity and the longitude of the periapsis of thei-th planet, ψ1 is the Delaunay's anomaly), which is inconvenient for the analytical investigation of the evolution of the major semi-axesa j , the eccentricitiese j and the resonance phases ϕ j =ψ1−π j . Later, a different method for the analytical integration of the general three-body problem, in the variablesa j ,e j and ϕ j , was considered by the author (Shinkin, 1993). A disadvantage of both methods is the fact that they use non-canonical changes of variables. But there exists a third very beautiful canonical method of analytical integration of the general planetary problem, which is briefly considered in the present paper and allows us to describe the bifurcations of separatrices (i.e. appearance, disappearance, splitting and confluence of separatrices) separating the domains of libration and circulation of the resonance phase on the phase plane in the averaged planar general three-body problem at first-order resonance. The bifurcation parameter is analytically found and plays an important role in a qualitative description of all kinds of motion in the examined problem.
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    Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 181-196 
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    ISSN: 1572-9478
    Keywords: Periodic solutions ; stability ; restricted three-body problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.
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    Uniform stability at permanently acting disturbances of solutions of Navier-Stokes equations for compressible isothermic fluids (1994)
    Springer
    Acta applicandae mathematicae 37 (1994), S. 129-136 
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    ISSN: 1572-9036
    Keywords: 35B35 ; 35Q30 ; 76N10 ; stability ; Navier-Stokes equations ; compressible fluids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that the uniform stability at permanently acting disturbances of a given solution of the Navier-Stokes equations for viscous compressible isothermic fluid is a consequence of the uniform exponential stability of the zero solution of so-called linearized equations.
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    Growth and long-run stability (1987)
    Springer
    Acta applicandae mathematicae 9 (1987), S. 219-237 
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    ISSN: 1572-9036
    Keywords: 34A34 ; 34D99 ; 90A16 ; Nonlinear differential equations ; stability ; growth ; economic dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.
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    Stability and Geometry of Third-Order Resonances in four-Dimensional Symplectic Mappings (1997)
    Springer
    Celestial mechanics and dynamical astronomy 67 (1997), S. 181-204 
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    ISSN: 1572-9478
    Keywords: Hamiltonian systems ; symplectic mappings ; normal forms ; resonances ; stability ; three degrees of freedom
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We analyze four-dimensional symplectic mappings in the neighbourhood of an elliptic fixed point whose eigenvalues are close to satisfy a third-order resonance. Using the perturbative tools of resonant normal forms, the geometry of the orbits and the existence of elliptic or hyperbolic one-dimensional tori (fixed lines) is worked out. This allows one to give an analytical estimate of the stability domain when the resonance is unstable. A comparison with numerical results for the four-dimensional Hénon mapping is given.
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    URL: http://dx.doi.org/10.1023/A:1008288826727
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    Position and velocity sensitivities at the triangular libration points (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 1-19 
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    ISSN: 1572-9478
    Keywords: Three body problem ; stability ; surface of section ; commensurability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The model of the circular restricted problem of three bodies is used to investigate the sensitivity of the third body motion when it is given a positional or velocity deviation away from the L4 triangular libration point. The x-axis is used as a criteria for defining the stability of the third body motion. Poincaré's surfaces of section are used to compare the regions of periodic, quasi-periodic and stochastic motion to the trajectories found using the definition of stability (not crossing the x-axis) defined in this study. Values of the primary/secondary mass ratios (μ) ranging from 0 to the linear critical value 0.038521... are investigated. Using this new form of stability measure, it is determined that certain values of μ are more stable than others. The results of this study are compared, and found, to give agreeable results to other studies which investigate commensurabilities of the long and short period terms of periodic orbits.
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    Stability of axial orbits in analytical galactic potentials (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 261-285 
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    ISSN: 1572-9478
    Keywords: galactic dynamics ; periodic orbits ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the stability of axial orbits in analytical galactic potentials as a function of the energy of the orbit and the ellipticity of the potential. The problem is solved by an analytical method, the validity of which is not limited to small amplitudes. The lines of neutral stability divide the parameter space in regions corresponding to different organizations of the main families of orbits in the symmetry planes.
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    Effects of small external forces on the planar oscillation of a cable connected satellites system (1992)
    Springer
    Celestial mechanics and dynamical astronomy 53 (1992), S. 219-226 
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    ISSN: 1572-9478
    Keywords: Artificial satellite ; dissipative forces ; stability
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    Topics: Physics
    Notes: Abstract The effects of small external dissipative and disturbing forces on the non-linear planar oscillation of a cable connected satellites system in the central gravitational field of earth have been studied. Typical non-linear oscillation's phenomena arizing from the aforesaid external forces are shown to take place. The presence of these forces enables the application of asymptotic methods of the theory of non-linear oscillations due to Bogoliubov and Mitropolsky to the equation characterizing the non-linear oscillation of the system.
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    Dynamics and self-organization of catalytic systems (1994)
    Springer
    Topics in catalysis 1 (1994), S. 305-314 
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    ISSN: 1572-9028
    Keywords: non-Langmuir ; kinetics ; non-linear dynamics ; oscillations ; chaos ; self-organization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The kinetics of a catalytic reaction is frequently formulated in terms of simple concepts of the Langmuir type. Apart from limitations arising from the non-uniformity of the catalyst's surface and from the coverage dependence of the rate “constants”, several other complications may come into play. These may arise on the “quantum level” where energy flow between the various degrees of freedom may cause failure of simple transition state theory, as well as on the “continuum level” where formulation of rate equations in terms of coupled non-linear differential equations may give rise to a rich scenario of spatio-temporal self-organization, including kinetic oscillations, chaos, and formation of concentration patterns. Several of these phenomena are illustrated by selected examples.
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    Runge–Kutta–Nyström‐type parallel block predictor–corrector methods (1999)
    Springer
    Advances in computational mathematics 10 (1999), S. 115-133 
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    ISSN: 1572-9044
    Keywords: Runge–Kutta–Nyström methods ; predictor–corrector methods ; stability ; parallelism ; 65M12 ; 65M20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
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    Mechanism of the hydrodenitrogenation of o-toluidine and methylcyclohexylamine over NiMo/γ-Al2O3 (2000)
    Springer
    Topics in catalysis 11-12 (2000), S. 327-333 
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    ISSN: 1572-9028
    Keywords: hydrodenitrogenation ; toluidine ; methylcyclohexylamine ; kinetics ; nickel-promoted molybdenum sulphide
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The hydrodenitrogenation (HDN) of o-toluidine and its reaction intermediates was studied over a NiMo/γ-Al2O3 catalyst. The kinetics of the HDN of methylcyclohexylamine and of the hydrogenation of cyclohexene were also studied. Hydrogenation of o-toluidine alone produces methylcyclohexene and methylcyclohexane. When a sufficient quantity of cyclohexene is added during the HDN of toluidine, methylcyclohexylamine, the first intermediate in the hydrogenation of toluidine, becomes detectable. Because of its strong adsorption constant and high rate constant for reacting further to methylcyclohexene and methylcyclohexane, methylcyclohexylamine is not observed in the HDN of toluidine. Adding cyclohexene decreases the adsorption of methylcyclohexylamine, thus enabling its detection. The rate and adsorption constants of methylcyclohexylamine and cyclohexene in the HDN of methylcyclohexylamine were calculated by fitting the kinetic data to a Langmuir–Hinshelwood equation. A two-site model was used to describe the surface reactions, with one site for the methylcyclohexylamine reactions and the other for the cyclohexene reaction.
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    Stability of the triangular libration points of the circular restricted problem in the presence of resonances (1996)
    Springer
    Celestial mechanics and dynamical astronomy 66 (1996), S. 191-202 
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    ISSN: 1572-9478
    Keywords: resonance ; restricted problem ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases ω1 = 2ω2 and ω1 = 3ω2. The motion is unstable for all the values of parameters q and A when ω1 = 2ω2 and the motion is unstable and stable depending upon the values of the parameters q and A when ω1 = 3ω2. Here q is the radiation parameter and A is the oblateness parameter.
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    The structure of chaos in a potential without escapes (1994)
    Springer
    Celestial mechanics and dynamical astronomy 60 (1994), S. 249-271 
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    ISSN: 1572-9478
    Keywords: Chaos ; periodic orbits ; stability ; asymptotic curves ; homoclinic points ; heteroclinic points
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    Topics: Physics
    Notes: Abstract We study the structure of chaos in a simple Hamiltonian system that does no have an escape energy. This system has 5 main periodic orbits that are represented on the surface of section $$(y,\dot y)$$ by the points (1)O(0,0), (2)C 1,C 2(±y c, 0), (3)B 1,B 2(O,±1) and (4) the boundary $$y^2 + \dot y^2 = 1$$ . The periodic orbits (1) and (4) have infinite transitions from stability (S) to instability (U) and vice-versa; the transition values of ε are given by simple approximate formulae. At every transitionS →U a set of 4 asymptotic curves is formed atO. For larger ε the size and the oscillations of these curves grow until they destroy the closed invariant curves that surroundO, and they intersect the asymptotic curves of the orbitsC 1,C 2 at infinite heteroclinic points. At every transitionU →S these asymptotic curves are duplicated and they start at two unstable invariant points bifurcating fromO. At the transition itself the asymptotic curves fromO are tangent to each other. The areas of the lobes fromO increase with ε; these lobes increase even afterO becomes stable again. The asymptotic curves of the unstable periodic orbits follow certain rules. Whenever there are heteroclinic points the asymptotic curves of one unstable orbit approach the asymptotic curves of another unstable orbit in a definite way. Finally we study the tangencies and the spirals formed by the asymptotic curves of the orbitsB 1,B 2. We find indications that the number of spiral rotations tends to infinity as ε → ∞. Therefore new tangencies between the asymptotic curves appear for arbitrarily large ε. As a consequence there are infinite new families of stable periodic orbits that appear for arbitrarily large ε.
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    Nekhoroshev estimate for isochronous non resonant symplectic maps (1989)
    Springer
    Celestial mechanics and dynamical astronomy 47 (1989), S. 333-359 
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    ISSN: 1572-9478
    Keywords: symplectic maps ; stability ; normal forms
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    Topics: Physics
    Notes: Abstract We prove that non resonant isochronous symplectic maps in a neighborhood of an elliptic fixed point are stable for exponentially long times with the inverse of the distance from the fixed point. In the proof we make use of the majorant series method together with an idea for optimizing remainder estimates first applied to Hamiltonian problems by Nekhoroshev.
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    Existence and Stability of L4,5 In The Relativistic Restricted Three-Body Problem (1997)
    Springer
    Celestial mechanics and dynamical astronomy 69 (1997), S. 271-281 
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    ISSN: 1572-9478
    Keywords: restricted three-body problem ; libration points ; stability
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    Topics: Physics
    Notes: Abstract The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied. It is found that L4,5 are unstable in the whole range 0 ≤ µ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable for 0 〈 µ 〈 µ0, where µ is the mass parameter and µ0 = 0.03852....
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    Long Time Stability for the Main Problem of Artificial Satellites (1997)
    Springer
    Celestial mechanics and dynamical astronomy 69 (1997), S. 317-330 
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    ISSN: 1572-9478
    Keywords: artificial satellite ; Nekhoroshev's theory ; normal form ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the significance of long time stabilty predictions in the light of Nekhoroshev's theory by studying the orbits of artificial satellites. As a simplified model problem we consider the so-called J2problem for an earth's satellite, neglecting luni-solar perturbations and nonconservative effects. We consider a wide range of orbits, excluding those which are too close to the critical inclination. Most of the orbits turn out to be stable for times larger than the estimated age of the solar system, thus proving that, as far as dissipation can be neglected, stability in Nekhoroshev's sense may be effective for physically realistic systems.
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    Nonlinear Stability of the Lagrangian Libration Points in the Chermnykh Problem (1998)
    Springer
    Celestial mechanics and dynamical astronomy 70 (1998), S. 41-58 
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    ISSN: 1572-9478
    Keywords: three-body problem ; libration points ; stability ; normal forms.
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    Topics: Physics
    Notes: Abstract In this paper we consider the problem of motion of an infinitesimal point mass in the gravity field of an uniformly rotating dumb-bell. The aim of our study is to investigate Liapunov stability of Lagrangian libration points of this problem. We analyze the stability of libration points in the whole range of parameters ω, μ of the problem. In particular, we consider all resonance cases when the order of resonance is not greater than five.
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    The integrable cases of the planetary three-body problem at first-order resonance (1993)
    Springer
    Celestial mechanics and dynamical astronomy 55 (1993), S. 249-259 
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    ISSN: 1572-9478
    Keywords: Asteroid ; libration ; resonance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper investigates the stability of the motion in the averaged planar general three-body problem in the case of first-order resonance. The equations of the averaged motion of bodies near the resonance surface is obtained and is analytically integrated by quadratures. The stability of the averaged motion is analytically investigated in relation to the semi-major axes, the eccentricities and the resonance phases. An autonomous second-order equation is obtained for the deviation of semiaxes from the resonance surface. This equation has an energy integral and is analytically integrated by quadratures. The quasi-periodic dependence on time with two-frequency basis of the averaged motion of bodies is found. The basic frequencies are analytically calculated. With the help of the mean functionals calculated along integral curves of the averaged problem the new analytic first integrals are constructed with coefficients periodic in time. The analytic conditions of librations of resonance phases are obtained.
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    About the periodic solutions of a rigid body in a central Newtonian field (1993)
    Springer
    Celestial mechanics and dynamical astronomy 55 (1993), S. 323-330 
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    ISSN: 1572-9478
    Keywords: Periodic orbits ; rigid body dynamics ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The equations of motion of a rigid body about a fixed point in a central Newtonian field is reduced to the equation of plane motion under the action of potential and gyroscopic forces, using the isothermal coordinates on the inertia ellipsoid. The construction of periodic solutions near the equilibrium points, by using the Lipaunov theorem of holomorphic integral, is obtained and the necessary and sufficient conditions for the stability of the system are given.
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    Invariant rotational curves in Sitnikov's Problem (1993)
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    Celestial mechanics and dynamical astronomy 55 (1993), S. 351-367 
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    ISSN: 1572-9478
    Keywords: Sitnikov's problem ; invariant rotational curves ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Sitnikov's Problem is a Restricted Three-Body Problem of Celestial Mechanics depending on a parameter, the eccentricity,e. The Hamiltonian,H(z, v, t, e), does not depend ont ife=0 and we have an integrable system; ife is small the KAM Theory proves the existence of invariant rotational curves, IRC. For larger eccentricities, we show that there exist two complementary sequences of intervals of values ofe that accumulate to the maximum admissible value of the eccentricity, 1, and such that, for one of the sequences IRC around a fixed point persist. Moreover, they shrink to the planez=0 ase tends to 1.
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    On the families of periodic orbits which bifurcate from the circular Sitnikov motions (1994)
    Springer
    Celestial mechanics and dynamical astronomy 60 (1994), S. 99-129 
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    ISSN: 1572-9478
    Keywords: Sitnikov motions ; periodic orbits ; stability ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we deal with the circular Sitnikov problem as a subsystem of the three-dimensional circular restricted three-body problem. It has a first analytical part where by using elliptic functions we give the analytical expressions for the solutions of the circular Sitnikov problem and for the period function of its family of periodic orbits. We also analyze the qualitative and quantitative behavior of the period function. In the second numerical part, we study the linear stability of the family of periodic orbits of the Sitnikov problem, and of the families of periodic orbits of the three-dimensional circular restricted three-body problem which bifurcate from them; and we follow these bifurcated families until they end in families of periodic orbits of the planar circular restricted three-body problem. We compare our results with the previous ones of other authors on this problem. Finally, the characteristic curves of some bifurcated families obtained for the mass parameter close to 1/2 are also described.
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    The stability of rational approximations of analytic semigroups (1993)
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    BIT 33 (1993), S. 74-84 
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    ISSN: 1572-9125
    Keywords: 65J10 ; 65M12 ; Analytic semigroup ; Banach space ; rational approximation ; A-acceptable ; A(θ)-acceptable ; stability ; Crank-Nicolson method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown thatA-acceptable and, more generally,A(θ)-arational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method.
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    Stiffness of ODEs (1993)
    Springer
    BIT 33 (1993), S. 285-303 
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    ISSN: 1572-9125
    Keywords: 65L05 ; stiffness ; stability ; pseudospectra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pseudospectra instead of spectra. Numerical experiments with an adaptive ODE solver illustrate these findings.
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    Exponential Integrators for Quantum-Classical Molecular Dynamics (1999)
    Springer
    BIT 39 (1999), S. 620-645 
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    ISSN: 1572-9125
    Keywords: Numerical integrator ; oscillatory solutions ; Schrödinger equation ; quantum-classical coupling ; error bounds ; stability
    Source: Springer Online Journal Archives 1860-2000
    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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    Stochastic Methods for Ill-Posed Problems (2000)
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    BIT 40 (2000), S. 226-240 
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    ISSN: 1572-9125
    Keywords: Stochastic differential equations ; regularisation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is devoted to the numerical analysis of ill-posed problems of evolution equations in Banach spaces using certain classes of stochastic one-step methods. The linear stability properties of these methods are studied. Regularisation is given by the choice of the regularisation parameter as α = $$\sqrt {\tau _n }$$ , where τ n is the stepsize and provides the convergence on smooth initial data. The case of the approximation of well-posed problems is also considered.
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    On integrating vertex singularities using extrapolation (1994)
    Springer
    BIT 34 (1994), S. 62-79 
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    ISSN: 1572-9125
    Keywords: AMS(MOS) 65D30 ; 65B05 ; adaptive ; cubature ; singularity ; extrapolation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new approach to the integration of vertex singularities is described. This approach is based on a non-uniform subdivision of the region of integration and the technique fits well to the subdivision strategy used in many adaptive algorithms. A nice feature with this approach is that it can be used in any dimension and on any region of integration which can be subdivided into subregions of the same form. The strategy can be applied both to vertex singularities and internal point singularities. In the latter case this can be done without an initial subdivision of the region in order to put the singular point in a vertex. It turns out that the technique has excellent numerical stability properties.
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    Three Dimensional Laser Simulation Code on a Desktop Personal Computer (1999)
    Springer
    Optical review 6 (1999), S. 28-36 
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    ISSN: 1349-9432
    Keywords: optical propagation equation ; stability ; picosecond pulse ; 3-dimensional computation ; Fresnel’s distribution ; fast Fourier transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a new simulation code able to simulate the entire propagation of laser pulse, from the amplifiers level up to the focusing stage. This algorithm has some new characteristics that we intend to present. It computes the three-dimensional optical propagation equation using no approximation other than its picosecond expression. The stability has been carefully studied so that it can be applied to any geometry. This is a great improvement since, up to now only cylindrical geometry was accessible for accuracy. In this paper we also present a method using Fast Fourier Transform able to evaluate with a high accuracy, Fresnel’s distribution of a focused laser pulse. The advantages provided by our algorithm are its rapidity and its high physical understanding of the focusing phenomena.
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    The influence of a flood event on phytoplankton succession (1990)
    Springer
    Aquatic sciences 52 (1990), S. 330-344 
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    ISSN: 1420-9055
    Keywords: Flood ; phytoplankton succession ; reversion ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The effect of the August 1987 River Reuss flood event on the phytoplankton biocoenosis in Lake Uri (Urnersee, part of Lake Lucerne, Switzerland) was investigated firstly by comparing biological, chemical and physical data sampled before the event with equivalent data sampled after the event; and secondly by comparing the phytoplankton succession in 1987 with that occurring in the “floodfree” year 1989. As a consequence of the flood, the physical and chemical environment of the phytoplankton was found to have undergone a change which resulted in an alteration in the composition of the phytoplankton community. The phytoplankton community existing previous to the flood event, which had been dominated byTabellaria fenestrata sensu Husted 1930 (K-strategist), was replaced by a biocoenosis characterized mainly by various species of flagellates, which represent a typical spring successional stage (r-strategists). After the externally-imposed perturbation, the return to stable physical and chemical conditions was followed by the re-establishment of the successional stage which had existed before the flood (termed “reversion” by Reynolds, 1980).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00879761
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  • 199
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    Stability of axial motions of nonlinearly elastic loops (1996)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 809-816 
    Details
    ISSN: 1420-9039
    Keywords: 34D20 ; 34D35 ; 35Q72 ; 73H10 ; 73K03 ; Elastic string ; stability ; energy-momentum ; axial motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish “orbitai” stability (modulo this collection of relative equilibria). For a well-defined class of “soft” materials, there is an upper bound on the axial speed sufficient for stability; “stiff” materials are shown to be orbitally stable at any axial speed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00915277
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    The polymerization of sickle hemoglobin in solutions and cells (1993)
    Springer
    Cellular and molecular life sciences 49 (1993), S. 110-117 
    Details
    ISSN: 1420-9071
    Keywords: Polymerization ; sickle hemoglobin ; sickle cell disease ; kinetics ; thermodynamics ; polymer domains ; nucleation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Abstract The polymerization of sickle hemoglobin occurs by the same mechanisms in solutions and in cells, and involves the formation of 14 stranded fibers from hemoglobin molecules which have assumed a deoxy quaternary structure. The fibers form via two types of highly concentration-dependent nucleation processes: homogeneous nucleation in solutions with hemoglobin activity above a critical activity, and heterogeneous nucleation in similarly supersaturated solutions which also contain hemoglobin polymers. The latter pathway is dominant, and creates polymer arrays called domains. The individual polymers bend, but also cross-link, and the resulting mass behaves as a solid. The concentration of polymerized hemoglobin increases exponentially unless clamped by rate limiting effects such as oxygen delivery.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01989414
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