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  • stability  (61)
  • Springer  (61)
  • 1995-1999  (61)
  • 1999  (61)
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  • 1995-1999  (61)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Neural processing letters 10 (1999), S. 267-271 
    ISSN: 1573-773X
    Keywords: recurrent neural networks ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract In this paper, we point out that the conditions given in [1] are sufficient but unnecessary for the global asymptotically stable equilibrium of a class of delay differential equations. Instead, we prove that under weaker conditions, it is still global asymptotically stable.
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  • 2
    ISSN: 1432-0770
    Keywords: Key words: Hebbian learning rule ; attractor dynamics ; symmetric connections ; multiplicative normalization ; self-organization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract. While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs.
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  • 3
    ISSN: 1573-904X
    Keywords: calcitonin ; polyethylene glycol ; PEGylation ; peptide ; tryptic digestion ; stability ; HPLC
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Purpose. To separate and characterize the different positional isomers of mono-PEGylated salmon calcitonins (mono-PEG-sCTs) and to evaluate the effects of the PEGylation site on the stability of different mono-PEG-sCTs in rat kidney homogenate. Methods. Mono-PEG-sCTs were prepared using succinimidyl carbonate monomethoxy polyethylene glycol (5,000 Da) and separated by gel-filtration HPLC followed by reversed-phase HPLC. To characterize PEGylated sCTs, matrix-assisted laser desorption ionization time of flight mass spectrometry (M ALDI-TOF MS) and reversed-phase HPLC of the trypsin digested samples were performed. Mono-PEG-sCTs and sCT in rat kidney homogenates were measured by column-switching reversed-phase HPLC with on-line detection of the radioiodinated samples using a flow-through radioisotope detector. Results. Three different mono-PEGylated sCTs were separated by reversed-phase gradient HPLC. From the MALDI-TOF MS analysis, the average molecular weight of mono-PEG-sCTs was confirmed as around 8650 Da. The presence of PEG moiety in the mono-PEG-sCTs was also manifested by the fact that the distance between two adjacent mass spectum lines was 44 Da which corresponds to PEG monomer unit. Tryptic digestion analysis demonstrated that these mono-PEG-sCTs are 3 positional isomers of N-terminus, Lys18- and Lys11-residue modified mono-PEGylated sCTs. The degradation half-life of these 3 positional isomers in rat kidney homogenates significantly increased in order of the N-terminus (125.5 min), Lys11- (157.3 min), and Lysl8-residue modified mono-PEGylated sCT (281.5 min) over the native sCT (4.8 min). Conclusions. Three positional isomers of mono-PEGylated sCTs were purified and characterized. Of these, the resistance to proteolytic degradation was highest for the Lysl8-residue modified mono-PEG-sCT. These studies demonstrate that the in vivo stability of PEGylated sCTs is highly dependent on the site of PEG molecule attachment.
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  • 4
    ISSN: 1573-904X
    Keywords: polymer implant ; brain cancer ; carmustine ; polyanhydride ; stability ; controlled release
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
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  • 5
    ISSN: 1573-904X
    Keywords: nanoparticles ; poly(lactic acid) ; poly(lactic acid-co-ethylene oxide) ; freeze-drying ; stability ; flow cytometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Purpose. To investigate the feasibility of producing freeze-dried poly-(ethylene oxide) (PEO)-surface modified nanoparticles and to study their ability to avoid the mononuclear phagocytic system (MPS), as a function of the PEO chain length and surface density. Methods. The nanoparticles were produced by the salting-out method using blends of poly(D,L-lactic acid) (PLA) and poly(D,L-lactic acid-co-ethylene oxide) (PLA-PEO) copolymers. The nanoparticles were purified by cross-flow filtration and freeze-dried as such or with variable amounts of trehalose as a lyoprotectant. The redispersibility of the particles was determined immediately after freeze-drying and after 12 months of storage at −25° C. The uptake of the nanoparticles by human monocytes was studied in vitro by flow cytometry. Results. PLA-PEO nanoparticles could be produced from all the polymeric blends used. Particle aggregation after freeze-drying was shown to be directly related to the presence of PEO. Whereas this problem could be circumvented by use of trehalose, subsequent aggregation was shown to occur during storage. These phenomena were possibly related to the specific thermal behaviours of PEO and trehalose. In cell studies, a clear relationship between the PEO content and the decrease of uptake was demonstrated. Conclusions. The rational design of freeze-dried PEO-surface modified nanoparticles with potential MPS avoidance ability is feasible by using the polymer blends approach combined with appropriate lyoprotection and optimal storage conditions.
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  • 6
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    Optical review 6 (1999), S. 28-36 
    ISSN: 1349-9432
    Keywords: optical propagation equation ; stability ; picosecond pulse ; 3-dimensional computation ; Fresnel’s distribution ; fast Fourier transform
    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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  • 7
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    Computational mechanics 23 (1999), S. 8-19 
    ISSN: 1432-0924
    Keywords: Keywords: Material characteristic length ; strain-rate gradient ; dominant growth rate ; viscoplastic material ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract We study thermomechanical deformations of a viscoplastic body deformed in simple shear. The strain gradients are taken as independent kinematic variables and the corresponding higher order stresses are included in the balance laws, and the equation for the yield surface. Three different functional relationships, the power law, and those proposed by Wright and Batra, and Johnson and Cook are used to relate the effective strain rate to the effective stress and temperature. Effects of strain hardening of the material and elastic deformations are neglected. The homogeneous solution of the problem is perturbed and the stability of the problem linear in the perturbation variables is studied. Following Wright and Ockendon's postulate that the wavelength whose initial growth rate is maximum determines the minimum spacing between adjacent shear bands, the shear band spacing is computed. It is found that the minimum shear band spacing is very sensitive to the thermal softening coefficient/exponent, the material characteristic length and the nominal strain-rate. Approximate analytical expressions for the critical wave length for heat conducting nonpolar materials and locally adiabatic deformations of gradient dependent materials are also derived.
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  • 8
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    Archive of applied mechanics 69 (1999), S. 47-54 
    ISSN: 1432-0681
    Keywords: Key words Bifurcation ; stability ; multibody system dynamics ; singularity theory ; Liapunov's direct method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary In this paper, the global behavior of relative equilibrium states of a three-body satellite with flexible connection under the action of the gravitational torque is studied. With geometric method, the conditions of existence of nontrivial solutions to the relative equilibrium equations are determined. By using reduction method and singularity theory, the conditions of occurrence of bifurcation from trivial solutions are derived, which agree with the existence conditions of nontrivial solutions, and the bifurcation is proved to be pitchfork-bifurcation. The Liapunov stability of each equilibrium state is considered, and a stability diagram in terms of system parameters is presented.
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  • 9
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    Journal of inclusion phenomena and macrocyclic chemistry 34 (1999), S. 277-289 
    ISSN: 1573-1111
    Keywords: complexes ; stability ; extraction ; transport ; tetrathiolactams
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The synthesis of tetrathiolactams and related di- and tetrathioamide compounds is described. The formation constants of their heavy-metal complexes are determined by using the strong UV absorption of the thioamide chromophore. Extraction and transport abilities of tetrathioamide ionophores show selectivities for Ag(I) and Hg(II) cations over alkali, alkaline-earth or other heavy metal cations including transition metals such as Co(II).
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  • 10
    ISSN: 1573-1111
    Keywords: hexacyclen ; pentacyclen ; anion complexes ; stoichiometry ; stability ; polarography
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The complexation of protonated hexacyclen and pentacyclen with pyrophosphate, selenite, selenate, molybdate and tungstate anions was studied by differential pulse polarography at 25 °C. The stoichiometry and stability of the resulting anion complexes were evaluated from the pH and concentration-dependence of the peak potentials, respectively. The results established 1 : 1 anion receptor complexation in all cases. In the case of all anions studied, hexacyclen was found to form more stable anion complexes than pentacyclen. The fact that the anion-receptor complexation depends on the structural features of both the anions and the macrocycles used is indicative of a steric controlled interaction.
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  • 11
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    Journal of productivity analysis 12 (1999), S. 55-75 
    ISSN: 1573-0441
    Keywords: Data envelopment analysis (DEA) ; returns to scale (RTS) ; sensitivity ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract Sensitivity of the returns to scale (RTS) classifications in data envelopment analysis is studied by means of linear programming problems. The stability region for an observation preserving its current RTS classification (constant, increasing or decreasing returns to scale) can be easily investigated by the optimal values to a set of particular DEA-type formulations. Necessary and sufficient conditions are determined for preserving the RTS classifications when input or output data perturbations are non-proportional. It is shown that the sensitivity analysis method under proportional data perturbations can also be used to estimate the RTS classifications and discover the identical RTS regions yielded by the input-based and the output-based DEA methods. Thus, our approach provides information on both the RTS classifications and the stability of the classifications. This sensitivity analysis method can easily be applied via existing DEA codes.
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  • 12
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    Journal of intelligent and robotic systems 26 (1999), S. 91-100 
    ISSN: 1573-0409
    Keywords: robots ; neural networks ; adaptiveness ; stability ; approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract An indirect adaptive control approach is developed in this paper for robots with unknown nonlinear dynamics using neural networks (NNs). A key property of the proposed approach is that the actual joint angle values in the control law are replaced by the desired joint angles, angle velocities and accelerators, and the bound on the NN reconstruction errors is assumed to be unknown. Main theoretical results for designing such a neuro-controller are given, and the control performance of the proposed controller is verified with simulation studies.
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  • 13
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    Earth, moon and planets 87 (1999), S. 103-115 
    ISSN: 1573-0794
    Keywords: Accretion ; exoplanetary system ; extrasolar planets ; numerical integration ; orbital migration ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A number of extrasolar planets have been detected in close orbits around nearby stars. It is probable that these planets did not form in these orbits but migrated from their formation locations beyond the ice line. Orbital migration mechanisms involving angular momentum transfer through tidal interactions between the planets and circumstellar gas-dust disks or by gravitational interaction with a residual planetesimal disk together with several means of halting inward migration have been identified. These offer plausible schemes to explain the orbits of observed extrasolar giant planets and giant planets within the Solar System. Recent advances in numerical integration methods and in the power of computer workstations have allowed these techniques to be applied to modelling directly the mechanisms and consequences of orbital migration in the Solar System. There is now potential for these techniques also to be applied to modelling the consequences of the orbital migration of planets in the observed exoplanetary systems. In particular the detailed investigation of the stability of terrestrial planets in the habitable zone of these systems and the formation of terrestrial planets after the dissipation of the gas disk is now possible. The stability of terrestrial planets in the habitable zone of selected exoplanetary systems has been established and the possibility of the accretion of terrestrial planets in these systems is being investigated by the author in collaboration with Barrie W. Jones (Open University), and with John Chambers (NASA-Ames) and Mark Bailey of Armagh Observatory, using numerical integration. The direct simulation of orbital migration by planetesimal scattering must probably await faster hardware and/or more efficient algorithms.
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  • 14
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    Celestial mechanics and dynamical astronomy 74 (1999), S. 19-57 
    ISSN: 1572-9478
    Keywords: stability ; Hamiltonian ; two centers ; oblate planet ; galactic disks ; dipole
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Relative equilibria occur in a wide variety of physical applications, including celestial mechanics, particle accelerators, plasma physics, and atomic physics. We derive sufficient conditions for Lyapunov stability of circular orbits in arbitrary axisymmetric gravitational (electrostatic) and magnetic fields, including the effects of local mass (charge) and current density. Particularly simple stability conditions are derived for source‐free regions, where the gravitational field is harmonic (∇2U = 0) or the magnetic field irrotational (∇ × B = 0). In either case the resulting stability conditions can be expressed geometrically (coordinate‐free) in terms of dimensionless stability indices. Stability bounds are calculated for several examples, including the problem of two fixed centers, the J2 planetary model, galactic disks, and a toroidal quadrupole magnetic field.
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  • 15
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    BIT 39 (1999), S. 385-402 
    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; backward error analysis ; growth factor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new backward error analysis of LU factorization is presented. It allows to obtain a sharper upper bound for the forward error and a new definition of the growth factor that we compare with the well known Wilkinson growth factor for some classes of matrices. Numerical experiments show that the new growth factor is often of order approximately log2 n whereas Wilkinson's growth factor is of order n or $$\sqrt n$$ .
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  • 16
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    BIT 39 (1999), S. 620-645 
    ISSN: 1572-9125
    Keywords: Numerical integrator ; oscillatory solutions ; Schrödinger equation ; quantum-classical coupling ; error bounds ; stability
    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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  • 17
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    Celestial mechanics and dynamical astronomy 75 (1999), S. 251-285 
    ISSN: 1572-9478
    Keywords: unrestricted problem ; rotational motion ; rigid body dynamics ; libration points ; stability ; resonances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present an analysis of the model introduced by Kokoriev and Kirpichnikov (1988) for the study of unrestricted planar motion of a point mass and a symmetric rigid body whose gravity field is approximated by two point masses (a dumb-bell model). To show possible generalization of the model, we give a systematic derivation of equations of motion for a more general unrestricted problem of a point and a rigid body possessing a plane of dynamical symmetry. We give a simple description of bifurcation of triangular libration points, and we perform an analysis of their linear stability. We propose to extend the model of Kokoriev and Kirpichnikov (1988) to a case when the symmetric body is oblate. In the proposed model the gravity field of moving and rotating body is approximated by two complex masses at complex distance (a complex dumb-bell model). An analysis of bifurcation of the triangular libration points in this model is also presented.
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  • 18
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    Flow, turbulence and combustion 62 (1999), S. 137-162 
    ISSN: 1573-1987
    Keywords: laminar wall jet ; heat transfer ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The hydrodynamic stability of a low speed, plane, non-isothermal laminar wall jet at a constant temperature boundary condition was investigated theoretically and experimentally. The mean velocity and temperature profiles used in the stability analysis were obtained by implementing the Illingworth–Stewartson transformation that allows one to extend the classical Glauert solution to a thermally non-uniform flow. The stability calculations showed that the two unstable eigenmodes coexisting at moderate Reynolds numbers are significantly affected by the heat transfer. Heating is destabilizing the flow while cooling is stabilizing it. However, the large-scale instabilities associated with the inflection point of the velocity profile still amplify in spite of the high level of the stabilizing temperature difference. The calculated stability characteristics of the wall jet with heat transfer were compared with experimental data. The comparison showed excellent agreement for small amplitudes of the imposed perturbations. The agreement is less good for the phase velocities of the sub-harmonic wave and this is attributed to experimental difficulties and to nonlinear effects.
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  • 19
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    International tax and public finance 6 (1999), S. 621-639 
    ISSN: 1573-6970
    Keywords: expectations ; bubbles ; uniqueness ; stability ; state variables ; multiplicity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract This paper concerns the minimal-state-variable (MSV) criterion for selection among solutions in rational expectationsmodels that feature a multiplicity of paths that satisfy all of the model's conditions. It compares the MSVcriterion with others, including the widely used saddle-path (dynamic stability) criterion. It is emphasized that theMSV criterion can be viewed as a scientifically useful classification scheme that delineates the unique solutionthat is free of bubble components. In the process of demonstrating uniqueness for a broad class of linear models,the paper exposits a convenient computational procedure. Applications to current issues are outlined.
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  • 20
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    Agroforestry systems 45 (1999), S. 131-158 
    ISSN: 1572-9680
    Keywords: competition ; fertility ; microclimate ; risk ; stability ; water
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract The first ecosystem mimic hypothesis suggests clear advantages if man-made land use systems do not deviate greatly in their resource use patterns from natural ecosystems typical of a given climatic zone. The second hypothesis claims that additional advantages will accrue if agroecosystems also maintain a substantial part of the diversity of natural systems. We test these hypotheses for the savannah zone of sub-Saharan Africa, with its low soil fertility and variable rainfall. Where annual food crops replace the natural grass understorey of savannah systems, water use will decrease and stream and groundwater flow change, unless tree density increases relative to the natural situation. Increasing tree density, however, will decrease crop yields, unless the trees meet specific criteria. Food crop production in the parkland systems may benefit from lower temperatures under tree canopies, but water use by trees providing this shade will prevent crops from benefiting. In old parkland trees that farmers have traditionally retained when opening fields for crops, water use per unit shade is less than in most fast growing trees introduced for agroforestry trials. Strong competition between plants adapted to years with different rainfall patterns may stabilise total system productivity -- but this will be appreciated by a farmer only if the components are of comparable value. The best precondition for farmers to maintain diversity in their agroecosystem hinges on the availability of a broad basket of choices, without clear winners or 'best bets'.
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  • 21
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    Journal of statistical physics 95 (1999), S. 867-902 
    ISSN: 1572-9613
    Keywords: kinetics of phase transitions ; domain coarsening ; asymptotic behavior ; self-similarity ; stability ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The classical Lifshitz–Slyozov–Wagner theory of domain coarsening predicts asymptotically self-similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field. Here we consider the long-time behavior of measure-valued solutions for systems in which particle size is uniformly bounded, i.e., for initial measures of compact support. We prove that the long-time behavior of the size distribution depends sensitively on the initial distribution of the largest particles in the system. Convergence to the classically predicted smooth similarity solution is impossible if the initial distribution function is comparable to any finite power of distance to the end of the support. We give a necessary criterion for convergence to other self-similar solutions, and conditional stability theorems for some such solutions. For a dense set of initial data, convergence to any self-similar solution is impossible.
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    Journal of statistical physics 95 (1999), S. 835-850 
    ISSN: 1572-9613
    Keywords: quasicrystals ; nonperiodic tilings ; classical lattice-gas models ; nonperiodic ground states ; nonperiodic Gibbs states ; stability ; frustration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract One of the fundamental problems of quasicrystals is to understand their occurrence in microscopic models of interacting particles. We review here recent attempts to construct stable quasicrystalline phases. In particular, we compare two recently constructed classical lattice-gas models with translation-invariant interactions and without periodic ground-state configurations. The models are based on nonperiodic tilings of the plane by square-like tiles. In the first model, all interactions can be minimized simultaneously. The second model is frustrated; its nonperiodic ground state can arise only by the minimization of the energy of competing interactions. We put forward some hypotheses concerning stabilities of nonperiodic ground states. In particular, we introduce two criteria, the so-called strict boundary conditions, and prove their equivalence to the zero-temperature stability of ground states against small perturbations of potentials of interacting particles. We discuss the relevance of these conditions for the low-temperature stability, i.e., for the existence of thermodynamically stable nonperiodic equilibrium states.
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    Journal of biomolecular NMR 13 (1999), S. 187-191 
    ISSN: 1573-5001
    Keywords: alignment ; bicelle ; dipolar coupling ; liquid crystal ; pH ; stability ; ubiquitin
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Abstract It is demonstrated that mixtures of ditetradecyl- phosphatidylcholine or didodecyl-phoshatidylcholine and dihexyl- phosphatidylcholine in water form lyotropic liquid crystalline phases under similar conditions as previously reported for bicelles consisting of dimyristoyl-phosphatidylcholine (DMPC) and dihexanoyl- phosphatidylcholine (DHPC). The carboxy-ester bonds present in DMPC and DHPC are replaced by ether linkages in their alkyl analogs, which prevents acid- or base-catalyzed hydrolysis of these compounds. 15N-1H dipolar couplings measured for ubiquitin over the 2.3–10.4pH range indicate that this protein retains a backbone conformation which is very similar to its structure at pH 6.5 over this entire range.
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    Nonlinear dynamics 20 (1999), S. 221-246 
    ISSN: 1573-269X
    Keywords: Coulomb friction ; asymmetric damping ; exact periodic motions ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Dynamics of a class of strongly nonlinear single degree of freedom oscillators is investigated. Their common characteristic is that they possess piecewise linear damping properties, which can be expressed in a general asymmetric form. More specifically, the damping coefficient and a constant parameter appearing in the equation of motion are functions of the velocity direction. This class of oscillators is quite general and includes other important categories of mechanical systems as special cases, like systems with Coulomb friction. First, an analysis is presented for locating directly exact periodic responses of these oscillators to harmonic excitation. Due to the presence of dry friction, these responses may involve intervals where the oscillator is stuck temporarily. Then, an appropriate stability analysis is also presented together with some quite general bifurcation results. In the second part of the work, this analysis is applied to several example systems with piecewise linear damping, in order to reveal the most important aspects of their dynamics. Initially, systems with symmetric characteristics are examined, for which the periodic response is found to be symmetric or asymmetric. Then, dynamical systems with asymmetric damping characteristics are also examined. In all cases, emphasis is placed on investigating the low forcing frequency ranges, where interesting dynamics is noticed. The analytical predictions are complemented with results obtained by proper integration of the equation of motion, which among other responses reveal the existence of quasiperiodic, chaotic and unbounded motions.
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    Journal of engineering mathematics 35 (1999), S. 385-404 
    ISSN: 1573-2703
    Keywords: Bénard-Marangini convection ; conducting fluids ; stability ; two-layer system.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The onset of steady Bénard-Marangoni convection in two horizontal liquid layers of electrically conducting immiscible fluids subjected to a uniform vertical magnetic field and temperature gradient is analysed by means of a combination of analytical and numerical techniques. The free surface can be either deformable or nondeformable and the interface between the fluids is always assumed to be flat. The effect of the lower layer on the critical values of Rayleigh, Marangoni and wave numbers for the onset of steady convection is investigated. When the free surface is nondeformable, the critical parameters for the onset of pure Marangoni convection are increased, whereas for the onset of pure Bénard convection they are decreased compared to the single-layer model. The results for a single-layer and for two-layers are qualitatively similar for Bénard-Marangoni convection when the free surface is deformable. All disturbances can be stabilized with sufficiently strong magnetic field when the free surface is nondeformable. If the free surface is allowed to deform and gravity waves are excluded, then the layers are always unstable to disturbances with sufficiently small wave number with magnetic field. Inclusion of gravity waves has a stabilizing effect on certain disturbances of small wave number in the presence of weak or moderate magnetic field.
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    Multidimensional systems and signal processing 10 (1999), S. 7-20 
    ISSN: 1573-0824
    Keywords: multivariate polynomials ; stability ; robust stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract This paper presents a detailed analysis of some classes of stable multivariate polynomials. The main aim of the analysis is to give conditions under which polynomials preserve stability when they are subjected to small coefficient variations. The maximal class of such polynomials is introduced. Some basic properties of polynomials from this class are obtained.
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    Nonlinear dynamics 19 (1999), S. 135-158 
    ISSN: 1573-269X
    Keywords: perturbation methods ; higher-order approximations ; dynamical systems ; codimension ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Higher-order multiple-scale methods for general multiparameter mechanical systems are studied. The role played by the control and imperfection parameters in deriving the perturbative equations is highlighted. The definition of the codimension of the problem, borrowed from the bifurcation theory, is extended to general systems, excited either externally or parametrically. The concept of a reduced dynamical system is then invoked. Different approaches followed in the literature to deal with reconstituted amplitude equations are discussed, both in the search for steady-state solutions and in the analysis of stability. Four classes of methods are considered, based on the consistency or inconsistency of the approach, and on the completeness or incompleteness of the terms retained in the analysis. The four methods are critically compared and general conclusions drawn. Finally, three examples are illustrated to corroborate the findings and to show the quantitative differences between the various approaches.
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    Nonlinear dynamics 19 (1999), S. 173-193 
    ISSN: 1573-269X
    Keywords: fluid conveying pipes ; high-frequency pulsating fluid ; separation of slow and fast motion ; stability ; nonlinear dynamics
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    Topics: Mathematics
    Notes: Abstract Stability and nonlinear dynamics of two articulated pipes conveying fluid with a high-frequency pulsating component is investigated. The non-autonomous model equations are converted into autonomous equations by approximating the fast excitation terms with slowly varying terms. The downward hanging pipe position will lose stability if the mean flow speed exceeds a certain critical value. Adding a pulsating component to the fluid flow is shown to stabilize the hanging position for high values of the ratio between fluid and pipe-mass, and to marginally destabilize this position for low ratios. An approximate nonlinear solution for small-amplitude flutter oscillations is obtained using a fifth-order multiple scales perturbation method, and large-amplitude oscillations are examined by numerical integration of the autonomous model equations, using a path-following algorithm. The pulsating fluid component is shown to affect the nonlinear behavior of the system, e.g. bifurcation types can change from supercritical to subcritical, creating several coexisting stable solutions and also anti-symmetrical flutter may appear.
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    Nonlinear dynamics 19 (1999), S. 313-332 
    ISSN: 1573-269X
    Keywords: double pendulum system ; double Hopf bifurcation ; stability ; chaos
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    Topics: Mathematics
    Notes: Abstract A double pendulum system is studied for analyzing the dynamic behaviour near a critical point characterized by nonsemisimple 1:1 resonance. Based on normal form theory, it is shown that two phase-locked periodic solutions may bifurcate from an initial equilibrium, one of them is unstable and the other may be stable for certain values of parameters. A secondary bifurcation from the stable periodic solution yields a family of quasi-periodic solutions lying on a two-dimensional torus. Further cascading bifurcations from the quasi-periodic motions lead to two chaoses via a period-doubling route. It is shown that all the solutions and chaotic motions are obtained under positive damping.
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    Journal of optimization theory and applications 100 (1999), S. 575-597 
    ISSN: 1573-2878
    Keywords: Queueing networks ; scheduling ; stability ; performance evaluation
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    Topics: Mathematics
    Notes: Abstract We obtain new linear programs for bounding the performance and proving the stability of queueing networks. They exploit the key facts that the transition probabilities of queueing networks are shift invariant on the relative interiors of faces and the cost functions of interest are linear in the state. A systematic procedure for choosing different quadratic functions on the relative interiors of faces to serve as surrogates of the differential costs in an inequality relaxation of the average cost function leads to linear program bounds. These bounds are probably better than earlier known bounds. It is also shown how to incorporate additional features, such as the presence of virtual multi-server stations to further improve the bounds. The approach also extends to provide functional bounds valid for all arrival rates.
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    Journal of optimization theory and applications 102 (1999), S. 299-313 
    ISSN: 1573-2878
    Keywords: Comparison of methods ; optimal control ; sensitivity ; shooting methods ; stability
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    Topics: Mathematics
    Notes: Abstract A new method for solving optimal control problems, here called multiple NOC shooting, is presented. It is developed from NOC shooting. It has some advantages over its parent and over multiple shooting, which are both successful, high-accuracy methods for optimal control. A comparison of the three methods is given, incorporating two examples.
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    Set-valued analysis 7 (1999), S. 209-238 
    ISSN: 1572-932X
    Keywords: nonsmooth analysis ; subdifferentials ; coderivatives ; implicit function theorem ; solvability ; stability ; open mapping theorem ; metric regularity ; multidirectional mean value inequality
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    Topics: Mathematics
    Notes: Abstract We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.
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    Queueing systems 32 (1999), S. 195-231 
    ISSN: 1572-9443
    Keywords: window flow control ; TCP ; stability ; multiclass networks ; stationary ergodic point processes ; (max,+)-linear system
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    Topics: Computer Science
    Notes: Abstract We focus on window flow control as used in packet-switched communication networks. The approach consists in studying the stability of a system where each node on the path followed by the packets of the controlled connection is modeled by a FIFO (First-In-First-Out) queue of infinite capacity which receives in addition some cross traffic represented by an exogenous flow. Under general stochastic assumptions, namely for stationary and ergodic input processes, we show the existence of a maximum throughput allowed by the flow control. Then we establish bounds on the value of this maximum throughput. These bounds, which do not coincide in general, are reached by time-space scalings of the exogenous flows. Therefore, the performance of the window flow control depends not only on the traffic intensity of the cross flows, but also on fine statistical characteristics such as the burstiness of these flows. These results are illustrated by several examples, including the case of a nonmonotone, nonconvex and fractal stability region.
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    Queueing systems 31 (1999), S. 171-206 
    ISSN: 1572-9443
    Keywords: scheduling ; open multiclass queueing networks ; discrete-review policies ; fluid models ; stability
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    Topics: Computer Science
    Notes: Abstract This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value r k (q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable. In such a policy, system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed. Stability is proved by combining elementary large deviations theory with an analysis of an associated fluid control problem. These results are extended to systems with class dependent setup times as well as systems with alternate routing and admission control capabilities.
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    Computational & mathematical organization theory 5 (1999), S. 5-30 
    ISSN: 1572-9346
    Keywords: network models ; organization theory ; rule following ; self organized ; stability ; work teams ; work routine
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    Topics: Mathematics
    Notes: Abstract Self-organized rule-following systems are increasingly relevant objects of study in organization theory due to such systems&2018; capacity to maintain control while enabling decentralization of authority. This paper proposes a network model for such systems and examines the stability of the networks&2018; repetitive behavior. The networks examined are Ashby nets, a fundamental class of binary systems: connected aggregates of nodes that individually compute an interaction rule, a binary function of their three inputs. The nodes, which we interpret as workers in a work team, have two network inputs and one self-input. All workers in a given team follow the same interaction rule. We operationalize the notion of stability of the team&2018;s work routine and determine stability under small perturbations for all possible rules these teams can follow. To study the organizational concomitants of stability, we characterize the rules by their memory, fluency, homogeneity, and autonomy. We relate these measures to work routine stability, and find that stability in ten member teams is enhanced by rules that have low memory, high homogeneity, and low autonomy.
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    Queueing systems 32 (1999), S. 131-168 
    ISSN: 1572-9443
    Keywords: stability ; positive recurrence ; fluid limit ; polling system ; exhaustive service policy
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    Topics: Computer Science
    Notes: Abstract We introduce a generalized criterion for the stability of Markovian queueing systems in terms of stochastic fluid limits. We consider an example in which this criterion may be applied: a polling system with two stations and two heterogeneous servers.
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    Queueing systems 33 (1999), S. 293-325 
    ISSN: 1572-9443
    Keywords: stability ; fluid models ; multiclass queueing networks ; piecewise linear Lyapunov functions ; linear Lyapunov functions ; monotone global stability ; static buffer priority disciplines
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    Topics: Computer Science
    Notes: Abstract This paper studies the stability of a three‐station fluid network. We show that, unlike the two‐station networks in Dai and Vande Vate [18], the global stability region of our three‐station network is not the intersection of its stability regions under static buffer priority disciplines. Thus, the “worst” or extremal disciplines are not static buffer priority disciplines. We also prove that the global stability region of our three‐station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three‐station network. We also show that the LP proposed by Bertsimas et al. [1] does not characterize either the global stability region or even the monotone global stability region of our three‐station network. Further, we demonstrate that the LP related to the linear Lyapunov function proposed by Chen and Zhang [11] does not characterize the stability region of our three‐station network under a static buffer priority discipline.
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    Queueing systems 32 (1999), S. 99-130 
    ISSN: 1572-9443
    Keywords: neural network ; inhibition ; stability ; Markov process ; fluid limit ; Harris-recurrence ; transience
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    Topics: Computer Science
    Notes: Abstract The subject of the paper is the stability analysis of some neural networks consisting of a finite number of interacting neurons. Following the approach of Dai [5] we use the fluid limit model of the network to derive a sufficient condition for positive Harris-recurrence of the associated Markov process. This improves the main result in Karpelevich et al. [11] and, at the same time, sheds some new light on it. We further derive two different conditions that are sufficient for transience of the state process and illustrate our results by classifying some examples according to positive recurrence or transience.
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    Journal of thermal analysis and calorimetry 56 (1999), S. 1177-1184 
    ISSN: 1572-8943
    Keywords: differential scanning calorimetry ; DNA triple helix ; oligonucleotides ; stability
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    Topics: Chemistry and Pharmacology
    Notes: Abstract In this work we report a thermodynamic characterization of stability and melting behaviour of two 24-mer DNA triplexes. The third strand, that binds the Watson-Crick double helix with Hoogsteen hydrogen bonds, contains 3′-3′ phosphodiester junction that determines the polarity inversion. The target double helix is composed of adjacent and alternate fragments of oligopurine-oligopyrimidine tracts. The two helices differ from the substitution of the cytosine, involved in the junction, with the thymine. Calorimetric data reported here provide a quantitative measure of the influence of pH and base modification on the stability of a DNA triplex.
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    Journal of thermal analysis and calorimetry 56 (1999), S. 1285-1304 
    ISSN: 1572-8943
    Keywords: amorphous state ; combined techniques ; drug design ; drug product development ; drug substance ; drug technology ; DSC ; excipients ; failure investigations ; hydrates ; MDSC ; microcalorimetry ; pharmaceuticals ; polymorphism ; polymers ; preformulation ; process optimization ; purity ; quality control ; solvates ; stability ; sub-ambient DSC ; TG ; temperature resolved X-ray diffraction ; water interactions ; thermal microscopy ; water sorption-desorption
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    Topics: Chemistry and Pharmacology
    Notes: Abstract Modern thermal analysis, microcalorimetry and new emerging combined techniques which deliver calorimetric, microscopic and spectroscopic data offer a powerful analytical battery for the study of pharmaceuticals. These techniques are very useful in all steps of development of new drug products as well as methods for quality control in production. The characterization of raw materials enables to understand the relationships between polymorphs, solvates and hydrates and to choose the proper development of new drug products with very small amount of material in a very short time. Information on stability, purity is valuable for new entities as well as for marketed drug substances from different suppliers. Excipients which vary from single organic or inorganic entity to complexes matrixes or polymers need to be characterized and properly controlled. The thermodynamic phase-diagrams are the basis of the studies of drug-excipients interactions. They are very useful for the development of new delivery systems. A great number of new formulations need proper knowledge of the behaviour of the glass transition temperature of the components. Semi-liquid systems, interactions in aqueous media are also successfully studied by these techniques.
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    Journal of thermal analysis and calorimetry 55 (1999), S. 727-739 
    ISSN: 1572-8943
    Keywords: ignition ; polymer combustion modelling ; stability ; steady state
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    Topics: Chemistry and Pharmacology
    Notes: Abstract A mathematical model of ignition and burning of organic polymers was used for evaluation and quantification of the tendency of polymers to ignition. The model permits investigation of the influence of one parameter of the polymer on the others. It was found that the model could be used for the verification of the ignitability method developed by Miller et al. [1]. Different steady states of combustion were found when using the model proposed. There is a characteristic steady state for normal flaming combustion, another for non-flaming combustion, and there are also unstable steady states that have no real physical meaning.
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    Advances in computational mathematics 10 (1999), S. 115-133 
    ISSN: 1572-9044
    Keywords: Runge–Kutta–Nyström methods ; predictor–corrector methods ; stability ; parallelism ; 65M12 ; 65M20
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    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
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    Advances in computational mathematics 10 (1999), S. 271-289 
    ISSN: 1572-9044
    Keywords: delay differential equations ; steady state solutions ; stability ; 34K20 ; 65J10
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    Topics: Mathematics
    Notes: Abstract The characteristic equation of a system of delay differential equations (DDEs) is a nonlinear equation with infinitely many zeros. The stability of a steady state solution of such a DDE system is determined by the number of zeros of this equation with positive real part. We present a numerical algorithm to compute the rightmost, i.e., stability determining, zeros of the characteristic equation. The algorithm is based on the application of subspace iteration on the time integration operator of the system or its variational equations. The computed zeros provide insight into the system’s behaviour, can be used for robust bifurcation detection and for efficient indirect calculation of bifurcation points.
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    ISSN: 1572-9036
    Keywords: (discrete-time) Markov control processes ; expected total cost ; value iteration ; policy iteration ; stability ; transient control models
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    Topics: Mathematics
    Notes: Abstract This paper studies the expected total cost (ETC) criterion for discrete-time Markov control processes on Borel spaces, and possibly unbounded cost-per-stage functions. It presents optimality results which include conditions for a control policy to be ETC-optimal and for the ETC-value function to be a solution of the dynamic programming equation. Conditions are also given for the ETC-value function to be the limit of the α-discounted cost value function as α ↑ 1, and for the Markov control process to be `stable" in the sense of Lagrange and almost surely. In addition, transient control models are fully analized. The paper thus provides a fairly complete, up-dated, survey-like presentation of the ETC criterion for Markov control processes on Borel spaces.
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    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
    ISSN: 1531-5851
    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
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    Topics: Mathematics
    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
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    ISSN: 1573-3025
    Keywords: aerosolisation effects ; bioaerosol ; bioaerosol sampling ; effects of recovery agents ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The sampling and assay of bioaerosols are important ina number of industrial and health-care applications. Airborne microorganisms are notoriously difficult toenumerate accurately under such conditions and nosingle procedure is suitable for all applications. Problems are compounded by the differences in assaymethod or sampler type selected, making theinterpretation of results difficult.Understanding the airborne behaviour of microorganismsover a range of environmental conditions is vital ifprocedures are to be defined and recommended for theassessment of bioaerosols. Microorganisms that arerobust over a wide range of conditions are ideal astracer particles. Unfortunately, the large majorityof non-fungal bioaerosols are susceptible to damage. A predictable assessment procedure is required whichwill not affect the viability of the collectedsample. This paper examines how aerosolisation may affect the characteristics of two speciesof microorganism (Pseudomonas fluorescens andMS2 coliphage). It forms part of a larger programmeto develop standards for the assessment of biologicalparticles. The aim of the work was to develop procedures toexamine the effects of aerosolisation onmicroorganisms, with particular reference topre-aerosolisation protocol (spray suspension age) andpost-sampling handling protocol (aerosol age incollection solution). These procedures were then usedto examine the effect of recovery agents, addedto the spray suspension prior to aerosolisation, onthe culturability of E.coli. Aerosolisation reduces the culturability of P. fluorescensand the viability of viability of MS2coliphage. Pre-sampling and post-collection handlingand storage of these aerosolised microorganisms werealso found to have an effect. This and earlierstudies have shown that the culturable fraction ofmicroorganisms can be affected by the same factorsdescribed above. Of five microorganisms tested so farin the main programme, only Penicillium expansumspores were shown to be robust and stable with aconstant culturable fraction. Therefore, recommendinga particular microorganism (apart from P. expansum) as an airborne biological standard foraerosol studies is not advised. It is recommendedthat a microorganism, representative of the envisagedapplication, be characterised it in terms of theaerosolisation parameters, storage time and conditionsin the manner reported in this study. This can beachieved using the experimental equipment described.The addition of 0.1 mM concentrations of the sugarsinositol, trehalose and raffinose to spray suspensionsof Escherichia coli, prior to aerosolisation,made no significant difference to the culturablefraction of the aerosol.
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    Multibody system dynamics 3 (1999), S. 287-299 
    ISSN: 1573-272X
    Keywords: multibody dynamics ; symbol manipulation ; linearization ; stability ; Floquet theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract It is shown that use of AUTOLEV, a symbol manipulation computer program for mechanics analyses, can greatly facilitate the stability analysis of motions of multibody systems.
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    Nonlinear dynamics 20 (1999), S. 181-196 
    ISSN: 1573-269X
    Keywords: monitoring ; stability ; compressors ; axial flow compressors ; stall ; surge ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Monitoring systems are proposed for the detection of incipient instability in axial flow compression systems. The work employs generic features associated with the response to noise inputs of systems bordering on instability. Based on these generic features, a closed-loop monitoring system is proposed. Numerical simulation is used to illustrate the operation of the proposed closed-loop monitoring system.
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    Journal of engineering mathematics 36 (1999), S. 327-348 
    ISSN: 1573-2703
    Keywords: Bingham fluids ; multi-layer flow ; no-flow/yield criteria ; stability ; variational methods.
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    Topics: Mathematics , Technology
    Notes: Abstract The mechanically unstable situation of a heavy Bingham fluid resting on top of a light Bingham fluid in an inclined closed-ended pipe can be stabilised if the fluids have sufficiently large yield stresses. This paper focuses on determining the yield stresses that are sufficient to keep the fluids statically stable for a given fluid density difference, pipe diameter and pipe inclination. The results are applicable to a broad class of practically observable flows. This situation provides an idealised model for the oilfield process of plug cementing.
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    Discrete event dynamic systems 9 (1999), S. 45-64 
    ISSN: 1573-7594
    Keywords: hybrid dynamic systems ; event feedback ; real-time scheduling ; stability
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    Topics: Mathematics
    Notes: Abstract Based on some practical engineering problems arising from process control and space-structure control, this paper studies a class of hybrid dynamic systems in which N plants are controlled by a central controller in sharing time manner, where the plants are described by differential equations and the controller works according to the mechanism of discrete events. An event feedback strategy is suggested to be a scheduling policy such that one and only one plant among N plants is chosen to be controlled at any time. Some conditions of asymptotical and exponential stability are then given and an exponential upper bound of states norm is also estimated for the event feedback scheduling strategy. An algorithm based on event feedback strategy is presented to determine the control laws of the plants to meet the given performance. An example follows to illustrate the application and effect of the results.
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    Applied mathematics and mechanics 20 (1999), S. 1384-1388 
    ISSN: 1573-2754
    Keywords: nonlinear dynamic system ; bifurcation ; stability ; TB123 ; O322
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A computation algorithm based on the Poincaré Mapping in combination with Pseudo-Arc Length Continuation Method is presented for calculating the unstable response with saddle-node bifurcation, and the singularity, which occurs using the general continuation method combined with Poincaré Mapping to follow the path, is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too. There will be two directions in which the path can be continued at each point, but only one can be used. The method of determining the direction will be presented in the paper. It can be concluded that is method is effective in analysis of nonlinear dynamic system with saddle-node bifurcations.
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    Applied mathematics and mechanics 20 (1999), S. 233-240 
    ISSN: 1573-2754
    Keywords: viscoelasticity ; cylindrical shell ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the dynamic stability of a viscoelastic circular cylindrical shell subject to an axial compressive force and a uniformly distributed radial compressive load is discussed. By using the Laplace transformation, stability conditions of viscoelastic shell under constant loads are yielded. By using synthetically the classical dynamic methods, the various dynamical properties for the dynamical system defined by the viscoelastic shell and the effect of parameters on the stability of structure are obtained.
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    Applied mathematics and mechanics 20 (1999), S. 564-567 
    ISSN: 1573-2754
    Keywords: generalized Birkhoff's system ; equilibrium state ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, equilibrium stability of generalized Birkhoff's autonomous system is discussed. First, equilibrium equations of generalized Birkhoff's autonomous system are set up, and then the linear approximate method and direct method of stability in equilibrium state are studied. Some results on equilibrium of generalized Birkhoff's autonomous system are obtained on the basis of Lyapunov's thorem. Last, the application of the results is illustrated with an example.
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    Applied mathematics and mechanics 20 (1999), S. 912-916 
    ISSN: 1573-2754
    Keywords: delay ; neural network ; stability ; TN911.23 ; O332
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, by using Liapunov functional, some sufficient conditions are obtained for the stability of the equilibrium of a neural network model with delay of the type $$u'_i \left( t \right) = - b_i u_i \left( t \right) + \sum\limits_{j = 1}^n {T_{ij} f_j } \left( {\mu _j u_j \left( {t - \tau _j } \right)} \right) + c_i ,\tau _j \geqslant 0,i = 1,2 \cdots ,n.$$
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    Reaction kinetics and catalysis letters 68 (1999), S. 243-247 
    ISSN: 1588-2837
    Keywords: Methane partial oxidation ; nickel-based catalysts ; stability ; sintering and loss of nickel
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The thermal stability and an 80 h life test over nickel-based catalysts for CH4/O2 to syngas reaction were investigated by flow-reactor, XPS, XRD and AAS analysis. The results indicate that the introduction of Li and La not only stabilized the support γ-Al2O3 phase, but also suppressed the sintering and loss of nickel, and in addition, enhanced the ability to suppress the carbon-deposition over NiO/Al2O3 during the high-temperature reaction.
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  • 56
    ISSN: 1573-5117
    Keywords: disturbance ; stability ; resilience ; Trichoptera ; Ephemeroptera ; Psychomyia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Benthic macroinvertebrate assemblages of Bushkill Creek, Northampton County, PA were studied at the same site during the 1970s (11 dates) and 1990s (8 dates) to evaluate stability and resilience. In the 1970s, a Surber sampler was used, and in the 1990s, a Hess sampler. Assemblages appeared stable over a wide range of environmental stresses with the exception of 1994–1995 when total numbers and total Trichoptera decreased. Taxa richness and EPT indices varied little in 1994–1995 from other sampled years. By July 1996, all metrics (Trichoptera numbers, total numbers, taxa richness, EPT index, Bray-Curtis Index) resembled the 1970s exception for lower wet weight. Bray-Curtis indices and taxa composition were similar in July 1972 and July 1996, suggesting assemblage stability over 25 years. The Trichoptera, Psychomyia (Psychomiidae) and Leucotrichia (Hydroptilidae), decreased during the 1990s and never rebounded to 1970s numbers. During winter 1994, the coldest temperatures and greatest cumulative snowfall occurred in the region. These conditions probably stressed the assemblage with low temperatures, anchor/frazil ice and ice break-up. The assemblage was then exposed to four bankful floods in winter/spring 1994 and five bankful floods in winter/spring 1996. Recovery time following these multiple disturbances was 27 months. Previous recovery times from winter and flood disturbances were considerably shorter (2–5 months). The 1990s recovery time (5–9 times previusly recorded) for this assemblage was apparently extended by multiple physical disturbances, outside the predicted range. The assemblages had not been previously exposed to such severe conditions and, therefore, recovery time was extended. Despite severe weather conditions, the assemblage recovered and exhibited both stability and resilience in its return to an assemblage similar to the 1970s.
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  • 57
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    Journal of dynamical and control systems 5 (1999), S. 501-507 
    ISSN: 1573-8698
    Keywords: Singular perturbation ; invariant manifold ; overflowing manifold ; stability ; characteristic numbers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A singularly perturbed system with a small parameter ε at the velocity of the slow variable y and with the fast variable x is considered. The main hypothesis is that for all y from some bounded domain D, the fast subsystem has a stable invariant or overflowing manifold M 0(y) and that the motions in this system going in the directions transversal to M 0(y) are more fast than the mutual approaching of trajectories on M 0(y) (a precise statement is given in terms of appropriate Lyapunov-type characteristic numbers). It is proved that for a sufficiently small ε, the whole system has an invariant manifold close to $$\bigcup\limits_{y \in D} {M_0 (y) \times \{ y\}}$$ the degree of its smoothness is specifed.
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  • 58
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    Lithuanian mathematical journal 39 (1999), S. 20-32 
    ISSN: 1573-8825
    Keywords: Schrödinger equation ; explicit finite-difference schemes ; stability ; energy conservation ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider three-level explicit schemes for solving the nonlinear variable coefficient Schrödinger-type equation. Using spectral and energy methods we establish the stability and convergence of these schemes. The existence of discrete conservation laws is investigated. General results are applied for the DuFort-Frankel and leap-frog diffenrence schemes.
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  • 59
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    Mechanics of composite materials 35 (1999), S. 495-506 
    ISSN: 1573-8922
    Keywords: layered structure ; shells ; frames ; stringers ; nonlinearity ; stability ; pulsed loading ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Nonlinear three-dimensional problems of dynamic deformation, buckling, and posteritical behavior of composite shell structures under pulsed loads are analyzed. The structure is assumed to be made of rigidly joined plates and shells of revolution along the lines coinciding with the coordinate directions of the joined elements. Individual structural elements can be made of both composite and conventional isotropic materials. The kinematic model of deformation of the structural elements is based on Timoshenko-type hypotheses. This approach is oriented to the calculation of nonstationary deformation processes in composite structures under small deformations but large displacements and rotation angles, and is implemented in the context of a simplified version of the geometrically nonlinear theory of shells. The physical relations in the composite structural elements are based on the theory of effective moduli for individual layers or for the package as a whole, whereas in the metallic elements this is done in the framework of the theory of plastic flow. The equations of motion of a composite shell structure are derived based on the principle of virtual displacements with some additional conditions allowing for the joint operation of structural elements. To solve the initial boundary-value problem formulated, an efficient numerical method is developed based on the finite-difference discretization of variational equations of motion in space variables and an explicit second-order time-integration scheme. The permissible time-integration step is determined using Neumann's spectral criterion. The above method is especially efficient in calculating thin-walled shells, as well as in the case of local loads acting on the structural element, when the discretization grid has to be condensed in the zones of rapidly changing solutions in space variables. The results of analyzing the nonstationary deformation processes and critical loads are presented for composite and isotropic cylindrical shells reinforced with a set of discrete ribs in the case of pulsed axial compression and external pressure.
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  • 60
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    Mathematical methods of operations research 50 (1999), S. 245-270 
    ISSN: 1432-5217
    Keywords: Key words: Portfolio optimization ; stochastic programming ; stability ; postoptimality ; worst-case analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. Solutions of portfolio optimization problems are often influenced by errors or misspecifications due to approximation, estimation and incomplete information. Selected methods for analysis of results obtained by solving stochastic programs are presented and their scope illustrated on generic examples – the Markowitz model, a multiperiod bond portfolio management problem and a general strategic investment problem. The approaches are based on asymptotic and robust statistics, on the moment problem and on results of parametric optimization.
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  • 61
    ISSN: 1573-5125
    Keywords: Chironomidae ; interspecific competition ; streams ; stability ; succession
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract New streams formed following ice recession in Glacier Bay National Park, southeastern Alaska allow insights into the role of abiotic and biotic interactions in the assemblage of benthic communities. Reductions in abundance of a pioneer chironomid colonizer, Diamesa alpina/lupus, in one new stream, Wolf Point Creek, is considered to be a result of competitive interactions with subsequent colonizers, as opposed to intolerance of warmer water temperature as previously suggested. Reduced densities of potential competitors (25–50 larvae per 500 cm2) in a cobble transplant experiment between streams, allowed persistence of D. alpina/lupus at low densities. In addition, significantly more D. alpina/lupus larvae emigrated from artificial stream channels containing other chironomid taxa than channels without potential competitors while there was no significant correlation of emigration with water temperature. A small number of D. alpina/lupus transplanted from a cold stream (4–6 °C) survived at water temperatures of 10–15 °C for 1 week. These results infer that interference competition is the causal mechanism in the decline of D. alpina/lupus. Complete exclusion of D. alpina/lupus from the stream has not occurred and water temperature may play a role in partitioning D. alpina/lupus from other taxa on a temporal or a spatial basis.
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