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  • stability
  • Springer  (35)
  • Amsterdam ; Boston : Elsevier
  • Berlin : Reimer
  • Berlin ; Heidelberg : Springer
  • Berlin [u.a.] : Springer
  • Berlin, Heidelberg : Springer
  • Leningrad : Gidrometeoizdat
  • München : Beck
  • Obninsk : VNIIGMI-MCD
  • Wabern : Federal Office of Topography, Swiss Geological Survey
  • 2005-2009
  • 1995-1999
  • 1985-1989  (35)
  • 1925-1929
  • 1989  (23)
  • 1985  (12)
Collection
Publisher
  • Springer  (35)
  • Amsterdam ; Boston : Elsevier
  • Berlin : Reimer
  • Berlin ; Heidelberg : Springer
  • Berlin [u.a.] : Springer
  • +
Years
  • 2005-2009
  • 1995-1999
  • 1985-1989  (35)
  • 1925-1929
Year
  • 1
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    Journal of dynamics and differential equations 1 (1989), S. 269-298 
    ISSN: 1572-9222
    Keywords: Geometric mechanics ; reduction ; stability ; chaos ; rigid body dynamics ; periodic orbits ; 58F
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give a complete bifurcation and stability analysis for the relative equilibria of the dynamics of three coupled planar rigid bodies. We also use the equivariant Weinstein-Moser theorem to show the existence of two periodic orbits distinguished by symmetry type near the stable equilibrium. Finally we prove that the dynamics is chaotic in the sense of Poincaré-Birkhoff-Smale horseshoes using the version of Melnikov's method suitable for systems with symmetry due to Holmes and Marsden.
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  • 2
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    Journal of dynamics and differential equations 1 (1989), S. 299-325 
    ISSN: 1572-9222
    Keywords: Commodity markets ; time delays ; stability ; Hopf bifurcation ; 34K15 ; 45J05 ; 90A16
    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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  • 3
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    Celestial mechanics and dynamical astronomy 47 (1989), S. 333-359 
    ISSN: 1572-9478
    Keywords: symplectic maps ; stability ; normal forms
    Source: Springer Online Journal Archives 1860-2000
    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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  • 4
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    Journal of statistical physics 54 (1989), S. 1427-1427 
    ISSN: 1572-9613
    Keywords: Kink propagation ; kink width ; characteristic functions ; stability ; continuum of modes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider the propagation of kinks in an elastic chain in a bistable or multistable potential under the action of a driving force [M. Büttiker and H. Thomas,Phys. Rev. A 37:235 (1988)]. Each element of the chain is subject to a damping force proportional to its velocity. We show that both the propagation velocity of the kinks as a function of the driving field, and the kink width as a function of propagation velocity, are determined by characteristic functions which depend only on the form of the potential. These functions can be found by considering a single particle moving in the upside-down potential of the chain. The general properties of these functions are studied and illustrated by several examples. The stability of these driven kinks is discussed. Interestingly, we find in addition to the expected discrete localized eigenmodes a two-dimensional continuum of oscillatory modes with a localized envelope.
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  • 5
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    Journal of statistical physics 55 (1989), S. 141-156 
    ISSN: 1572-9613
    Keywords: Kosterlitz-Thouless ; Coulomb gas ; hierarchical model ; renormalization group ; screening ; stability ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A hierarchical version of two-dimensional lattice Coulomb gases is investigated. Forβ〉β c=8π there is a locally stable line of fixed points for the renormalization group (“block charges”) transformations. For $$\beta 〉 \bar \beta _c (\beta _c \leqslant \bar \beta _c \leqslant \tfrac{3}{2}\pi \beta _c )$$ , these fixed points are globally stable. As a consequence we show that there is no screening of external charges for any activity if $$\beta 〉 \bar \beta _c $$ . Atβ c a supercritical bifurcation takes place and we investigate the behavior of the model forβ≲β c to show a weak form of screening.
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  • 6
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    Landscape ecology 3 (1989), S. 43-51 
    ISSN: 1572-9761
    Keywords: Czechoslovakia ; CSSR ; Slovakia ; ecological model ; planning ; landscape management ; stability ; disturbance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Development of the general ecological model (EM) of the CSSR has been included in the state program for environmental policy - the Ecoprogramme of the CSSR — at a scale of 1:1 000 000 for the entire Czechoslovak territory and at a scale of 1:500 000 for the Czech Socialist Republic (CSR) and the Slovak Socialist Republic (SSR). The objective of the first EM stage was to make a survey of spatial differentiation of the major ecological problems of the country. The EM consists of four parts, three analytical and one synthetic. These parts are: a. The ecological state (value) of the current spatial structure of the landscape. b. Ecological stress factors in the landscape. c. Protection of nature and natural resources. From the spatial synthesis of these three groups (from their spatial encounters), the following synthetic group of conditions was obtained: d. Regional ecological problems, a system of ecologically stable areas, environmental stress factors and factors endangering the ecological stability of the landscape, the natural resources and the human environment.
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  • 7
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    Acta mechanica solida Sinica 2 (1989), S. 285-294 
    ISSN: 0894-9166
    Keywords: Liapunov function ; stability ; discrete time system ; decision matrix
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The purpose of this paper is to present a new method for constructing Liapunov function and determining the stability of discrete time systems with a computer on the basis of the similarity transformation theory by directly applying the system matrix of the system under discussion instead of solving the discrete Liapunov's matrix equation.
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  • 8
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    Pure and applied geophysics 130 (1989), S. 743-749 
    ISSN: 1420-9136
    Keywords: Dynamic systems ; multiple equilibrium ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A set of ordinary differential equations describing a mechanical system subject to forcing and dissipation is considered. A topological argument is employed to show that if all time-dependent solutions of the governing equations are bounded, the equations admitN steady solutions, whereN is a positive odd integer and where at least (N−1)/2 of the steady solutions are unstable. The results are discussed in the context of atmospheric flows, and it is shown that truncated forms of the quasigeostrophic equations of dynamic meteorology and of Budyko-Sellers climate models satisfy the hypotheses of the theorem.
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  • 9
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    Acta mechanica Sinica 5 (1989), S. 109-117 
    ISSN: 1614-3116
    Keywords: stability ; boundary layer ; compliant wall
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The stability characteristics of laminar boundary layers over compliant walls was studied by the linear theory. Unlike the previous authors, the coupled motion of the fluid and solid was required to satisfy the continuity conditions of both the velocity and stress at the interface. Results of calculations show that as the speed ratio or density ratio exceeds a certain threshold value, the two types of unstable waves will no longer be distinguishable, and the tangential component of the disturbance stress is no longer negligible. So the neglect of it, as the previous authors did, is unjustified.
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  • 10
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    Aquatic ecology 23 (1989), S. 73-83 
    ISSN: 1573-5125
    Keywords: model ; fish ; vegetation ; eutrophication ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract A simple mathematical model was constructed, describing the relationships between pike, bream, aquatic macrophytes and the nutrient loading of shallow lakes. The model is analyzed with the use of zero-isoclines. It is concluded that, over a certain range of nutrient concentrations, the ecological relations incorporated in the model can give rise to the existence of two alternative stable equilibria;viz. a turbid bream-dominated one, and a clear state in which pike and aquatic vegetation are abundant. Under oligotrophic conditions, the clear-water state represents the only stable equilibrium; however, at high nutrient levels, the clear state is absent, or only locally stable. The response of the model to both increase and decrease of the nutrient level is characterised by hysteresis. The results indicate that manipulation of fish densities as a measure to improve water quality is only likely to produce long-term results when the nutrient level is below a certain threshold.
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  • 11
    ISSN: 1573-5060
    Keywords: Vigna radiata ; mungbean ; stability ; genotype-environment interaction ; wide adaptability ; AVRDC ; segmented regression
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Summary Yield data from the 5th–12th international mungbean nursery (IMN) trials conducted at 23 sites in 15 countries were analyzed by conventional stability analysis—regression of genotype mean on the environmental index, and by segmented regression analysis—fitting separate linear regressions in low yielding and high yielding environments. The gene pool base concept allows comparison of genotypes from different IMN trials grown in different years and sites. A very high positive linear relationship was observed between the regression coefficient and the average yield of cultivars, indicating that high yielding cultivars were less stable across environments. When data points of the regression of genotype mean and site mean for VC 1973A, a high yielding and widely adapted cultivar, were examined, the relationship appeared not to be linear. The segmented regression analysis improved the coefficient of determination (r2) and the genotypes were grouped based on regression coefficients in high yielding and low yielding environments. Different categories of genotypes suitable for high input environments, widely adaptable genotypes, and highly stable genotypes were identified.
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  • 12
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    Hydrobiologia 171 (1989), S. 159-170 
    ISSN: 1573-5117
    Keywords: Daphnia galeata mendotae ; Daphnidae ; Cladocera ; Crustacea ; cyclomorphosis ; phenotypic variability ; stability ; temperate lake ; coefficient of variation ; invertebrate predation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Phenotypic change is studied in a cyclomorphicDaphnia galeata mendotae population known from previous studies to be clonally diverse. Morphological analyses revealed cyclical changes in both adult and juvenile helmet length and tailspine length which were: 1) strongly correlated with mean water temperature; and 2) repeated annually during the 3-year study period. Field populations exhibited high (5% to 30%) coefficients of variation (CV) for both helmet length and tailspine length; the CV also exhibited seasonal fluctuations such that it was lowest in late summer. The period of highestDaphnia helmet development coincides with peak densities of the common invertebrate predatorsChaoborus andLeptodora. The fluctuations in CV may be due to both differential phenotypic expression of the coexisting clones and invertebrate predation.
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  • 13
    ISSN: 1573-5117
    Keywords: thermal structure ; heat content ; stability ; annual cycle ; diel variation ; tropical lakes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The thermal structure, heat content and stability were studied in Lakes Dom Helvécio and Carioca during an annual cycle. It was found that the maximum heat content, stability and work of the wind in Lake Dom Helvécio correspond to two, four and four times, respectively, the values for the Lake Carioca. These difference can be attributed to morphometric differences in the lakes. A long-term record of heat content and stability for lake Carioca is also presented. Diel variations were studied in summer and winter. The tropicality of the lakes is discussed and compared with other lacustrine systems.
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  • 14
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    Rheologica acta 28 (1989), S. 504-510 
    ISSN: 1435-1528
    Keywords: Taylor-Couette flow ; stability ; Doi-Edwards equation ; inertia
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract The stability of Taylor-Couette flow of entangled polymeric solutions to small axisymmetric stationary disturbances is analyzed using the Doi-Edwards constitutive equation in the small gap limit. A previous analysis of Karlsson, Sokolov, and Tanner for the general K-BKZ equation, of which the Doi-Edwards equation is a special case, reduces the problem to one of numerically evaluating seven viscoelastic functions of the shear rate $$\dot \gamma$$ in the gap. Of these seven, only three — two of which are related to the second normal stress difference, and one of them to shear thinning — significantly affect the flow stability. The negative second normal stress difference of the Doi-Edwards fluid stabilizes the flow at low values of the Weissenberg number λ1 $$\dot \gamma$$ , while shear thinning produces strong destabilization at moderate Weissenberg number. Hereλ 1 is the longest relaxation time. Non-monotonic effects of viscoelasticity on Taylor-Couette stability analogous to those predicted here have been observed in experiments of Giesekus. The extreme shear thinning of the Doi-Edwards fluid is also predicted to produce a large growth in the height of the Taylor cells, a phenomenon that has been seen experimentally by Beavers and Joseph.
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  • 15
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    Rheologica acta 28 (1989), S. 499-503 
    ISSN: 1435-1528
    Keywords: Taylor-Couetteflow ; stability ; Boger fluid ; Oldroyd-B equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Experimental evidence of a non-inertial, cellular instability in the Taylor-Couette flow of a viscoelastic fluid is presented. A linear stability analysis for an Oldroyd-B fluid, which is successful in describing many features of the experimental fluid, predicts the critical Deborah number,De c , at which the instability is observed. The dependence ofDe c on the value of the dimensionless gap between the cylinders is also determined.
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  • 16
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    Acta applicandae mathematicae 14 (1989), S. 125-133 
    ISSN: 1572-9036
    Keywords: 92A07 ; stationary solution ; immune response ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Some results connected with a simple mathematical model of infectious disease are discussed in order to demonstrate the approach to the modelling of such real processes. A more complicated model of antiviral immune response is presented. A new modification of this model in which targets for the viruses are immunocompetent cells is suggested.
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  • 17
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    Acta applicandae mathematicae 15 (1989), S. 211-234 
    ISSN: 1572-9036
    Keywords: 70F99 ; 70K20 ; 73C02 ; 35P30 ; Flexible body ; Lagrangian and Hamiltonian dynamics ; stability ; partial differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We analyse here the equations of motion of a planar body consisting of a rigid body with attached flexible rod. These equations take the form of coupled ordinary and partial differential equations. We analyse the equations both with and without centrifugal stiffening effects. Using the ‘energy-momentum’ method, we analyse nonlinear stability of the equilibria in each case. We also analyse the Hamiltonian and Poisson bracket structure of the system as well as the energy-momentum map and associated relative equilibria.
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  • 18
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    Journal of statistical physics 56 (1989), S. 533-545 
    ISSN: 1572-9613
    Keywords: Immune system ; dormant B cells ; cycles ; Jerne theory ; memory ; nonlinear phenomena ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The role of dormant B cells and cycles is analyzed in the context of a Lotka-Volterra network. It is shown that dormant B cells stabilize a cycle and that in this way both cooperate to preserve the internal image (memory) of an antigen. The network is embedded in a hierarchical scheme which allows adaptation, learning, and innovation by biased and random mutation.
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  • 19
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    Pharmaceutical research 6 (1989), S. 971-975 
    ISSN: 1573-904X
    Keywords: lyophilization ; stability ; pH effect ; moexipril
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Because of the limited stability of moexipril (RS-10085; 1) in aqueous solution, lyophilized parenteral formulations were evaluated as a function of pH in this study. In general, the lyophilized powder of 1 showed about two orders of magnitude less reactivity at 50°C than in aqueous solution at pH values below 3 or above 6. At pH 5.1, however, the lyophilized powder had maximum reactivity, with the rate actually comparable to that observed in aqueous solution. When the distribution of the two major products, diketopiperazine (DKP) 2 and ester hydrolysis analogue 3, was compared to the observed kinetics as a function of pH, it was clear that removal of water via lyophilization suppressed the spontaneous k 1 cyclization process, the spontaneous k 3 hydrolysis process, and the specific base-catalyzed k 4 hydrolysis process. The overall spontaneous k 2 cyclization process, however, was not affected by lyophilization. The latter result is accounted for by the increased equilibrium constant for the formation of the tetrahedral intermediate, To, as a result of lyophilization. This study demonstrates that stability data in solution can not be used for predicting the stability of moexipril in lyophilized powder form.
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  • 20
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    Journal of optimization theory and applications 63 (1989), S. 79-89 
    ISSN: 1573-2878
    Keywords: Probabilistic constrained programs ; feasible solution sets ; stability ; point-to-set maps
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we show the continuity of the feasibility set with respect to the reliability levels and with respect to the distribution of the random elements of a stochastic program with probabilistic constraints. Continuity is then used to obtain stability results for this type of stochastic program. An easy criterion is given for checking the conditions which guarantee the continuity of the feasibility set.
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  • 21
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    Journal of optimization theory and applications 61 (1989), S. 73-94 
    ISSN: 1573-2878
    Keywords: Decentralized control ; stabilization by output feedback ; stability ; numerical methods ; discrete-time linear systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we present an approach for designing structural constrained controllers for discrete-time linear systems, based on a new stabilizability property of the Riccati equation solution. First, the feedback stabilization problem under a general structural constraint is considered and a simple numerical procedure to solve it is presented. Special attention is given to the output feedback stabilization problem, for which sufficient conditions for the existence and convergence toward a stabilizing matrix are provided. Some examples are solved and comparisons with other methods available in the literature are made.
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  • 22
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    Journal of optimization theory and applications 61 (1989), S. 403-408 
    ISSN: 1573-2878
    Keywords: Isoperimetric inequalities ; stability ; circular rings ; structural optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of determining the optimal cross section of a circular ring so as to maximize the buckling pressure under a given total volume is formulated and solved. An isoperimetric inequality is proved: Among all the circular rings of given mass and radius, the ring with constant bending rigidity along the arc length has the largest critical buckling pressure.
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  • 23
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    Journal of optimization theory and applications 62 (1989), S. 419-447 
    ISSN: 1573-2878
    Keywords: Minimax optimization ; parametric optimization ; transversality ; sensitivity ; stability ; Chebyshev approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider functions of maximum type (max functions for short), subject to (in)equality constraints. The space dimension is finite, and the maximum is taken over a compact manifold with boundary. Effective local minimization algorithms based on Newton's method can be derived in the case where a local minimum is nondegenerate (in a two-level sense). In fact, nondegeneracy refers on the one hand to a local (implicit) reduction of the original max function to another one, where the maximum is taken over a finite set. On the other hand, it refers to strict complementarity and nondegeneracy of the underlying quadratic form with respect to the reduced stationary situation. As the main goal, we show that the set ofn-parameter families of functions, for which the stationary points of the corresponding max function are nondegenerate, constitutes an open and dense subset in the space of alln-parameter families (the topology used takes derivatives up to second order into account). An application to approximation problems of Chebyshev type is presented.
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  • 24
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    Computing 35 (1985), S. 85-91 
    ISSN: 1436-5057
    Keywords: 65M05 ; 65M10 ; 65M25 ; Second order ; characteristic difference schemes ; quasilinear hyperbolic systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Wir stellen ein Charakteristikenverfahren zweiter Ordnung für die numerische Lösung der Anfangswertaufgabe von quasilinearen hyperbolischen Systemen vor und beweisen die Stabilität des Verfahrens für Systeme mit konstanten Koeffizienten.
    Notes: Abstract We present two-step, second-order explicit characteristic difference schemes for the numerical solution of initialvalue problems for quasilinear hyperbolic system and show that the method is stable for systems with constant coefficients.
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  • 25
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    Computing 35 (1985), S. 325-344 
    ISSN: 1436-5057
    Keywords: 65L05 ; Numerical analysis ; Nyström methods ; stiff problems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Abstract The stability of adaptive Nyström-Runge-Kutta procedures is studied for a wide class of nonlinear stiff systems of second order differential equations. We show that for a large class of semi-discrete hyperbolic and parabolic problems the restriction of the stepsize is not due to the stiffness of the differential equation. Furthermore we use the scalar test equation $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ to derive conditions which ensure that the numerical forced oscillation is in phase with the analytical forced oscillation. The order of adaptive Nyström-Runge-Kutta methods (with a stability-matrix based on a diagonal Padéapproximation) for which the forced oscillation is in phase with its analytical counterpart cannot be greater than two. This barrier of order is not true forr-stage implicit Nyström methods of orderp=2r.
    Notes: Zusammenfassung Für eine umfangreiche Klasse nichtlinearer steifer Differentialgleichungssysteme zweiter Ordnung wird die Stabilität adaptiver Nyström-Runge-Kutta-Verfahren untersucht. Wir zeigen, daß für eine große Klasse semidiskretisierter hyperbolischer und parabolischer Probleme die Restriktion der Schrittweite unabhängig von der Steifheit des Differentialgleichungssystems ist. Weiterhin verwenden wir die skalare Testgleichung $$y'' = - \omega ^2 y + q \cdot e^{iv(t - t_0 )} $$ und geben Bedingungen dafür an, daß die numerische erzwungene Schwingung mit der analytischen erzwungenen Schwingung in Phase ist. Die Konsistenzordnung adaptiver Nyström-Runge-Kutta-Verfahren (mit einer Stabilitätsmatrix, die auf einer diagnolen Padé-Approximation beruht), für die die erzwungene Schwingung mit ihrem analytischen Gegenstück in Phase ist, kann nicht größer als zwei sein. Diese Ordnungsbarriere gilt nicht fürr-stufige implizite Nyström-Methoden der Ordnungp=2r.
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  • 26
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    Acta applicandae mathematicae 4 (1985), S. 225-258 
    ISSN: 1572-9036
    Keywords: 92A15 ; Prey ; predator ; competition ; dynamical system ; ordinary differential equation ; phase diagram ; equilibrium ; trajectory ; stability ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a problem of the dynamics of prey-predator populations suggested by the content of a letter of the biologist Umberto D'Ancona to Vito Volterra. The main feature of the problem is the special type of competition between predators of the same species as well as of different species. Two classes of cases are investigated: a first class in which the behaviour of the predator is ‘blind’ and the second one in which the behaviour is ‘intelligent’. A qualitative analysis of the dynamical systems under consideration is followed by a numerical analysis of the most significant cases.
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  • 27
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    Journal of mathematical biology 21 (1985), S. 285-298 
    ISSN: 1432-1416
    Keywords: Population dynamics ; coexistence ; mutualism ; persistence ; predator-mediated coexistence ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract We address the question of the long term coexistence of three interacting species whose dynamics are governed by the ordinary differential equations x i = X i f i (i = 1, 2, 3). In order for any theory in this area to be useful in practice, it must utilize as little information as possible concerning the forms of the f i , in view of the great difficulty of determining these experimentally. Here we obtain, under rather general conditions on the equations, a criterion for judging whether the species will coexist in a biologically realistic manner. This criterion depends only on the behaviour near the one or two species equilibria of the two dimensional subsystems, the behaviour there being relatively easy to examine experimentally. We show that with the exception of one class of cases, which is a generalization of a classical example of May and Leonard [21], invasibility at each such equilibrium suitably interpreted is both necessary and sufficient for a strong form of coexistence to hold. In the exceptional case, a single additional condition at the equilibria is enough to ensure coexistence.
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  • 28
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    Journal of mathematical biology 22 (1985), S. 81-104 
    ISSN: 1432-1416
    Keywords: FitzHugh-Nagumo equation ; pulse solution ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The FitzHugh-Nagumo equation u t =u xx +f(u)-w, u t =b(u-dw), is a simplified mathematical description of a nerve axon. If the parameters b〉0 and d⩾0 are taken suitably, this equation has two travelling pulse solutions with different propagation speeds. We study the stability of the fast pulse solution when b〉0 is sufficiently small. It is proved analytically by eigenvalue analysis that the fast pulse solution is “exponentially stable” if d〉0, and is “marginally stable” but not exponentially stable if d=0.
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  • 29
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    Rheologica acta 24 (1985), S. 551-555 
    ISSN: 1435-1528
    Keywords: Torsional flow ; Oldroyd-B fluid ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract It is shown that the exact solution of the torsional flow of a class of Oldroyd-type fluids is kinematically similar to that for a Newtonian fluid. Furthermore, it is shown by a linearized stability analysis and by numerical integration, that the basic flow is unstable at high Weissenberg numbers. An Oldroyd fluid which has a negative second-normal stress coefficient is found to be more stable than one with zero (or positive) second-normal stress coefficient in this flow.
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  • 30
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    Rheologica acta 24 (1985), S. 321-322 
    ISSN: 1435-1528
    Keywords: Viscometric flow ; stability ; short memory approximation ; change of type ; upper convected Maxwell model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 31
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    Rheologica acta 24 (1985), S. 469-473 
    ISSN: 1435-1528
    Keywords: Liquid crystal ; nematic ; semigroup ; stability ; tumbled state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract In shear flow of a nematic liquid crystal withα 3 ≧ 0 flow alignment cannot occur. The stability of the stationary in-plane solution, “the tumbled state”, is investigated using abstract techniques. Employing the existence of an elastic energy a sufficient criterion for stability is formulated. This criterion depends on the in-plane solution which is obtainable as a quadrature that is non-elementary except in special cases. It is shown that the tumbled state is stable and asymptotically stable for some physical configurations. The criterion presented is not a necessary condition for stability and thus only gives a lower bound.
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  • 32
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    Mathematical methods of operations research 29 (1985), S. 65-104 
    ISSN: 1432-5217
    Keywords: Additive cost criterion ; analytic behaviour of strategies ; ES strategy ; list schedule ; MES strategy ; priority rule ; quasi-stability ; regular measure of performance ; scheduling problems ; set strategy ; shift property ; stability ; stochastic scheduling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The paper introduces the finite class of set strategies for stochastic scheduling problems. It is shown that the knownstable classes of strategies such as ES and MES strategies are of this type, as arelist-scheduling strategies such as LEPT and SEPT and other, more complicatedpriority-type strategies. Roughly speaking, set strategies are characterized by the fact that the decision as to which jobs should be started at timet depends only on the knowledge of the two sets of jobs finished up to timet and being processed at timet. Contrary to list scheduling strategies, set strategies may involve deliberate idleness of machines, i.e. may not be greedy and can therefore not generally be induced by priority rules. It is demonstrated that set strategies have useful properties. They are e.g.λ n -almost everywhere continuous and therefore show satisfactorystability behaviour w.r.t. weak convergence of the joint distribution of job durations. Furthermore, the optimum w.r.t.all strategies is already attained on this class if job durations are independent and exponentially distributed and the performance measure fulfills a certainshift condition. This shift property is a quite natural concept and generalizes aspects of the notion ofadditivity in semi-Markov decision theory and stochastic dynamic optimization. Its complete analytical characterization is a major object of this paper. Typical additive cost criteria such as makespan and flowtime are of course covered, which yields simultaneously a first step towards generalization of optimality of LEPT and SEPT rules, as known for special cases. In fact, in view of the obtained optimality result, the question of when deliberate idleness of machines can be avoided, gains considerable interest, as it characterizes stochastic environments in whichpriority strategies are optimal. This provides a major link with current research on the analysis of networks of queues in the context of computer systems.
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  • 33
    ISSN: 1573-0646
    Keywords: 2,5-diaziridinyl-3,6-bis(2-hydroxyethylamino)-1,4-benzoquinone ; BZQ ; light-sensitive ; solution ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Medicine
    Notes: Summary The stability of the potential antitumour agent 2,5-diaziridinyl-3,6-bis(2-hydroxyethylamino)-1,4-benzoquinone (BZQ; NSC 224070) has been investgated by high-performance liquid chromatography. At 22°C in 0.05M buffer, BZQ was most stable at pH 9 with an apparent first-order rate constant (k) of about 0.014 h−11. There was reduced stability at pH values above and below 9.0. At a pH of 3 and 12 the values of k were 38 and 0.3 h−1, respectively. Stability of BZQ was adversely affected by increased temperatures (above 0°C), increased buffer concentration and light. Solutions of BZQ could not be frozen for any length of time, as the drug precipitated out in a form that would not redissolve (possibly a polymer). For parenteral administration to patients, it is suggested that BZQ would be most stable in 1.26% sodium bicarbonate solution when at room temperature, under normal laboratory lighting, 5% of the drug degraded (t0.95) in 5.5 h. Increased stability is obtainable in this medium by refrigeration and vigorous exclusion of light. Long term (24 h) infusions of BZQ could be considered in hypotonic sodium bicarbonate (30 mM) with careful exclusion of light as long as the volume of the infusion was small, e.g. 1 ml/h. Under these conditions to.95 was 42 h at 21.5°C.
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    Periodica mathematica Hungarica 16 (1985), S. 1-5 
    ISSN: 1588-2829
    Keywords: Primary 34A50, 65L05 ; Secondary 41A15 ; Differential equations ; initial value problem ; spline function ; linear multistep method ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we continue the study [4] of the stability question of the quasidouble step spline function approximations,s(x) ∈ C m−2 , to the initial value problemy (n) = f(x, y, ⋯, y (n−1) ). It will be shown that the method is unstable and hence divergent form ≥ n + 4.
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    Journal of optimization theory and applications 47 (1985), S. 235-252 
    ISSN: 1573-2878
    Keywords: Uncertain dynamical systems ; robotic tracking ; stability ; deterministic feedback control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The tracking problem for a robotic manipulator withn controlled degrees of freedom and uncertain dynamics is considered. Based on the deterministic theory of Refs. 1–15 and requiring only knowledge of bounds on the system uncertainty, a classC of continuous feedback controls (adapted from Ref. 11) is proposed with respect to which the uncertain tracking system is practically stabilizable in the sense that, given a feasible path to be tracked and an arbitrarily small neighborhood σ of the origin in the appropriate error space, there exists a control inC such that the tracking error for the feedback controlled uncertain system is ultimately bounded with respect to σ. The theory is illustrated in a numerical example of a robot with two degrees of freedom.
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