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  • 1
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    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
    ISSN: 1531-5851
    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
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  • 2
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    OR spectrum 20 (1998), S. 101-107 
    ISSN: 1436-6304
    Keywords: Competitive location model ; Nash equilibria ; stability ; reachability ; Wettbewerbsmodelle in der Standorttheorie ; Nash Gleichgewicht ; Stabilität ; Erreichbarkeit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In der Arbeit werden die Standorte von Duopolisten in einem Baum untersucht. Unter der Annahme festgesetzter Preise werden notwendige und hinreichende Bedingungen für Nash Gleichgewichte für Standorte auf Bäumen hergeleitet. Unter Verwendung dieser Bedingungen wird dann gezeigt, daß — angenommen Nash Gleichgewichte existieren — diese in einem wiederholt angewandten sequentiellen Standortfindungsprozeß, in dem beide Duopolisten als Zielfunktion kurzfristige Gewinnmaximierung haben, auch erreicht werden.
    Notes: Abstract This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.
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  • 3
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    OR spectrum 20 (1998), S. 101-107 
    ISSN: 1436-6304
    Keywords: Key words: Competitive location model ; Nash equilibria ; stability ; reachability ; Schlüsselwörter: Wettbewerbsmodelle in der Standorttheorie ; Nash Gleichgewicht ; Stabilität ; Erreichbarkeit
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung. In der Arbeit werden die Standorte von Duopolisten in einem Baum untersucht. Unter der Annahme festgesetzter Preise werden notwendige und hinreichende Bedingungen für Nash Gleichgewichte für Standorte auf Bäumen hergeleitet. Unter Verwendung dieser Bedingungen wird dann gezeigt, daß– angenommen Nash Gleichgewichte existieren – diese in einem wiederholt angewandten sequentiellen Standortfindungsprozeß, in dem beide Duopolisten als Zielfunktion kurzfristige Gewinnmaximierung haben, auch erreicht werden. “Equilibrium is a place in heaven, but how do we get there from here?”
    Notes: Abstract. This paper examines the location of duopolists on a tree. Given parametric prices, we first delineate necessary and sufficient conditions for locational Nash equilibria on trees. Given these conditions, we then show that Nash equilibria, provided they exist, can be reached in a repeated sequential relocation process in which both facilities follow short-term profit maximization objectives.
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  • 4
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    OR spectrum 18 (1996), S. 231-239 
    ISSN: 1436-6304
    Keywords: Generalized polymatrix games ; generalized linear complementarity problem ; stability ; degree theory ; Verallgemeinerte Polymatrix-Spiele ; verallgemeinertes lineares Komplementaritätsproblem ; Stabilität ; Grad-Theorie
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung In dieser Arbeit führen wir eine Verallgemeinerung des Polymatrix-Spiels (eines Nicht-Nullsummen- und nicht-kooperativenn-Personen-Spiels), das von Howson betrachtet wurde, ein und führen das Problem, eine Gleichgewichtsmenge von Strategien für ein solches Spiel zu berechnen, auf das verallgemeinerte lineare Komplementaritätsproblem von Cottle und Dantzig zurück. Für eine noch allgemeinere Version des Spiels beweisen wir die Existenz einerε-Gleichgewichtsmenge von Strategien. Wir präsentieren auch ein Ergebnis über die Stabilität der Gleichgewichte, das auf der Grad-Theorie beruht.
    Notes: Abstract In this paper, we introduce a generalization of the polymatrix game (a nonzero sum noncooperativen-person game) considered by Howson and relate the problem of computing an equilibrium set of strategies for such a game to the generalized linear complementarity problem of Cottle and Dantzig. For an even more general version of the game we prove the existence of anε-equilibrium set of strategies. We also present a result on the stability of the equilibria based on degree theory.
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  • 5
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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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  • 6
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    Journal of dynamics and differential equations 10 (1998), S. 151-188 
    ISSN: 1572-9222
    Keywords: Fourth-order solitary waves ; stability ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study ground-state traveling wave solutions of a fourth-order wave equation. We find conditions on the speed of the waves which imply stability and instability of the solitary waves. The analysis depends on the variational characterization of the ground states rather than information about the linearized operator.
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  • 7
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    Positivity 1 (1997), S. 319-330 
    ISSN: 1572-9281
    Keywords: delay equations ; stability ; positive solutions ; spectral growth condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove stability for a semilinear delay equation, whose nonlinearity is majorized by a linear positive operator. The key ingredients are a spectral condition, positivity of solutions to the linear problem, and lattice properties of the Banach space.
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  • 8
    ISSN: 1572-9281
    Keywords: asymptotic stability ; dichotomic maps ; retarded functional differential equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the study of the stability of nonautonomous retarded functional differential equations using the theory of dichotomic maps. After some preliminaries, we prove the theorems on simple and asymptotic stability. Some examples are given to illustrate the application of the method. Main results about asymptotic stability of the equation $$x'(t) = - b(t)x(t - r)$$ and of itsnonlinear generalization $$x'(t) = b(t)f(x(t - r))$$ are established.
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  • 9
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    Set-valued analysis 5 (1997), S. 73-88 
    ISSN: 1572-932X
    Keywords: differential inclusion ; invariance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The properties of invariance, stability, asymptotic stability and attainability of a given compact set $$K \subset \mathbb{R}^n $$ with respect to a differential inclusion, have weak and strong versions: the weak version requires existence of a trajectory with the corresponding property, while the strong one requires this property for all trajectories. The following statement is proven in the paper (under slight restrictions) for each of the above-mentioned properties: if K has the weak property with respect to $$\dot x \in F(x) $$ , then there is a (regulation) mapping G such that G(x) ⊂ F(x) ∀ x and G has the strong property with respect to $${\dot x}$$ ε G(x). In addition, certain regularity of the set of solutions of the last inclusion is claimed.
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  • 10
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    Set-valued analysis 5 (1997), S. 365-375 
    ISSN: 1572-932X
    Keywords: set-valued mappings ; vector optimization ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We establish optimization results for set-valued mappings, with the image space given by a topological vector space partially ordered by a cone. Moreover, we obtain stability results relative to parametrized optimization problems. We use a weak semicontinuity concept related to the order structure of the image space and show how compactness assumptions used in previous papers can be lightened.
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  • 11
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    Annals of operations research 56 (1995), S. 79-93 
    ISSN: 1572-9338
    Keywords: Multistage stochastic programs ; optimization in Banach spaces ; stability ; approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Multistage stochastic programs are regarded as mathematical programs in a Banach spaceX of summable functions. Relying on a result for parametric programs in Banach spaces, the paper presents conditions under which linearly constrained convex multistage problems behave stably when the (input) data process is subjected to (small) perturbations. In particular, we show the persistence of optimal solutions, the local Lipschitz continuity of the optimal value and the upper semicontinuity of optimal sets with respect to the weak topology inX. The linear case with deterministic first-stage decisions is studied in more detail.
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  • 12
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    Computational & mathematical organization theory 5 (1999), S. 5-30 
    ISSN: 1572-9346
    Keywords: network models ; organization theory ; rule following ; self organized ; stability ; work teams ; work routine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Self-organized rule-following systems are increasingly relevant objects of study in organization theory due to such systems&2018; capacity to maintain control while enabling decentralization of authority. This paper proposes a network model for such systems and examines the stability of the networks&2018; repetitive behavior. The networks examined are Ashby nets, a fundamental class of binary systems: connected aggregates of nodes that individually compute an interaction rule, a binary function of their three inputs. The nodes, which we interpret as workers in a work team, have two network inputs and one self-input. All workers in a given team follow the same interaction rule. We operationalize the notion of stability of the team&2018;s work routine and determine stability under small perturbations for all possible rules these teams can follow. To study the organizational concomitants of stability, we characterize the rules by their memory, fluency, homogeneity, and autonomy. We relate these measures to work routine stability, and find that stability in ten member teams is enhanced by rules that have low memory, high homogeneity, and low autonomy.
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  • 13
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    Journal of dynamics and differential equations 9 (1997), S. 463-505 
    ISSN: 1572-9222
    Keywords: Difference equations ; random perturbation ; averaging ; diffusion approximation ; randomly perturbed iterations ; stability ; 3SR60 ; 60H15 ; 60J99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let (X, ℬ) and (Y,C) be two measurable spaces withX being a linear space. A system is determined by two functionsf(X): X→ X andϕ:X×Y→X, a (small) positive parameterε and a homogeneous Markov chain {y n } in (Y,C) which describes random perturbations. States of the system, say {x n ɛ ∈X, n=0, 1,⋯}, are determined by the iteration relations:x n+1 ɛ =f(x n ɛ )+ɛϕ(x n ɛ ,Yn+1) forn≥0, wherex 0 ɛ =x 0 is given. Here we study the asymptotic behavior of the solutionx n ɛ asε → 0 andn → ∞ under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.
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  • 14
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    Set-valued analysis 5 (1997), S. 377-390 
    ISSN: 1572-932X
    Keywords: differential inclusions ; stability ; boundedness of solutions ; Lyapunov functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions.
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  • 15
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    Set-valued analysis 4 (1996), S. 361-374 
    ISSN: 1572-932X
    Keywords: 34A60 ; 34E15 ; 34C29 ; differential inclusion ; singular perturbation ; averaging method ; controlability ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider nonlinear, singularly perturbed differential inclusions and apply the averaging method in order to construct a limit differential inclusion for slow motion. The main approximation result states that the existence and regularity of the limit differential inclusion suffice to describe the limit behavior of the slow motion. We give explicit approximation rates for the uniform convergence on compact time intervals. The approach works under controllability or stability properties of fast motion.
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  • 16
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    Set-valued analysis 7 (1999), S. 209-238 
    ISSN: 1572-932X
    Keywords: nonsmooth analysis ; subdifferentials ; coderivatives ; implicit function theorem ; solvability ; stability ; open mapping theorem ; metric regularity ; multidirectional mean value inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.
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  • 17
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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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  • 18
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    Advances in computational mathematics 10 (1999), S. 271-289 
    ISSN: 1572-9044
    Keywords: delay differential equations ; steady state solutions ; stability ; 34K20 ; 65J10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The characteristic equation of a system of delay differential equations (DDEs) is a nonlinear equation with infinitely many zeros. The stability of a steady state solution of such a DDE system is determined by the number of zeros of this equation with positive real part. We present a numerical algorithm to compute the rightmost, i.e., stability determining, zeros of the characteristic equation. The algorithm is based on the application of subspace iteration on the time integration operator of the system or its variational equations. The computed zeros provide insight into the system’s behaviour, can be used for robust bifurcation detection and for efficient indirect calculation of bifurcation points.
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  • 19
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    BIT 36 (1996), S. 531-541 
    ISSN: 1572-9125
    Keywords: Meromorphic resolvent ; stability ; power bounded
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Tools to estimate resolvents are developed and a model result is given for power bounded operators: the dimension showing up in the Kreiss matrix theorem can be replaced by the trace norm.
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  • 20
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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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  • 21
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    Advances in computational mathematics 9 (1998), S. 145-171 
    ISSN: 1572-9044
    Keywords: periodic pseudodifferential equations ; multiwavelets ; splines with multiple knots ; generalized Galerkin–Petrov schemes ; boundary element methods ; error analysis ; stability ; Strang–Fix condition ; 65J10 ; 65N30 ; 65N35 ; 65R20 ; 47G30 ; 45P05 ; 41A25 ; 41A30 ; 41A15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We develop a stability and convergence analysis of Galerkin–Petrov schemes based on a general setting of multiresolution generated by several refinable functions for the numerical solution of pseudodifferential equations on smooth closed curves. Particular realizations of such a multiresolution analysis are trial spaces generated by biorthogonal wavelets or by splines with multiple knots. The main result presents necessary and sufficient conditions for the stability of the numerical method in terms of the principal symbol of the pseudodifferential operator and the Fourier transforms of the generating multiscaling functions as well as of the test functionals. Moreover, optimal convergence rates for the approximate solutions in a range of Sobolev spaces are established.
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  • 22
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    Advances in computational mathematics 4 (1995), S. 1-26 
    ISSN: 1572-9044
    Keywords: Wavelets ; biorthogonal wavelets ; stability ; primary 15A12 ; 65F35 ; secondary 42C15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL → ∞. These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.
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  • 23
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    Annals of global analysis and geometry 13 (1995), S. 141-148 
    ISSN: 1572-9060
    Keywords: Gauss curvature ; stability ; 53
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    Topics: Mathematics
    Notes: Abstract We prove that a domain on a surface of constant curvature is stable provided the integral of the mean curvature is small enough.
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  • 24
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    Annals of global analysis and geometry 15 (1997), S. 277-297 
    ISSN: 1572-9060
    Keywords: mean curvature ; $$r$$ -mean curvature ; sphere ; stability ; stable
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We deal with compact hypersurfaces immersed in space forms with constant $$r$$ -mean curvature. They are critical points for a variational problem. We show they are stable if and only if they are geodesic spheres, generalizing results on constant curvature hypersurfaces.
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  • 25
    ISSN: 1572-9125
    Keywords: finite difference methods ; wave equation ; accuracy ; stability ; Padé approximants ; order stars ; Riemann surface
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation,u tt =c 2 u xx , given by $$\sum\limits_{j = - S}^S {b_j U_{n + 1,m + j} + } \sum\limits_{j = - S}^S {a_j U_{n,m + j} + } \sum\limits_{j = - S}^S {b_j U_{n - 1,m + j} } = 0.$$ It has already been proved that the maximal order of accuracyp of such schemes is given byp ≤ 2(s + S). In this paper we show that the requirement of stability does not reduce this maximal order for any choice of the pair (s, S). The result is proved by introducing an order star on the Riemann surface of the algebraic function associated with the scheme. Furthermore, Padé schemes, withS = 0,s 〉 0, ands = 0,S 〉 0, are proved to be stable for 0 〈 μ 〈 1, where μ is the Courant number. These schemes can be implemented with high-order absorbing boundary conditions without reducing the range of μ for which stable solutions are obtained.
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  • 26
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    BIT 26 (1986), S. 93-99 
    ISSN: 1572-9125
    Keywords: Primary 65HO5 ; nonlinear equation ; multiple roots ; multipoint iterative methods ; error constant ; stability ; efficiency
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A one-parameter family of derivative free multipoint iterative methods of orders three and four are derived for finding the simple and multiple roots off(x)=0. For simple roots, the third order methods require three function evaluations while the fourth order methods require four function evaluations. For multiple roots, the third order methods require six function evaluations while the fourth order methods require eight function evaluations. Numerical results show the robustness of these methods.
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    BIT 27 (1987), S. 424-437 
    ISSN: 1572-9125
    Keywords: 65 L 05 ; 65 L 20 ; stability ; contractivity ; numerical solution of stiff initial value problems in ordinary differential equations ; Runge-Kutta methods ; Rosenbrock methods ; rational Runge-Kutta methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper concerns the stability analysis of numerical methods for approximating the solutions to (stiff) initial value problems. Our analysis includes the case of (nonlinear) systems of differential equations that are essentially more general than the classical test equationU′=λU, with λ a complex constant. We explore the relation between two stability concepts, viz. the concepts of contractivity and weak contractivity. General Runge-Kutta methods, one-stage Rosenbrock methods and a notable rational Runge-Kutta method are analysed in some detail.
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    Acta applicandae mathematicae 49 (1997), S. 35-54 
    ISSN: 1572-9036
    Keywords: dynamical systems ; stability ; pseudo orbit tracing property ; nonstandard analysis
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    Topics: Mathematics
    Notes: Abstract It is known that it is not possible to introduce C0 -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rn. Classically these amount to considering the space of all systems on a given subset of Rn as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.
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    Geometriae dedicata 62 (1996), S. 281-298 
    ISSN: 1572-9168
    Keywords: 53C23 ; Hyperbolicity ; stability ; quasi-geodesics
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    Topics: Mathematics
    Notes: Abstract It is known that for a geodesic metric space hyperbolicity in the sense of Gromov implies geodesic stability. In this paper it is shown that the converse is also true. So Gromov hyperbolicity and geodesic stability are equialent for geodesic metric spaces.
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    Acta applicandae mathematicae 9 (1987), S. 219-237 
    ISSN: 1572-9036
    Keywords: 34A34 ; 34D99 ; 90A16 ; Nonlinear differential equations ; stability ; growth ; economic dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.
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    Advances in computational mathematics 10 (1999), S. 115-133 
    ISSN: 1572-9044
    Keywords: Runge–Kutta–Nyström methods ; predictor–corrector methods ; stability ; parallelism ; 65M12 ; 65M20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
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    BIT 39 (1999), S. 620-645 
    ISSN: 1572-9125
    Keywords: Numerical integrator ; oscillatory solutions ; Schrödinger equation ; quantum-classical coupling ; error bounds ; stability
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    Topics: Mathematics
    Notes: Abstract We study time integration methods for equations of mixed quantum-classical molecular dynamics in which Newtonian equations of motion and Schrödinger equations are nonlinearly coupled. Such systems exhibit different time scales in the classical and the quantum evolution, and the solutions are typically highly oscillatory. The numerical methods use the exponential of the quantum Hamiltonian whose product with a state vector is approximated using Lanczos' method. This allows time steps that are much larger than the inverse of the highest frequencies. We describe various integration schemes and analyze their error behaviour, without assuming smoothness of the solution. As preparation and as a problem of independent interest, we study also integration methods for Schrödinger equations with time-dependent Hamiltonian.
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    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 809-816 
    ISSN: 1420-9039
    Keywords: 34D20 ; 34D35 ; 35Q72 ; 73H10 ; 73K03 ; Elastic string ; stability ; energy-momentum ; axial motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish “orbitai” stability (modulo this collection of relative equilibria). For a well-defined class of “soft” materials, there is an upper bound on the axial speed sufficient for stability; “stiff” materials are shown to be orbitally stable at any axial speed.
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    Monatshefte für Mathematik 126 (1998), S. 117-124 
    ISSN: 1436-5081
    Keywords: 52A20 ; 52A22 ; star bodies ; spherical integral transformations ; convex bodies ; stability
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    Topics: Mathematics
    Notes: Abstract LetK be ad-dimensional star body (with respect to the origino). It is known that the (d−1)-dimensional volume of the intersections ofK with the hyperplanes througho does not uniquely determineK. Uniqueness can only be achieved under additional assumptions, such as central symmetry. Here it is pointed out that if one uses, instead of intersections by hyperplanes, intersections by half-planes that containo on the boundary, then, without any additional assumptions, the volume of these intersections determinesK uniquely. This assertion, and more general results of this kind, together with stability estimates, are obtained from uniqueness results and estimates concerning a particular spherical integral transformation.
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    K-Theory 1 (1987), S. 185-196 
    ISSN: 1573-0514
    Keywords: Quadratic space ; patching diagram ; projective module ; stability
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    Topics: Mathematics
    Notes: Abstract We prove that every quadratic space of sufficiently large index contains a hyperbolic orthogonal summand.
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    K-Theory 10 (1996), S. 491-516 
    ISSN: 1573-0514
    Keywords: 57M60 ; 57N13 ; 57R91 ; 19G38 ; topological 4-manifold ; pseudofree action ; equivariant intersection form ; stability ; topological rigidity
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    Topics: Mathematics
    Notes: Abstract This paper is concerned with the algebraic aspects of the classification of pseudofree, locally linear group actions on a simply connected 4-manifold, particularly with the splitting and stability properties of the associated Hermitian intersection module and its isometry group. Our main result is the proof of stability of the equivariant intersection form for a large class of pseudofree actions. We also prove a topological rigidity theorem stating that two locally linear, pseudofree actions on a closed, oriented, simply connected 4-manifold, with the equivariant intersection forms indefinite and of rank at least 3 at each irreducible character, are topologically conjugate by an orientation preserving homeomorphism if and only if their oriented local representations at the corresponding fixed points are linearly equivalent.
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    K-Theory 2 (1988), S. 1-355 
    ISSN: 1573-0514
    Keywords: Pseudoisotopy ; stability ; Morse theory
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    Topics: Mathematics
    Notes: Abstract The stability theorem states that the suspension map C(M) → C(M X I) defined on the pseudoisotopy space C(M)=Diff(M X I rel M X O U ∂M X I) of a compact smooth n-manifold M is ∼ n/3-connected. This implies that C(M) has the R~ n/3-homotopy type of the stable pseudoisotopy space P(M) which is related to Waldhausen's algebraic K-theory of spaces by Waldhausen's formula A(X) Ω∞S∞(X+) X B2P(X). This paper gives a detailed proof of the smooth stability theorem following ideas by Hatcher for the proof of a PL stability theorem.
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    Journal of nonlinear science 5 (1995), S. 373-418 
    ISSN: 1432-1467
    Keywords: Hamiltonian system with symmetry ; relative equilibria ; perturbation ; linearization ; stability
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    Topics: Mathematics , Physics
    Notes: Summary A relative equilibrium of a Hamiltonian system with symmetry is a point of phase space giving an evolution which is a one-parameter orbit of the action of the symmetry group of the system. The evolutions of sufficiently small perturbations of a formally stable relative equilibrium are arbitrarily confined to that relative equilibrium's orbit under the isotropy subgroup of its momentum. However, interesting evolution along that orbit, here called drift, does occur. In this article, linearizations of relative equilibria are used to construct a first order perturbation theory explaining drift, and also to determine when the set of relative equilibria near a given relative equilibrium is a smooth symplectic submanifold of phase space.
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    International journal of game theory 25 (1996), S. 1-12 
    ISSN: 1432-1270
    Keywords: Bimatrix game ; ɛ-equilibrium ; optimal strategies ; vertical linear complementarity problem ; degree ; stability
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    Topics: Mathematics , Economics
    Notes: Abstract In this article, we consider a two-person game in which the first player picks a row representative matrixM from a nonempty set $$A$$ ofm ×n matrices and a probability distributionx on {1,2,...,m} while the second player picks a column representative matrixN from a nonempty set ℬ ofm ×n matrices and a probability distribution y on 1,2,...,n. This leads to the respective costs ofx t My andx t Ny for these players. We establish the existence of an ɛ-equilibrium for this game under the assumption that $$A$$ and ℬ are bounded. When the sets $$A$$ and ℬ are compact in ℝmxn, the result yields an equilibrium state at which stage no player can decrease his cost by unilaterally changing his row/column selection and probability distribution. The result, when further specialized to singleton sets, reduces to the famous theorem of Nash on bimatrix games.
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    Journal of nondestructive evaluation 14 (1995), S. 127-136 
    ISSN: 1573-4862
    Keywords: Nondestructive evaluation ; corrosion monitoring ; electrical impedance tomography ; stability ; numerical methods
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    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics
    Notes: Abstract We investigate the problem of detecting and assessing, by means of static electrical measurements, damage due to corrosion in a structure. Corrosion damage, which is assumed to occur in an inaccessible part of a specimen, is modelled as material loss. The detection device consists of electrodes which inject DC current and measure voltage potentials in the accessible part of the specimen. The topography of the damaged surface is estimated from the measured data. This research is meant to evaluate if a method based on static electrical measurements has the potential to be developed into a useful nondestructive evaluation tool. We propose computational methods that take the measured data and estimate the unknown damaged surface. The methods are studied in order to understand their properties. Several example calculations from synthetic data are presented. Our findings indicate that such a device has limited resolution. However, it offers several advantages that make it worthwhile to pursue further research.
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  • 41
    ISSN: 1573-4919
    Keywords: heart mitochondria ; lability ; muscle mitochondria ; oxidative phosphorylation ; stability ; taurine
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    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract We modified the isolation procedure of muscle and heart mitochondria. In human muscle, this resulted in a 3.4 fold higher yield of better coupled mitochondria in half the isolation time. In a preparation from rat muscle we studied factors that affected the stability of oxidative phosphorylation (oxphos) and found that it decreased by shaking the preparation on a Vortex machine, by exposure to light and by an increase in storage temperature. The decay was found to be different for each substrate tested. The oxidation of ascorbate was most stable and less sensitive to the treatments. When mitochondria were stored in the dark and the cold, the decrease in oxidative phosphorylation followed first order kinetics. In individual preparations of muscle and heart mitochondria, protection of oxidative phosphorylation was found by adding candidate stabilizers, such as desferrioxamine, lazaroids, taurine, carnitine, phosphocreatine, N-acetylcysteine, Trolox-C and ruthenium red, implying a role for reactive oxygen species and calcium-ions in the in vitro damage at low temperature to oxidative phosphorylation. In heart mitochondria oxphos with pyruvate and palmitoylcarnitine was most labile followed by glutamate, succinate and ascorbate.We studied the effect of taurine, hypotaurine, carnitine, and desferrioxamine on the decay of oxphos with these substrates. 1 mM taurine (n = 6) caused a significant protection of oxphos with pyruvate, glutamate and palmitoylcarnitine, but not with the other substrates. 5 mM L-carnitine (n = 6), 1 mM hypotaurine (n = 3) and 0.1 mM desferrioxamine (n = 3) did not protect oxphos with any of the substrates at a significant level. These experiments were undertaken in the hope that the in vitro stabilizers can be used in future treatment of patients with defects in oxidative phosphorylation. (Mol Cell Biochem 174: 61–66, 1997)
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  • 42
    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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    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
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    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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  • 44
    ISSN: 1573-4919
    Keywords: microtubules ; assembly/diassembly ; ATP ; cAMP ; phosphorylation ; stability
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    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract The relevance of protein phosphorylation, transphosphorylation and binding phenomena in the kinetics of the ATP-induced assembly of cycle-purified microtubule protein from mammalian brain were studied. ATP was able to induce the polymerization of microtubules of normal appearance. However, the assembled structures, were unstable and microtubules depolymerized after achievement of a transitory maximum. Cyclic AMP reduced the amplitude of the polymerization maximum in a concentration-dependent manner, correlating with the stimulation of the endogenous phosphorylation reaction. When microtubule assembly was induced by GTP, in the presence of various concentrations of ATP, the slope of the depolymerization phase was found to depend on the concentration of ATP. Fluoride ion inhibited the endogenous phosphorylation reaction and reduced the disassembly rate, in a concentration-dependent manner. Evidence is also presented indicating that ATP did not bind to phosphocellulose-purified tubulin. These results further contribute to indicate that ATP and cyclic AMP, acting coordinately to control the phosphorylation extent of microtubule proteins are important factors to determine microtubule stability within the cell. Some implications of this mechanism for the regulation by cAMP of the initiation of DNA synthesis and mitosis are considered.
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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
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    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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    Journal of mathematical biology 22 (1985), S. 81-104 
    ISSN: 1432-1416
    Keywords: FitzHugh-Nagumo equation ; pulse solution ; stability
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    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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    Acta mathematicae applicatae sinica 12 (1996), S. 216-224 
    ISSN: 1618-3932
    Keywords: Dynamics of populations ; enemy-pest system ; persistence ; stability
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    Topics: Mathematics
    Notes: Abstract The model of a kind of predator-parasite-pest system is built in this paper in which the parasite population is controlled by predator in such a way that it preys upon the pest individuals parasitized. A disgusty of predator for preying upon the pest individuals parasitized is introduced in the model to measure the intensity that the parasite population was controlled by the predator. The persistence and the stability are studied for this system mathematically. And the influence of the disgusty on the persistence of the system is also noticed in biology.
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    Acta mathematicae applicatae sinica 13 (1997), S. 176-187 
    ISSN: 1618-3932
    Keywords: Spherical surface ; pseudospectral method ; vorticity equations ; stability ; convergence
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    Topics: Mathematics
    Notes: Abstract The pseudospectral method for solving vorticity equations on spherical surface is discussed. An interpolation procedure, which is different from the usual ones, is proposed. Based on such an interpolation, the pseudospectral scheme is constructed. Its generalized stability and convergence are analyzed rigorously. The theoretical analysis and computational skills can also be applied to other nonlinear partial differential equations defined on spherical surface.
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    Numerical algorithms 10 (1995), S. 225-244 
    ISSN: 1572-9265
    Keywords: Cholesky factorization error analysis ; Hankel matrix ; least squares ; normal equations ; orthogonal factorization ; QR factorization ; semi-normal equations ; stability ; Toeplitz matrix ; weak stability ; Primary 65F25 ; Secondary 47B35 ; 65F05 ; 65F30 ; 65Y05 ; 65Y10
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    Topics: Computer Science , Mathematics
    Notes: Abstract We show that a fast algorithm for theQR factorization of a Toeplitz or Hankel matrixA is weakly stable in the sense thatR T R is close toA T A. Thus, when the algorithm is used to solve the semi-normal equationsR TRx=AT b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear systemAx=b. The algorithm also applies to the solution of the full-rank Toeplitz or Hankel least squares problem min ||Ax-b||2.
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    Numerical algorithms 14 (1997), S. 343-359 
    ISSN: 1572-9265
    Keywords: progressive interpolation ; stability ; spline ; shape parameters ; geometric continuity ; 41A05 ; 41A15 ; 65D05 ; 65D07
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    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, we study several interpolating and smoothing methods for data which are known “progressively”. The algorithms proposed are governed by recurrence relations and our principal goal is to study their stability. A recurrence relation will be said stable if the spectral radius of the associated matrix is less than one. The iteration matrices depend on shape parameters which come either from the connection at the knots, or from the nature of the interpolant between two knots. We obtain various stability domains. Moving the parameters inside these domains leads to interesting shape effects.
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    Numerical algorithms 10 (1995), S. 245-260 
    ISSN: 1572-9265
    Keywords: Multistep methods ; differential-algebraic equations ; stability ; existence and uniqueness ; convergence of iterative method ; 65L06 ; 65L20 ; 65N22
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    Topics: Computer Science , Mathematics
    Notes: Abstract Multistep methods for the differential/algebraic equations (DAEs) in the form of $$F_1 (x) = 0, F_2 (x,x',z) = 0$$ are presented, whereF 1 maps from ℝ n to ℝ ′ ,F 2 from ℝ n x ℝ n x ℝ m to ℝ s andr〈n≤r+s=n+m. By employing the deviations of the available existence theories, a new form of the multistep method for solutions of (1) is developed. Furthermore, it is shown that this method has no typical instabilities such as those that may occur in the application of multistep method to DAEs in the traditional manner. A proof of the solvability of the multistep system is provided, and an iterative method is developed for solving these nonlinear algebraic equations. Moreover, a proof of the convergence of this iterative method is presented.
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    Acta mathematicae applicatae sinica 13 (1997), S. 33-44 
    ISSN: 1618-3932
    Keywords: Inverse problem ; hyperbolic equations ; eigenvalue problem ; spectral function ; integral kernel ; stability
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    Topics: Mathematics
    Notes: Abstract In this paper, the inverse boundary value problem of the hyperbolic system of first-order differential equations is discussed. The estimate of the solution and the quantitative analysis about its stability are obtained, and some stability criteria are established.
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  • 53
    ISSN: 1573-0646
    Keywords: Antagonist G ([Arg6, D-Trp7,9,,MePhe 8 ]-Substance P {6-11}) ; analytical characterization ; parenteral formulation ; stability ; oxidative degradation products
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Medicine
    Notes: Abstract The aim of this study was to develop a stable parenteral dosage form for the investigational cytotoxic drug [Arg6, D-Trp7,9, MePhe8]-Substance P {6-11} (Substance P Antagonist G; Antagonist G). Antagonist G bulk drug was structurally and analytically characterized. The drug exhibits excellent aqueous solubility, although relatively poor aqueous stability characteristics. Lyophilization was, therefore, selected as the manufacturing process. Differential scanning calorimetry studies were conducted to determine the freeze-drying cycle parameters which resulted in a stable, lyophilized formulation of Antagonist G. The prototype, containing 50 mg Antagonist G per vial, was found to be the optimal formulation in terms of solubility, length of the freeze-drying cycle, stability, and dosage requirements in the planned phase I clinical trials. Quality control of the freeze-dried formulation showed that the manufacturing process does not change the integrity of Antagonist G. Shelf life studies demonstrated that the formulation is stable for at least 3 years, when stored at 2–8°C in a dark environment. Oxidative degradation products of Antagonist G were isolated and structurally characterized by mass spectrometry, nuclear magnetic resonance spectroscopy, and infrared spectroscopy.
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    Applied mathematics and mechanics 16 (1995), S. 195-202 
    ISSN: 1573-2754
    Keywords: nonlinear ; stability ; Lyapunov function
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In the paper Lyapumov function for a fourth order linear system is given and stability of the trivial solutions to a class of fourth order nonlinear systems is studied.
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    Applied mathematics and mechanics 16 (1995), S. 635-642 
    ISSN: 1573-2754
    Keywords: analytic mechanics ; nonholonomic system ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The stability for the equilibrium states of Chaplygin's systems is considered. The equations of motion of Chaplygin's systems and the existence conditions of their equilibrium states are given. Some criteria of stability for the equilibrium. states of Chaplygin's systems are obtained. Two examples are finally given.
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    Applied mathematics and mechanics 17 (1996), S. 869-877 
    ISSN: 1573-2754
    Keywords: thermohaline double-diffusive system ; periodic solution ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A shortout analytic method of stability in strong nonlinear autonomous system is introduced into stability analysis of the thermohaline double-diffusive system. Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions. For linear periodic solution in infinitesimal motion, the existence range of monotomic branch and oscillatory branch are outilined. The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value µ c in this case of 0〈rs-rsc≪1. The stability conclusions under different direction of vortex are drawn out.
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    Applied mathematics and mechanics 19 (1998), S. 163-168 
    ISSN: 1573-2754
    Keywords: nonlinear equation ; stability ; Newton's method ; auto-adjustable damping method ; the vector of damping factors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The general approach for solving the nonlinear equations is linearizing the equations and forming various iterative procedures, then executing the numerical simulation. For the strongly nonlinear problems, the solution obtained in the iterative process is always difficult, even divergent due to the numerical instability. It can not fulfill the engineering requirements. Newton's method and its variants can not settle this problem. As a result, the application of numerical simulation for the strongly nonlinear problems is limited. An auto-adjustable damping method has been presented in this paper. This is a further improvement of Newton's method with damping factor. A set of vector of damping factor is introduced. This set of vector can be adjusted continuously during the iterative process in accordance with the judgement and adjustment. An effective convergence coefficient and quichening coefficient are employed to relax the restricted requirements for the initial values and to shorten the iterative process. Then, the numerical stability will be ensured for the solution of complicated strongly nonlinear equations. Using this method, some complicated strongly nonlinear heat transfer problems in airplanes and aeroengines have been numerically simulated successfully. It can be used for the numerical simulation of strongly nonlinear problems in engineering such as nonlinear hydrodynamics and aerodynamics, heat transfer and structural dynamic response etc.
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    Applied mathematics and mechanics 19 (1998), S. 861-867 
    ISSN: 1573-2754
    Keywords: rotating fluids ; motion of body ; small disturbances ; stability
    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, the disturbances to a uniformly rotating ideal fluid with a sphere moving steadily along the axis of rotation are analysed by using linearization theory, the equations of disturbance, pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method of normal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that three are three kinds of possible forms of neutral disturbances.
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    Applied mathematics and mechanics 20 (1999), S. 912-916 
    ISSN: 1573-2754
    Keywords: delay ; neural network ; stability ; TN911.23 ; O332
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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, by using Liapunov functional, some sufficient conditions are obtained for the stability of the equilibrium of a neural network model with delay of the type $$u'_i \left( t \right) = - b_i u_i \left( t \right) + \sum\limits_{j = 1}^n {T_{ij} f_j } \left( {\mu _j u_j \left( {t - \tau _j } \right)} \right) + c_i ,\tau _j \geqslant 0,i = 1,2 \cdots ,n.$$
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    Applied mathematics and mechanics 19 (1998), S. 457-462 
    ISSN: 1573-2754
    Keywords: neural networks ; equilibrium ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, some sufficient conditions are obtained for the global asymptotic stability of the equilibrium of neural networks with interneuronal transmission delays of the type $$x'_i (t) = - b_i x_i (t) + \sum\limits_{j = 1}^n {\omega _{\ddot y} f_j (x_j (t - \tau _j )) + p_i (t 〉 0;i = 1,2, \cdots ,n)} $$
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    Applied mathematics and mechanics 20 (1999), S. 1384-1388 
    ISSN: 1573-2754
    Keywords: nonlinear dynamic system ; bifurcation ; stability ; TB123 ; O322
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    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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  • 63
    ISSN: 1573-8221
    Keywords: D-amino acid ; dipeptides ; stability ; integrative functions of the brain
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    Topics: Biology , Medicine
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  • 64
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    Discrete event dynamic systems 5 (1995), S. 383-403 
    ISSN: 1573-7594
    Keywords: Discrete event systems ; stability ; boundedness ; Petri nets ; manufacturing systems
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    Topics: Mathematics
    Notes: Abstract Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of “logical” discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications including manufacturing systems and computer networks (Passino et al. 1994, Burgess and Passino 1994). In this paper we extend the conventional notions and analysis of uniform boundedness, uniform ultimate boundedness, practical stability, finite time stability, and Lagrange stability so that they apply to the class of logical DES that can be defined on a metric space. Within this stability-theoretic framework we show that the standard Petri net-theoretic notions of boundedness are special cases of Lagrange stability and uniform boundedness. In addition we show that the Petri ent-theoretic approach to boundedness analysis is actually a Lyapunov approach in that the net-theoretic analysis actually produces an appropriate Lyapunov function. Moreover, via the Lyapunov approach we provide a sufficient condition for the uniform ultimate boundedness of General Petri nets. To illustrate the Petri net results, we study the boundedness properties of a rate synchronization network for manufacturing systems. In addition, we provide a detailed analysis of the Lagrange stability of a single-machine manufacturing system that uses a priority-based part servicing policy.
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    Discrete event dynamic systems 8 (1998), S. 137-173 
    ISSN: 1573-7594
    Keywords: hybrid systems ; switched systems ; timed Petri nets ; stability ; supervisory control
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    Topics: Mathematics
    Notes: Abstract In this paper, timed Petri nets are used to model and control hybrid systems. Petri nets are used instead of finite automata primarily because of the advantages they offer in dealing with concurrency and complexity issues. A brief overview of existing results on hybrid systems that are based on Petri nets is first presented. A class of timed Petri nets named programmable timed Petri nets (PTPN) is then used to model hybrid systems. Using the PTPN, the stability and supervisory control of hybrid systems are addressed and efficient algorithms are introduced. In particular, we present sufficient conditions for the uniform ultimate boundness of hybrid systems composed of multiple linear time invariant plants which are switched between using a logical rule described by a Petri net. This paper also examines the supervisory control of a hybrid system in which the continuous state is transfered to a region of the state space in a way that respects safety specifications on the plant's discrete and continuous dynamics.
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    Discrete event dynamic systems 7 (1997), S. 209-232 
    ISSN: 1573-7594
    Keywords: Stochastic recurrence equations ; performance evaluation ; ergodicity ; stability ; subadditive ergodic theory
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    Topics: Mathematics
    Notes: Abstract This paper deals with the asymptotic behavior of the stochastic dynamics of discrete event systems. In this paper we focus on a wide class of models arising in several fields and particularly in computer science. This class of models may be characterized by stochastic recurrence equations in ℝK of the form T(n+1) = φ n+1(T(n)) where φ n is a random operator monotone and 1—linear. We establish that the behaviour of the extremas of the process T(n) are linear. The results are an application of the sub-additive ergodic theorem of Kingman. We also give some stability properties of such sequences and a simple method of estimating the limit points.
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    Journal of mathematical imaging and vision 7 (1997), S. 309-323 
    ISSN: 1573-7683
    Keywords: relaxation labeling processes ; consistency ; growth transformations ; Liapunov functions ; stability
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    Topics: Mathematics
    Notes: Abstract We present some new results which definitively explain thebehavior of the classical, heuristic nonlinear relaxation labelingalgorithm of Rosenfeld, Hummel, and Zucker in terms of theHummel-Zucker consistency theory and dynamical systems theory. Inparticular, it is shown that, when a certain symmetry condition is met,the algorithm possesses a Liapunov function which turns out to be (thenegative of) a well-known consistency measure. This follows almostimmediately from a powerful result of Baum and Eagon developed in thecontext of Markov chain theory. Moreover, it is seen that most of theessential dynamical properties of the algorithm are retained when thesymmetry restriction is relaxed. These properties are also shown tonaturally generalize to higher-order relaxation schemes. Someapplications and implications of the presented results are finallyoutlined.
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    Discrete event dynamic systems 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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  • 69
    ISSN: 1573-7594
    Keywords: Decentralized scheduling ; manufacturing systems ; corridor policies ; stability
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    Notes: Abstract Sharifnia, Caramanis, and Gershwin [1991] introduced a class of policies for manufacturing systems, called by themlinear corridor policies. They proved that their stability can be discussed by the study of a simpler subset of such policies (cone policies). This paper revisits their work presenting a different description of the dynamics of the systems under study and explores it to device a necessary and sufficient condition for stability, obtained by the strengthening of the assumptions in Sharifnia et al. (1991). This condition is shown to be simply tested (M −1≥0) and valid for various realizations.
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    Neuroscience and behavioral physiology 16 (1986), S. 333-339 
    ISSN: 1573-899X
    Keywords: adaptability ; stability ; electroencephalogram ; connectability of EEG components
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    Topics: Biology , Medicine
    Notes: Abstract The problem of the stability and adaptability of regulatory processes is considered, taking as a point of departure N. P. Bekhtereva's theory regarding stable pathological states, and inflexible and adaptable links in control systems. The need to introduce a probabilistic approach is emphasized. Generalizations are made on materials relating to the connectability of the separate components of the biorhythms of functional systems, and to the stability of their amplitude-frequency characteristics. The corpus of facts permitted the successful development in clinical practice of functional biocontrol and feedback.
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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
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    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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    Mathematical notes 63 (1998), S. 396-400 
    ISSN: 1573-8876
    Keywords: ordinary differential equations ; fast and slow time ; periodic solutions ; existence ; stability
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    Topics: Mathematics
    Notes: Abstract We consider a system of ordinary first-order differential equations. The right-hand sides of the system are proportional to a small parameter and depend almost periodically on fast time and periodically on slow time. With this system, we associate the system averaged over fast time. We assume that the averaged system has a structurally unstable periodic solution. We prove a theorem on the existence and stability of almost periodic solutions of the original system.
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    Mathematical notes 60 (1996), S. 269-273 
    ISSN: 1573-8876
    Keywords: abstract Cauchy problem ; uniform correctness ; perturbation theory ; stability
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    Topics: Mathematics
    Notes: Abstract The stability of the uniform correctness of the Cauchy problem $$u(t) + \frac{k}{t}u'(t) = \mathbb{A}u(t)$$ ,t〉0,u(0)=u 0,u′(0)=0 fork〉0 with respect to perturbations of the operator $$\mathbb{A}$$ is studied.
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    Acta applicandae mathematicae 14 (1989), S. 125-133 
    ISSN: 1572-9036
    Keywords: 92A07 ; stationary solution ; immune response ; stability
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    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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    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
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    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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    Journal of optimization theory and applications 57 (1988), S. 265-293 
    ISSN: 1573-2878
    Keywords: Discrete-time systems ; infinite-horizon optimal control ; moving-horizon control ; state-control constraints ; nonquadratic cost functions ; stability
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    Topics: Mathematics
    Notes: Abstract Stability results are given for a class of feedback systems arising from the regulation of time-varying discrete-time systems using optimal infinite-horizon and moving-horizon feedback laws. The class is characterized by joint constraints on the state and the control, a general nonlinear cost function and nonlinear equations of motion possessing two special properties. It is shown that weak conditions on the cost function and the constraints are sufficient to guarantee uniform asymptotic stability of both the optimal infinite-horizon and moving-horizon feedback systems. The infinite-horizon cost associated with the moving-horizon feedback law approaches the optimal infinite-horizon cost as the moving horizon is extended.
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    Journal of optimization theory and applications 84 (1995), S. 415-431 
    ISSN: 1573-2878
    Keywords: Kalman filtering ; Karhunen-Loève expansion ; stability ; observability ; controllability
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    Topics: Mathematics
    Notes: Abstract Several state-space models for estimating a second-order stochastic process are proposed in this paper on the basis of the approximate Karhunen-Loève expansion. Properties of these models are studied and then the Kalman filtering method is applied. The accuracy of the models on the basis of two different situations, deterministic or random inputs, is studied by means of a simulation of a Brownian motion.
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    Journal of optimization theory and applications 88 (1996), S. 671-688 
    ISSN: 1573-2878
    Keywords: Infinite-horizon problems ; optimal control ; transversality condition ; stability ; Lyapunov exponents
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    Notes: Abstract We present necessary conditions of optimality for an infinitehorizon optimal control problem. The transversality condition is derived with the help of stability theory and is formulated in terms of the Lyapunov exponents of solutions to the adjoint equation. A problem without an exponential factor in the integral functional is considered. Necessary and sufficient conditions of optimality are proved for linear quadratic problems with conelike control constraints.
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    Journal of optimization theory and applications 97 (1998), S. 707-729 
    ISSN: 1573-2878
    Keywords: Nonlinear integral equations ; optimal control in L p-spaces ; relaxation ; existence ; stability ; nonconcentration ; optimality conditions ; Pontryagin maximum principle
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    Topics: Mathematics
    Notes: Abstract Optimal control problems with nonlinear equations usually do not possess optimal solutions, so that their natural (i.e., continuous) extension (relaxation) must be done. The relaxed problem may also serve to derive first-order necessary optimality condition in the form of the Pontryagin maximum principle. This is done here for nonlinear Fredholm integral equations and problems coercive in an L p-space of controls with p〈+∞. Results about a continuous extension of the Uryson operator play a key role.
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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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  • 81
    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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    Applied mathematics and mechanics 19 (1998), S. 135-146 
    ISSN: 1573-2754
    Keywords: nonholonomic system ; Lagrange's theorem ; manifold ; stability ; Liapunov's direct method
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The stability problem for the manifold of equilibrium positions of a class of nonholonomic systems is studied in this paper. Based on Liapunov's direct method and the definition of stability. Lagrange's theorem of holonomic systems is extended to a class of nonholonomic conservative systems and dissipative systems, and a new expression is made to the relation between asymptotic stability for the manifold of equilibrium positions of this class of nonholonomic systems and dissipative forces. Two examples are finally given to illustrate the application of the theorems.
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  • 83
    ISSN: 1573-0778
    Keywords: CHO cells ; DHFR ; IGFBP-1 ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract Stable expression of human insulin-like growth factor of binding protein-1 (hIGFBP-1)at high levels has been achieved in Chinese hamster ovary (CHO) cells by co-transfection and subsequent co-amplification of expression vectors containing the hIGFBP-1 cDNA and a dihydrofolate reductase (DHFR) cDNA gene into DHFR-deficient cells. Stepwise selection of the DHFR+ transformants in increasing concentrations of methotrexate (MTX) generated cells which had high copy numbers of the hIGFBP-1 gene (around 100 copies in cells amplified in medium containing 100 nM MTX). Expression of hIGFBP-1 in mixed clones was found to increase with increasing copy number and an apparent correlation between intra- and extracellular levels of hIGFBP-1 produced by these cells was observed. It was further observed that continuous cultivation over eight months in medium supplemented with 100 nM MTX increased the production of hIGFBP-1 25 times. The productivity did not increase further after five more months cultivation in MTX containing medium. A subcloning of this cell line gave clones with an even higher productivity. Further amplification in 500 nM or 1 uM MTX did not increase the hIGFBP-1 production.
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    Applied mathematics and mechanics 16 (1995), S. 1161-1169 
    ISSN: 1573-2754
    Keywords: shell ; stability ; critical load
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper gives the resultant forces and moments, strain energy and work of external forces on the basis of the deformation theory of flexible body. Therefore, in accordance with the principle of virtual displacement, the energy criterion of critical load is obtained and the equilibrium equation and boundary conditions of stability problem are derived.
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    Applied mathematics and mechanics 17 (1996), S. 65-75 
    ISSN: 1573-2754
    Keywords: impacting vibration ; stability ; codimension two bifurcation
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Bifurcation problems of a spring-mass system vibrating against an infinite large plane are studied in this paper. It is shown that there exist phenomena of codimension two bifurcations when the ratios of frequencies are in the neigborhood of the same special values and the coefficient of restitution approach unity. By theory of normal forms, we reduce Poincare maps to normal forms, and find flip bifurcations, Hopf bifurcations of fixed points and that of period two points. The theoretical solutions are verified by numerical computations.
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    Applied mathematics and mechanics 17 (1996), S. 1039-1049 
    ISSN: 1573-2754
    Keywords: nonlinear differential equations of the fourth order ; Lyapunov function ; stability ; boundedness ; intrinsic method
    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, we first present constructing a Lyapunov function for (1.1) and then we show the asymptotic stability in the large of the trivial solution x=0 for case p≡0, and the boundedness result of the solutions of (1.1) for case p≠0. These results improve several well-known results.
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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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    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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    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
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    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 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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    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
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    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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    Journal of optimization theory and applications 84 (1995), S. 145-169 
    ISSN: 1573-2878
    Keywords: Stackelberg problem ; multifunctions ; Γ-limits ; existence ; stability ; ε-solutions ; strict ε-solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The aim of this paper is to study, in a topological framework, existence and stability for the solutions to a parametrized Stackelberg problem. To this end, approximate solutions are used, more precisely, ε-solutions and strict ε-solutions. The results given are of minimal character and the standard types of constraints are considered, that is, constant constraints, constraints defined by a finite number of inequalities, and more generally constraints defined by an arbitrary multifunction.
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    Journal of optimization theory and applications 90 (1996), S. 357-380 
    ISSN: 1573-2878
    Keywords: Polyhedral sets ; extreme points ; multivalued maps ; continuity ; stability ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is focused on the stability properties of the extreme point set of a polyhedron. We consider a polyhedral setX(A,b) which is defined by a linear system of equality and inequality constraintsAx≤b, where the matrixA and the right-hand sideb are subject to perturbations. The extreme point setE(X(A,b)) of the polyhedronX(A,b) defines a multivalued map ℳ:(A,b)→E(X(A,b)). In the paper, characterization of continuity and Lipschitz continuity of the map ℳ is obtained. Boundedness of the setX(A,b) is not assumed It is shown that lower Lipschitz continuity is equivalent to the lower semicontinuity of the map ℳ and to the Robinson and Mangasarian-Fromovitz constraint qualifications. Upper Lipschitz continuity is proved to be equivalent to the upper semicontinuity of the map ℳ. It appears that the upper semicontinuity of the map ℳ implies the lower semicontinuity of this map. Some examples of using the conditions obtained are provided.
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  • 94
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    Journal of optimization theory and applications 93 (1997), S. 635-638 
    ISSN: 1573-2878
    Keywords: Polynomial theory ; robustness ; Kharitonov theorem ; stability ; Hurwitz polynomials ; inverse Kharitonov problem ; Rouché theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of the robust stability of a Hurwitz polynomial which is the characteristic polynomial of a discrete-time linear time-invariant system is investigated. A new approach based on the Rouché theorem of classical complex analysis is adopted. An interesting sufficient condition for robust stability is derived. Three examples are included to support the theoretical result.
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  • 95
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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
    Source: Springer Online Journal Archives 1860-2000
    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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  • 96
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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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  • 97
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    Journal of optimization theory and applications 48 (1986), S. 81-93 
    ISSN: 1573-2878
    Keywords: Optimization ; duality ; stability ; nonconvex programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Using the concept of Φ-conjugate functions, a wide class of nonconvex optimization problems can be investigated. By generalized Lagrangians, the problems indicated and a generalized notion of stability can be treated. It is possible to give duality theorems for these problems such that the approach given by Rockafellar (1967) for convex problems can be extended to the nonconvex case.
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  • 98
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    Journal of optimization theory and applications 48 (1986), S. 245-263 
    ISSN: 1573-2878
    Keywords: Controlled invariants ; (A, ℬ)-invariants ; conditioned invariants ; (ℒ,A)-invariants ; stability ; stabilizability ; geometric approach ; linear system theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Self-bounded controlled and self-hidden conditioned invariant subspaces, recently introduced by the authors for a more direct and neat handling of some fundamental concepts of the geometric approach, such as controllability subspaces, are proved in this paper to be very useful tools also in dealing with synthesis problems with stability requirements. Definitions concerning stability of invariants and stabilizability of controlled invariants, simple and self-bounded, are first presented and discussed. In particular, it is shown that a more straightforward definition for controlled invariant stabilizability allows a simpler development of the theory, Then, some fundamental results relating self-boundedness to stabilizability are derived. For the sake of completeness, all statements are dualized to conditioned invariants, simple and self-hidden.
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  • 99
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    Journal of optimization theory and applications 50 (1986), S. 239-255 
    ISSN: 1573-2878
    Keywords: Uncertain dynamical systems ; robotic tracking ; stability ; nonlinear feedback control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The development of flexible manufacturing systems calls for industrial robots characterized by robustness of performance with regard to the variations of the loads and real time specification of the trajectory in the work space. In this paper, the design of a feedback controller guaranteeing such performance is considered. At first, the manipulator dynamics are embedded into a larger class of uncertain dynamical systems and a class of feedback controls is proposed that guarantees uniform ultimate boundedness of the tracking error. Successively, the methodology is specialized for the case of robotic manipulators to track trajectories described in task-oriented coordinates; the proposed control algorithm operates without requiring any explicit coordinate transformation.
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  • 100
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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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