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  • Articles  (349)
  • stability  (233)
  • global optimization  (117)
  • growth
  • Springer  (349)
  • Kiel: Kiel Institute for the World Economy (IfW)
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  • Mathematics  (338)
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  • Articles  (349)
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  • 1
    Electronic Resource
    Electronic Resource
    Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex (2000)
    Springer
    Annals of operations research 98 (2000), S. 171-187 
    Details
    ISSN: 1572-9338
    Keywords: global optimization ; cutting angle method ; increasing positively homogeneous function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper we study a method for global optimization of increasing positively homogeneous functions over the unit simplex, which is a version of the cutting angle method. Some properties of the auxiliary subproblem are studied and a special algorithm for its solution is proposed. A cutting angle method based on this algorithm allows one to find an approximate solution of some problems of global optimization with 50 variables. Results of numerical experiments are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019204407420
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  • 2
    Electronic Resource
    Electronic Resource
    A New ADI Scheme for Solving Three-Dimensional Parabolic Equations with First-Order Derivatives and Variable Coefficients (2000)
    Springer
    Journal of computational analysis and applications 2 (2000), S. 293-308 
    Details
    ISSN: 1572-9206
    Keywords: parabolic equations ; ADI scheme ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An ADI scheme for solving three-dimensional parabolic equations withfirst-order derivatives and variable coefficients has been developed basedon our previous papers and the idea of the modified upwind differencescheme. This ADI scheme is second-order accurate and unconditionallystable. Further, a small parameter can be chosen which makes it suitablefor simulating fast-transient phenomena or for computations on fine spatialmeshes. The method is illustrated with numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1010108620966
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  • 3
    Electronic Resource
    Electronic Resource
    A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions (2000)
    Springer
    Journal of heuristics 6 (2000), S. 191-213 
    Details
    ISSN: 1572-9397
    Keywords: genetic algorithm ; global optimization ; continuous variables
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Genetic algorithms are stochastic search approaches based on randomized operators, such as selection, crossover and mutation, inspired by the natural reproduction and evolution of the living creatures. However, few published works deal with their application to the global optimization of functions depending on continuous variables. A new algorithm called Continuous Genetic Algorithm (CGA) is proposed for the global optimization of multiminima functions. In order to cover a wide domain of possible solutions, our algorithm first takes care over the choice of the initial population. Then it locates the most promising area of the solution space, and continues the search through an “intensification” inside this area. The selection, the crossover and the mutation are performed by using the decimal code. The efficiency of CGA is tested in detail through a set of benchmark multimodal functions, of which global and local minima are known. CGA is compared to Tabu Search and Simulated Annealing, as alternative algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009626110229
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  • 4
    Electronic Resource
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    CHESS—Changing Horizon Efficient Set Search: A Simple Principle for Multiobjective Optimization (2000)
    Springer
    Journal of heuristics 6 (2000), S. 405-418 
    Details
    ISSN: 1572-9397
    Keywords: MOCO ; multiobjective optimization ; global optimization ; local search methods ; metaheuristics ; quad-trees
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a new concept for generating approximations to the non-dominated set in multiobjective optimization problems. The approximation set A is constructed by solving several single-objective minimization problems in which a particular function D(A, z) is minimized. A new algorithm to calculate D(A, z) is proposed. No general approach is available to solve the one-dimensional optimization problems, but metaheuristics based on local search procedures are used instead. Tests with multiobjective combinatorial problems whose non-dominated sets are known confirm that CHESS can be used to approximate the non-dominated set. Straightforward parallelization of the CHESS approach is illustrated with examples. The algorithm to calculate D(A, z) can be used in any other applications that need to determine Tchebycheff distances between a point and a dominant-free set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009638700683
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  • 5
    Electronic Resource
    Electronic Resource
    Bifurcation Phenomena from Standing Pulse Solutions in Some Reaction-Diffusion Systems (2000)
    Springer
    Journal of dynamics and differential equations 12 (2000), S. 117-167 
    Details
    ISSN: 1572-9222
    Keywords: singular perturbation ; standing pulses ; stability ; Hopf bifurcation ; reaction-diffusion system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Bifurcation phenomena from standing pulse solutions of the problem $$\varepsilon \tau u_t = \varepsilon ^2 u_{xx} + f(u,v),{\text{ }}v_t = v_{xx} + g(u,v)$$ is considered. ε(〉0) is a sufficiently small parameter and τ is a positive one. It is shown that there exist two types of destabilization of standing pulse solutions when τ decreases. One is the appearance of travelling pulse solutions via the static bifurcation and the other is that of in-phase breathers via the Hopf bifurcation. Furthermore which type of destabilization occurs first with decreasing τ is discussed for the piecewise linear nonlinearities f and g.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009098719440
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  • 6
    Electronic Resource
    Electronic Resource
    Stability of Linear Inequality Systems Measured by the Hausdorff Metric (2000)
    Springer
    Set-valued analysis 8 (2000), S. 253-266 
    Details
    ISSN: 1572-932X
    Keywords: Hausdorff metric ; linear inequality systems ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we propose a Hausdorff metric to measure the “distance” between two linear inequality systems on a real normed space X. For this topology, which comes through a pseudo-metric in the set Σ of linear inequality systems, the closedness of the feasible set mapping is studied, and at the same time a characterization of the stability of the subset Σ c of consistent sytems is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008701026782
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  • 7
    Electronic Resource
    Electronic Resource
    Stability Properties of a Bond Portfolio Management Problem (2000)
    Springer
    Annals of operations research 99 (2000), S. 251-265 
    Details
    ISSN: 1572-9338
    Keywords: stochastic programming ; bond portfolio management ; interest ratescenarios ; stability ; sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract The bond portfolio management problem is formulated as a multiperiod two-stage or multistage stochastic program based on interest rate scenarios. These scenarios depend on the available market data, on the applied estimation and sampling techniques, etc., and are used to evaluate coefficients of the resulting large scale mathematical program. The aim of the contribution is to analyze stability and sensitivity of this program on small changes of the coefficients – the (scenario dependent) values of future interest rates and prices. We shall prove that under sensible assumptions, the scenario subproblems are stable linear programs and that also the optimal first-stage decisions and the optimal value of the considered stochastic program possess acceptable continuity properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019275817688
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  • 8
    Electronic Resource
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    Destabilization for quasivariational inequalities of reaction-diffusion type (2000)
    Springer
    Applications of mathematics 45 (2000), S. 161-176 
    Details
    ISSN: 1572-9109
    Keywords: reaction-diffusion system ; unilateral conditions ; quasivariational inequality ; Leray-Schauder degree ; eigenvalue ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a reaction-diffusion system of the activator-inhibitor type with unilateral boundary conditions leading to a quasivariational inequality. We show that there exists a positive eigenvalue of the problem and we obtain an instability of the trivial solution also in some area of parameters where the trivial solution of the same system with Dirichlet and Neumann boundary conditions is stable. Theorems are proved using the method of a jump in the Leray-Schauder degree.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023033910657
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  • 9
    Electronic Resource
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    Diagonally implicit Runge–Kutta methods for 3D shallow water applications (2000)
    Springer
    Advances in computational mathematics 12 (2000), S. 229-250 
    Details
    ISSN: 1572-9044
    Keywords: numerical analysis ; shallow water problems ; DIRK methods ; stability ; 65L06 ; 65L20 ; 65M12 ; 65M20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We construct A‐stable and L‐stable diagonally implicit Runge–Kutta methods of which the diagonal vector in the Butcher matrix has a minimal maximum norm. If the implicit Runge–Kutta relations are iteratively solved by means of the approximately factorized Newton process, then such iterated Runge–Kutta methods are suitable methods for integrating shallow water problems in the sense that the stability boundary is relatively large and that the usually quite fine vertical resolution of the discretized spatial domain is not involved in the stability condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1018969203026
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  • 10
    Electronic Resource
    Electronic Resource
    On the Robustness of Gaussian Elimination with Partial Pivoting (2000)
    Springer
    BIT 40 (2000), S. 62-73 
    Details
    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; pivoting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It has been recently shown that large growth factors might occur in Gaussian Elimination with Partial Pivoting (GEPP) also when solving some plausibly natural systems. In this note we argue that this potential problem could be easily solved, with much smaller risk of failure, by very small (and low cost) modifications of the basic algorithm, thus confirming its inherent robustness. To this end, we first propose an informal model with the goal of providing further support to the comprehension of the stability properties of GEPP. We then report the results of numerical experiments that confirm the viewpoint embedded in the model. Basing on the previous observations, we finally propose a simple scheme that could be turned into (even more) accurate software for the solution of linear systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022314201484
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  • 11
    Electronic Resource
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    Runge-Kutta Methods for the Numerical Solution of Stiff Semilinear Systems (2000)
    Springer
    BIT 40 (2000), S. 611-639 
    Details
    ISSN: 1572-9125
    Keywords: Runge-Kutta methods ; stability ; convergence ; stiff problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper studies the stability and convergence properties of general Runge-Kutta methods when they are applied to stiff semilinear systems y′(t) = J(t)y(t) + g(t, y(t)) with the stiffness contained in the variable coefficient linear part. We consider two assumptions on the relative variation of the matrix J(t) and show that for each of them there is a family of implicit Runge-Kutta methods that is suitable for the numerical integration of the corresponding stiff semilinear systems, i.e. the methods of the family are stable, convergent and the stage equations possess a unique solution. The conditions on the coefficients of a method to belong to these families turn out to be essentially weaker than the usual algebraic stability condition which appears in connection with the B-stability and convergence for stiff nonlinear systems. Thus there are important RK methods which are not algebraically stable but, according to our theory, they are suitable for the numerical integration of semilinear problems. This paper also extends previous results of Burrage, Hundsdorfer and Verwer on the optimal convergence of implicit Runge-Kutta methods for stiff semilinear systems with a constant coefficients linear part.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022332200092
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  • 12
    Electronic Resource
    Electronic Resource
    Stochastic Methods for Ill-Posed Problems (2000)
    Springer
    BIT 40 (2000), S. 226-240 
    Details
    ISSN: 1572-9125
    Keywords: Stochastic differential equations ; regularisation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is devoted to the numerical analysis of ill-posed problems of evolution equations in Banach spaces using certain classes of stochastic one-step methods. The linear stability properties of these methods are studied. Regularisation is given by the choice of the regularisation parameter as α = $$\sqrt {\tau _n }$$ , where τ n is the stepsize and provides the convergence on smooth initial data. The case of the approximation of well-posed problems is also considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022386822865
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  • 13
    Electronic Resource
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    Perron–Frobenius Theory and Symmetry of Solutions to Nonlinear PDE's (2000)
    Springer
    Letters in mathematical physics 53 (2000), S. 313-320 
    Details
    ISSN: 1573-0530
    Keywords: partial differential equations ; nonlinearities ; symmetries ; stability ; minimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We suggest a simple but general method of establishing symmetry properties of stable solutions of nonlinear elliptic equations. The method relies on characterization of symmetry breaking with a help of zero modes and on a generalization of the Perron–Frobenius theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007622208894
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  • 14
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    On the Stability of Functional Equations and a Problem of Ulam (2000)
    Springer
    Acta applicandae mathematicae 62 (2000), S. 23-130 
    Details
    ISSN: 1572-9036
    Keywords: stability ; functional equations ; Cauchy difference ; semigroup ; inequalities ; approximate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study the stability of functional equations that has its origins with S. M. Ulam, who posed the fundamental problem 60 years ago and with D. H. Hyers, who gave the first significant partial solution in 1941. In particular, during the last two decades, the notion of stability of functional equations has evolved into an area of continuing research from both pure and applied viewpoints. Both classical results and current research are presented in a unified and self-contained fashion. In addition, related problems are investigated. Some of the applications deal with nonlinear equations in Banach spaces and complementarity theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006499223572
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  • 15
    Electronic Resource
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    Numerical solutions for a coupled non-linear oscillator (2000)
    Springer
    Journal of mathematical chemistry 28 (2000), S. 325-340 
    Details
    ISSN: 1572-8897
    Keywords: numerical method ; stability ; Hopf bifurcation ; coupled oscillator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract A second-order accurate numerical method has been proposed for the solution of a coupled non-linear oscillator featuring in chemical kinetics. Although implicit by construction, the method enables the solution of the model initial-value problem (IVP) to be computed explicitly. The second-order method is constructed by taking a linear combination of first-order methods. The stability analysis of the system suggests the existence of a Hopf bifurcation, which is confirmed by the numerical method. Both the critical point of the continuous system and the fixed point of the numerical method will be seen to have the same stability properties. The second-order method is more competitive in terms of numerical stability than some well-known standard methods (such as the Runge–Kutta methods of order two and four).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011025104111
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  • 16
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    The Equation of State of Lakes (2000)
    Springer
    Aquatic geochemistry 6 (2000), S. 1-17 
    Details
    ISSN: 1573-1421
    Keywords: lakes ; density ; compressibility ; expansibility ; conductivity ; stability ; pvt properties
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract In recent years, a number of workers have studied the stability of deep lakes such as Lake Tanganyika, Lake Baikal and Lake Malawi. In this paper, the methods that can be used to determine the effect that the components of lakes have on the equation of state are examined. The PVT properties of Lakes have been determined by using apparent molal volume data for the major ionic components of the lake. The estimated PVT properties (densities, expansibility and compressibilities) of the lakes are found to be in good agreement with the PVT properties (P) of seawater diluted to the same salinity. This is similar to earlier work that showed that the PVT properties of rivers and estuarine waters could also be estimated from the properties of seawater. The measured densities of Lake Tanganyika were found to be in good agreement (± 2 × 10-6 g cm-3) with the values estimated from partial molal properties and the values of seawater at the same total salinity (ST = 0.568‰). The increase in the densities of Lake Tanganyika waters increased due to changes in the composition of the waters. The measured increase in the measured density (45 × 10-6 g cm-3) is in good agreement (46 × 10-6 g cm-3) with the values calculated for the increase in Na+, HCO3 -, Mg2+, Ca2+ and Si(OH)4. Methods are described that can be used to determine the conductivity salinity of lakes using the equations developed for seawater. By combining these relationships with apparent molal volume data, one can relate the PVT properties of the lake to those of seawater.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009626325650
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  • 17
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    Outcome-Space Cutting-Plane Algorithm for Linear Multiplicative Programming (2000)
    Springer
    Journal of optimization theory and applications 104 (2000), S. 301-322 
    Details
    ISSN: 1573-2878
    Keywords: global optimization ; multiplicative programming ; cutting plane ; nonconvex programming ; outcome space ; extreme-point search
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This article presents an outcome-space pure cutting-plane algorithm for globally solving the linear multiplicative programming problem. The framework of the algorithm is taken from a pure cutting-plane decision set-based method developed by Horst and Tuy for solving concave minimization problems. By adapting this method to an outcome-space reformulation of the linear multiplicative programming problem, rather than applying directly the method to the original decision-set formulation, it is expected that considerable computational savings can be obtained. Also, we show how additional computational benefits might be obtained by implementing the new algorithm appropriately. To illustrate the new algorithm, we apply it to the solution of a sample problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004657629105
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  • 18
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    Approximation of an Analog Diffusion Network with Applications to Image Estimation (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 391-414 
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    ISSN: 1573-2878
    Keywords: diffusion networks ; image estimation ; global optimization ; simulated annealing ; weak convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This work is concerned with a numerical procedure for approximating an analog diffusion network. The key idea is to take advantage of the separable feature of the noise for the diffusion machine and use a parallel processing method to develop recursive algorithms. The asymptotic properties are studied. The main result of this paper is to establish the convergence of a continuous-time interpolation of the discrete-time algorithm to that of the analog diffusion network via weak convergence methods. The parallel processing feature of the network makes it attractive for solving large-scale optimization problems. Applications to image estimation are considered. Not only is this algorithm useful for the image estimation problems, but it is widely applicable to many related optimization problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026485504384
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  • 19
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    Duality Bound Method for the General Quadratic Programming Problem with Quadratic Constraints (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 331-354 
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    ISSN: 1573-2878
    Keywords: general quadratic programming problem with quadratic constraints ; global optimization ; branch-and-bound algorithms ; duality bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this article is to develop a branch-and-bound algorithm using duality bounds for the general quadratically-constrained quadratic programming problem and having the following properties: (i) duality bounds are computed by solving ordinary linear programs; (ii) they are at least as good as the lower bounds obtained by solving relaxed problems, in which each nonconvex function is replaced by its convex envelope; (iii) standard convergence properties of branch-and-bound algorithms for nonconvex global optimization problems are guaranteed. Numerical results of preliminary computational experiments for the case of one quadratic constraint are reported.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026437621223
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  • 20
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    Global Optimization of Costly Nonconvex Functions Using Radial Basis Functions (2000)
    Springer
    Optimization and engineering 1 (2000), S. 373-397 
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    ISSN: 1573-2924
    Keywords: global optimization ; nonconvex optimization ; software ; black box
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The paper considers global optimization of costly objective functions, i.e. the problem of finding the global minimum when there are several local minima and each function value takes considerable CPU time to compute. Such problems often arise in industrial and financial applications, where a function value could be a result of a time-consuming computer simulation or optimization. Derivatives are most often hard to obtain, and the algorithms presented make no use of such information. Several algorithms to handle the global optimization problem are described, but the emphasis is on a new method by Gutmann and Powell, A radial basis function method for global optimization. This method is a response surface method, similar to the Efficient Global Optimization (EGO) method of Jones. Our Matlab implementation of the Radial Basis Function (RBF) method is described in detail and we analyze its efficiency on the standard test problem set of Dixon-Szegö, as well as its applicability on a real life industrial problem from train design optimization. The results show that our implementation of the RBF algorithm is very efficient on the standard test problems compared to other known solvers, but even more interesting, it performs extremely well on the train design optimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1011584207202
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  • 21
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    Stability and chaotic motion in columns of nonlinear viscoelastic material (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 987-994 
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    ISSN: 1573-2754
    Keywords: stability ; chaos ; averaging method ; Galerkin method ; viscoelastic column ; O322
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The dynamical stability of a homogeneous, simple supported column, subjected to a periodic axial force, is investigated. The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive relation. The equation of motion was derived as a nonlinear integro-partial-differential equation, and was simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method was employed to carry out the stability analysis. Numerical results are presented to compare with the analytical ones. Numerical results also indicate that chaotic motion appears.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02459307
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  • 22
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    Analysis of coupled-mode flutter of pipes conveying fluid on the elastic foundation (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 1177-1186 
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    ISSN: 1573-2754
    Keywords: elastic foundation ; pipe conveying fluid ; coupled-mode flutter ; stability ; power series method ; 0353
    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 governing equation of solid-liquid couple vibration of pipe conveying fluid on the elastic foundation was derived. The critical velocity and complex frequency of pipe conveying fluid on Winkler elastic foundation and two-parameter foundation were calculated by power series method. Compared with pipe without considering elastic foundation, the numerical results show that elastic foundation can increase the critical flow velocity of static instability and dynamic instability of pipe. And the increase of foundation parameters may increase the critical flow velocity of static instability and dynamic instability of pipe, thereby delays the occurrence of divergence and flutter instability of pipe. For higher mass ratio β, in the combination of certain foundation parameters, pipe behaves the phenomenon of restabilization and redivergence after the occurrence of static instability, and then coupled-mode flutter takes place.
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    URL: http://dx.doi.org/10.1007/BF02458996
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  • 23
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    Research on stability of moving jet containing dense suspended solid particles (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 1390-1400 
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    ISSN: 1573-2754
    Keywords: suspended solid particles ; continuum phase-coupled model ; stability ; moving jet ; numerical computation ; O359
    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 spatial stability equation of moving jet containing dense suspended solid particles was derived out by means of the continuum phase-coupled model. The stability curves of moving jet for different downstream distances, Reynolds number of flow-field, particle properties and velocities of jetting device are got by the finite difference method based on the asymptotic method and the Eulerian conservative difference scheme. Founded on the analysis of the obtained stability curves it is found that the positive velocity of jetting device widens the unstable frequency range of flow-field but the effect of the negative one is contrary. In addition, particles existing in the flow-field curb the instability of flow-field and the effect enhances with the decrease of Reynolds number of flow-field. These conclusions benefit learning the development of moving two-phase jet.
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    URL: http://dx.doi.org/10.1007/BF02459217
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  • 24
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    Analysis and calculation of the nonlinear stability of the rotational composite shell (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 209-216 
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    ISSN: 1573-2754
    Keywords: composite material ; rotational shell ; stability ; nonlinear ; O347.3
    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 By adopting the energy method, a new method to calculate the stability of the composite shell of revolution is presented. This method takes the influence of nonlinear prebuckling deformations and stresses on the buckling of the shell into account. The relationships between the prebuckling deformations and strains are calculated by nonlinear Kármán equations. The numerical method is used to calculate the energy of the total system. The nonlinear equations are solved by combining gradient method and amendatory Newton iterative method. The computer program is also developed. An example is given to demonstrate the accuracy of the method presented.
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    Convergence and stability of recursive damped least square algorithm (2000)
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    Applied mathematics and mechanics 21 (2000), S. 237-242 
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    ISSN: 1573-2754
    Keywords: system identification ; damped least square ; recursive algorithm ; convergence ; stability ; O231 ; O241
    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 recursive least square is widely used in parameter identification. But it is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. It is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.
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    Almost Surely Convergent Global Optimization Algorithm Using Noise-Corrupted Observations (2000)
    Springer
    Journal of optimization theory and applications 104 (2000), S. 343-376 
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    ISSN: 1573-2878
    Keywords: random search ; stochastic approximation ; global optimization
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    Topics: Mathematics
    Notes: Abstract A new recursive algorithm for searching the global minimizer of a function is proposed when the function is observed with noise. The algorithm is based on switches between the stochastic approximation and the random search. The combination of SA with RS is not a new idea in such combination, the difficulty consists in creating a good switching rule and in designing an efficient method to reduce the noise effect. The proposed switching rule is easily realizable, the noise reducing method is effective, and the whole recursive optimization algorithm is simply calculated. It is proved that the algorithm a.s. converges to the global minimizer and is asymptotically normal. In comparison with existing methods, the proposed algorithm not only requires much weaker conditions, but also is more efficient as shown by simulation.
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    URL: http://dx.doi.org/10.1023/A:1004661730014
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    Convergence of the Simulated Annealing Algorithm for Continuous Global Optimization (2000)
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    Journal of optimization theory and applications 104 (2000), S. 691-716 
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    ISSN: 1573-2878
    Keywords: simulated annealing ; cooling schedule ; global optimization ; convergence analysis
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    Topics: Mathematics
    Notes: Abstract A class of simulated annealing algorithms for continuous global optimization is considered in this paper. The global convergence property is analyzed with respect to the objective value sequence and the minimum objective value sequence induced by simulated annealing algorithms. The convergence analysis provides the appropriate conditions on both the generation probability density function and the temperature updating function. Different forms of temperature updating functions are obtained with respect to different kinds of generation probability density functions, leading to different types of simulated annealing algorithms which all guarantee the convergence to the global optimum.
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    Mixed Solutions for Weak Stackelberg Problems: Existence and Stability Results (2000)
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    Journal of optimization theory and applications 105 (2000), S. 417-440 
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    ISSN: 1573-2878
    Keywords: mixed solutions ; weak Stackelberg problems ; existence ; stability ; weak convergence of probability measures
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    Topics: Mathematics
    Notes: Abstract We are concerned with ∈-mixed solutions for weak Stackelberg problems corresponding to two-player nonzero-sum noncooperative games. Two cases are considered: (i) mixed strategies for only the second player; (ii) mixed strategies for both players. After giving basic results relating convergence of functions and weak convergence of probability measures, we establish existence and stability results for ∈-mixed solutions under general assumptions of minimal character without any convexity assumption. Our results improve previous work of Mallozzi and Morgan (Refs. 1–2).
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    Inner Approximation Method for a Reverse Convex Programming Problem (2000)
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    Journal of optimization theory and applications 107 (2000), S. 355-389 
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    ISSN: 1573-2878
    Keywords: global optimization ; reverse convex programming problem ; dual problem ; inner approximation method ; penalty function method
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    Notes: Abstract In this paper, we consider a reverse convex programming problem constrained by a convex set and a reverse convex set, which is defined by the complement of the interior of a compact convex set X. We propose an inner approximation method to solve the problem in the case where X is not necessarily a polytope. The algorithm utilizes an inner approximation of X by a sequence of polytopes to generate relaxed problems. It is shown that every accumulation point of the sequence of optimal solutions of the relaxed problems is an optimal solution of the original problem.
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    Optimization of the Norm of a Vector-Valued DC Function and Applications (2000)
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    Journal of optimization theory and applications 107 (2000), S. 245-260 
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    ISSN: 1573-2878
    Keywords: global optimization ; difference of convex functions ; location theory ; multiple-criteria decision making
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    Notes: Abstract In this paper, we show that a DC representation can be obtained explicitly for the composition of a gauge with a DC mapping, so that the optimization of certain functions involving terms of this kind can be made by using standard DC optimization techniques. Applications to facility location theory and multiple-criteria decision making are presented.
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    Global Optimization Techniques for Mixed Complementarity Problems (2000)
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    Journal of global optimization 16 (2000), S. 1-21 
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    ISSN: 1573-2916
    Keywords: Mixed complementarity problems ; semismooth Newton method ; global optimization ; tunneling method ; filled function method
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    Notes: Abstract We investigate the theoretical and numerical properties of two global optimization techniques for the solution of mixed complementarity problems. More precisely, using a standard semismooth Newton-type method as a basic solver for complementarity problems, we describe how the performance of this method can be improved by incorporating two well-known global optimization algorithms, namely a tunneling and a filled function method. These methods are tested and compared with each other on a couple of very difficult test examples.
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    Simulated Annealing Algorithms for Continuous Global Optimization: Convergence Conditions (2000)
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    Journal of optimization theory and applications 104 (2000), S. 121-133 
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    ISSN: 1573-2878
    Keywords: global optimization ; simulated annealing ; convergence conditions
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    Topics: Mathematics
    Notes: Abstract In this paper, simulated annealing algorithms for continuous global optimization are considered. After a review of recent convergence results from the literature, a class of algorithms is presented for which strong convergence results can be proved without introducing assumptions which are too restrictive. The main idea of the paper is that of relating both the temperature value and the support dimension of the next candidate point, so that they are small at points with function value close to the current record and bounded away from zero otherwise.
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    Optimum Radius of Robust Stability for Schur Polynomials (2000)
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    Journal of optimization theory and applications 104 (2000), S. 165-174 
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    ISSN: 1573-2878
    Keywords: Systems theory ; stability ; robust stability ; linear systems ; discrete-time systems ; robustness ; polynomial theory ; Kharitonov theorem ; inverse Kharitonov problem ; Rouche theorem
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    Notes: Abstract The paper investigates the problem of the robust stability of Schur polynomials. Recently, a new approach based on the Rouche theorem of classical complex analysis has been adopted for the solution of this problem. In this paper, an improvement of the previous solution is presented. This is the optimum solution of the robust stability problem for Schur polynomials, which is obtained by solving a minimization problem and is better than other methods in robust stability literature. Three numerical examples are given to illustrate the proposed method.
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    Branch-and-Bound Variant of an Outcome-Based Algorithm for Optimizing over the Efficient Set of a Bicriteria Linear Programming Problem (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 37-54 
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    ISSN: 1573-2878
    Keywords: multiple-criteria decision making ; efficient set ; global optimization ; branch-and-bound methods
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    Notes: Abstract The paper presents a finite branch-and-bound variant of an outcome-based algorithm proposed by Benson and Lee for minimizing a lower-semicontinuous function over the efficient set of a bicriteria linear programming problem. Similarly to the Benson-Lee algorithm, we work primarily in the outcome space. Dissimilarly, instead of constructing a sequence of consecutive efficient edges in the outcome space, we use the idea of generating a refining sequence of partitions covering the at most two-dimensional efficient set in the outcome space. Computational experience is also presented.
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    Extended Well-Posedness Properties of Vector Optimization Problems (2000)
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    Journal of optimization theory and applications 106 (2000), S. 165-182 
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    ISSN: 1573-2878
    Keywords: Vector optimization ; asymptotically minimizing sequences ; extended well-posedness ; stability ; vector variational principle
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    Notes: Abstract In this paper, the concept of extended well-posedness of scalar optimization problems introduced by Zolezzi is generalized to vector optimization problems in three ways: weakly extended well-posedness, extended well-posedness, and strongly extended well-posedness. Criteria and characterizations of the three types of extended well-posedness are established, generalizing most of the results obtained by Zolezzi for scalar optimization problems. Finally, a stronger vector variational principle and Palais-Smale type conditions are used to derive sufficient conditions for the three types of extended well-posedness.
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    On the Robust Stability of 2D Schur Polynomials (2000)
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    Journal of optimization theory and applications 106 (2000), S. 431-439 
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    ISSN: 1573-2878
    Keywords: multidimensional polynomial theory ; robustness ; Kharitonov theorem ; stability ; Schur polynomials ; inverse Kharitonov problem ; Rouché theorem
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract In this note, the problem of the robust stability for a two-dimensional (two-variable) Schur polynomial which is the characteristic polynomial of a discrete-time linear time-invariant system is investigated. A new approach based on the Rouché theorem is adopted. The extension to the robust stability for multidimensional (multivariable) polynomials is also provided. Interesting sufficient conditions for such robust stability are derived. A two-dimensional example is included to support the theoretical result.
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    Upper and Lower Semicontinuity for Set-Valued Mappings Involving Constraints (2000)
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    Journal of optimization theory and applications 106 (2000), S. 527-550 
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    Keywords: vector optimization ; set-valued mappings ; constraint sets ; stability
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    Notes: Abstract In vector optimization, several authors have studied the upper and lower semicontinuity for mappings involving constraints in topological vector spaces partially ordered through a cone with nonempty interior. In this paper, we give conditions about the upper and lower semicontinuity in the case that the ordering cone in the parameter space has possibly empty interior, as it happens in many function spaces and seqence spaces.
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    Efficient Strategy for Adaptive Partition of N-Dimensional Intervals in the Framework of Diagonal Algorithms (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 145-168 
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    ISSN: 1573-2878
    Keywords: diagonal algorithms ; partitioning ; minimal description ; global optimization
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract In this paper, the problem of the minimal description of the structure offunctional f(x) over an N-dimensional interval is considered. Thedescription is obtained by applying diagonal algorithms, i.e., proceduressequentially partitioning the given hyperinterval and evaluating f(x)at the vertices corresponding to the main diagonal of each generatedsubinterval. Two partition strategies traditionally used for solving thisproblem are analyzed and it is demonstrated that using them can result ina high number of redundant evaluations of the functional f(x). Anew efficient partition strategy is proposed; it reduces considerably thenumber of evaluations of f(x) and the memory complexity.
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    Stability and Hopf Bifurcation of Four-Wheel-Steering Vehicles Involving Driver's Delay (2000)
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    Nonlinear dynamics 22 (2000), S. 361-374 
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    ISSN: 1573-269X
    Keywords: 4WS vehicle ; time delay ; stability ; Hopf bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A mathematical model is presented for four-wheel-steeringvehicles, with the time delay in driver's response and the nonlinearityin lateral tyre forces taken into account. It is proved that thevehicle-driver system has a trivial steady state motion, as well aseight non-trivial steady state motions due to the nonlinearity of tyreforces. The asymptotic stability and Hopf bifurcation of the trivialsteady state are analyzed for two control strategies ofrear-wheel-steering. It is shown through the numerical simulations thatthe four-wheel-steering technique based on the bilinear control strategyworks better when the driver's response involves time delay.
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    On the stability of wavelet and Gabor frames (Riesz bases) (1999)
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    The journal of Fourier analysis and applications 5 (1999), S. 105-125 
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    ISSN: 1531-5851
    Keywords: 26B05 ; 42B10 ; 42C99 ; frame ; Gabor system ; Riesz basis ; stability ; wavelet
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    Topics: Mathematics
    Notes: Abstract If the sequence of functions ϕj, k is a wavelet frame (Riesz basis) or Gabor frame (Riesz basis), we obtain its perturbation system ψj,k which is still a frame (Riesz basis) under very mild conditions. For example, we do not need to know that the support of ϕ or ψ $$(\hat \phi or\hat \psi )$$ is compact as in [14]. We also discuss the stability of irregular sampling problems. In order to arrive at some of our results, we set up a general multivariate version of Littlewood-Paley type inequality which was originally considered by Lemarié and Meyer [17], then by Chui and Shi [9], and Long [16].
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    The Stability of Self-Organized Rule-Following Work Teams (1999)
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    Computational & mathematical organization theory 5 (1999), S. 5-30 
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    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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    Implicit Multifunction Theorems (1999)
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    Set-valued analysis 7 (1999), S. 209-238 
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    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
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    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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    Numerical computation of stability and detection of Hopf bifurcations of steady state solutions of delay differential equations (1999)
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    Advances in computational mathematics 10 (1999), S. 271-289 
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    ISSN: 1572-9044
    Keywords: delay differential equations ; steady state solutions ; stability ; 34K20 ; 65J10
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    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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    A New Approach to Backward Error Analysis of Lu Factorization (1999)
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    BIT 39 (1999), S. 385-402 
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    ISSN: 1572-9125
    Keywords: Gaussian elimination ; stability ; backward error analysis ; growth factor
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    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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    Runge–Kutta–Nyström‐type parallel block predictor–corrector methods (1999)
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    Advances in computational mathematics 10 (1999), S. 115-133 
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    ISSN: 1572-9044
    Keywords: Runge–Kutta–Nyström methods ; predictor–corrector methods ; stability ; parallelism ; 65M12 ; 65M20
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    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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    Exponential Integrators for Quantum-Classical Molecular Dynamics (1999)
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    BIT 39 (1999), S. 620-645 
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    ISSN: 1572-9125
    Keywords: Numerical integrator ; oscillatory solutions ; Schrödinger equation ; quantum-classical coupling ; error bounds ; stability
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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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    The Cross-Entropy Method for Combinatorial and Continuous Optimization (1999)
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    Methodology and computing in applied probability 1 (1999), S. 127-190 
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    ISSN: 1387-5841
    Keywords: combinatorial optimization ; global optimization ; importance sampling ; markov chain monte carlo ; simulated annealing ; simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present a new and fast method, called the cross-entropy method, for finding the optimal solution of combinatorial and continuous nonconvex optimization problems with convex bounded domains. To find the optimal solution we solve a sequence of simple auxiliary smooth optimization problems based on Kullback-Leibler cross-entropy, importance sampling, Markov chain and Boltzmann distribution. We use importance sampling as an important ingredient for adaptive adjustment of the temperature in the Boltzmann distribution and use Kullback-Leibler cross-entropy to find the optimal solution. In fact, we use the mode of a unimodal importance sampling distribution, like the mode of beta distribution, as an estimate of the optimal solution for continuous optimization and Markov chains approach for combinatorial optimization. In the later case we show almost surely convergence of our algorithm to the optimal solution. Supporting numerical results for both continuous and combinatorial optimization problems are given as well. Our empirical studies suggest that the cross-entropy method has polynomial in the size of the problem running time complexity.
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    Markov Control Processes with the Expected Total Cost Criterion: Optimality, Stability, and Transient Models (1999)
    Springer
    Acta applicandae mathematicae 59 (1999), S. 229-269 
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    ISSN: 1572-9036
    Keywords: (discrete-time) Markov control processes ; expected total cost ; value iteration ; policy iteration ; stability ; transient control models
    Source: Springer Online Journal Archives 1860-2000
    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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    Stability of a class of neural network models with delay (1999)
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    Applied mathematics and mechanics 20 (1999), S. 912-916 
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    ISSN: 1573-2754
    Keywords: delay ; neural network ; stability ; TN911.23 ; O332
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, by using Liapunov functional, some sufficient conditions are obtained for the stability of the equilibrium of a neural network model with delay of the type $$u'_i \left( t \right) = - b_i u_i \left( t \right) + \sum\limits_{j = 1}^n {T_{ij} f_j } \left( {\mu _j u_j \left( {t - \tau _j } \right)} \right) + c_i ,\tau _j \geqslant 0,i = 1,2 \cdots ,n.$$
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    A method for following the unstable path between two saddle-node bifurcation points in nonlinear dynamic system (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 1384-1388 
    Details
    ISSN: 1573-2754
    Keywords: nonlinear dynamic system ; bifurcation ; stability ; TB123 ; O322
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract A computation algorithm based on the Poincaré Mapping in combination with Pseudo-Arc Length Continuation Method is presented for calculating the unstable response with saddle-node bifurcation, and the singularity, which occurs using the general continuation method combined with Poincaré Mapping to follow the path, is also proved. A normalization equation can be introduced to avoid the singularity in the process of iteration, and a new iteration algorithm will be presented too. There will be two directions in which the path can be continued at each point, but only one can be used. The method of determining the direction will be presented in the paper. It can be concluded that is method is effective in analysis of nonlinear dynamic system with saddle-node bifurcations.
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    URL: http://dx.doi.org/10.1007/BF02459172
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    Some dynamical properties of a viscoelastic cylindrical shell (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 233-240 
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    ISSN: 1573-2754
    Keywords: viscoelasticity ; cylindrical shell ; 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 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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    URL: http://dx.doi.org/10.1007/BF02463847
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    Stable and Real-Time Scheduling of a Class of Hybrid Dynamic Systems (1999)
    Springer
    Discrete event dynamic systems 9 (1999), S. 45-64 
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    ISSN: 1573-7594
    Keywords: hybrid dynamic systems ; event feedback ; real-time scheduling ; stability
    Source: Springer Online Journal Archives 1860-2000
    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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    URL: http://dx.doi.org/10.1023/A:1008320614629
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    Explicit second-order accurate schemes for the nonlinear Schrödinger equations (1999)
    Springer
    Lithuanian mathematical journal 39 (1999), S. 20-32 
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    ISSN: 1573-8825
    Keywords: Schrödinger equation ; explicit finite-difference schemes ; stability ; energy conservation ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider three-level explicit schemes for solving the nonlinear variable coefficient Schrödinger-type equation. Using spectral and energy methods we establish the stability and convergence of these schemes. The existence of discrete conservation laws is investigated. General results are applied for the DuFort-Frankel and leap-frog diffenrence schemes.
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    URL: http://dx.doi.org/10.1007/BF02465532
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    Orbital Migration Of Giant Planets: Using Numerical Integration To Investigate Consequences For Other Bodies (1999)
    Springer
    Earth, moon and planets 87 (1999), S. 103-115 
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    ISSN: 1573-0794
    Keywords: Accretion ; exoplanetary system ; extrasolar planets ; numerical integration ; orbital migration ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A number of extrasolar planets have been detected in close orbits around nearby stars. It is probable that these planets did not form in these orbits but migrated from their formation locations beyond the ice line. Orbital migration mechanisms involving angular momentum transfer through tidal interactions between the planets and circumstellar gas-dust disks or by gravitational interaction with a residual planetesimal disk together with several means of halting inward migration have been identified. These offer plausible schemes to explain the orbits of observed extrasolar giant planets and giant planets within the Solar System. Recent advances in numerical integration methods and in the power of computer workstations have allowed these techniques to be applied to modelling directly the mechanisms and consequences of orbital migration in the Solar System. There is now potential for these techniques also to be applied to modelling the consequences of the orbital migration of planets in the observed exoplanetary systems. In particular the detailed investigation of the stability of terrestrial planets in the habitable zone of these systems and the formation of terrestrial planets after the dissipation of the gas disk is now possible. The stability of terrestrial planets in the habitable zone of selected exoplanetary systems has been established and the possibility of the accretion of terrestrial planets in these systems is being investigated by the author in collaboration with Barrie W. Jones (Open University), and with John Chambers (NASA-Ames) and Mark Bailey of Armagh Observatory, using numerical integration. The direct simulation of orbital migration by planetesimal scattering must probably await faster hardware and/or more efficient algorithms.
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    URL: http://dx.doi.org/10.1023/A:1017996927696
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    Risk measurement with maximum loss (1999)
    Springer
    Mathematical methods of operations research 50 (1999), S. 121-134 
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    ISSN: 1432-5217
    Keywords: Key words: Risk measurement ; global optimization ; quadratic programming ; nonlinear programming ; polynomial-approximation algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. Effective risk management requires adequate risk measurement. A basic problem herein is the quantification of market risks: what is the overall effect on a portfolio if market rates change? First, a mathematical problem statement is given and the concept of `Maximum Loss' (ML) is introduced as a method for identifying the worst case in a given set of scenarios, called `Trust Region'. Next, a technique for calculating efficiently the Maximum Loss for quadratic functions is described; the algorithm is based on the Levenberg-Marquardt theorem, which reduces the high dimensional optimization problem to a one dimensional root finding.  Following this, the idea of the `Maximum Loss Path' is presented: repetitive calculation of ML for growing trust regions leads to a sequence of worst case scenarios, which form a complete path; similarly, the path of `Maximum Profit' (MP) can be determined. Finally, all these concepts are applied to nonquadratic portfolios: so-called `Dynamic Approximations' are used to replace arbitrary profit and loss functions by a sequence of quadratic functions, which can be handled with efficient solution procedures. A description of the overall algorithm rounds off the discussion of nonlinear portfolios.
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    URL: http://dx.doi.org/10.1007/s001860050039
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    Equilibrium stability of generalized Birkhoff's autonomous system (1999)
    Springer
    Applied mathematics and mechanics 20 (1999), S. 564-567 
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    ISSN: 1573-2754
    Keywords: generalized Birkhoff's system ; equilibrium state ; 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, 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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    Portfolio optimization via stochastic programming: Methods of output analysis (1999)
    Springer
    Mathematical methods of operations research 50 (1999), S. 245-270 
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    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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    URL: http://dx.doi.org/10.1007/s001860050097
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    A Multiple-Shooting Technique for Optimal Control (1999)
    Springer
    Journal of optimization theory and applications 102 (1999), S. 299-313 
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    ISSN: 1573-2878
    Keywords: Comparison of methods ; optimal control ; sensitivity ; shooting methods ; stability
    Source: Springer Online Journal Archives 1860-2000
    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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    URL: http://dx.doi.org/10.1023/A:1021728407151
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    New Linear Program Performance Bounds for Queueing Networks (1999)
    Springer
    Journal of optimization theory and applications 100 (1999), S. 575-597 
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    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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    URL: http://dx.doi.org/10.1023/A:1022638523391
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    DC Programming: Overview (1999)
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    Journal of optimization theory and applications 103 (1999), S. 1-43 
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    ISSN: 1573-2878
    Keywords: DC functions ; DC programming ; global optimization ; nonconvex programming ; optimality conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Mathematical programming problems dealing with functions, each of which can be represented as a difference of two convex functions, are called DC programming problems. The purpose of this overview is to discuss main theoretical results, some applications, and solution methods for this interesting and important class of programming problems. Some modifications and new results on the optimality conditions and development of algorithms are also presented.
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    URL: http://dx.doi.org/10.1023/A:1021765131316
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    Generalized γ-Valid Cut Procedure for Concave Minimization (1999)
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    Journal of optimization theory and applications 102 (1999), S. 289-298 
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    ISSN: 1573-2878
    Keywords: Concave minimization ; γ-valid cut ; Tuy cut ; global optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The concept of a γ-valid cutting plane has been used in many types of algorithms for solving concave minimization problems. Unfortunately, the procedures proposed to date for constructing these cuts are valid only under certain assumptions that often may not hold in practice. Chief among these is the requirement that the feasible region of the concave minimization problem in question have full dimension, and that the objective function of this problem be concave rather than quasiconcave. In this article, we propose, validate, and show how to implement a more general γ-valid cutting plane procedure which eliminates these restrictions.
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    URL: http://dx.doi.org/10.1023/A:1021776323080
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    Closed-Loop Stability Monitoring of Axial Flow Compression Systems (1999)
    Springer
    Nonlinear dynamics 20 (1999), S. 181-196 
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    ISSN: 1573-269X
    Keywords: monitoring ; stability ; compressors ; axial flow compressors ; stall ; surge ; bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Monitoring systems are proposed for the detection of incipient instability in axial flow compression systems. The work employs generic features associated with the response to noise inputs of systems bordering on instability. Based on these generic features, a closed-loop monitoring system is proposed. Numerical simulation is used to illustrate the operation of the proposed closed-loop monitoring system.
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    URL: http://dx.doi.org/10.1023/A:1004596213600
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    On the Reconstitution Problem in the Multiple Time-Scale Method (1999)
    Springer
    Nonlinear dynamics 19 (1999), S. 135-158 
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    ISSN: 1573-269X
    Keywords: perturbation methods ; higher-order approximations ; dynamical systems ; codimension ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Higher-order multiple-scale methods for general multiparameter mechanical systems are studied. The role played by the control and imperfection parameters in deriving the perturbative equations is highlighted. The definition of the codimension of the problem, borrowed from the bifurcation theory, is extended to general systems, excited either externally or parametrically. The concept of a reduced dynamical system is then invoked. Different approaches followed in the literature to deal with reconstituted amplitude equations are discussed, both in the search for steady-state solutions and in the analysis of stability. Four classes of methods are considered, based on the consistency or inconsistency of the approach, and on the completeness or incompleteness of the terms retained in the analysis. The four methods are critically compared and general conclusions drawn. Finally, three examples are illustrated to corroborate the findings and to show the quantitative differences between the various approaches.
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    Articulated Pipes Conveying Fluid Pulsating with High Frequency (1999)
    Springer
    Nonlinear dynamics 19 (1999), S. 173-193 
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    ISSN: 1573-269X
    Keywords: fluid conveying pipes ; high-frequency pulsating fluid ; separation of slow and fast motion ; stability ; nonlinear dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Stability and nonlinear dynamics of two articulated pipes conveying fluid with a high-frequency pulsating component is investigated. The non-autonomous model equations are converted into autonomous equations by approximating the fast excitation terms with slowly varying terms. The downward hanging pipe position will lose stability if the mean flow speed exceeds a certain critical value. Adding a pulsating component to the fluid flow is shown to stabilize the hanging position for high values of the ratio between fluid and pipe-mass, and to marginally destabilize this position for low ratios. An approximate nonlinear solution for small-amplitude flutter oscillations is obtained using a fifth-order multiple scales perturbation method, and large-amplitude oscillations are examined by numerical integration of the autonomous model equations, using a path-following algorithm. The pulsating fluid component is shown to affect the nonlinear behavior of the system, e.g. bifurcation types can change from supercritical to subcritical, creating several coexisting stable solutions and also anti-symmetrical flutter may appear.
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    Double Hopf Bifurcations and Chaos of a Nonlinear Vibration System (1999)
    Springer
    Nonlinear dynamics 19 (1999), S. 313-332 
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    ISSN: 1573-269X
    Keywords: double pendulum system ; double Hopf bifurcation ; stability ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A double pendulum system is studied for analyzing the dynamic behaviour near a critical point characterized by nonsemisimple 1:1 resonance. Based on normal form theory, it is shown that two phase-locked periodic solutions may bifurcate from an initial equilibrium, one of them is unstable and the other may be stable for certain values of parameters. A secondary bifurcation from the stable periodic solution yields a family of quasi-periodic solutions lying on a two-dimensional torus. Further cascading bifurcations from the quasi-periodic motions lead to two chaoses via a period-doubling route. It is shown that all the solutions and chaotic motions are obtained under positive damping.
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    Preventing buoyancy-driven flows of two Bingham fluids in a closed pipe – Fluid rheology design for oilfield plug cementing (1999)
    Springer
    Journal of engineering mathematics 36 (1999), S. 327-348 
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    ISSN: 1573-2703
    Keywords: Bingham fluids ; multi-layer flow ; no-flow/yield criteria ; stability ; variational methods.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The mechanically unstable situation of a heavy Bingham fluid resting on top of a light Bingham fluid in an inclined closed-ended pipe can be stabilised if the fluids have sufficiently large yield stresses. This paper focuses on determining the yield stresses that are sufficient to keep the fluids statically stable for a given fluid density difference, pipe diameter and pipe inclination. The results are applicable to a broad class of practically observable flows. This situation provides an idealised model for the oilfield process of plug cementing.
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    URL: http://dx.doi.org/10.1023/A:1004511113745
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    The onset of steady Bénard-Marangoni convection in a two-layer system of conducting fluid in the presence of a uniform magnetic field (1999)
    Springer
    Journal of engineering mathematics 35 (1999), S. 385-404 
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    ISSN: 1573-2703
    Keywords: Bénard-Marangini convection ; conducting fluids ; stability ; two-layer system.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The onset of steady Bénard-Marangoni convection in two horizontal liquid layers of electrically conducting immiscible fluids subjected to a uniform vertical magnetic field and temperature gradient is analysed by means of a combination of analytical and numerical techniques. The free surface can be either deformable or nondeformable and the interface between the fluids is always assumed to be flat. The effect of the lower layer on the critical values of Rayleigh, Marangoni and wave numbers for the onset of steady convection is investigated. When the free surface is nondeformable, the critical parameters for the onset of pure Marangoni convection are increased, whereas for the onset of pure Bénard convection they are decreased compared to the single-layer model. The results for a single-layer and for two-layers are qualitatively similar for Bénard-Marangoni convection when the free surface is deformable. All disturbances can be stabilized with sufficiently strong magnetic field when the free surface is nondeformable. If the free surface is allowed to deform and gravity waves are excluded, then the layers are always unstable to disturbances with sufficiently small wave number with magnetic field. Inclusion of gravity waves has a stabilizing effect on certain disturbances of small wave number in the presence of weak or moderate magnetic field.
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    Dynamics of Oscillators with Strongly Nonlinear Asymmetric Damping (1999)
    Springer
    Nonlinear dynamics 20 (1999), S. 221-246 
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    ISSN: 1573-269X
    Keywords: Coulomb friction ; asymmetric damping ; exact periodic motions ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Dynamics of a class of strongly nonlinear single degree of freedom oscillators is investigated. Their common characteristic is that they possess piecewise linear damping properties, which can be expressed in a general asymmetric form. More specifically, the damping coefficient and a constant parameter appearing in the equation of motion are functions of the velocity direction. This class of oscillators is quite general and includes other important categories of mechanical systems as special cases, like systems with Coulomb friction. First, an analysis is presented for locating directly exact periodic responses of these oscillators to harmonic excitation. Due to the presence of dry friction, these responses may involve intervals where the oscillator is stuck temporarily. Then, an appropriate stability analysis is also presented together with some quite general bifurcation results. In the second part of the work, this analysis is applied to several example systems with piecewise linear damping, in order to reveal the most important aspects of their dynamics. Initially, systems with symmetric characteristics are examined, for which the periodic response is found to be symmetric or asymmetric. Then, dynamical systems with asymmetric damping characteristics are also examined. In all cases, emphasis is placed on investigating the low forcing frequency ranges, where interesting dynamics is noticed. The analytical predictions are complemented with results obtained by proper integration of the equation of motion, which among other responses reveal the existence of quasiperiodic, chaotic and unbounded motions.
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    Reachability of locational Nash equilibria (1998)
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    OR spectrum 20 (1998), S. 101-107 
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    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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    Reachability of locational Nash equilibria (1998)
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    OR spectrum 20 (1998), S. 101-107 
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    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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    Discrete stability of the Differential System Method evaluated with geostatistical techniques (1998)
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    Stochastic environmental research and risk assessment 12 (1998), S. 191-204 
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    ISSN: 1436-3259
    Keywords: Keywords: groundwater flow ; inverse problems ; stability ; geostatistical interpolation ; kriging.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The Differential System Method (DSM) permits identification of the physical parameters of finite-difference groundwater flow models in a confined aquifer when piezometric head and source terms are known at each point of the finite-difference lattice for at least two independent flow situations for which the hydraulic gradients are not parallel. Since piezometric head data are usually few and sparse, interpolation of the measured data onto a regular grid can be performed with geostatistical techniques. We apply kriging to the sparse data of a synthetic aquifer to evaluate the stability of the DSM with respect to uncorrelated measurement errors and interpolation errors. The numerical results show that the DSM is stable.
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    Stability and Instability of Fourth-Order Solitary Waves (1998)
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    Journal of dynamics and differential equations 10 (1998), S. 151-188 
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    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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    Some Results on Stability of Retarded Functional Differential Equations Using Dichotomic Map Techniques (1998)
    Springer
    Positivity 2 (1998), S. 229-238 
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    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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    Multiwavelet approximation methods for pseudodifferential equations on curves. Stability and convergence analysis (1998)
    Springer
    Advances in computational mathematics 9 (1998), S. 145-171 
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    ISSN: 1572-9044
    Keywords: periodic pseudodifferential equations ; multiwavelets ; splines with multiple knots ; generalized Galerkin–Petrov schemes ; boundary element methods ; error analysis ; stability ; Strang–Fix condition ; 65J10 ; 65N30 ; 65N35 ; 65R20 ; 47G30 ; 45P05 ; 41A25 ; 41A30 ; 41A15
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    Notes: Abstract We develop a stability and convergence analysis of Galerkin–Petrov schemes based on a general setting of multiresolution generated by several refinable functions for the numerical solution of pseudodifferential equations on smooth closed curves. Particular realizations of such a multiresolution analysis are trial spaces generated by biorthogonal wavelets or by splines with multiple knots. The main result presents necessary and sufficient conditions for the stability of the numerical method in terms of the principal symbol of the pseudodifferential operator and the Fourier transforms of the generating multiscaling functions as well as of the test functionals. Moreover, optimal convergence rates for the approximate solutions in a range of Sobolev spaces are established.
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    On a spherical integral transformation and sections of star bodies (1998)
    Springer
    Monatshefte für Mathematik 126 (1998), S. 117-124 
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    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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    The auto-adjustable damping method for solving nonlinear equations (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 163-168 
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    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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    Disturbances to a rotating fluid with a sphere moving along the axis of rotation (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 861-867 
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    ISSN: 1573-2754
    Keywords: rotating fluids ; motion of body ; small disturbances ; stability
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the disturbances to a uniformly rotating ideal fluid with a sphere moving steadily along the axis of rotation are analysed by using linearization theory, the equations of disturbance, pressure and disturbance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric. The equation of disturbance stream function is analysed with the method of normal modes, and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral disturbances are obtained. The conclusion is drawn that three are three kinds of possible forms of neutral disturbances.
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    Bifurcations in Spherical MHD Models (1998)
    Springer
    Studia geophysica et geodaetica 42 (1998), S. 320-327 
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    ISSN: 1573-1626
    Keywords: MHD ; stability ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics
    Notes: Abstract A series of numerical studies on the behaviour of magnetic fields and motions in a spherical body of an electrically conducting incompressible fluid have been carried out. The magnetic field was assumed to be maintained by a given electromotive force inside the body and to continue as a potential field in outer space. In view of the motion an external forcing was taken into account, and boundary conditions were considered which correspond to a stress-free surface. The stability of several steady states has been studied as well as the evolutions starting from unstable states. In this paper a configuration with a poloidal magnetic field and a differential rotation, both symmetric about the same axis, is considered. This configuration is stable only for sufficiently small Hartmann numbers but evolves, if disturbed, in the case of larger Hartmann numbers toward a non-axisymmetric state. In this case the well-known symmetrization effect of differential rotation in magnetic fields is destroyed.
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    The stability in neural networks with interneuronal transmission delays (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 457-462 
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    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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    Timed Petri Nets in Hybrid Systems: Stability and Supervisory Control (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 137-173 
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    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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    Robust Estimation of Rotation Angles from Image Sequences Using the Annealing M-Estimator (1998)
    Springer
    Journal of mathematical imaging and vision 8 (1998), S. 181-192 
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    ISSN: 1573-7683
    Keywords: deterministic annealing ; global optimization ; M-estimator ; motion analysis ; robust statistics
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    Topics: Mathematics
    Notes: Abstract A robust method is presented for computing rotation angles of image sequences from a set of corresponding points containing outliers. Assuming known rotation axis, a least-squares (LS) solution are derived to compute the rotation angle from a clean data set of point correspondences. Since clean data is not guaranteed, we introduce a robust solution, based on the M-estimator, to deal with outliers. Then we present an enhanced robust algorithm, called the annealing M-estimator (AM-estimator), for reliable robust estimation. The AM-estimator has several attractive advantages over the traditional M-estimator: By definition, the AM-estimator involves neither scale estimator nor free parameters and hence avoids instabilities therein. Algorithmically, it uses a deterministic annealing technique to approximate the global solution regardless of the initialization. Experimental results are presented to compare the performance of the LS, M- and AM-estimators for the angle estimation. Experiments show that in the presence of outliers, the M-estimator outperforms the LS estimator and the AM-estimator outperforms the M-estimator.
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    Almost-periodic solutions to systems of differential equations with fast and slow time in the degenerate case (1998)
    Springer
    Mathematical notes 63 (1998), S. 396-400 
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    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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    Optimal Control of Nonlinear Fredholm Integral Equations (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 707-729 
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    ISSN: 1573-2878
    Keywords: Nonlinear integral equations ; optimal control in L p-spaces ; relaxation ; existence ; stability ; nonconcentration ; optimality conditions ; Pontryagin maximum principle
    Source: Springer Online Journal Archives 1860-2000
    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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    Lagrange's theorem for a class of nonholonomic systems and its application (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 135-146 
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    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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    On a Class of Functionals Whose Local Minima are Global (1998)
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    Journal of global optimization 12 (1998), S. 101-104 
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    ISSN: 1573-2916
    Keywords: Increasing functional ; integral functional ; global optimization
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    Topics: Mathematics
    Notes: Abstract In this note we introduce a suitable class of functionals, including the class of integral functionals, and prove that any (strict) local minimum of a functional of this class, defined on a decomposable space, is a (strict) global minimum. So, the recent result obtained by Giner in [1] is specified and extended.
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    Generalized Trajectory Methods for Finding Multiple Extrema and Roots of Functions (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 211-227 
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    ISSN: 1573-2878
    Keywords: Homotopy ; relaxation ; trajectory tracking ; global optimization ; roots ; nonlinear equations
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    Topics: Mathematics
    Notes: Abstract Two generalized trajectory methods are combined to provide a novel and powerful numerical procedure for systematically finding multiple local extrema of a multivariable objective function. This procedure can form part of a strategy for global optimization in which the greatest local maximum and least local minimum in the interior of a specified region are compared to the largest and smallest values of the objective function on the boundary of the region. The first trajectory method, a homotopy scheme, provides a globally convergent algorithm to find a stationary point of the objective function. The second trajectory method, a relaxation scheme, starts at one stationary point and systematically connects other stationary points in the specified region by a network of trjectories. It is noted that both generalized trajectory methods actually solve the stationarity conditions, and so they can also be used to find multiple roots of a set of nonlinear equations.
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    A Discrete Lagrangian-Based Global-Search Method for Solving Satisfiability Problems (1998)
    Springer
    Journal of global optimization 12 (1998), S. 61-99 
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    ISSN: 1573-2916
    Keywords: Discrete Lagrangian methods ; global optimization ; satisfiability ; NP-completeness
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    Topics: Mathematics
    Notes: Abstract Satisfiability is a class of NP-complete problems that model a wide range of real-world applications. These problems are difficult to solve because they have many local minima in their search space, often trapping greedy search methods that utilize some form of descent. In this paper, we propose a new discrete Lagrange-multiplier-based global-search method (DLM) for solving satisfiability problems. We derive new approaches for applying Lagrangian methods in discrete space, we show that an equilibrium is reached when a feasible assignment to the original problem is found and present heuristic algorithms to look for equilibrium points. Our method and analysis provides a theoretical foundation and generalization of local search schemes that optimize the objective alone and penalty-based schemes that optimize the constraints alone. In contrast to local search methods that restart from a new starting point when a search reaches a local trap, the Lagrange multipliers in DLM provide a force to lead the search out of a local minimum and move it in the direction provided by the Lagrange multipliers. In contrast to penalty-based schemes that rely only on the weights of violated constraints to escape from local minima, DLM also uses the value of an objective function (in this case the number of violated constraints) to provide further guidance. The dynamic shift in emphasis between the objective and the constraints, depending on their relative values, is the key of Lagrangian methods. One of the major advantages of DLM is that it has very few algorithmic parameters to be tuned by users. Besides the search procedure can be made deterministic and the results reproducible. We demonstrate our method by applying it to solve an extensive set of benchmark problems archived in DIMACS of Rutgers University. DLM often performs better than the best existing methods and can achieve an order-of-magnitude speed-up for some problems.
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    Hybrid Approach for Solving Multiple-Objective Linear Programs in Outcome Space (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 17-35 
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    ISSN: 1573-2878
    Keywords: Multiple-objective linear programming ; vector maximization ; efficient set ; outcome set ; global optimization
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    Topics: Mathematics
    Notes: Abstract Various difficulties arise in using decision set-based vector maximization methods to solve a multiple-objective linear programming problem (MOLP). Motivated by these difficulties, some researchers in recent years have begun to develop tools for analyzing and solving problem (MOLP) in outcome space, rather than in decision space. In this article, we present and validate a new hybrid vector maximization approach for solving problem (MOLP) in outcome space. The approach systematically integrates a simplicial partitioning technique into an outer approximation procedure to yield an algorithm that generates the set of all efficient extreme points in the outcome set of problem (MOLP) in a finite number of iterations. Some key potential practical and computational advantages of the approach are indicated.
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    Construction of Test Problems for Concave Minimization Under Linear and Nonlinear Constraints (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 83-108 
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    ISSN: 1573-2878
    Keywords: Concave minimization ; reverse convex programs ; non-convex optimization ; global optimization ; test problems ; linear programming ; nonlinear programming ; computational experiments
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    Topics: Mathematics
    Notes: Abstract This paper presents a method for constructing test problems with known global solutions for concave minimization under linear constraints with an additional convex constraint and for reverse convex programs with an additional convex constraint. The importance of such a construction can be realized from the fact that the well known d.c. programming problem can be formulated in this form. Then, the method is further extended to generate test problems with more than one convex constraint, tight or untight at the global solution.
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    Symbolic Computation of Local Stability and Bifurcation Surfaces for Nonlinear Time-Periodic Systems (1998)
    Springer
    Nonlinear dynamics 17 (1998), S. 1-21 
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    ISSN: 1573-269X
    Keywords: Symbolic computation ; stability ; bifurcation ; nonlinear ; time-periodic
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    Topics: Mathematics
    Notes: Abstract A new technique is presented for symbolic computation of local stability boundaries and bifurcation surfaces for nonlinear multidimensional time-periodic dynamical systems as an explicit function of the system parameters. This is made possible by the recent development of a symbolic computational algorithm for approximating the parameter-dependent fundamental solution matrix of linear time-periodic systems. By evaluating this matrix at the end of the principal period, the parameter-dependent Floquet Transition Matrix (FTM), or the linear part of the Poincaré map, is obtained. The subsequent use of well-known criteria for the local stability and bifurcation conditions of equilibria and periodic solutions enables one to obtain the equations for the bifurcation surfaces in the parameter space as polynomials of the system parameters. Further, the method may be used in conjunction with a series expansion to obtain perturbation-like expressions for the bifurcation boundaries. Because this method is not based on expansion in terms of a small parameter, it can be successfully applied to periodic systems whose internal excitation is strong. Also, the proposed method appears to be more efficient in terms of cpu time than the truncated point mapping method. Two illustrative example problems, viz., a parametrically excited simple pendulum and a double inverted pendulum subjected to a periodic follower force, are included.
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    Resonances of a Harmonically Forced Duffing Oscillator with Time Delay State Feedback (1998)
    Springer
    Nonlinear dynamics 15 (1998), S. 311-327 
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    ISSN: 1573-269X
    Keywords: Time delay ; stability ; vibration control ; periodic motion
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    Topics: Mathematics
    Notes: Abstract The paper presents analytical and numerical studies of the primary resonance and the 1/3 subharmonic resonance of a harmonically forced Duffing oscillator under state feedback control with a time delay. By using the method of multiple scales, the first order approximations of the resonances are derived and the effect of time delay on the resonances is analyzed. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. In order to numerically solve the problem of history dependence prior to the start of excitation, the concepts of the Poincaré section and fixed points are generalized. Then, a modified shooting scheme associated with the path following technique is proposed to locate the periodic motion of the delayed system. The numerical results show the efficacy of the first order approximations of the resonances.
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    Parametrically Excited Non-Linear Traveling Beams with and without External Forcing (1998)
    Springer
    Nonlinear dynamics 17 (1998), S. 301-324 
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    ISSN: 1573-269X
    Keywords: parametric excitation ; non-linear complex ; stability ; jump phenomena
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    Topics: Mathematics
    Notes: Abstract The effects of parametric excitation on a traveling beam, both with and without an external harmonic excitation, have been studied including the non-linear terms. Non-linear, complex normal modes have been used for the response analysis. Detailed numerical results are presented to show the effects of non-linearity on the stability of the parametrically excited system. In the presence of both parametric and external harmonic excitations, the response characteristics are found to be similar to that of a Duffing oscillator. The results are sensitive to the relative strengths of and the phase difference between the two forms of excitations.
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    Global Stability Analysis of Cylindrical and Dual Offset Rotor Bearing Systems (1998)
    Springer
    Nonlinear dynamics 16 (1998), S. 187-202 
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    ISSN: 1573-269X
    Keywords: Chaos ; stability ; offset ; bearings
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Extensive numerical simulation studies with a short bearing film model show that a balanced dual offset rotor bearing subjected to a fixed external load can improve bearing performance for load and speed conditions known to produce undesirable half-speed whirl in conventional zero-offset cylindrical systems. For specific values of dimensionless load, offset ratio, and load orientation, parametric changes in speed show that the dual offset bearing can undergo a variety of bifurcations which produce coexisting period 1–4 subharmonic, quasi-periodic, and chaotic attractors, all of which may be driven by lower-order dynamic processes. For a specific set of initial conditions, the transition to chaos via period doubling in the dual offset bearing actually produces lubricant films which are significantly thicker than those found in the corresponding cylindrical system.
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    Stability of Semilinear Delay Equations with Positive Solutions (1997)
    Springer
    Positivity 1 (1997), S. 319-330 
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    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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    Stability-Like Properties of Differential Inclusions (1997)
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    Set-valued analysis 5 (1997), S. 73-88 
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    ISSN: 1572-932X
    Keywords: differential inclusion ; invariance ; stability
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    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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    Optimization and Stability Results Through Cone Lower Semicontinuity (1997)
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    Set-valued analysis 5 (1997), S. 365-375 
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    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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    Discrete time semigroup transformations with random perturbations (1997)
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    Journal of dynamics and differential equations 9 (1997), S. 463-505 
    Details
    ISSN: 1572-9222
    Keywords: Difference equations ; random perturbation ; averaging ; diffusion approximation ; randomly perturbed iterations ; stability ; 3SR60 ; 60H15 ; 60J99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let (X, ℬ) and (Y,C) be two measurable spaces withX being a linear space. A system is determined by two functionsf(X): X→ X andϕ:X×Y→X, a (small) positive parameterε and a homogeneous Markov chain {y n } in (Y,C) which describes random perturbations. States of the system, say {x n ɛ ∈X, n=0, 1,⋯}, are determined by the iteration relations:x n+1 ɛ =f(x n ɛ )+ɛϕ(x n ɛ ,Yn+1) forn≥0, wherex 0 ɛ =x 0 is given. Here we study the asymptotic behavior of the solutionx n ɛ asε → 0 andn → ∞ under various assumptions on the data. General results are applied to some problems in epidemics, genetics and demographics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02227491
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  • 98
    Electronic Resource
    Electronic Resource
    On Stability and Boundedness for Lipschitzian Differential Inclusions: The Converse of Lyapunov's Theorems (1997)
    Springer
    Set-valued analysis 5 (1997), S. 377-390 
    Details
    ISSN: 1572-932X
    Keywords: differential inclusions ; stability ; boundedness of solutions ; Lyapunov functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008603707291
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  • 99
    Electronic Resource
    Electronic Resource
    Stability of Hypersurfaces with Constant $$r$$ -Mean Curvature (1997)
    Springer
    Annals of global analysis and geometry 15 (1997), S. 277-297 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006514303828
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  • 100
    Electronic Resource
    Electronic Resource
    Stability Concepts in Topological Dynamics by Nonstandard Methods (1997)
    Springer
    Acta applicandae mathematicae 49 (1997), S. 35-54 
    Details
    ISSN: 1572-9036
    Keywords: dynamical systems ; stability ; pseudo orbit tracing property ; nonstandard analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is known that it is not possible to introduce C0 -structural stability for whole systems in topological dynamics. Using the methods of Nonstandard Analysis, we suggest four different purely topological stability concepts for dynamical systems on compact subsets of Rn. Classically these amount to considering the space of all systems on a given subset of Rn as the fundamental entity when deforming a continuous system (instead of the space of all continuous systems as is normally done in topological dynamics). For two of the introduced stability concepts, we will show that all minimal flows are stable in this sense. Besides this, we will show that one of our stability concepts is related to what is called the pseudo orbit tracing property in a recently published book by Aoki and Hiraide and compare some of our results to the theory of dynamical systems as presented there.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005840309425
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