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  • stability  (558)
  • Springer  (558)
  • American Meteorological Society
  • 2000-2004  (58)
  • 1995-1999  (301)
  • 1990-1994  (198)
  • 1965-1969  (1)
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Year
  • 101
    Electronic Resource
    Electronic Resource
    Numerical stability of biorthogonal wavelet transforms (1995)
    Springer
    Advances in computational mathematics 4 (1995), S. 1-26 
    Details
    ISSN: 1572-9044
    Keywords: Wavelets ; biorthogonal wavelets ; stability ; primary 15A12 ; 65F35 ; secondary 42C15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For orthogonal wavelets, the discrete wavelet and wave packet transforms and their inverses are orthogonal operators with perfect numerical stability. For biorthogonal wavelets, numerical instabilities can occur. We derive bounds for the 2-norm and average 2-norm of these transforms, including efficient numerical estimates if the numberL of decomposition levels is small, as well as growth estimates forL → ∞. These estimates allow easy determination of numerical stability directly from the wavelet coefficients. Examples show that many biorthogonal wavelets are in fact numerically well behaved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02123471
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  • 102
    Electronic Resource
    Electronic Resource
    Some remarks on the second variation formula for the area (1993)
    Springer
    Annals of global analysis and geometry 11 (1993), S. 221-235 
    Details
    ISSN: 1572-9060
    Keywords: Second variation formula ; Morse index ; stability ; 53C
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Iff is a minimal, isometric immersion of the Riemannian manifoldM of dimensionn in a Riemannian manifold $$\overline M$$ of dimensionm and ifI N is the „differential Jacobi operator” acting on the cross sections of the normal bundleN(M), we obtain some information on the Morse index and on the stability ofM through a detailed geometric analysis of the immersionf obtained when considering the higher fundamental forms off.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00773368
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  • 103
    Electronic Resource
    Electronic Resource
    On stable surfaces of constant gauss curvature in space forms (1995)
    Springer
    Annals of global analysis and geometry 13 (1995), S. 141-148 
    Details
    ISSN: 1572-9060
    Keywords: Gauss curvature ; stability ; 53
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that a domain on a surface of constant curvature is stable provided the integral of the mean curvature is small enough.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01120329
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  • 104
    Electronic Resource
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    Stability of Hypersurfaces with Constant $$r$$ -Mean Curvature (1997)
    Springer
    Annals of global analysis and geometry 15 (1997), S. 277-297 
    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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  • 105
    Electronic Resource
    Electronic Resource
    The maximal accuracy of stable difference schemes for the wave equation (1995)
    Springer
    BIT 35 (1995), S. 83-115 
    Details
    ISSN: 1572-9125
    Keywords: finite difference methods ; wave equation ; accuracy ; stability ; Padé approximants ; order stars ; Riemann surface
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider three time-level difference schemes, symmetric in time and space, for the solution of the wave equation,u tt =c 2 u xx , given by $$\sum\limits_{j = - S}^S {b_j U_{n + 1,m + j} + } \sum\limits_{j = - S}^S {a_j U_{n,m + j} + } \sum\limits_{j = - S}^S {b_j U_{n - 1,m + j} } = 0.$$ It has already been proved that the maximal order of accuracyp of such schemes is given byp ≤ 2(s + S). In this paper we show that the requirement of stability does not reduce this maximal order for any choice of the pair (s, S). The result is proved by introducing an order star on the Riemann surface of the algebraic function associated with the scheme. Furthermore, Padé schemes, withS = 0,s 〉 0, ands = 0,S 〉 0, are proved to be stable for 0 〈 μ 〈 1, where μ is the Courant number. These schemes can be implemented with high-order absorbing boundary conditions without reducing the range of μ for which stable solutions are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01732980
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  • 106
    Electronic Resource
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    Netwon interpolation at Leja points (1990)
    Springer
    BIT 30 (1990), S. 332-346 
    Details
    ISSN: 1572-9125
    Keywords: 65D05 ; polynomial interpolaton ; Newton form ; stability ; Leja points ; ordering of interpolation points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The Newton form is a convenient representation for interpolation polynomials. Its sensitivity to perturbations depends on the distribution and ordering of the interpolation points. The present paper bounds the growth of the condition number of the Newton form when the interpolation points are Leja points for fairly general compact sets K in the complex plane. Because the Leja points are defined recursively, they are attractive to use with the Newton form. If K is an interval, then the Leja points are distributed roughly like Chebyshev points. Our investigation of the Newton form defined by interpolation at Leja points suggests an ordering scheme for arbitrary interpolation points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02017352
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  • 107
    Electronic Resource
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    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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  • 108
    Electronic Resource
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    A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations (1992)
    Springer
    BIT 32 (1992), S. 634-649 
    Details
    ISSN: 1572-9125
    Keywords: AMS(MOS): 65L20 ; CR: 5.17 ; delay differential equations ; numerical solution ; Runge-Kutta methods ; interpolation procedures ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with adapting Runge-Kutta methods to differential equations with a lagging argument. A new interpolation procedure is introduced which leads to numerical processes that satisfy an important asymptotic stability condition related to the class of testproblemsU′(t)=λU(t)+μU(t−τ) with λ, μ ε C, Re(λ)〈−|μ|, and τ〉0. Ifc i denotes theith abscissa of a given Runge-Kutta method, then in thenth stept n−1→t n :=t n−1+h of the numerical process our interpolation procedure computes an approximation toU(t n−1+c i h−τ) from approximations that have already been generated by the process at pointst j−1+c i h(j=1,2,3,...). For two of these new processes and a standard process we shall consider the convergence behaviour in an actual application to a given, stiff problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01994847
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  • 109
    Electronic Resource
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    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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  • 110
    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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  • 111
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    Quasi-geodesic segments and Gromov hyperbolic spaces (1996)
    Springer
    Geometriae dedicata 62 (1996), S. 281-298 
    Details
    ISSN: 1572-9168
    Keywords: 53C23 ; Hyperbolicity ; stability ; quasi-geodesics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is known that for a geodesic metric space hyperbolicity in the sense of Gromov implies geodesic stability. In this paper it is shown that the converse is also true. So Gromov hyperbolicity and geodesic stability are equialent for geodesic metric spaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00181569
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  • 112
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    Sur l'instabilite de certaines positions d'equilibre relatif dans le probleme des n corps (1990)
    Springer
    Celestial mechanics and dynamical astronomy 49 (1990), S. 219-231 
    Details
    ISSN: 1572-9478
    Keywords: n-body problem ; stability ; relative equilibrium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Description / Table of Contents: Abstract We prove in this paper the instability, for all n ⩾ 4, of the configurations of relative equilibrium in the n-body problem where the n bodies submitted to newtonian mutual attractions are at the vertices of a regular polypon with n sides. For this proof we show that the equations of variations projected to the n bodies plan P have at least two conjugate characteristic exponents with a strictly positive real part; while these equations projected to an orthogonal axis to P have some solutions with secular terms.
    Notes: Resumé On démontre dans cet article l'instabilité, pour tout n ⩾ 4, des configurations d'équilibre relatif dans le problème des n corps, oú les n corps soumises aux attractions newtonniennes mutuelles se trouvent aux sommets d'un polygone régulier de n cotés. La preuve consiste à montrer que les équations aux variations, projetées sur le plan P des n corps, possèdent au moins deux exposants caractéristiques complexes connugués dont la parr'e réelle est strictement positive; alors que ces equations projetées sur un axe orthogonal à P possèdent des solutions ayant des termes séculaires.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00049414
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  • 113
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    On a class of variational equations transformable to the Gauss hypergeometric equation (1992)
    Springer
    Celestial mechanics and dynamical astronomy 53 (1992), S. 145-150 
    Details
    ISSN: 1572-9478
    Keywords: Monodromy matrix ; Gauss hypergeometric equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new class of linear ordinary differential equations with periodic coefficients is found which can be transformed to the Gauss hypergeometric equation, and therefore the monodromy matrices are computable explicitly. These equations appear as the variational equations around a straight-line solution in Hamiltonian systems of the form H = T(p) + V(q), where T(p) and V(q) are homogeneous functions of p and q, respectively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00049462
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  • 114
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    Asteroid 522 Helga is chaotic and stable (1993)
    Springer
    Celestial mechanics and dynamical astronomy 56 (1993), S. 323-324 
    Details
    ISSN: 1572-9478
    Keywords: chaos ; stability ; asteroids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00699743
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  • 115
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    The Trojan asteroid belt: Proper elements, stability, chaos and families (1993)
    Springer
    Celestial mechanics and dynamical astronomy 57 (1993), S. 59-94 
    Details
    ISSN: 1572-9478
    Keywords: asteroids ; libration ; proper elements ; stability ; chaos ; families
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract I have computed proper elements for 174 asteroids in the 1 : 1 resonance with Jupiter, that is for all the reliable orbits available (numbered and multi-opposition). The procedure requires numerical integration, under the perturbations by the four major planets, for 1,000,000 years; the output is digitally filtered and compressed into a “synthetic theory” (as defined within theLONGSTOP project). The proper modes of oscillation of the variables related to eccentricity, perihelion, inclination and node define proper elements. A third proper element is defined as the amplitude of the oscillation of the semimajor axis associated with the libration period; because of the strong nonlinearity of the problem, this component cannot be determined by a simple Fourier transform to the frequency domain. I therefore give another definition, which results in very good stability with time. For 87% of the computed orbits, the stability of the proper elements-at least over 1M yr-is within the following bounds: 0.001AU in semimajor axis, 0.0025 in eccentricity and sine of inclination. Half of the cases with degraded stability of the proper elements are found to be chaotic, with e-folding times between 16,000 and 660,000yr; in some other cases, chaotic behaviour does not result in a significantly decreased stability of the proper elements (stable chaos). The accuracy and stability of these proper elements is good enough to allow a search for asteroid families; however, the dynamical structure of the Trojan belt is very different from the one of the main belt, and collisional events among Trojans can result in a distribution of fragments difficult to identify. The occurrence of couples of Trojans with very close proper elements is proven not to be statistically significant in almost all cases. As the only exception, the couple 1583 Antilochus — 3801 Thrasimedes is significant; however, it is not easy to account for it by a conventional collisional theory. The Menelaus group is confirmed as a strong candidate collisional family; Teucer and Sarpedon could be considered as significant clusters. A number of other clumps are detected (by the same automated clustering method used for the main belt by Zappalà et al., 1990, 1992), but the total number of Trojans with reliable orbits is not large enough to detect many significant candidate families.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00692462
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  • 116
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    The dynamics of solar sails with a non-point source of radiation pressure (1990)
    Springer
    Celestial mechanics and dynamical astronomy 49 (1990), S. 249-264 
    Details
    ISSN: 1572-9478
    Keywords: Solar sails ; radiation pressure ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The form of the solar radiation pressure on a heliocentric orbiting solar sail is obtained for a finite angular sized and limb darkened solar disk by the use of the radiation pressure tensor. It is found that the usual inverse square variation of the solar radiation pressure is modified by the finite angular size, and to a lesser extent by the solar limb darkening. The actual magnitude of the modification is in itself small, except at close heliocentric distances. However, its existence has implications for the dynamical stability of solar sails both in parked and circular orbital configurations and for the accuracy of trajectory calculations, particularly for sails in the inner solar system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00049416
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  • 117
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    Bifurcations of separatrices in the averaged planar general three-body problem at first-order resonance (1994)
    Springer
    Celestial mechanics and dynamical astronomy 60 (1994), S. 307-315 
    Details
    ISSN: 1572-9478
    Keywords: Asteroid ; libration ; resonance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract It is known that an abridged case of the averaged planar general three-body problem, at first-order resonance, is analytically integrated, using an expansion of the disturbing function linear in the eccentricities. There exist different methods with the help of which the integration can be performed. For the first time Sessin and Ferraz-Mello in the years 1981–88 (Sessin, 1981, 1983; Ferraz-Mello and Sessin, 1984; Ferraz-Mello, 1987, 1988) did an analytic integration for the restricted elliptic three-body problem, in terms of the variablesK andH (K=ΣD j e j cos (ψ1−π j ),H=ΣD j e j sin (ψ1−π j ),D j = const, wheree j and π j are, respectively, the eccentricity and the longitude of the periapsis of thei-th planet, ψ1 is the Delaunay's anomaly), which is inconvenient for the analytical investigation of the evolution of the major semi-axesa j , the eccentricitiese j and the resonance phases ϕ j =ψ1−π j . Later, a different method for the analytical integration of the general three-body problem, in the variablesa j ,e j and ϕ j , was considered by the author (Shinkin, 1993). A disadvantage of both methods is the fact that they use non-canonical changes of variables. But there exists a third very beautiful canonical method of analytical integration of the general planetary problem, which is briefly considered in the present paper and allows us to describe the bifurcations of separatrices (i.e. appearance, disappearance, splitting and confluence of separatrices) separating the domains of libration and circulation of the resonance phase on the phase plane in the averaged planar general three-body problem at first-order resonance. The bifurcation parameter is analytically found and plays an important role in a qualitative description of all kinds of motion in the examined problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00691899
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  • 118
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    Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 181-196 
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    ISSN: 1572-9478
    Keywords: Periodic solutions ; stability ; restricted three-body problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00048514
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  • 119
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    Uniform stability at permanently acting disturbances of solutions of Navier-Stokes equations for compressible isothermic fluids (1994)
    Springer
    Acta applicandae mathematicae 37 (1994), S. 129-136 
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    ISSN: 1572-9036
    Keywords: 35B35 ; 35Q30 ; 76N10 ; stability ; Navier-Stokes equations ; compressible fluids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove that the uniform stability at permanently acting disturbances of a given solution of the Navier-Stokes equations for viscous compressible isothermic fluid is a consequence of the uniform exponential stability of the zero solution of so-called linearized equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00995135
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  • 120
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    Stability and Geometry of Third-Order Resonances in four-Dimensional Symplectic Mappings (1997)
    Springer
    Celestial mechanics and dynamical astronomy 67 (1997), S. 181-204 
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    ISSN: 1572-9478
    Keywords: Hamiltonian systems ; symplectic mappings ; normal forms ; resonances ; stability ; three degrees of freedom
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We analyze four-dimensional symplectic mappings in the neighbourhood of an elliptic fixed point whose eigenvalues are close to satisfy a third-order resonance. Using the perturbative tools of resonant normal forms, the geometry of the orbits and the existence of elliptic or hyperbolic one-dimensional tori (fixed lines) is worked out. This allows one to give an analytical estimate of the stability domain when the resonance is unstable. A comparison with numerical results for the four-dimensional Hénon mapping is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008288826727
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  • 121
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    Position and velocity sensitivities at the triangular libration points (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 1-19 
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    ISSN: 1572-9478
    Keywords: Three body problem ; stability ; surface of section ; commensurability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The model of the circular restricted problem of three bodies is used to investigate the sensitivity of the third body motion when it is given a positional or velocity deviation away from the L4 triangular libration point. The x-axis is used as a criteria for defining the stability of the third body motion. Poincaré's surfaces of section are used to compare the regions of periodic, quasi-periodic and stochastic motion to the trajectories found using the definition of stability (not crossing the x-axis) defined in this study. Values of the primary/secondary mass ratios (μ) ranging from 0 to the linear critical value 0.038521... are investigated. Using this new form of stability measure, it is determined that certain values of μ are more stable than others. The results of this study are compared, and found, to give agreeable results to other studies which investigate commensurabilities of the long and short period terms of periodic orbits.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00051686
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  • 122
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    Stability of axial orbits in analytical galactic potentials (1995)
    Springer
    Celestial mechanics and dynamical astronomy 61 (1995), S. 261-285 
    Details
    ISSN: 1572-9478
    Keywords: galactic dynamics ; periodic orbits ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the stability of axial orbits in analytical galactic potentials as a function of the energy of the orbit and the ellipticity of the potential. The problem is solved by an analytical method, the validity of which is not limited to small amplitudes. The lines of neutral stability divide the parameter space in regions corresponding to different organizations of the main families of orbits in the symmetry planes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00051897
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  • 123
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    Effects of small external forces on the planar oscillation of a cable connected satellites system (1992)
    Springer
    Celestial mechanics and dynamical astronomy 53 (1992), S. 219-226 
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    ISSN: 1572-9478
    Keywords: Artificial satellite ; dissipative forces ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The effects of small external dissipative and disturbing forces on the non-linear planar oscillation of a cable connected satellites system in the central gravitational field of earth have been studied. Typical non-linear oscillation's phenomena arizing from the aforesaid external forces are shown to take place. The presence of these forces enables the application of asymptotic methods of the theory of non-linear oscillations due to Bogoliubov and Mitropolsky to the equation characterizing the non-linear oscillation of the system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00052610
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  • 124
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    Runge–Kutta–Nyström‐type parallel block predictor–corrector methods (1999)
    Springer
    Advances in computational mathematics 10 (1999), S. 115-133 
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    ISSN: 1572-9044
    Keywords: Runge–Kutta–Nyström methods ; predictor–corrector methods ; stability ; parallelism ; 65M12 ; 65M20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes the construction of block predictor–corrector methods based on Runge–Kutta–Nyström correctors. Our approach is to apply the predictor–corrector method not only with stepsize h, but, in addition (and simultaneously) with stepsizes a i h, i = 1 ...,r. In this way, at each step, a whole block of approximations to the exact solution at off‐step points is computed. In the next step, these approximations are used to obtain a high‐order predictor formula using Lagrange or Hermite interpolation. Since the block approximations at the off‐step points can be computed in parallel, the sequential costs of these block predictor–corrector methods are comparable with those of a conventional predictor–corrector method. Furthermore, by using Runge–Kutta–Nyström corrector methods, the computation of the approximation at each off‐step point is also highly parallel. Numerical comparisons on a shared memory computer show the efficiency of the methods for problems with expensive function evaluations.
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    URL: http://dx.doi.org/10.1023/A:1018930732643
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    Stability of the triangular libration points of the circular restricted problem in the presence of resonances (1996)
    Springer
    Celestial mechanics and dynamical astronomy 66 (1996), S. 191-202 
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    ISSN: 1572-9478
    Keywords: resonance ; restricted problem ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of triangular libration points, when the bigger primary is a source of radiation and the smaller primary is an oblate spheroid. has been investigated in the resonance cases ω1 = 2ω2 and ω1 = 3ω2. The motion is unstable for all the values of parameters q and A when ω1 = 2ω2 and the motion is unstable and stable depending upon the values of the parameters q and A when ω1 = 3ω2. Here q is the radiation parameter and A is the oblateness parameter.
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    URL: http://dx.doi.org/10.1007/BF00054964
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    The structure of chaos in a potential without escapes (1994)
    Springer
    Celestial mechanics and dynamical astronomy 60 (1994), S. 249-271 
    Details
    ISSN: 1572-9478
    Keywords: Chaos ; periodic orbits ; stability ; asymptotic curves ; homoclinic points ; heteroclinic points
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the structure of chaos in a simple Hamiltonian system that does no have an escape energy. This system has 5 main periodic orbits that are represented on the surface of section $$(y,\dot y)$$ by the points (1)O(0,0), (2)C 1,C 2(±y c, 0), (3)B 1,B 2(O,±1) and (4) the boundary $$y^2 + \dot y^2 = 1$$ . The periodic orbits (1) and (4) have infinite transitions from stability (S) to instability (U) and vice-versa; the transition values of ε are given by simple approximate formulae. At every transitionS →U a set of 4 asymptotic curves is formed atO. For larger ε the size and the oscillations of these curves grow until they destroy the closed invariant curves that surroundO, and they intersect the asymptotic curves of the orbitsC 1,C 2 at infinite heteroclinic points. At every transitionU →S these asymptotic curves are duplicated and they start at two unstable invariant points bifurcating fromO. At the transition itself the asymptotic curves fromO are tangent to each other. The areas of the lobes fromO increase with ε; these lobes increase even afterO becomes stable again. The asymptotic curves of the unstable periodic orbits follow certain rules. Whenever there are heteroclinic points the asymptotic curves of one unstable orbit approach the asymptotic curves of another unstable orbit in a definite way. Finally we study the tangencies and the spirals formed by the asymptotic curves of the orbitsB 1,B 2. We find indications that the number of spiral rotations tends to infinity as ε → ∞. Therefore new tangencies between the asymptotic curves appear for arbitrarily large ε. As a consequence there are infinite new families of stable periodic orbits that appear for arbitrarily large ε.
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    URL: http://dx.doi.org/10.1007/BF00693324
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    Existence and Stability of L4,5 In The Relativistic Restricted Three-Body Problem (1997)
    Springer
    Celestial mechanics and dynamical astronomy 69 (1997), S. 271-281 
    Details
    ISSN: 1572-9478
    Keywords: restricted three-body problem ; libration points ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied. It is found that L4,5 are unstable in the whole range 0 ≤ µ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable for 0 〈 µ 〈 µ0, where µ is the mass parameter and µ0 = 0.03852....
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    URL: http://dx.doi.org/10.1023/A:1008271021060
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    Long Time Stability for the Main Problem of Artificial Satellites (1997)
    Springer
    Celestial mechanics and dynamical astronomy 69 (1997), S. 317-330 
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    ISSN: 1572-9478
    Keywords: artificial satellite ; Nekhoroshev's theory ; normal form ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the significance of long time stabilty predictions in the light of Nekhoroshev's theory by studying the orbits of artificial satellites. As a simplified model problem we consider the so-called J2problem for an earth's satellite, neglecting luni-solar perturbations and nonconservative effects. We consider a wide range of orbits, excluding those which are too close to the critical inclination. Most of the orbits turn out to be stable for times larger than the estimated age of the solar system, thus proving that, as far as dissipation can be neglected, stability in Nekhoroshev's sense may be effective for physically realistic systems.
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    URL: http://dx.doi.org/10.1023/A:1008277122375
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    Nonlinear Stability of the Lagrangian Libration Points in the Chermnykh Problem (1998)
    Springer
    Celestial mechanics and dynamical astronomy 70 (1998), S. 41-58 
    Details
    ISSN: 1572-9478
    Keywords: three-body problem ; libration points ; stability ; normal forms.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we consider the problem of motion of an infinitesimal point mass in the gravity field of an uniformly rotating dumb-bell. The aim of our study is to investigate Liapunov stability of Lagrangian libration points of this problem. We analyze the stability of libration points in the whole range of parameters ω, μ of the problem. In particular, we consider all resonance cases when the order of resonance is not greater than five.
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    URL: http://dx.doi.org/10.1023/A:1008250207046
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    The integrable cases of the planetary three-body problem at first-order resonance (1993)
    Springer
    Celestial mechanics and dynamical astronomy 55 (1993), S. 249-259 
    Details
    ISSN: 1572-9478
    Keywords: Asteroid ; libration ; resonance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper investigates the stability of the motion in the averaged planar general three-body problem in the case of first-order resonance. The equations of the averaged motion of bodies near the resonance surface is obtained and is analytically integrated by quadratures. The stability of the averaged motion is analytically investigated in relation to the semi-major axes, the eccentricities and the resonance phases. An autonomous second-order equation is obtained for the deviation of semiaxes from the resonance surface. This equation has an energy integral and is analytically integrated by quadratures. The quasi-periodic dependence on time with two-frequency basis of the averaged motion of bodies is found. The basic frequencies are analytically calculated. With the help of the mean functionals calculated along integral curves of the averaged problem the new analytic first integrals are constructed with coefficients periodic in time. The analytic conditions of librations of resonance phases are obtained.
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    URL: http://dx.doi.org/10.1007/BF00692513
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    About the periodic solutions of a rigid body in a central Newtonian field (1993)
    Springer
    Celestial mechanics and dynamical astronomy 55 (1993), S. 323-330 
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    ISSN: 1572-9478
    Keywords: Periodic orbits ; rigid body dynamics ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The equations of motion of a rigid body about a fixed point in a central Newtonian field is reduced to the equation of plane motion under the action of potential and gyroscopic forces, using the isothermal coordinates on the inertia ellipsoid. The construction of periodic solutions near the equilibrium points, by using the Lipaunov theorem of holomorphic integral, is obtained and the necessary and sufficient conditions for the stability of the system are given.
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    URL: http://dx.doi.org/10.1007/BF00692992
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    Invariant rotational curves in Sitnikov's Problem (1993)
    Springer
    Celestial mechanics and dynamical astronomy 55 (1993), S. 351-367 
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    ISSN: 1572-9478
    Keywords: Sitnikov's problem ; invariant rotational curves ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Sitnikov's Problem is a Restricted Three-Body Problem of Celestial Mechanics depending on a parameter, the eccentricity,e. The Hamiltonian,H(z, v, t, e), does not depend ont ife=0 and we have an integrable system; ife is small the KAM Theory proves the existence of invariant rotational curves, IRC. For larger eccentricities, we show that there exist two complementary sequences of intervals of values ofe that accumulate to the maximum admissible value of the eccentricity, 1, and such that, for one of the sequences IRC around a fixed point persist. Moreover, they shrink to the planez=0 ase tends to 1.
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    On the families of periodic orbits which bifurcate from the circular Sitnikov motions (1994)
    Springer
    Celestial mechanics and dynamical astronomy 60 (1994), S. 99-129 
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    ISSN: 1572-9478
    Keywords: Sitnikov motions ; periodic orbits ; stability ; bifurcations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In this paper we deal with the circular Sitnikov problem as a subsystem of the three-dimensional circular restricted three-body problem. It has a first analytical part where by using elliptic functions we give the analytical expressions for the solutions of the circular Sitnikov problem and for the period function of its family of periodic orbits. We also analyze the qualitative and quantitative behavior of the period function. In the second numerical part, we study the linear stability of the family of periodic orbits of the Sitnikov problem, and of the families of periodic orbits of the three-dimensional circular restricted three-body problem which bifurcate from them; and we follow these bifurcated families until they end in families of periodic orbits of the planar circular restricted three-body problem. We compare our results with the previous ones of other authors on this problem. Finally, the characteristic curves of some bifurcated families obtained for the mass parameter close to 1/2 are also described.
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    URL: http://dx.doi.org/10.1007/BF00693095
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    The stability of rational approximations of analytic semigroups (1993)
    Springer
    BIT 33 (1993), S. 74-84 
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    ISSN: 1572-9125
    Keywords: 65J10 ; 65M12 ; Analytic semigroup ; Banach space ; rational approximation ; A-acceptable ; A(θ)-acceptable ; stability ; Crank-Nicolson method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown thatA-acceptable and, more generally,A(θ)-arational approximations of bounded analytic semigroups in Banach space are stable. The result applies, in particular, to the Crank-Nicolson method.
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    URL: http://dx.doi.org/10.1007/BF01990345
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    Stiffness of ODEs (1993)
    Springer
    BIT 33 (1993), S. 285-303 
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    ISSN: 1572-9125
    Keywords: 65L05 ; stiffness ; stability ; pseudospectra
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is argued that even for a linear system of ODEs with constant coefficients, stiffness cannot properly be characterized in terms of the eigenvalues of the Jacobian, because stiffness is a transient phenomenon whereas the significance of eigenvalues is asymptotic. Recent theory from the numerical solution of PDEs is adapted to show that a more appropriate characterization can be based upon pseudospectra instead of spectra. Numerical experiments with an adaptive ODE solver illustrate these findings.
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    URL: http://dx.doi.org/10.1007/BF01989751
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    Exponential Integrators for Quantum-Classical Molecular Dynamics (1999)
    Springer
    BIT 39 (1999), S. 620-645 
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    ISSN: 1572-9125
    Keywords: Numerical integrator ; oscillatory solutions ; Schrödinger equation ; quantum-classical coupling ; error bounds ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study time integration methods for equations of mixed quantum-classical molecular dynamics in which Newtonian equations of motion and Schrödinger equations are nonlinearly coupled. Such systems exhibit different time scales in the classical and the quantum evolution, and the solutions are typically highly oscillatory. The numerical methods use the exponential of the quantum Hamiltonian whose product with a state vector is approximated using Lanczos' method. This allows time steps that are much larger than the inverse of the highest frequencies. We describe various integration schemes and analyze their error behaviour, without assuming smoothness of the solution. As preparation and as a problem of independent interest, we study also integration methods for Schrödinger equations with time-dependent Hamiltonian.
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    URL: http://dx.doi.org/10.1023/A:1022335122807
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    Stochastic Methods for Ill-Posed Problems (2000)
    Springer
    BIT 40 (2000), S. 226-240 
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    ISSN: 1572-9125
    Keywords: Stochastic differential equations ; regularisation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is devoted to the numerical analysis of ill-posed problems of evolution equations in Banach spaces using certain classes of stochastic one-step methods. The linear stability properties of these methods are studied. Regularisation is given by the choice of the regularisation parameter as α = $$\sqrt {\tau _n }$$ , where τ n is the stepsize and provides the convergence on smooth initial data. The case of the approximation of well-posed problems is also considered.
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    URL: http://dx.doi.org/10.1023/A:1022386822865
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    On integrating vertex singularities using extrapolation (1994)
    Springer
    BIT 34 (1994), S. 62-79 
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    ISSN: 1572-9125
    Keywords: AMS(MOS) 65D30 ; 65B05 ; adaptive ; cubature ; singularity ; extrapolation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new approach to the integration of vertex singularities is described. This approach is based on a non-uniform subdivision of the region of integration and the technique fits well to the subdivision strategy used in many adaptive algorithms. A nice feature with this approach is that it can be used in any dimension and on any region of integration which can be subdivided into subregions of the same form. The strategy can be applied both to vertex singularities and internal point singularities. In the latter case this can be done without an initial subdivision of the region in order to put the singular point in a vertex. It turns out that the technique has excellent numerical stability properties.
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    URL: http://dx.doi.org/10.1007/BF01935016
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    Three Dimensional Laser Simulation Code on a Desktop Personal Computer (1999)
    Springer
    Optical review 6 (1999), S. 28-36 
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    ISSN: 1349-9432
    Keywords: optical propagation equation ; stability ; picosecond pulse ; 3-dimensional computation ; Fresnel’s distribution ; fast Fourier transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a new simulation code able to simulate the entire propagation of laser pulse, from the amplifiers level up to the focusing stage. This algorithm has some new characteristics that we intend to present. It computes the three-dimensional optical propagation equation using no approximation other than its picosecond expression. The stability has been carefully studied so that it can be applied to any geometry. This is a great improvement since, up to now only cylindrical geometry was accessible for accuracy. In this paper we also present a method using Fast Fourier Transform able to evaluate with a high accuracy, Fresnel’s distribution of a focused laser pulse. The advantages provided by our algorithm are its rapidity and its high physical understanding of the focusing phenomena.
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    URL: http://dx.doi.org/10.1007/s10043-999-0028-1
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    The influence of a flood event on phytoplankton succession (1990)
    Springer
    Aquatic sciences 52 (1990), S. 330-344 
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    ISSN: 1420-9055
    Keywords: Flood ; phytoplankton succession ; reversion ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The effect of the August 1987 River Reuss flood event on the phytoplankton biocoenosis in Lake Uri (Urnersee, part of Lake Lucerne, Switzerland) was investigated firstly by comparing biological, chemical and physical data sampled before the event with equivalent data sampled after the event; and secondly by comparing the phytoplankton succession in 1987 with that occurring in the “floodfree” year 1989. As a consequence of the flood, the physical and chemical environment of the phytoplankton was found to have undergone a change which resulted in an alteration in the composition of the phytoplankton community. The phytoplankton community existing previous to the flood event, which had been dominated byTabellaria fenestrata sensu Husted 1930 (K-strategist), was replaced by a biocoenosis characterized mainly by various species of flagellates, which represent a typical spring successional stage (r-strategists). After the externally-imposed perturbation, the return to stable physical and chemical conditions was followed by the re-establishment of the successional stage which had existed before the flood (termed “reversion” by Reynolds, 1980).
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    Stability of axial motions of nonlinearly elastic loops (1996)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 47 (1996), S. 809-816 
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    ISSN: 1420-9039
    Keywords: 34D20 ; 34D35 ; 35Q72 ; 73H10 ; 73K03 ; Elastic string ; stability ; energy-momentum ; axial motion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We establish the stability of axial motions (steady motions along the lengthwise direction) of nonlinearly elastic loops of string. A key observation here is that a linear combination of the total energy and the total circulation of the string, both of which are conserved quantities, yields an appropriate Liapunov function. From our previous work [5], we know that there are uncountably many shapes corresponding to a given axial speed. Accordingly, we establish “orbitai” stability (modulo this collection of relative equilibria). For a well-defined class of “soft” materials, there is an upper bound on the axial speed sufficient for stability; “stiff” materials are shown to be orbitally stable at any axial speed.
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    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
    Source: Springer Online Journal Archives 1860-2000
    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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    Thermal and chemical stability of titanium-substituted MCM-41 (1996)
    Springer
    Catalysis letters 40 (1996), S. 261-264 
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    ISSN: 1572-879X
    Keywords: Ti-substituted MCM-41 ; stability ; dehydrogenation of ethanol ; hydroxylation of phenol ; XRD ; XANES
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The thermal and chemical stability of a titanium-substituted MCM-41 (TiMCM-41) with Si/Ti mole ratio of 39 and pore diameter of 2.4 nm was studied with the small-angle X-ray diffraction and X-ray absorption near-edge structure techniques. The TiMCM-41 was stable in helium flow below 1273 K and under gas-phase reaction conditions of ethanol dehydrogenation (ethanol/ O2 = 1 mol/mol, 373–723 K). Under liquid-phase reaction conditions of phenol hydroxylation (phenol/35% H2O2 /acetone in moles=3∶1∶7,333K), however, it lost the MCM-41structure and titanium was leached out of the silicalite framework.
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    Ethene hydroformylation on Co/SiO2 catalysts (1998)
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    Catalysis letters 53 (1998), S. 97-101 
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    ISSN: 1572-879X
    Keywords: ethene hydroformylation ; heterogeneous catalysts ; cobalt catalysts ; gas‐phase deposition ; dispersion ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The results from ethene hydroformylation at 173°C showed that a Co(acac)3/SiO2 catalyst prepared from Co(acac)3 precursor by gas‐phase deposition was three times as active as a catalyst prepared by impregnation from cobalt nitrate, but oxo‐selectivities were similar. The high propanal selectivities on the Co(acac)3/SiO2 seem to be related to the presence of highly dispersed active sites favouring CO insertion. As dispersion is decreased from 23 to 8% due to increasing metal content (from 5 to 16 wt%), oxo‐selectivity decreased from 39 to 25%. The activity of Co(acac)3/SiO2 remained unchanged during 68 h on stream. The gas‐phase deposition technique described here is a promising method for the preparation of active, selective and stable heterogeneous hydroformylation catalysts.
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    Preparation of model catalysts by laser interference nanolithography followed by metal cluster deposition (1998)
    Springer
    Catalysis letters 56 (1998), S. 1-6 
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    ISSN: 1572-879X
    Keywords: nanolithography ; model catalyst ; palladium ; copper ; stability ; spin-coating ; SEM ; AFM ; XPS
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Metal clusters arranged on nanostructured oxidized silicon wafers are presented as new model catalyst systems. A photoresist layer spun on top of a wafer was patterned by laser interference exposure. The grid obtained after removing the exposed parts of the resist is used as an etching mask. Hollows with diameters of 300 nm and depths between 50 and 60 nm were etched into the oxide layer using wet chemical methods. Two methods were applied to deposit metal clusters (Pd or Cu) in a defined way within the hollows. The particles ranged from 10 to 50 nm in height and from 80 to 200 nm in diameter. The model catalyst systems were characterized by atomic force microscopy and X-ray photoelectron spectroscopy. The method presented here allows us to produce 4 inch wafers that are covered completely by nanometer-sized structures in a reasonable period of time.
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    Long-term stability of the V2O5/Al2O3 catalyst for the selective reduction of nitrogen oxides (1994)
    Springer
    Catalysis letters 28 (1994), S. 25-31 
    Details
    ISSN: 1572-879X
    Keywords: vanadia/alumina ; stability ; NO x selective reduction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Changes of the V2O5/Al3O3 catalyst aged for up to 10 years under real conditions of the selective catalytic reduction of NO x by ammonia (SCR) at the tail gases of the nitric acid plant were characterized by51V NMR spectroscopy, porosimetry, temperature programmed reduction (TPR) and catalytic activity measurements. The catalytic activity and the redox properties of the catalyst were found intact. Only small variations of the ratio of the octahedral and tetrahedral vanadia species were documented by51V NMR on aged catalyst.
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    On the rotating rod with variable cross section (1997)
    Springer
    Archive of applied mechanics 67 (1997), S. 447-456 
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    ISSN: 1432-0681
    Keywords: Key words rotation ; stability ; energy criterion ; variational analysis ; functional analysis ; eigenvalue problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Stability of a heavy rotating rod with a variable cross section is studied by energy method. Bifurcation points for the system of equilibrium equations are analyzed. It is shown that for the case when the rotation speed exceeds the critical one, the trivial solution ceases to be the minimizer of the potential energy, so that rod loses stability, according to the energy criteria. Also, a new estimate of the maximal rod deflection in the post-critical state is obtained.
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    URL: http://dx.doi.org/10.1007/s004190050130
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    Vibration of rods with a concentrated mass in the presence of non-conservative forces (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 507-521 
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    ISSN: 1432-0681
    Keywords: rod vibrations ; stability ; tip mass ; non-conservative forces ; non-selfadjoint problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Separable and non-selfadjoint boundary-value problems representing the vibration of linearly elastic unidimensional systems are considered. The elastic system is modelled as a continuous distributed-parameter system where singularities in the mass distribution function can be neatly taken into account. Specifically, extending Green's function approach, the free vibration, stability and forced vibration of fixed-free rods with a tip mass and under the action of uniformly distributed non-conservative loads have been investigated analytically.
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    Stability of bars made of linear elastic materials with voids (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 99-109 
    Details
    ISSN: 1432-0681
    Keywords: Key words Bars ; voids ; viscoelasticity ; stability ; critical load
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  Dynamic stability of an elastic bar with voids is considered. Using the Lyapunov approach some new sufficient stability conditions are obtained and explicit expressions for the critical load are derived.
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    URL: http://dx.doi.org/10.1007/BF00787903
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    Influence of shear deformation on the buckling of elastically supported beams (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 133-141 
    Details
    ISSN: 1432-0681
    Keywords: Shear deformation ; elastically supported beams ; axial compression ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary The influence of shear deformation on the buckling behavior of a beam supported laterally by a Winkler elastic foundation is studied. A full investigation of the bifurcation points at which, under axial load, the beam becomes critical with respect to one or two simultaneous buckling modes is made. The configurations and stabilities of the equilibrium paths that bifurcate from the critical points are derived. From the results of theoretical analysis, it becomes evident that shear deformation has a considerable effect upon the equilibriums and stabilities of the post-buckling of the beam. The results for the Bernoulli-Euler beam can be obtained as a limiting case for those of the present beam by letting the shear stiffness tend to infinity.
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    URL: http://dx.doi.org/10.1007/BF00799294
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    Modale Behandlung linearer periodisch zeitvarianter Bewegungsgleichungen (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 178-193 
    Details
    ISSN: 1432-0681
    Keywords: Periodic motion ; modal treatment ; itrations ; time variance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Übersicht Lineare, periodisch zeitvariante Bewegungsgleichungen treten im Hubschrauber- und Windturbinenbau auf. Der Getriebebau und die Rotordynamik liefern weitere Beispiele. In diesem Bericht wird ein systematischer Weg zu ihrer Lösung dargestellt. Mit dem Ansatz von Hill wird die homogene Lösung über die Lösung eines Eigenwertproblems gewonnen. Nach Anpassung an die Anfangsbedingungen liefert sie die Fundamentalmatrix des Systems. Ähnlich wie bei zeitinvarianten Systemen, existieren auch bei zeitvarianten Systemen Orthogonalitätsbedingungen, die die Eigenvektoren erfüllen. Die Eigenvektoren selbst sind allerdings zeitabhängig. Benutzt man die Eigenvektoren als Ansatzvektor zur Berechnung der erzwungenen Schwingungen (Transformation mit der zeitvarianten Modalmatrix des Systems), so gelingt es, die Bewegungsgleichungen des Systems in entkoppelte, zeitinvariante zu überführen. Sie lassen sich in bekannter Weise lösen. Dieses Vorgehen wird auf eine moderne Windkraftanlage angewandt. Sie wurde zunächst mit 372 Freiheitsgraden modelliert, die aber auf 18 vor der numerischen Weiterbehandlung kondensiert wurden. Das Stabilitätsverhalten und die Antwortspektren auf stochastische Anregung durch den Wind wurden auf dem oben beschriebenen Weg ermittelt.
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    URL: http://dx.doi.org/10.1007/BF00799297
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  • 152
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    Modale Behandlung linearer periodisch zeitvarianter Bewegungsgleichungen (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 178-193 
    Details
    ISSN: 1432-0681
    Keywords: Key words Periodic motion ; modal treatment ; itrations ; time variance ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Übersicht  Lineare, periodisch zeitvariante Bewegungsgleichungen treten im Hubschrauber- und Windturbinenbau auf. Der Getriebebau und die Rotordynamik liefern weitere Beispiele. In diesem Bericht wird ein systematischer Weg zu ihrer Lösung dargestellt. Mit dem Ansatz von Hill wird die homogene Lösung über die Lösung eines Eigenwertproblems gewonnen. Nach Anpassung an die Anfangsbedingungen liefert sie die Fundamentalmatrix des Systems. Ähnlich wie bei zeitinvarianten Systemen, existieren auch bei zeitvarianten Systemen Orthogonalitätsbedingungen, die die Eigenvektoren erfüllen. Die Eigenvektoren selbst sind allerdings zeitabhängig. Benutzt man die Eigenvektoren als Ansatzvektor zur Berechnung der erzwungenen Schwingungen (Transformation mit der zeitvarianten Modalmatrix des Systems), so gelingt es, die Bewegungsgleichungen des Systems in entkoppelte, zeitinvariante zu überführen. Sie lassen sich in bekannter Weise lösen. Dieses Vorgehen wird auf eine moderne Windkraftanlage angewandt. Sie wurde zunächst mit 372 Freiheitsgraden modelliert, die aber auf 18 vor der numerischen Weiterbehandlung kondensiert wurden. Das Stabilitätsverhalten und die Antwortspektren auf stochastische Anregung durch den Wind wurden auf dem oben beschriebenen Weg ermittelt.
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    URL: http://dx.doi.org/10.1007/BF00799297
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    Constitutive branching in compressible elastic materials (1996)
    Springer
    Archive of applied mechanics 66 (1996), S. 291-299 
    Details
    ISSN: 1432-0681
    Keywords: stability ; elasticity ; singularities ; bifurcation ; material instabilities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Branching analysis for the homogeneous deformations of a compressible elastic unit cube under dead loading is performed. Critical conditions for branching of the equilibrium paths are derived and the post-critical equilibrium paths are described. Special attention is given to the compound branching.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00787357
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  • 154
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    Influence of shear deformation on the buckling of elastically supported beams (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 133-141 
    Details
    ISSN: 1432-0681
    Keywords: Key words Shear deformation ; elastically supported beams ; axial compression ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  The influence of shear deformation on the buckling behavior of a beam supported laterally by a Winkler elastic foundation is studied. A full investigation of the bifurcation points at which, under axial load, the beam becomes critical with respect to one or two simultaneous buckling modes is made. The configurations and stabilities of the equilibrium paths that bifurcate from the critical points are derived. From the results of theoretical analysis, it becomes evident that shear deformation has a considerable effect upon the equilibriums and stabilities of the post-buckling of the beam. The results for the Bernoulli-Euler beam can be obtained as a limiting case for those of the present beam by letting the shear stiffness tend to infinity.
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    URL: http://dx.doi.org/10.1007/BF00799294
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    Hydraulic analysis of free-surface flows with solidification (2000)
    Springer
    Archive of applied mechanics 70 (2000), S. 17-29 
    Details
    ISSN: 1432-0681
    Keywords: Key words free-surface flow ; solidification ; strip casting ; steady state ; nonuniqueness ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary The paper is concerned with a one-dimensional analysis of plane open-channel flow with continuous solidification. The process is of relevance for recent developments in the casting of steel and other metals. The bottom of the channel consists of a rotating casting roll and a horizontal cooling table, where the solidified material is withdrawn with given velocity. The study is restricted to the region downstream of the top of the casting roll. Surface tension is neglected. In the main part of the analysis inviscid fluid flow is considered since the Reynolds number is very large in the applications. It is found that the steady-state solutions are nonunique in a certain parameter range. In addition to a continuous solution, there are two solutions including hydraulic jumps, with one hydraulic jump being located on the casting roll, the other one on the cooling table. Regarding the stability of the non unique solutions, the evolution of disturbances is investigated numerically as an initial-value problem. It is concluded that the hydraulic jump on the cooling table is unstable, while the other discontinuous solution as well as the continuous solution are stable for sufficiently small disturbances. Which stable solution is attained in the steady state, depends on the history of the process. Friction at the liquid/solid interface is taken into account in the last part of the analysis. A constant friction coefficient is assumed. It is found that the history of the process determines the steady-state solution if, and only if, the friction coefficient is sufficiently small. For larger values of the friction coefficient, the steady-state solution is unique and independent of the history of the transient process. Furthermore, for sufficiently large friction coefficients, stable hydraulic jumps are found, in contrast to the inviscid case, also on the cooling table.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004199900031
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    Vibration of rods with a concentrated mass in the presence of non-conservative forces (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 507-521 
    Details
    ISSN: 1432-0681
    Keywords: Key words rod vibrations ; stability ; tip mass ; non-conservative forces ; non-selfadjoint problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  Separable and non-selfadjoint boundary-value problems representing the vibration of linearly elastic unidimensional systems are considered. The elastic system is modelled as a continuous distributed-parameter system where singularities in the mass distribution function can be neatly taken into account. Specifically, extending Green’s function approach, the free vibration, stability and forced vibration of fixed-free rods with a tip mass and under the action of uniformly distributed non-conservative loads have been investigated analytically.
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    URL: http://dx.doi.org/10.1007/BF00789092
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    A combined perturbation/finite-difference procedure applied to temperature effects and stability in a laminar boundary layer (1996)
    Springer
    Archive of applied mechanics 66 (1996), S. 264-272 
    Details
    ISSN: 1432-0681
    Keywords: asymptotic expansion ; stability ; boundary layer ; laminar flow ; heat transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary By means of a combined method it is demonstrated for regular perturbation problems how the higher order terms of an asymptotic expansion may be determined from numerical solutions of the non-expanded basic equations. The method is applied to heat transfer effects in a laminar boundary layer and to the analysis of its stability. All first- and second-order coefficients of the problem are determined from numerical solutions of the basic set of equations.
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    URL: http://dx.doi.org/10.1007/BF00787354
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    A combined perturbation/finite-difference procedure applied to temperature effects and stability in a laminar boundary layer (1996)
    Springer
    Archive of applied mechanics 66 (1996), S. 264-272 
    Details
    ISSN: 1432-0681
    Keywords: Key words asymptotic expansion ; stability ; boundary layer ; laminar flow ; heat transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary  By means of a combined method it is demonstrated for regular perturbation problems how the higher order terms of an asymptotic expansion may be determined from numerical solutions of the non-expanded basic equations. The method is applied to heat transfer effects in a laminar boundary layer and to the analysis of its stability. All first- and second-order coefficients of the problem are determined from numerical solutions of the basic set of equations.
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    Global dynamical behavior of a three-body system with flexible connection in the gravitational field (1999)
    Springer
    Archive of applied mechanics 69 (1999), S. 47-54 
    Details
    ISSN: 1432-0681
    Keywords: Key words Bifurcation ; stability ; multibody system dynamics ; singularity theory ; Liapunov's direct method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary In this paper, the global behavior of relative equilibrium states of a three-body satellite with flexible connection under the action of the gravitational torque is studied. With geometric method, the conditions of existence of nontrivial solutions to the relative equilibrium equations are determined. By using reduction method and singularity theory, the conditions of occurrence of bifurcation from trivial solutions are derived, which agree with the existence conditions of nontrivial solutions, and the bifurcation is proved to be pitchfork-bifurcation. The Liapunov stability of each equilibrium state is considered, and a stability diagram in terms of system parameters is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004190050203
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    Stability of bars made of linear elastic materials with voids (1995)
    Springer
    Archive of applied mechanics 65 (1995), S. 99-109 
    Details
    ISSN: 1432-0681
    Keywords: Bars ; voids ; viscoelasticity ; stability ; critical load
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Summary Dynamic stability of an elastic bar with voids is considered. Using the Lyapunov approach some new sufficient stability conditions are obtained and explicit expressions for the critical load are derived.
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    URL: http://dx.doi.org/10.1007/BF00787903
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    The finite volume element method with quadratic basis functions (1996)
    Springer
    Computing 57 (1996), S. 281-299 
    Details
    ISSN: 1436-5057
    Keywords: 65N15 ; 65N99 ; 35A40 ; Finite volume method ; box scheme ; stability ; error estimates
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Es wird eine Box-Methode mit quadratischen Ansatzfunktionen zur Diskretisierung elliptischer Randwertaufgaben vorgestellt. Die entstehende Diskretisierungsmatrix ist nichsymmetrisch. Die Stabilitätsanalyse basiert auf einer elementweisen Abschätzung des Skalarproduktes 〈A h u h ,u h 〉. Hinreichende Bedingungen an die Geometrie der Dreiecke der Triangulierung führen zur diskreten Elliptizität. Unter diesen Voraussetzungen wird eineO(h 2)-Fehlerabschätzung bewiesen.
    Notes: Abstract The paper presents a box scheme with quadratic basis functions for the discretisation of elliptic boundary value problems. The resulting discretisation matrix is non-symmetrical (and also not an M-matrix). The stability analysis is based on an elementwise estimation of the scalar product 〈A h u h ,u h 〉. Sufficient conditions placed on the triangles of the triangulation lead to discrete ellipticity. Proof of anO(h 2) error estimate is given for these conditions.
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    URL: http://dx.doi.org/10.1007/BF02252250
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    Sequential stability of the constant cost dynamic lot size model-searching for monotonicity (1994)
    Springer
    OR spectrum 15 (1994), S. 197-203 
    Details
    ISSN: 1436-6304
    Keywords: Inventory ; dynamic programming ; stability ; Lagerhaltung ; Dynamische Optimierung ; Stabilität
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Die Menge der Kostenparameter, für die eine optimale Lösung des dynamischen Losgrößenmodells optimal bleibt wird hier Stabilitätsregion genannt. Die Größe einer solchen Menge kann als Maß der Robustheit einer Lösung angesehen werden. Es ist zu erwarten, daß die Stabilitätsregionen mit wachsendem Zeithorizont schrumpfen und daß sie in diesem Sinne monoton sind. In der vorliegenden Arbeit werden verschiedene hinreichende Bedingungen für diese Monotonie untersucht. Die Bedingungen setzen unter anderem die Existenz von Planungs- und Vorhersage-Horizonten voraus und verallgemeinern so Ergebnisse einer früheren Arbeit, in der Aussagen für gewöhnliche Planungs-Horizonte vorgestellt wurden.
    Notes: Abstract The set of cost inputs for which an optimal solution of the dynamic lot size model remains valid is called stability region. The size of this region may be viewed as a measure of robustness of a solution. It is an expectation that the stability regions shrink with growing time horizons and that they are monotonous in this sense. In the present paper several sufficient conditions implying monotonicity will be studied. The conditions cover the existence of planning and forecast horizons and generalize the results of a previous paper in wich monotonicity results were presented for the case of ordinary planning horizons.
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    URL: http://dx.doi.org/10.1007/BF01719450
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    Surf-riding and oscillations of a ship in quartering waves (1995)
    Springer
    Journal of marine science and technology 1 (1995), S. 24-36 
    Details
    ISSN: 1437-8213
    Keywords: surf-riding ; nonlinear ; wave ; ship motion ; stability ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The behavior of a ship encountering large regular waves from astern at low frequency is the object of investigation, with a parallel study of surf-riding and periodic motion paterns. First, the theoretical analysis of surf-riding is extended from purely following to quartering seas. Steady-state continuation is used to identify all possible surf-riding states for one wavelength. Examination of stability indicates the existence of stable and unstable states and predicts a new type of oscillatory surf-riding. Global analysis is also applied to determine the areas of state space which lead to surf-riding for a given ship and wave conditions. In the case of overtaking waves, the large rudder-yaw-surge oscillations of the vessel are examined, showing the mechanism and conditions responsible for loss of controllability at certain vessel headings.
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    URL: http://dx.doi.org/10.1007/BF01240010
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    A survey on stability of chemical species in solution during storage: the BCR experience (1995)
    Springer
    Microchimica acta 118 (1995), S. 131-141 
    Details
    ISSN: 1436-5073
    Keywords: stability ; chemical species ; solutions ; calibration ; interlaboratory studies ; measurement and testing programme
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The stability of chemical species in solution during storage is one of the critical aspect that has to be carefully studied e.g. for calibration purposes or prior to the organization of interlaboratory studies using synthetic solutions. The Measurements and Testing Programme (formerly BCR) is currently undertaking projects to improve the quality of speciation analysis for a variety of species (e.g. As, Hg, Sn, Pb, Cr). In all the cases the stability of these species was carefully studied in the solutions provided to the participants. This paper gives an overview of some of the results obtained in different BCR-projects on speciation analysis.
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    URL: http://dx.doi.org/10.1007/BF01242236
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    Multivariate exploratory data analysis in chemical industry (1991)
    Springer
    Microchimica acta 104 (1991), S. 467-482 
    Details
    ISSN: 1436-5073
    Keywords: prediction ; stability ; multivariate methods ; graphical analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract Sizeable data bases are now being routinely generated in a variety of contexts in chemical industry. Statistical investigations of such data bases are aimed both at initially uncovering structure and eventually proposing models, in particular for predicting product quality by the mix or characteristics of the chemical compounds. “Online Multivariate Exploratory Graphical Analysis” (OMEGA) stands for a structured exploratory study of the relationships in a multivariate data set, where, rather than testing for one specific property, as many clues as possible for interesting structures are searched for by different dimension reductions and succeeding interactive graphical analyses. The stability of the projections obtained by the different dimension reduction methods is assessed by simulation producing graphical displays particularly supporting the identification of influential points. The variation of the predictions obtained by the different dimension reduction methods is assessed by cross-validation delivering misclassification rates or cross-validated R2 values. The interpretation of the new coordinates corresponding to dimension reduction is supported by loading simplifications and graphical displays for judging its adequacy. The OMEGA strategy has been found to be an effective tool for routine searching for structure.
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    URL: http://dx.doi.org/10.1007/BF01245532
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    On some problems of stability of systems with an infinite number of degrees of freedom (1994)
    Springer
    Meccanica 29 (1994), S. 195-210 
    Details
    ISSN: 1572-9648
    Keywords: Chetaev functional ; pendulum ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Sommario Si considera il problema di stabilità di punti di equilibrio di un pendolo fisico con un filo inestensibile appeso ad esso dal punto di vista del teorema di Lagrange sulla stabilità e sulla sua inversione. Difficoltà specifiche relative allo studio di un sistema meccanico di dimensione infinita sono discusse. Si suggerisce un nuovo metodo per lo studio della stabilità rispetto a due metriche. L'influenza di fenomeni di risonanza sul moto del sistema ridotto (linearizzato) è considerata.
    Notes: Abstract The problem of stability of equilibria of a physical pendulum with a nonstretchable thread attached to it is considered from the standpoint of the Lagrange theorem on stability and its inversion. Specific difficulties which one faces when studying an infinite dimensional mechanical system are discussed. A new approach to the study of stability with respect to two metrics is suggested. The influence of resonant phenomena on the motion of the shortened (linearized) system is considered.
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    URL: http://dx.doi.org/10.1007/BF01007501
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    Concerning a Technique for Increasing Stability of Climbing Robots (2000)
    Springer
    Journal of intelligent and robotic systems 27 (2000), S. 195-209 
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    ISSN: 1573-0409
    Keywords: wall-climbing robot ; electromagnetic grippers ; stability ; additional support element ; sliding and turning over conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Legged-climbing robot is considered. Each foot of the robot has an electromagnet system for robot"s holding on a metal surface. This surface can be both vertical and inclined, including negative slope. Analytical calculation of robot stability under turn over or sliding conditions has been made. Critical slopes have been determined. One of these slopes corresponds to minimal reserve of robot stability towards sliding and another to minimal reserve of robot stability towards turning-over. As total reserve of stability of a robot is always equal to the minimal one of these reserves. Additional support elements of elastic material with high coefficient of friction, along with electromagnet, allows to increase minimal reserve of robot stability towards sliding. The use of such support elements leads to redistributing force of normal support reaction between electromagnet (which surface has low coefficient of friction) and additional support element (which surface has high coefficient of friction). It is just what leads to increasing the total friction force and as a consequence to increasing of minimal reserve of robot stability towards sliding.
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    URL: http://dx.doi.org/10.1023/A:1008158332368
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    Robust pole assignment for incomplete nonlinear decoupling applied to robots (1990)
    Springer
    Journal of intelligent and robotic systems 3 (1990), S. 259-289 
    Details
    ISSN: 1573-0409
    Keywords: Nonlinear decoupling ; feedback linearization ; functional analysis ; elastic robots ; robustness ; stability ; pole assignment ; nonlinear systems ; robot control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A robustness analysis and synthesis for incomplete nonlinear decoupling for a class of nonlinear systems is discussed. Rigid and elastic-joint robot models belong to this class. For the elastic case, a transformation facilitates the robustness analysis under a weak assumption. Charts with H 1- and H ∞- norms of closed-loop disturbance transfer functions of the nonlinear-decoupled system are presented for a robust pole assignment.
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    URL: http://dx.doi.org/10.1007/BF00126073
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    Real-time feedback scheduling of flexible manufacturing systems (1992)
    Springer
    Journal of intelligent and robotic systems 6 (1992), S. 51-63 
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    ISSN: 1573-0409
    Keywords: Scheduling ; flexible manufacturing systems ; stability ; feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A genetic manufacturing environment is considered. The emphasis is on small-lot, discrete, and asynchronous type of manufacturing systems rather than high volume and continuous type. Two classes of scheduling policies are proposed to render the machine stable. The policies are of feedback type. The decision is made in real-time and on-line.
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    URL: http://dx.doi.org/10.1007/BF00314697
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    Force control of robots with nonlinearities (1992)
    Springer
    Journal of intelligent and robotic systems 6 (1992), S. 219-240 
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    ISSN: 1573-0409
    Keywords: Force control ; slip-stick friction ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper explores two practical issues related to the force control of manipulators. The first issue examined is how system stability is effected by commonly occurring manipulator nonlinearities, such as sampled-data, control signal saturation and slip-stick friction. It is shown that discretely implemented force control algorithms can drive the feedback force controlled manipulator into a limit cycle, even for a very small sampling period that by far satisfies Shannon's sampling theorem. The bounds of stability are enhanced by the presence of control signal saturation and slip stick friction. The second issue investigated is the inclusion of a high gain inner position loop as a means to minimize the unpredictability in the steady state error due to slip-stick friction. In order to support the theoretical conclusions, experiments were performed with the PUMP 560 industrial robot testbed facility developed at Colorado State University.
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    URL: http://dx.doi.org/10.1007/BF00248017
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    On the topological classification of pseudofree group actions on 4-manifolds: II (1996)
    Springer
    K-Theory 10 (1996), S. 491-516 
    Details
    ISSN: 1573-0514
    Keywords: 57M60 ; 57N13 ; 57R91 ; 19G38 ; topological 4-manifold ; pseudofree action ; equivariant intersection form ; stability ; topological rigidity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the algebraic aspects of the classification of pseudofree, locally linear group actions on a simply connected 4-manifold, particularly with the splitting and stability properties of the associated Hermitian intersection module and its isometry group. Our main result is the proof of stability of the equivariant intersection form for a large class of pseudofree actions. We also prove a topological rigidity theorem stating that two locally linear, pseudofree actions on a closed, oriented, simply connected 4-manifold, with the equivariant intersection forms indefinite and of rank at least 3 at each irreducible character, are topologically conjugate by an orientation preserving homeomorphism if and only if their oriented local representations at the corresponding fixed points are linearly equivalent.
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    URL: http://dx.doi.org/10.1007/BF00536601
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    Nonabelian K-theory: The nilpotent class of K 1 and general stability (1991)
    Springer
    K-Theory 4 (1991), S. 363-397 
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    ISSN: 1573-0514
    Keywords: Nonabelian K 1 ; noncommutative homotopy ; general linear group ; superspecial linear groups ; descending central series ; stability ; relative normal subgroups ; nilpotent sandwich classifications ; quasi-finite algebras
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A functorial filtration GL n =S−1L n $$ \supseteq$$ S0L n $$ \supseteq$$ ⋯ $$ \supseteq$$ S i L n $$ \supseteq$$ ⋯ $$ \supseteq$$ E n of the general linear group GL n, n ⩾ 3, is defined and it is shown for any algebra A, which is a direct limit of module finite algebras, that S−1 L n (A)/S0L n (A) is abelian, that S0L n (A) $$ \supseteq$$ S1L n (A) $$ \supseteq$$ ⋯ is a descending central series, and that S i L n (A) = E n(A) whenever i ⩾ the Bass-Serre dimension of A. In particular, the K-functors k 1 S i L n =S i L n /E n are nilpotent for all i ⩾ 0 over algebras of finite Bass-Serre dimension. Furthermore, without dimension assumptions, the canonical homomorphism S i L n (A)/S i+1 L n (A)→S i L n+ 1(A)/S i+1 L n + 1 (A) is injective whenever n ⩾ i + 3, so that one has stability results without stability conditions, and if A is commutative then S0L n (A) agrees with the special linear group SL n (A), so that the functor S0L n generalizes the functor SL n to noncommutative rings. Applying the above to subgroups H of GL n (A), which are normalized by E n(A), one obtains that each is contained in a sandwich GL′ n (A, ρ) $$ \supseteq$$ H $$ \supseteq$$ E n(A, ρ) for a unique two-sided ideal ρ of A and there is a descending S0L n (A)-central series GL′ n (A, ρ) $$ \supseteq$$ S0L n (A, ρ) $$ \supseteq$$ S1L n (A, ρ) $$ \supseteq$$ ⋯ $$ \supseteq$$ S i L n (A, ρ) $$ \supseteq$$ ⋯ $$ \supseteq$$ E n(A, ρ) such that S i L n (A, ρ)=E n(A, ρ) whenever i ⩾ Bass-Serre dimension of A.
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    Representing homology classes by locally flat 2-spheres (1993)
    Springer
    K-Theory 7 (1993), S. 333-367 
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    ISSN: 1573-0514
    Keywords: Locally flat embedding ; pointed Hermitian module ; splitting ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove an existence result for topologically locally flat embeddings of 2-spheres in simply connected 4-manifolds. This topological result is deduced from a splitting theorem for pointed Hermitian modules over a cyclic group ring. A stability result for such modules is also proved. This applies to the isotopy classification of locally flat embeddings.
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    Autonomous Intelligent Cruise Control with Actuator Delays (1998)
    Springer
    Journal of intelligent and robotic systems 23 (1998), S. 27-43 
    Details
    ISSN: 1573-0409
    Keywords: autonomous control ; actuator delays ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper, we consider the control design problem of vehicle following systems with actuator delays. An upper bound for the time delays is first constructed to guarantee the vehicle stability. Second, sufficient conditions are presented to avoid slinky-effects in the vehicle following. Next, zero steady state achieved by the proposed controller is proven. Finally, simulations are given to examine our claims.
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    URL: http://dx.doi.org/10.1023/A:1007946007601
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    Sensitivity and Stability of the Classifications of Returns to Scale in Data Envelopment Analysis (1999)
    Springer
    Journal of productivity analysis 12 (1999), S. 55-75 
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    ISSN: 1573-0441
    Keywords: Data envelopment analysis (DEA) ; returns to scale (RTS) ; sensitivity ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract Sensitivity of the returns to scale (RTS) classifications in data envelopment analysis is studied by means of linear programming problems. The stability region for an observation preserving its current RTS classification (constant, increasing or decreasing returns to scale) can be easily investigated by the optimal values to a set of particular DEA-type formulations. Necessary and sufficient conditions are determined for preserving the RTS classifications when input or output data perturbations are non-proportional. It is shown that the sensitivity analysis method under proportional data perturbations can also be used to estimate the RTS classifications and discover the identical RTS regions yielded by the input-based and the output-based DEA methods. Thus, our approach provides information on both the RTS classifications and the stability of the classifications. This sensitivity analysis method can easily be applied via existing DEA codes.
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    Perron–Frobenius Theory and Symmetry of Solutions to Nonlinear PDE's (2000)
    Springer
    Letters in mathematical physics 53 (2000), S. 313-320 
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    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.
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    URL: http://dx.doi.org/10.1023/A:1007622208894
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    A structural approach to robust stability of polynomials (1992)
    Springer
    Multidimensional systems and signal processing 3 (1992), S. 421-425 
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    ISSN: 1573-0824
    Keywords: Convex combination ; polynomial ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A sufficient condition for Hurwitz stability of a convex combination of two stable polynomials is obtained.
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    Fertilizer value of pig slurries processed by the Promest procedure (1992)
    Springer
    Nutrient cycling in agroecosystems 32 (1992), S. 61-70 
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    ISSN: 1573-0867
    Keywords: Pig slurry ; processing ; relative efficiency index ; N ; P ; K ; organic carbon ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract In the Netherlands, pig slurries are processed to improve their fertilizer value as well as handling and application. The relative efficiency index (REI) of N, P and K and the stability of organic carbon (C) in test products of processed pig slurries (PPS) were determined in pot and incubation experiments. The dry and easily manageable PPS were produced according to the Promest procedure. The mineral fraction of total N varied from 60 to 88%. It consisted mainly of nitrate. About 25% of the organic N was rapidly mineralized. The REI of N varied from 66 to 92%. After application REI of P from pelletized PPS varied from 41 to 62% in the first half year. The REI of P in ground but non-pelletized PPS varied from 81 to 100%. The REI of K was estimated to be 100%. PPS contained less easily decomposable organic C than untreated pig slurry due to the anaerobic digestion step in the processing procedure. About 34% of the organic C disappeared as methane and carbon dioxide during processing. It was concluded that processing improved the fertilizer value of PPS compared with that of untreated pig slurry.
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    Stability regions of Schur andG-stable polynomials (1993)
    Springer
    Multidimensional systems and signal processing 4 (1993), S. 91-101 
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    ISSN: 1573-0824
    Keywords: Bilinear transformation ; polynomial ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The paper presents a unified approach to calculation, for a given, nominal,G-stable polynomial, a corresponding stability region in the space of perturbed coefficients
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    URL: http://dx.doi.org/10.1007/BF00986008
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    Stability determination of two-dimensional discrete-time systems (1993)
    Springer
    Multidimensional systems and signal processing 4 (1993), S. 331-354 
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    ISSN: 1573-0824
    Keywords: two-dimensional discrete-time systems ; two-dimensional digital filters ; bivariate polynomials ; stability ; Bistritz tabular form ; Jury tabular form ; Schur-Cohn minors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In determining root distribution of univariate polynomials with real or complex-valued coefficients, the Bistritz tabular form offers a significant computational advantage. Stability studies of two-dimensional (2-D) discrete-time systems involve univariate polynomials possessing parameter-dependent coefficients, where the parameter takes values on the unit circle in the complex plane. This paper investigates the application of Bistritz tabular form in determining stability of 2-D discrete-time systems, and for this purpose we present two algorithms. Both algorithms utilize a recent result that has established the relationship between Schur-Cohn minors and the entries of the Bistritz tabular form corresponding to a given polynomial. A comparison between the use of the modified Jury table and the Bistritz table in stability checking of 2-D discrete-time systems is also presented.
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    Can the ecosystem mimic hypotheses be applied to farms in African savannahs? (1999)
    Springer
    Agroforestry systems 45 (1999), S. 131-158 
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    ISSN: 1572-9680
    Keywords: competition ; fertility ; microclimate ; risk ; stability ; water
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract The first ecosystem mimic hypothesis suggests clear advantages if man-made land use systems do not deviate greatly in their resource use patterns from natural ecosystems typical of a given climatic zone. The second hypothesis claims that additional advantages will accrue if agroecosystems also maintain a substantial part of the diversity of natural systems. We test these hypotheses for the savannah zone of sub-Saharan Africa, with its low soil fertility and variable rainfall. Where annual food crops replace the natural grass understorey of savannah systems, water use will decrease and stream and groundwater flow change, unless tree density increases relative to the natural situation. Increasing tree density, however, will decrease crop yields, unless the trees meet specific criteria. Food crop production in the parkland systems may benefit from lower temperatures under tree canopies, but water use by trees providing this shade will prevent crops from benefiting. In old parkland trees that farmers have traditionally retained when opening fields for crops, water use per unit shade is less than in most fast growing trees introduced for agroforestry trials. Strong competition between plants adapted to years with different rainfall patterns may stabilise total system productivity -- but this will be appreciated by a farmer only if the components are of comparable value. The best precondition for farmers to maintain diversity in their agroecosystem hinges on the availability of a broad basket of choices, without clear winners or 'best bets'.
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    Acid-base equilibrium—A thermodynamic study of formation and stability of the Bi-2223 phase (1993)
    Springer
    Journal of superconductivity 6 (1993), S. 55-57 
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    ISSN: 1572-9605
    Keywords: Superconductivity ; Bi-2223 ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract A general acid-base equilibrium theory was proposed to explain the formation and stability of the Bi-2223 phase based on the Lewis acid-base theory, and principle of metallurgical physical chemistry. The acid-base nature of oxide was defined according to the electrostatic force between cation and oxygen anion. A series of experimental facts were systematically explained based on the theory: substitution of Bi for Ca in. the Pb-free 2223 phase, and the effect of substitution of the high-valent cation for Bi3+; oxygen-pressure atmosphere, and the heat-schocking technique on the formation and stability of the 2223 phase.
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    Stable Quasicrystalline Ground States (1997)
    Springer
    Journal of statistical physics 88 (1997), S. 691-711 
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    ISSN: 1572-9613
    Keywords: Quasicrystals ; nonperiodic tilings ; classical lattice-gas models ; ground states ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We give strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions, but rather are generic in some regions of phase space. We show this by constructing classical lattice-gas models with translation-invariant finite-range interactions and with a unique quasiperiodic ground state which is stable against small perturbations of two-body potentials. More generally, we provide a criterion for stability of nonperiodic ground states.
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    URL: http://dx.doi.org/10.1023/B:JOSS.0000015168.25151.22
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    Renormalization of the Chapman–Enskog Expansion: Isothermal Fluid Flow and Rosenau Saturation (1998)
    Springer
    Journal of statistical physics 91 (1998), S. 285-305 
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    ISSN: 1572-9613
    Keywords: Chapman–Enskog expansion ; Burnett equation ; Boltzmann equation ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This paper continues the author's study of procedures for rewriting the well-known Chapman–Enskog expansion used in the kinetic theory of gases. The usual Chapman–Enskog expansion, when used in isothermal fluid motion, will introduce nonlinear instability at super-Burnett order O(ε3) truncation. The procedure given here eliminates the truncation instability and produces the desired dissipation inequality.
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    Classical Lattice-Gas Models of Quasicrystals (1999)
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    Journal of statistical physics 95 (1999), S. 835-850 
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    ISSN: 1572-9613
    Keywords: quasicrystals ; nonperiodic tilings ; classical lattice-gas models ; nonperiodic ground states ; nonperiodic Gibbs states ; stability ; frustration
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract One of the fundamental problems of quasicrystals is to understand their occurrence in microscopic models of interacting particles. We review here recent attempts to construct stable quasicrystalline phases. In particular, we compare two recently constructed classical lattice-gas models with translation-invariant interactions and without periodic ground-state configurations. The models are based on nonperiodic tilings of the plane by square-like tiles. In the first model, all interactions can be minimized simultaneously. The second model is frustrated; its nonperiodic ground state can arise only by the minimization of the energy of competing interactions. We put forward some hypotheses concerning stabilities of nonperiodic ground states. In particular, we introduce two criteria, the so-called strict boundary conditions, and prove their equivalence to the zero-temperature stability of ground states against small perturbations of potentials of interacting particles. We discuss the relevance of these conditions for the low-temperature stability, i.e., for the existence of thermodynamically stable nonperiodic equilibrium states.
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    Non-Self-Similar Behavior in the LSW Theory of Ostwald Ripening (1999)
    Springer
    Journal of statistical physics 95 (1999), S. 867-902 
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    ISSN: 1572-9613
    Keywords: kinetics of phase transitions ; domain coarsening ; asymptotic behavior ; self-similarity ; stability ; chaos
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The classical Lifshitz–Slyozov–Wagner theory of domain coarsening predicts asymptotically self-similar behavior for the size distribution of a dilute system of particles that evolve by diffusional mass transfer with a common mean field. Here we consider the long-time behavior of measure-valued solutions for systems in which particle size is uniformly bounded, i.e., for initial measures of compact support. We prove that the long-time behavior of the size distribution depends sensitively on the initial distribution of the largest particles in the system. Convergence to the classically predicted smooth similarity solution is impossible if the initial distribution function is comparable to any finite power of distance to the end of the support. We give a necessary criterion for convergence to other self-similar solutions, and conditional stability theorems for some such solutions. For a dense set of initial data, convergence to any self-similar solution is impossible.
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    Twenty years of cable-in-conduit conductors: 1975–1995 (1995)
    Springer
    Journal of fusion energy 14 (1995), S. 3-12 
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    ISSN: 1572-9591
    Keywords: Cable-in-conduit conductors ; stability ; quench pressure ; thermal hydraulic quenchback ; superfluid helium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract This paper reviews our progress during the last two decades in understanding cable-in-conduit conductors. The emphasis is on the physical principles governing the behavior of cable-in-conduit conductors, and no detailed mathematics is presented. The paper is constructed as a historical narrative.
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    Stability estimations and quench simulations for the ITER conductors (1995)
    Springer
    Journal of fusion energy 14 (1995), S. 59-67 
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    ISSN: 1572-9591
    Keywords: ITER ; stability ; quench ; superconductor ; CICC ; FCC ; calculation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract Quench simulations and stability estimations for the International Thermonuclear Experimental Reactor (ITER) are discussed. Especially numerical issues and associated benchmark actions are summarized. Satisfactory agreement between the various codes from the 4 ITER parties is now obtained after numerical convergence problems have been resolved. However, these require confirmation by experiments on relevant conductor geometries. In multistage cables, a non-uniform current distribution within the cable affects the stability of the conductor. A possible mechanism for the non-uniform distribution is flux loops between the strands or cable substages as the current is ramped up or down. A preliminary estimation of stability with non-uniform current distribution is also discussed.
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    Stability of Attractive Bose–Einstein Condensates (2000)
    Springer
    Journal of statistical physics 101 (2000), S. 731-746 
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    ISSN: 1572-9613
    Keywords: attractive Bose–Einstein condensates ; nonlinear Schrödinger equation ; stability ; ground state ; variational arguments
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We propose the critical nonlinear Schrödinger equation with a harmonic potential as a model of attractive Bose–Einstein condensates. By an elaborate mathematical analysis we show that a sharp stability threshold exists with respect to the number of condensate particles. The value of the threshold agrees with the existing experimental data. Moreover with this threshold we prove that a ground state of the condensate exists and is orbital stable. We also evaluate the minimum of the condensate energy.
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    Spatial scale influence on longterm temporal patterns of a semi-arid grassland (1996)
    Springer
    Landscape ecology 11 (1996), S. 107-113 
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    ISSN: 1572-9761
    Keywords: scaling ; temporal patterns ; equilibrium ; stability ; succession ; predictability ; variability ; grassland ; savannah ; chaos ; ecological scale ; vegetation dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract Longterm (45 years) temporal data were used to assess the influence of spatial scale on temporal patterns of a semi-arid west Texas grassland. Temporal basal area dynamics of common curlymesquite (Hilaria belangeri (Steud.) Nash) collected from permanent plots within two areas that were released from disturbance (longterm overgrazing and drought), were evaluated at two spatial scales (quadrat, site). Wiens (1989) proposed hypotheses to characterize the influence of scale on variability, predictability, and equilibrium. These hypotheses were tested for this grassland and temporal patterns observed were different for each spatial scale. The large scale (site) was characterized by low variation between units, high variation within units, high potential predictability, and possible movement toward a fluctuating but relatively stable or equilibrial state. At the small scale (quadrat), variation between units was high, predictability low, and there was no indication of movement toward a stable state; chaotic behavior may be expressed at this scale although the length of the temporal record may not be sufficient to evaluate this phenomenon.
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    Forest spread and phase transitions at forest-prairie ecotones in Kansas, U.S.A. (1996)
    Springer
    Landscape ecology 11 (1996), S. 225-235 
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    ISSN: 1572-9761
    Keywords: fire ; fractals ; grassland ; percolation ; stability ; succession
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The spread of gallery forest habitat into upland areas is of substantial interest to resource managers because such spread has many implications for the management of grassland and forest habitats. This study used a dynamic percolation model to examine the potential rates of spread or invasion of forest in eastern Kansas. Aerial photos taken 16 years apart at the Fort Riley training base were used to calibrate a spatially explicit contagion model of forest spread to interpolate and extrapolate the forest spread processes. Results fit the actual pattern of spread well, as measured by both visual inspection and a multiscale fractal measure of pattern. Comparisons to a long-term fire-exclusion experiment in Geary County, Kansas, and to the Konza Prairie also provided validation. Both the simulation and the 100-year Geary County series showed an interesting pattern of forest spread. Spread was slow and steady until about 20% forest cover was reached, at which point the rate increased. We conclude that this self-accelerating response is due to spatial patterns created by the spreading forest that tend to accelerate the growth process after a critical point is reached. On the basis of theoretical study and experimental simulation of the percolation phase transitions, we suggest that fractal dimensions in a transient ecotone of binary mixtures (e.g., trees and grasses) should range between 1.56 and 1.8958, and the critical fractal dimension during ecotonal phase transitions should be 1.7951. This critical point of about 18.5% forest cover that we predicted was close to the observed result and might represent a phase transition at the forest-prairie ecotone.
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    Stable Sampled-data Adaptive Control of Robot Arms Using Neural Networks (1997)
    Springer
    Journal of intelligent and robotic systems 20 (1997), S. 131-155 
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    ISSN: 1573-0409
    Keywords: robot adaptive control ; basis function-like networks ; stability ; discrete variable structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Stable neural network-based sampled-data indirect and direct adaptivecontrol approaches, which are the integration of a neural network (NN)approach and the adaptive implementation of the discrete variable structurecontrol, are developed in this paper for the trajectory tracking control ofa robot arm with unknown nonlinear dynamics. The robot arm is assumed tohave an upper and lower bound of its inertia matrix norm and its states areavailable for measurement. The discrete variable structure control servestwo purposes, i.e., one is to force the system states to be within the stateregion in which neural networks are used when the system goes out of neuralcontrol; and the other is to improve the tracking performance within the NNapproximation region. Main theory results for designing stable neuralnetwork-based sampled data indirect and direct adaptive controllers aregiven, and the extension of the proposed control approaches to the compositeadaptive control of a flexible-link robot is discussed. Finally, theeffectiveness of the proposed control approaches is illustrated throughsimulation studies.
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    Robust Regulator for Flexible-Joint Robots Using Integrator Backstepping (1998)
    Springer
    Journal of intelligent and robotic systems 22 (1998), S. 23-38 
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    ISSN: 1573-0409
    Keywords: robot dynamic model ; stiffness matrix ; constant disturbance ; integrator backstepping ; Liapunov functions ; Barbalat lemma ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A robust regulator for flexible-joint robots is proposed, which yields constant torque disturbance rejection acting on the links. The design uses the integrator backstepping technique [4,5] to cancel nonlinearities and disturbance not in the range space of the control. Stability of the closed loop system is shown using iterative Liapunov functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007947416837
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    Forward Assembly Planning Based on Stability (1997)
    Springer
    Journal of intelligent and robotic systems 19 (1997), S. 411-436 
    Details
    ISSN: 1573-0409
    Keywords: assembly planning ; stability ; robot ; forward ; operations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The paper presents an approach to sequence planning consisting in determining assembly sequences defined in terms of mating and non-mating operations and based on a dynamic expansion of the assembly tree obtained using a knowledge base management system. The planner considers the case of a single-robot assembly workcell. The use of stability and the detailed definition of sequences also by means of several non-mating operations are shown to be powerful instruments in the control of the tree expansion. Forward assembly planning has been chosen, in order to minimize the number of stability checks. Backtracking is avoided by combining precedence relations and stability analysis. Hard and soft constrains are introduced to drive the tree expansion. Hard constraints are precedence relations and stability analysis. All operations are associated to costs, which are used as soft constraints. The operation based approach enables one to manage even non-mating operations and to easily overcome the linearity constraint. Costs enable the planner to manage the association among tools and components. The first section of the paper concerns Stability Analysis that is subdivided into Static and Dynamic Stability Analysis. The former is mainly involved in analyzing gravity effects; the latter is mainly involved in evaluate inertia effects due to manipulation. Stability Analysis is implemented in a simplified form. Fundamental assumptions are: no rotational equilibrium condition is considered; for each reaction force only direction and versus, but not magnitude, are considered; friction is neglected. The second section discusses the structure of the planner and its implementation. The planner is a rule based system. Forward chaining and hypothetical reasoning are the inference strategies used. The knowledge base and the data base of the system are presented and the advantages obtained using a rule based system are discussed. The third section shows two planning examples, showing the performance of the system in a simple case and in an industrial test case, the assembly of a microwave branching filter composed of 26 components.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007928631050
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    Stable Neuro-Adaptive Control for Robots with the Upper Bound Estimation on the Neural Approximation Errors (1999)
    Springer
    Journal of intelligent and robotic systems 26 (1999), S. 91-100 
    Details
    ISSN: 1573-0409
    Keywords: robots ; neural networks ; adaptiveness ; stability ; approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract An indirect adaptive control approach is developed in this paper for robots with unknown nonlinear dynamics using neural networks (NNs). A key property of the proposed approach is that the actual joint angle values in the control law are replaced by the desired joint angles, angle velocities and accelerators, and the bound on the NN reconstruction errors is assumed to be unknown. Main theoretical results for designing such a neuro-controller are given, and the control performance of the proposed controller is verified with simulation studies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008195720685
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    A catastrophe analysis on the stability of the crack growth in three-point bending specimens (1996)
    Springer
    Acta mechanica solida Sinica 9 (1996), S. 179-183 
    Details
    ISSN: 0894-9166
    Keywords: crack growth ; stability ; cusp catastrophe ; J-integral ; three-point bending specimen
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This paper presents an attempt at the application of catastrophe theory to the stability analysis ofJ-controlled crack growth in three-point bending specimens. By introducing the solutions ofJ- integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02209162
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    Technical note: Bias and the quantification of stability (1995)
    Springer
    Machine learning 20 (1995), S. 23-33 
    Details
    ISSN: 0885-6125
    Keywords: stability ; bias ; accuracy ; repeatability ; agreement ; similarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is the stability of the algorithm; in other words, the repeatability of the results. If we obtain two sets of data from the same phenomenon, with the same underlying probability distribution, then we would like our learning algorithm to induce approximately the same concepts from both sets of data. This paper introduces a method for quantifying stability, based on a measure of the agreement between concepts. We also discuss the relationships among stability, predictive accuracy, and bias.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00993473
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    A reinforcement connectionist approach to robot path finding in non-maze-like environments (1992)
    Springer
    Machine learning 8 (1992), S. 363-395 
    Details
    ISSN: 0885-6125
    Keywords: Connectionism ; reinforcement learning ; robot path finding ; stability ; reactive systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper presents a reinforcement connectionist system which finds and learns the suitable situation-action rules so as to generate feasible paths for a point robot in a 2D environment with circular obstacles. The basic reinforcement algorithm is extended with a strategy for discovering stable solution paths. Equipped with this strategy and a powerful codification scheme, the path-finder (i) learns quickly, (ii) deals with continuous-valued inputs and outputs, (iii) exhibits good noise-tolerance and generalization capabilities, (iv) copes with dynamic environments, and (v) solves an instance of the path finding problem with strong performance demands.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00992702
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    A Reinforcement Connectionist Approach to Robot Path Finding in Non-Maze-Like Environments (1992)
    Springer
    Machine learning 8 (1992), S. 363-395 
    Details
    ISSN: 0885-6125
    Keywords: Connectionism ; reinforcement learning ; robot path finding ; stability ; reactive systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper presents a reinforcement connectionist system which finds and learns the suitable situation-action rules so as to generate feasible paths for a point robot in a 2D environment with circular obstacles. The basic reinforcement algorithm is extended with a strategy for discovering stable solution paths. Equipped with this strategy and a powerful codification scheme, the path-finder (i) learns quickly, (ii) deals with continuous-valued inputs and outputs, (iii) exhibits good noise-tolerance and generalization capabilities, (iv) copes with dynamic environments, and (v) solves an instance of the path finding problem with strong performance demands.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022684924132
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    Technical Note: Bias and the Quantification of Stability (1995)
    Springer
    Machine learning 20 (1995), S. 23-33 
    Details
    ISSN: 0885-6125
    Keywords: stability ; bias ; accuracy ; repeatability ; agreement ; similarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Research on bias in machine learning algorithms has generally been concerned with the impact of bias on predictive accuracy. We believe that there are other factors that should also play a role in the evaluation of bias. One such factor is the stability of the algorithm; in other words, the repeatability of the results. If we obtain two sets of data from the same phenomenon, with the same underlying probability distribution, then we would like our learning algorithm to induce approximately the same concepts from both sets of data. This paper introduces a method for quantifying stability, based on a measure of the agreement between concepts. We also discuss the relationships among stability, predictive accuracy, and bias.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022682001417
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