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  • Articles  (40)
  • stability  (21)
  • 17B37  (19)
  • 2005-2009
  • 1990-1994  (40)
  • 1994  (40)
  • Mathematics  (39)
  • Energy, Environment Protection, Nuclear Power Engineering  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Stability results for approximately efficient solutions (1994)
    Springer
    OR spectrum 16 (1994), S. 47-52 
    Details
    ISSN: 1436-6304
    Keywords: Vector optimization ; approximately efficient solutions ; stability ; Vektoroptimierung ; Näherungslösungen ; Stabilität
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Description / Table of Contents: Zusammenfassung Wir führen ein Konzept für Näherungslösungen in der Vektoroptimierung ein und vergleichen dieses mit einem neuen Konzept aus [8]. Weiterhin untersuchen wir Beziehungen zwischen der Menge der Näherungslösungen eines Vektoroptimierungsproblems und den Näherungslösungen eines entsprechenden parametrischen Ersatzproblems. Schließlich beweisen wir Stabilitätseigenschaften des skalaren Ersatzproblems.
    Notes: Abstract We introduce a concept for approximately efficient solutions in vector optimization and compare it with another recent concept given in [8]. Further, we study relations between the set of approximately efficient solutions of a vector optimization problem and the approximate solutions of a corresponding parametric surrogate optimization problem. Finally, we prove stability properties for the scalar surrogate problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01719703
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  • 2
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    Linear stability of relative equilibria with a dominant mass (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 37-51 
    Details
    ISSN: 1572-9222
    Keywords: Celestial mechanics ; relative equilibria ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A criterion for the linear stability of relative equilibria of the Newtoniann-body problem is found in the case whenn−1 of the masses are small. Several stable periodic orbits of the problem are presented as examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02219187
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  • 3
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    Symmetrization properties of parabolic equations in symmetric domains (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 639-658 
    Details
    ISSN: 1572-9222
    Keywords: Symmetry ; parabolic equations ; positive solutions ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Symmetry properties of positive solutions of a Dirichlet problem for a strongly nonlinear parabolic partial differential equation in a symmetric domainD ⊂ R n are considered. It is assumed that the domainD and the equation are invariant with respect to a group {Q} of transformations ofD. In examples {Q} consists of reflections or rotations. The main result of the paper is the theorem which states that any compact inC(D) negatively invariant set which consists of positive functions consists ofQ-symmetric functions. Examples of negatively invariant sets are (in autonomous case) equilibrium points, omega-limit sets, alpha-limit sets, unstable sets of invariant sets, and global attractors. Application of the main theorem to equilibrium points gives the Gidas-Ni-Nirenberg theorem. Applying the theorem to omega-limit sets, we obtain the asymptotical symmetrization property. That means that a bounded solutionu(t) asr→∞ approaches subspace of symmetric functions. One more result concerns properties of eigenfunctions of linearizations of the equations at positive equilibrium points. It is proved that all unstable eigenfunctions are symmetric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02218852
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  • 4
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    A free boundary problem modeling thermal instabilities: Stability and bifurcation (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 447-486 
    Details
    ISSN: 1572-9222
    Keywords: Free boundary problems ; gasless combustion ; stability ; Hopf bifurcation ; 35R35 ; 35B40 ; 80A25
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we analyze a simple free boundary model associated with solid combustion and some phase transition processes. There is strong evidence that this “one-phase” model captures all major features of dynamical behavior of more realistic (and complicated) combustion and phase transition models. The principal results concern the dynamical behavior of the model as a bifurcation parameter (which is related to the activation energy in the case of combustion) varies. We prove that the basic uniform front propagation is asymptotically stable against perturbations for the bifurcation parameter above the instability threshold and that a Hopf bifurcation takes place at the threshold value. Results of numerical simulations are presented which confirm that both supercritical and subcritical Hofp bifurcation may occur for physically reasonable nonlinear kinetic functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02218858
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  • 5
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    Stability of standing waves for the generalized Davey-Stewartson system (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 325-334 
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    ISSN: 1572-9222
    Keywords: Nonlinear Schrödinger equations ; anisotropic standing waves ; stability ; concentration compactness principle ; Davey-Stewartson system ; 35Q35 ; 35B35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study the stability of standing waves for a nonlinear Schrödinger equation, which derives from the generalized Davey-Stewartson system in the elliptic-elliptic case. We prove the existence of stable standing waves under certain conditions.
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    URL: http://dx.doi.org/10.1007/BF02218533
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  • 6
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    The index of lyapunov stable fixed points in two dimensions (1994)
    Springer
    Journal of dynamics and differential equations 6 (1994), S. 631-637 
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    ISSN: 1572-9222
    Keywords: stability ; fixed point index ; periodic solutions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR 2 has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.
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    URL: http://dx.doi.org/10.1007/BF02218851
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  • 7
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    Quantum homogeneous spaces, duality and quantum 2-spheres (1994)
    Springer
    Geometriae dedicata 52 (1994), S. 291-315 
    Details
    ISSN: 1572-9168
    Keywords: 16W30 ; 17B37 ; 22E99 ; quantum groups ; quantum homogeneous spaces ; coaction ; dual Hopf algebras ; two-sided coideals ; infinitesimal invariance ; quantum SU(2) ; sl(2) quantized universal enveloping algebra ; quantum 2-spheres
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a quantum groupG the notion of quantum homogeneousG-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more general one is based upon the notion of infinitesimal invariance with respect to certain two-sided coideals in the Hopf algebra dual to the Hopf algebra ofG. These methods are applied to the quantum group SU(2). As two-sided coideals we take the subspaces spanned by twisted primitive elements in the sl(2) quantized universal enveloping algebra. A one-parameter series of mutually non-isomorphic quantum 2-spheres is obtained, together with the spectral decomposition of the corresponding right regular representation of quantum SU(2). The link with the quantum spheres defined by Podleś is established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01278478
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  • 8
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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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  • 9
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01935016
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  • 10
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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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  • 11
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    An elliptic quantum algebra for $$\widehat{s1}_2 $$ 2 (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 259-268 
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    ISSN: 1573-0530
    Keywords: 17B37 ; 82A67
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract An elliptic deformation of $$\widehat{s1}_2 $$ is proposed. Our presentation of the algebra is based on the relationRLL = LLR *, whereR andR * are eight-vertexR-matrices with the elliptic moduli chosen differently. In the trigonometric limit, this algebra reduces to a quotient of that proposed by Reshetikhin and Semenov-Tian-Shansky. Conjectures concerning highest-weight modules and vertex operators are formulated, and the physical interpretation ofR * is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00750668
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  • 12
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    On affine yangians (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 269-274 
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    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 82B23
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A Yangian $$Y(\widetilde{sl}(2))$$ , a deformation of the universal enveloping algebra of the two-dimensional loop algebra sl(2) ⊗C [t −1,t;u], is constructed. This deformation is an analogue of a Yangian which was constructed by V. Drinfeld for any simple Lie algebra. The PBW theorem for $$Y(\widetilde{sl}(2))$$ is proved and some representations are constructed. Like usual Yangians, $$Y(\widetilde{sl}(2))$$ possesses a one-dimensional group of auto- morphisms and at zero level - a two-dimensional group of automorphisms. This observation allows one to conjecture that the representation theory of $$Y(\widetilde{sl}(2))$$ should give rise to new solutions of QYBE. Yangians of other affine algebras can be constructed similarly and they enjoy similar properties.
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    URL: http://dx.doi.org/10.1007/BF00761137
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  • 13
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    Heisenberg realization for U q (sl n ) on the flag manifold (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 35-43 
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    ISSN: 1573-0530
    Keywords: 17B37 ; 16S32 ; 81R10 ; 33D80
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give the Heisenberg realization for the quantum algebra U q (sl n ), which is written by theq-difference operator on the flag manifold. We construct it from the action of U q (sl n ) on theq-symmetric algebraA q (Mat n ) by the Borel-Weil-like approach. Our realization is applicable to the construction of the free field realization for U q $$(\widehat{s1_n })$$ [2].
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    URL: http://dx.doi.org/10.1007/BF00761420
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  • 14
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    Small representations of quantum affine algebras (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 131-145 
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    ISSN: 1573-0530
    Keywords: 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We characterize the finite-dimensional representations of the quantum affine algebra U q ( $$\widehat{sl}$$ n+1) (whereq ∈ ℂ× is not a root of unity) which are irreducible as representations of U q (sl n+1). We call such representations ‘small’. In 1986, Jimbo defined a family of homomorphismsev a from U q (sl n+1) to (an enlargement of) U q (sl,n+1), depending on a parametera ∈ ℂ·. A second family,ev a can be obtained by a small modification of Jimbo's formulas. We show that every small representation of U q ( $$\widehat{sl}$$ n+1) is obtained by pulling back an irreducible representation of U q (sl n+1) byev a orev a for somea ∈ ℂ·.
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    URL: http://dx.doi.org/10.1007/BF00939701
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  • 15
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    Free boson representation of $$U_q (\widehat{sl}_3 )$$ (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 207-216 
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    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A representation of the quantum affine algebra $$U_q (\widehat{sl}_3 )$$ of an arbitrary levelk is constructed in the Fock module of eight boson fields. This realization reduces the Wakimoto representation in theq → 1 limit. The analogues of the screening currents are also obtained. They commute with the action of $$U_q (\widehat{sl}_3 )$$ modulo total differences of some fields.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00805853
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  • 16
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    Algebraic deformation program on minimal nilpotent orbit (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 241-250 
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    ISSN: 1573-0530
    Keywords: 17B35 ; 17B37 ; 22E46
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct an algebraic star product on the minimal nilpotent coadjoint orbit of a simple complex Lie group with a Lie algebra which is not of typeA n. According to the deformation program, we study the representations of the Lie algebra associated to this orbit.
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    URL: http://dx.doi.org/10.1007/BF00805856
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  • 17
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    Quantized affine Lie algebras and diagonalization of braid generators (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 267-277 
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    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Let U q $$(\hat{\mathcal{G}})$$ be a quantized affine Lie algebra. It is proven that the universal R-matrix R of U q $$(\hat{\mathcal{G}})$$ satisfies the celebrated conjugation relationR + =TR withT the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight U q $$(\hat{\mathcal{G}})$$ -module and a spectral decomposition formula for the braid generator is obtained which is the generalization of Reshetikhin and Gould forms to the present affine case. Casimir invariants are constructed and their eigenvalues computed by means of the spectral decomposition formula. As a by-product, an interesting identity is found.
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    URL: http://dx.doi.org/10.1007/BF00751063
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  • 18
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    On aq-deformation of the discrete Painlevé I equation andq-orthogonal polynomials (1994)
    Springer
    Letters in mathematical physics 30 (1994), S. 327-336 
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    ISSN: 1573-0530
    Keywords: 17B37 ; 33D45 ; 39A70 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We present aq-analog of the discrete Painlevé I equation, and a special realization of it in terms ofq-orthogonal polynomials.
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    URL: http://dx.doi.org/10.1007/BF00751068
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  • 19
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    Metric on quantum spaces (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 35-39 
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    ISSN: 1573-0530
    Keywords: 46L87 ; 81R50 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We introduce the analogue of the metric tensor in the case ofq-deformed differential calculus. We analyse the consequences of the existence of the metric, showing that this enforces severe restrictions on the parameters of the theory. We discuss in detail examples of the Manin plane and theq-deformation of SU(2). Finally we touch the topic of relations with Connes' approach.
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    URL: http://dx.doi.org/10.1007/BF00751169
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  • 20
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    Casimir invariants for quantized affine Lie algebras (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 77-83 
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    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Casimir invariants for quantized affine Lie algebras are constructed and their eigenvalues computed in any irreducible highest-weight representation.
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    URL: http://dx.doi.org/10.1007/BF00751173
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  • 21
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    Quantum affine algebras and universalR-matrix with spectral parameter (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 101-110 
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    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Using the previously obtained universalR-matrix for the quantized nontwisted affine Lie algebras U q (A 1 (1) ) and U q (A 2 (1) ), we determine the explicitly spectral dependent universalR-matrix for the corresponding quantum Lie algebras U q (A 1) and U q (A 2). As applications, we reproduce the well known results in the fundamental representations and we also derive an extremely explicit formula of the spectral-dependentR-matrix for the adjoint representation of U q (A 2), the simplest nontrivial case when the tensor product decomposition of the representation with itself has nontrivial multiplicity.
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    URL: http://dx.doi.org/10.1007/BF00750144
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  • 22
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    Quantization of U q [so(2n + 1)] with deformed para-Fermi operators (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 151-157 
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    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The observation thatn pairs of para-Fermi (pF) operators generate the universal enveloping algebra of the orthogonal Lie algebra so(2n + 1) is used in order to define deformed pF operators. It is shown that these operators are an alternative to the Chevalley generators. With this background U q [so(2n + 1)] and its ‘Cartan-Weyl’ generators are written down entirely in terms of deformed para-Fermi operators.
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    URL: http://dx.doi.org/10.1007/BF00750149
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  • 23
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    R-matrix method for Heisenberg quantum groups (1994)
    Springer
    Letters in mathematical physics 31 (1994), S. 159-166 
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    ISSN: 1573-0530
    Keywords: 17B37 ; 81R50 ; 70H05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract TheR-matrix method is systematically applied to get several Heisenberg quantum groups depending on two or three parameters. It turns out that the associatedR-matrices have to verify a weaker form of the QYBE. Only for particular cases of quantum groups, we can imposeR to be a solution of the QYBE. The corresponding quantum Heisenberg Lie algebras are obtained by duality.
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    URL: http://dx.doi.org/10.1007/BF00750150
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    Poisson structures on the Lorentz group (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 11-23 
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    ISSN: 1573-0530
    Keywords: 22E46 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Poisson-Lie structures on the Lorentz group are completely classified. A method applicable to an arbitrary semisimple complex Lie group (treated as real) is developed.
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    URL: http://dx.doi.org/10.1007/BF00761120
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  • 25
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    Classification of three-dimensional covariant differential calculi on Podles' quantum spheres and on related spaces (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 25-36 
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    ISSN: 1573-0530
    Keywords: 17B37 ; 46L87 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Covariant differential calculi on the quantum space $$\mathfrak{X}_{q\lambda \rho }$$ for the quantum group SL q (2) are classified. Our main assumptions are thatq is not a root of unity and that the differentials de j of the generators of $$\mathfrak{X}_{q\lambda \rho }$$ form a free right module basis for the first-order forms. Our result says, in particular, that apart from the two casesc =c(3), ∞ there exists a unique differential calculus with the above properties on the space $$\mathfrak{X}_{q\lambda \rho }$$ which corresponds to Podles' quantum sphereS qc /2 .
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    URL: http://dx.doi.org/10.1007/BF00761121
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  • 26
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    Representation theory of quantized poincaré algebra. tensor operators and their applications to one-particle systems (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 85-101 
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    ISSN: 1573-0530
    Keywords: 81R50 ; 16W30 ; 17B37
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A representation theory of the quantized Poincaré (κ-Poincaré) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the nondeformed Poincaré algebra. A theory of tensor operators for QPA is considered in detail. Necessary and sufficient conditions are found in order for scalars to be invariants. Covariant components of the four-momenta and the Pauli-Lubanski vector are explicitly constructed. These results are used for the construction of someq-relativistic equations. The Wigner-Eckart theorem for QPA is proven.
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    URL: http://dx.doi.org/10.1007/BF00739419
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  • 27
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    Diagonalization of the braid generator on unitary irreps of quantum supergroups (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 231-240 
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    ISSN: 1573-0530
    Keywords: 81R10 ; 17B37 ; 16W30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown that the braid generator σ associated with the universalR-matrix is diagonalizable on all unitary representations of quantum supergroups. An example is considered using U q (gl(2|1)) and a family of eight-dimensional typical representations.
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    URL: http://dx.doi.org/10.1007/BF00750665
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  • 28
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    Left regular representation and contraction of sl q (2) to e q (2) (1994)
    Springer
    Letters in mathematical physics 32 (1994), S. 249-258 
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    ISSN: 1573-0530
    Keywords: 16W30 ; 17B37 ; 81R10 ; 81R50
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The left regular representation of the quantum algebras sl q (2) and e q (2) are discussed and shown to be related by contraction. The reducibility is studied andq-difference intertwining operators are constructed.
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    URL: http://dx.doi.org/10.1007/BF00750667
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    On the stability of solitary-wave solutions of model equations for long waves (1994)
    Springer
    Journal of nonlinear science 4 (1994), S. 449-470 
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    ISSN: 1432-1467
    Keywords: solitary waves ; stability ; nonlinear dispersive wave equations ; model equations for long waves ; Korteweg-de Vries-type equations ; regularized long-wave equations ; nonlinear Schrödinger equations ; 35B35 ; 35B40 ; 35Q35 ; 35Q51 ; 35Q53 ; 35Q55 ; 35S10 ; 76B15 ; 76B25 ; 76E30 ; 86A05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary After a review of the existing state of affairs, an improvement is made in the stability theory for solitary-wave solutions of evolution equations of Korteweg-de Vries-type modelling the propagation of small-amplitude long waves. It is shown that the bulk of the solution emerging from initial data that is a small perturbation of an exact solitary wave travels at a speed close to that of the unperturbed solitary wave. This not unexpected result lends credibility to the presumption that the solution emanating from a perturbed solitary wave consists mainly of a nearby solitary wave. The result makes use of the existing stability theory together with certain small refinements, coupled with a new expression for the speed of propagation of the disturbance. The idea behind our result is also shown to be effective in the context of one-dimensional regularized long-wave equations and multidimensional nonlinear Schrödinger equations.
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    URL: http://dx.doi.org/10.1007/BF02430641
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    On coupling of stochastic processes with embedded point processes (1994)
    Springer
    Acta applicandae mathematicae 34 (1994), S. 71-81 
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    ISSN: 1572-9036
    Keywords: 60F55 ; 60G10 ; 60K15 ; Coupling ; marked-point processes ; regeneration ; stationarity ; stability ; maximal coupling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Criteria for semi-, wide-sense-, traditional regeneration and a coupling construction of stochastic processes with embedded point processes are presented.
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    URL: http://dx.doi.org/10.1007/BF00994258
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    Persistence, stability and level crossings in an integrodifferential system (1994)
    Springer
    Journal of mathematical biology 32 (1994), S. 395-426 
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    ISSN: 1432-1416
    Keywords: Uniform persistence ; stability ; Lyapunov functional ; level-crossing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Dynamical characteristics of an integrodifferential system modelling two species competition with hereditary effects are investigated; in particular we derive sufficient conditions for the persistence of the species, existence of an attracting periodic solution and ‘level-crossings’ of solutions about the periodic solution.
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    URL: http://dx.doi.org/10.1007/BF00160166
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    Single-locus gametophytic incompatibility: the symmetric equilibrium is globally asymptotically stable (1994)
    Springer
    Journal of mathematical biology 32 (1994), S. 515-520 
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    ISSN: 1432-1416
    Keywords: Gametophytic incompatibility ; model ; equilibrium ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The deterministic dynamics of the classical single-locus multiple-allele model of gametophytic incompatibility is analyzed with the intention to prove the conjecture that the symmetric state (uniform distribution of genotypes) is the only polymorphic equilibrium and that this equilibrium is globally asymptotically stable in the interior of the frequency simplex. It is shown that the minimum allelic frequency increases strictly over the generations as long as a uniform allelic distribution is not realized. Hence, the minimum allelic frequency is a Ljapunov function for the invariant set of genotypic frequencies characterized by a uniform allelic distribution. Within this set, the uniform genotypic distribution is approached in an exponential fashion, which proves the assertion. An evolutionary optimization rule associated with the global convergence to the symmetric state is implied by the fact that at this state the overall amount of pollen elimination resulting from incompatible crosses is minimized.
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    URL: http://dx.doi.org/10.1007/BF00573457
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    DECUHR: an algorithm for automatic integration of singular functions over a hyperrectangular region (1994)
    Springer
    Numerical algorithms 8 (1994), S. 201-220 
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    ISSN: 1572-9265
    Keywords: Automatic ; adaptive ; cubature ; singularity ; extrapolation ; stability ; 65D30 ; 65-04 ; 65B05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We describe an automatic cubature algorithm for functions that have a singularity on the surface of the integration region. The algorithm combines an adaptive subdivision strategy with extrapolation. The extrapolation uses a non-uniform subdivision that can be directly incorporated into the subdivision strategy used for the adaptive algorithm. The algorithm is designed to integrate a vector function over ann-dimensional rectangular region and a FORTRAN implementation is included.
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    URL: http://dx.doi.org/10.1007/BF02142691
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    Fixed-order robust compensators via min-max principle (1994)
    Springer
    Journal of optimization theory and applications 81 (1994), S. 277-296 
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    ISSN: 1573-2878
    Keywords: Robust control ; min-max techniques ; synthesis methods ; stability ; multivariable control systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An important (some say, the major) reason for using feedback control is the presence of uncertain parameters which are a natural part of any real dynamical model. In this paper, we consider uncertain constant parameters in a time-invariant linear plant and announce some new results concerning robust compensator synthesis. Using the min-max principle, we derive necessary conditions for fixed-order linear robust controllers assuring asymptotic stability or relative stability. These necessary conditions are an extension of the Lagrange multiplier method. This is achieved using a cost function based on the inverse of the so-called critical constraint. We present both matrix and polynomial versions; the latter allows controllers of fixed structure. We suggest a probability-one homotopy algorithm and solve some examples from the literature.
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    URL: http://dx.doi.org/10.1007/BF02191665
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    The bounded extermination and stability of mutual interference system of four-dimensional species (1994)
    Springer
    Applied mathematics and mechanics 15 (1994), S. 1035-1045 
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    ISSN: 1573-2754
    Keywords: mutual interference system ; bounded ; extermination equilibrium ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper considers a typical mutual interference system of four-dimensional species, its bounded, extermination stability are studied, and their necessary-sufficient condition are given, and their ecology meaning set forth.
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    URL: http://dx.doi.org/10.1007/BF02455395
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    The application of multi-scale perturbation method to the stability analysis of plane couette flow (1994)
    Springer
    Applied mathematics and mechanics 15 (1994), S. 923-928 
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    ISSN: 1573-2754
    Keywords: stability ; multi-scale perturbation method ; bifurcation from infinity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper applies the multi-scale perturbation method suggested by Ref. [3] to investigate the linear stability behavior of distorted plane Couette flow. Using this method, the unstable Tollmien-Schlichting wave in plane Couette flow can be found. but not the most unstable mode. By comparing the results of this paper with those of Ref. [3], the effectiveness of this method is investigated.
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    URL: http://dx.doi.org/10.1007/BF02451035
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    Stability of solutions of generalized logistic difference equations (1994)
    Springer
    Periodica mathematica Hungarica 29 (1994), S. 81-87 
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    ISSN: 1588-2829
    Keywords: Primary 39 ; Secondary 58F ; Generalized logistic ; stability ; difference equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01876205
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    On the range sets of variational inequalities (1994)
    Springer
    Journal of optimization theory and applications 83 (1994), S. 565-586 
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    ISSN: 1573-2878
    Keywords: Variational inequalities ; range sets ; cones ; polyhedra ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper investigates the closedness and convexity of the range sets of the variational inequality (VI) problem defined by an affine mappingM and a nonempty closed convex setK. It is proved that the range set is closed ifK is the union of a polyhedron and a compact convex set. Counterexamples are given such that the range set is not closed even ifK is a simple geometrical figure such as a circular cone or a circular cylinder in a three-dimensional space. Several sufficient conditions for closedness and convexity of the range set are presented. Characterization for the convex hull of the range set is established in the case whereK is a cone, while characterization for the closure of the convex hull of the range set is established in general. Finally, some applications to stability of VI problems are derived.
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    URL: http://dx.doi.org/10.1007/BF02207642
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    Economic growth with environmental damage and technical progress (1994)
    Springer
    Environmental and resource economics 4 (1994), S. 241-249 
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    ISSN: 1573-1502
    Keywords: Economic growth ; pollution control ; technical progress ; tradeable pollution permits ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Economics
    Notes: Abstract The papers on economic growth with environmental constraints usually ignore the effect of technical progress, this results in static steady state solutions. This paper examines the problem of optimal economic growth with environmental damage, technical progress taken into account, which produces a steady state solution that corresponds to an equilibrium growth, with non-constant emissions and pollutant stock. As a means of steering the economy along the optimal path, two types of tradeable pollution permits are analyzed. The method of stabilizing the optimal path, leading to a steady state, is suggested.
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    URL: http://dx.doi.org/10.1007/BF00692326
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    Stability and bifurcation analysis of a nonlinear transversally loaded rotating shaft (1994)
    Springer
    Nonlinear dynamics 5 (1994), S. 39-52 
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    ISSN: 1573-269X
    Keywords: Shaft ; stability ; bifurcation ; analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dynamic stability and self-excited posteritical whirling of rotating transversally loaded shaft made of a standard material with elastic and viscous nonlinearities are analyzed in this paper using the theory of bifurcations as a mathematical tool. Partial differential equations of motion are derived under assumption that von Karman's nonlinearity is absent but geometric curvature nonlinearity is included. Galerkin's first-mode discretization procedure is then applied and the equations of motion are transformed to two third-order nonlinear equations that are analyzed using the theory of bifurcation. Condition for nontrivial equilibrium stability is determined and a bifurcating periodic solution of the second-order approximation is derived. The effects of dimensionless stress relaxation time and cubic elastic and viscous nonlinearities as well as the role of the transverse load are studied in the exemplary numerical calculations. A strongly stabilizing influence of the relaxation time is found that may eliminate self-excited vibration at all. Transition from super- to subcritical bifurcation is observed as a result of interaction between system nonlinearities and the transverse load.
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    URL: http://dx.doi.org/10.1007/BF00045079
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