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  • Articles  (24)
  • Springer  (24)
  • Molecular Diversity Preservation International
  • 2000-2004  (24)
  • Mathematics  (24)
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  • Articles  (24)
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  • 1
    Electronic Resource
    Electronic Resource
    Examples of Minimal Unit Vector Fields (2000)
    Springer
    Annals of global analysis and geometry 18 (2000), S. 385-404 
    Details
    ISSN: 1572-9060
    Keywords: geodesic ; normal ; strongly normal and minimal unit vector fields
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We provide a series of examples of Riemannian manifoldsequipped with a minimal unit vector field.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006788819180
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  • 2
    Electronic Resource
    Electronic Resource
    On the Starting Algorithms for Fully Implicit Runge-Kutta Methods (2000)
    Springer
    BIT 40 (2000), S. 685-714 
    Details
    ISSN: 1572-9125
    Keywords: Stiff initial value problems ; implicit Runge-Kutta methods ; solution of stage equations ; starting algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the behavior of starting algorithms to solve the algebraic equations of stages arising when fully implicit Runge-Kutta methods are applied to stiff initial value problems. The classical Lagrange extrapolation of the internal stages of the preceding step and some variants thereof that do not require any additional cost are analyzed. To study the order of the starting algorithms we consider three different approaches. First we analyze the classical order through the theory of Butcher's series, second we derive the order on the Prothero and Robinson model and finally we study the stiff order for a general class of dissipative problems. A detailed study of the orders of some starting algorithms for Gauss, Radau IA-IIA, Lobatto IIIA-C methods is also carried out. Finally, to compare the most relevant starting algorithms studied here, some numerical experiments on well known nonlinear stiff problems are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022340401909
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  • 3
    Electronic Resource
    Electronic Resource
    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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  • 4
    Electronic Resource
    Electronic Resource
    Ultrapowers and semigroups of operators (2000)
    Springer
    Integral equations and operator theory 37 (2000), S. 32-47 
    Details
    ISSN: 1420-8989
    Keywords: Primary: 47A53 ; 46B08 ; Secondary: 46B07
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study two semigroups $$\mathcal{U}^{up} _ + ,\mathcal{R}^{up} _ + $$ of operators between Banach spaces, related with the finite representability ofc 0 and ℓ1. We show that these semigroups are open, have nice duality properties and can be characterized in terms of compact perturbations, and in terms of the properties of their ultrapowers. We obtain analogous results for their associated dual semigroups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01673621
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  • 5
    Electronic Resource
    Electronic Resource
    Inversion de Fourier ponctuelle des distributions à support compact (2000)
    Springer
    Archiv der Mathematik 75 (2000), S. 290-298 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. On montre que l'intégrale de Fourier d'une distribution â support compact est sommable en moyenne de Cesâro uniformément vers zéro au voisinage d'un point si et seulement si ce point n'appartient pas au support de la distribution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000130050506
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  • 6
    Electronic Resource
    Electronic Resource
    The polynomial property (V) (2000)
    Springer
    Archiv der Mathematik 75 (2000), S. 299-306 
    Details
    ISSN: 1420-8938
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. Given Banach spaces E and F, we denote by ${\cal P}(^k\! E,F)$ the space of all k-homogeneous (continuous) polynomials from E into F, and by ${\cal P}_{\mathop {\rm wb}\nolimits }(^k\! E,F)$ the subspace of polynomials which are weak-to-norm continuous on bounded sets. It is shown that if E has an unconditional finite dimensional expansion of the identity, the following assertions are equivalent: (a) ${\cal P}(^k\! E,F) ={\cal P}_{\mathop {\rm wb}\nolimits }(^k\! E,F)$ ; (b) ${\cal P}_{\mathop {\rm wb}\nolimits}(^k\! E,F)$ contains no copy of c 0; (c) ${\cal P}(^k\! E,F)$ contains no copy of $\ell _\infty$ ; (d) ${\cal P}_{\mathop {\rm wb}\nolimits }(^k\! E,F)$ is complemented in ${\cal P}(^k\! E,F)$ . This result was obtained by Kalton for linear operators. As an application, we show that if E has Pełczyński's property (V) and satisfies ${\cal P}(^k\! E)={\cal P}_{\mathop {\rm wb}\nolimits }(^k\! E)$ then, for all F, every unconditionally converging $P\in {\cal P}(^k\! E,F)$ is weakly compact. If E has an unconditional finite dimensional expansion of the identity, then the converse is also true.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s000130050507
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  • 7
    Electronic Resource
    Electronic Resource
    Perturbation of the Drazin inverse for closed linear operators (2000)
    Springer
    Integral equations and operator theory 36 (2000), S. 92-106 
    Details
    ISSN: 1420-8989
    Keywords: 47A10 ; 47A60 ; 34G10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate the perturbation of the Drazin inverse of a closed linear operator recently introduced by second author and Tran, and derive explicit bounds for the perturbations under certain restrictions on the perturbing operators. We give applications to the solution of perturbed linear equations, to the asymptotic behaviour ofC 0-semigroups of linear operators, and to perturbed differential equations. As a special case of our results we recover recent perturbation theorems of Wei and Wang.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01236288
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  • 8
    Electronic Resource
    Electronic Resource
    Orlicz-Pettis Polynomials on Banach Spaces (2000)
    Springer
    Monatshefte für Mathematik 129 (2000), S. 341-350 
    Details
    ISSN: 1436-5081
    Keywords: 2000 Mathematics Subject Classification: 46G25; 46B20 ; Key words: Polynomial on c0 ; unconditionally converging polynomial ; weakly unconditionally Cauchy series ; unconditionally convergent series
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract.  We introduce the class of Orlicz-Pettis polynomials between Banach spaces, defined by their action on weakly unconditionally Cauchy series. We give a number of equivalent definitions, examples and counterexamples which highlight the differences between these polynomials and the corresponding linear operators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s006050050080
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  • 9
    Electronic Resource
    Electronic Resource
    Homomorphisms on Lipschitz Spaces (2000)
    Springer
    Monatshefte für Mathematik 129 (2000), S. 25-30 
    Details
    ISSN: 1436-5081
    Keywords: 1991 Mathematics Subject Classification: 26A16, 54D60 ; Key words: homomorphisms, Lipschitz spaces, realcompactness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract.  Denote by the family of all real valued functions on a metric space which satisfy a Lipschitz condition on the compact (bounded) subsets of X. We prove that every homomorphism on is the evaluation at some point of X if and only if X is realcompact (every closed bounded subset of X is compact).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s006050050003
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  • 10
    Electronic Resource
    Electronic Resource
    Simple Algorithms for the On-Line Multidimensional Dictionary and Related Problems (2000)
    Springer
    Algorithmica 28 (2000), S. 255-267 
    Details
    ISSN: 1432-0541
    Keywords: Key words. Multidimensional dictionary, On-line algorithms, Data structures.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. The on-line multidimensional dictionary problem consists of executing on-line any sequence of the following operations: INSERT(p) , DELETE(p) , and MEM-BER-SHIP(p) , where p is any (ordered) d -tuple (or string with d elements, or points in d -space where the dimensions have been ordered). We introduce a clean structure based on balanced binary search trees, which we call multidimensional balanced binary search trees, to represent the set of d -tuples. We present algorithms for each of the above operations that take O(d + log n) time, where n is the current number of d -tuples in the set, and each INSERT and DELETE operation requires no more than a constant number of rotations. Our structure requires dn words to represent the input, plus O(n) pointers and data indicating the first component where pairs of d -tuples differ. This information, which can be easily updated, enables us to test for MEMBERSHIP efficiently. Other operations that can be performed efficiently in our multidimensional balanced binary search trees are: print in lexicographic order (O(dn) time), find the (lexicographically) smallest or largest d -tuple (O( log n) time), and concatenation (O(d + log n) time). Finding the (lexicographically) k th smallest or largest d -tuple can also be implemented efficiently (O( log n) time), at the expense of adding an integer value at each node.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004530010039
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