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Träfflista för sökning "AMNE:(NATURAL SCIENCES Mathematics) srt2:(1975-1999)"

Sökning: AMNE:(NATURAL SCIENCES Mathematics) > (1975-1999)

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1.
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2.
  • Holmbom, Anders (författare)
  • Some modes of convergence and their application to homogenization and optimal composites design
  • 1996
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • In this thesis, we develop, extend, apply, and discuss a number of methods for the study of limits of sequences of functions and operators. The connection between the notion of two-scale convergence and more general concepts of convergence is investigated and some alternative classes of admissible test functions are characterized. These techniques are extended into compactness results suitable to prove homogenization and corrector results for linear parabolic equations. A further refinement of these methods, together with a characterization of the limits of certain sequences of parameter-dependent functions which has been subject to extension from a quite general class of periodic domains, is introduced. This provides an efficient tool for the homogenization of e.g. nonlinear evolution heat conduction in heterogeneous materials which vibrate with high frequencies or are perforated by periodically arranged nonconducting holes. Moreover, we prove compactness and homogenization for sequences of solutions of linear elliptic and monotone parabolic equations defined in some classes of nonperiodic domains and derive a Darcy's law for a type of nonperiodic porous media. In the linear elliptic case the convergence is strengthened by means of correctors. Finally, we present some numerical results for homogenized stiffness of fibre composites and demonstrate how homogenization techniques for elasticity in composite materials and for liquid flow in porous media can be combined with recent optimization techniques to obtain optimal layout of composite materials.
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4.
  • Klisinska, Anna (författare)
  • Clarkson type inequalities and geometric properties of banach spaces
  • 1999
  • Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • In this thesis Clarkson's inequalities and their generalizations are the main tools. The technique that can be used to prove Clarkson type inequalities in more dimensions is shown. We also establish Clarkson type inequalities in general Banach spaces and point out the connections between Clarkson's inequalities and the concept of type and cotype. The classical results on the von Neumann-Jordan constant, closely related to Clarkson's inequalities, are shortly presented. The concepts of moduli of convexity and smoothness, which are connected with the geometry of Banach spaces, are discussed. Some equivalent ways of describing modulus of convexity and some properties of this function are formulated. The estimation of the modulus of convexity for L(p)-spaces is presented as well. Finally, several examples of moduli of convexity and smoothness for different spaces are described.
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5.
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6.
  • Albeverio, Sergio, et al. (författare)
  • Estimates uniform in time for the transition probability ofdiusions with small drift and for stochastically perturbed Newton equations
  • 1999
  • Ingår i: Journal of theoretical probability. - 0894-9840 .- 1572-9230. ; 12:2, s. 293-300
  • Tidskriftsartikel (refereegranskat)abstract
    • An estimate uniform in time for the transition probability of di®usion processes with small drift is given. This also covers the case of a degenerate di®usion describing a stochastic perturbation of a particle moving according to the Newton's law. Moreover the random wave operator for such a particle is described and the analogue of asymptotic completeness is proven, the latter in the case of a su±ciently small drift.
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8.
  • Andersson, Pontus (författare)
  • Random tournaments and random circuits
  • 1999
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • This thesis is devoted to two different topics in the area of probabilistic combinatorics: asymptotic behaviour of subgraph counts in a random tournament and random circuit decompositions of complete graphs.Let Tn be a random tournament on n vertices, chosen uniformly from all 2(n2) such tournaments, and let D be an arbitrary directed graph. Then the number of copies of D in Tn is a random variable which, after normalization, converges in distribution as n tends to infinity. The limit distribution is determined, and it turns out to be normal for a typical D, but for some D it is a quadratic polynomial in normal variables. It is also shown that the variance of the number of copies of D in Tn is a polynomial in n and that the degree of this polynomial is, for a typical D, 2v - 3, where v is the number of vertices of D. However, examples are given for which this degree is as low as v.Some directed graphs turn out to appear the same number of times in all tournaments with a fixed number of vertices. A partial characterization of these directed graphs is given.In the complete undirected or directed graph on n vertices, choose a random decomposition of the set of all edges into circuits, uniformly from all such decompositions. Letting Lk be the fraction of edges contained in the k-th longest circuit in this decomposition, it is shown that (L1, L2,...) converges to a Poisson-Dirichlet distribution as n tends to infinity. It is also shown that the numbersof circuits of given lengths converge jointly to independent Poisson variables, and that the expected number of circuits is log n + O(1) in the undirected case and 2 log n + O(1) in the directed case.
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9.
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10.
  • Asekritova, Irina, et al. (författare)
  • On Equivalemce of K- and J-Methods for (n+1)-Tuples of Banach Spaces
  • 1997
  • Ingår i: Studia Mathematica. - 0039-3223 .- 1730-6337. ; 122:2, s. 99-116
  • Tidskriftsartikel (refereegranskat)abstract
    • It is shown that the main results of the theory of real interpolation, i.e. the equivalence and reiteration theorems, can be extended from couples to a class of (n+1)-tuples of Banach spaces, which includes (n+1)-tuples of Banach function lattices, Sobolev and Besov spaces. As an application of our results, it is shown that Lions' problem on interpolation of subspaces and Semenov's problem on interpolation of subcouples have positive solutions when all spaces are Banach function lattices or their retracts. In general, these problems have negative solutions.
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