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North Holland

    • Convex Cones

      • 1st Edition
      • Volume 56
      • August 18, 2011
      • B. Fuchssteiner + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 3 9 1
      • eBook
        9 7 8 0 0 8 0 8 7 1 6 7 7

    • Probabilities and Potential, C

      • 1st Edition
      • Volume 151
      • August 18, 2011
      • C. Dellacherie + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 0 7 0
      • eBook
        9 7 8 0 0 8 0 8 7 2 6 2 9
      This third volume of the monograph examines potential theory. The first chapter develops potential theory with respect to a single kernel (or discrete time semigroup). All the essential ideas of the theory are presented: excessive functions, reductions, sweeping, maximum principle. The second chapter begins with a study of the notion of reduction in the most general situation possible - the ``gambling house'' of Dubins and Savage. The beautiful results presented have never been made accessible to a wide public. These are then connected with the theory of sweeping with respect to a cone of continuous functions, and the integral representation in compact convex sets. The third chapter presents new or little-known results, with the aim of illustrating the effectiveness of capacitary methods in the most varied fields. The last two chapters are concerned with the theory of resolvents.The fourth and last part of the English edition will be devoted to the theory of Markov processes.

    • Differential Calculus and Holomorphy

      • 1st Edition
      • Volume 64
      • August 18, 2011
      • J.F. Colombeau
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 4 9 0
      • eBook
        9 7 8 0 0 8 0 8 7 1 7 5 2

    • Symmetric Banach Manifolds and Jordan C<SUP>*</SUP>-Algebras

      • 1st Edition
      • Volume 104
      • August 18, 2011
      • H. Upmeier
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 8 0 1 5
      • eBook
        9 7 8 0 0 8 0 8 7 2 1 5 5
      This book links two of the most active research areas in present day mathematics, namely Infinite Dimensional Holomorphy (on Banach spaces) and the theory of Operator Algebras (C*-Algebras and their non-associative generalizations, the Jordan C*-Algebras). It organizes in a systematic way a wealth of recent results which are so far only accessible in research journals and contains additional original contributions. Using Banach Lie groups and Banach Lie algebras, a theory of transformation groups on infinite dimensional manifolds is presented which covers many important examples such as Grassmann manifolds and the unit balls of operator algebras. The theory also has potential importance for mathematical physics by providing foundations for the construction of infinite dimensional curved phase spaces in quantum field theory.

    • Elementary Introduction to New Generalized Functions

      • 1st Edition
      • Volume 113
      • August 18, 2011
      • J.F. Colombeau
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 8 0 9 1
      • eBook
        9 7 8 0 0 8 0 8 7 2 2 4 7
      The author's previous book `New Generalized Functions and Multiplication of Distributions' (North-Holland, 1984) introduced `new generalized functions' in order to explain heuristic computations of Physics and to give a meaning to any finite product of distributions. The aim here is to present these functions in a more direct and elementary way. In Part I, the reader is assumed to be familiar only with the concepts of open and compact subsets of R&eegr;, of C∞ functions of several real variables and with some rudiments of integration theory. Part II defines tempered generalized functions, i.e. generalized functions which are, in some sense, increasing at infinity no faster than a polynomial (as well as all their partial derivatives). Part III shows that, in this setting, the partial differential equations have new solutions. The results obtained show that this setting is perfectly adapted to the study of nonlinear partial differential equations, and indicate some new perspectives in this field.

    • Combinatorial Set Theory: Partition Relations for Cardinals

      • 1st Edition
      • Volume 106
      • August 18, 2011
      • P. Erdös + 3 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 3 0 8
      • eBook
        9 7 8 0 4 4 4 5 3 7 4 5 4
      This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality.

    • Foundations of Infinitesimal Stochastic Analysis

      • 1st Edition
      • August 18, 2011
      • K.D. Stroyan + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 8 2 0 6
      • eBook
        9 7 8 0 0 8 0 9 6 0 4 2 5
      This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.

    • From Associations to Structure

      • 1st Edition
      • Volume 6
      • August 18, 2011
      • K.V. Wilson
      • English
      • Paperback
        9 7 8 0 4 4 4 5 5 7 2 6 1
      • eBook
        9 7 8 0 0 8 0 8 6 6 6 0 4
      Wilson's book proposes an associationistic form of psychological theory which is opposed to the more extreme structuralist claims. It brings together a relatively novel combination of topics from psychology, computational linguistics and artificial intelligence which support a viable associationistic position.

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