Seminars, 2002
  • 26.11.2002
    Professor David Shoikhet, ORT Braude College
    Some classical and modern mathematical models in biology. Stochastic, analytic, and geometrical solutions


  • 8.11.2002
    Professor Eva Matouskova, Mathematical Institute, Czech Academy of Sciences, Prague, Czech Republic
    Almost isometries of Euclidean balls


    Let f be a bi-Lipschitz mapping of the Euclidean ball BRn into l2 with both Lipschitz constants close to one. We investigate the shape of f(BRn). We give examples of such a mapping f, which has Lipschitz constants arbitrarily close to one and at the same time has in the supremum norm distance at least one from every isometry of Rn.

  • 28.10.2002
    Professor Andery E.Shishkov, Institute of Applied Mathrmatics and Mechanics of NAS of Ukraine, Donetsk
    Localized and nonlocalized boundary blow-up regimes for higher order uasilinear parabolic equations


    There are considered mixed problems for general parabolic PDE with boundary data blowing up in some finite time. We prove sharp sufficient conditions of localization of singularities of generalized energy solutions. For nonlocalized blow up regimes we investigate the propagation of corresponding blow-up wave.

  • 8.10.2002
    Prof. Uwe Brauer, Universidad Complutense de Madrid, Spain
    Local existence of solution of the Einstein--Euler system with non compact support of the density


    A class of local in time solutions of the Einstein-Euler system is discussed which were obtained in collaboration with Lavi Karp. These solutions generalize previous results of Rendall in various ways. First of all the restriction of time symmetry is removed, secondly the range of the equation of state is enhanced in such a way, that static solutions are included. The main tool in order to achieve this result is the introduction of a new class of weighted Sobolev spaces of fractional order. The properties of these spaces are discussed together with the corresponding elliptic theory, which has interest by their own. Finally some remarks are made concerning the singular limes of these solutions to the corresponding solutions of the Euler-Poisson system, obtained by Gamblin.

  • 27.06.2002
    Pr. Mihai Putinar, University of California, Santa Barbara, U.S.A.
    A skew normal dilation on the numerical range of an operator


    A generalization of Sz. Nagy-Foias dilation theorem valid for any Hilbert space operator will be presented. The main tool is a positivity result deduced from the investigation of the Neumann-Poincare double layer potential operator, on a convex planar curve. Former observations due to C.Berger, T.Kato and J.Stampfli can therefore be proved in an unifying way.

  • 11.06.2002
    Buma Abramovich, Technion and ORT Braude College
    Useful Mistakes


    We present a variety of examples of wrong proofs, misinterpreted definitions and mistaken use of the theory. The examples are based on our experience of teaching mathematics to engineering students. They include elementary examples and more advanced ones and are taken from different subjects. In analyzing the mistakes we try to use them to improve the students' understanding. A joint work with M. Berezina and A. Berman.

  • 04.06.2002
    Emil Suacan, Technion and ORT Braude College
    An Introduction to Automatic Groups (Continuation)


    We present a concise panorama of Automatic Group Theory (as developed by Cannon, Epstein and Thurston, i.e. that branch of Combinatorial Group Theory connecting (especially through the investigation of the geodesics in the Cayley Graph, a path already pioneered by Max Dehn) between Automata Theory, Combinatorial Group Theory and geometry (especially the Geometry of Hyperbolic Manifolds).

  • 27.05.2002
    Professor Vladimir Ovchinnikov, Voronezh, Russia
    On the K-functional for pairs of operator spaces