Now showing items 21-40 of 112

    • Isogonal prismatoids 

      Grünbaum, Branko (Springer New York, 1997)
      A prismatoid is a polyhedron with all vertices in two parallel planes. A polyhedron P is isogonal if all its vertices form one transitivity class under isometric symmetries of P. Although these restrictions appear very ...
    • What symmetry groups are present in the Alhambra? 

      Grünbaum, Branko (American Mathematical Society, 2006)
      The question which of the seventeen wallpaper groups are represented in the fabled ornamentation of the Alhambra has been raised and discussed quite often, with widely diverging answers. Some of the arguments from these ...
    • Small triangle-free configurations of points and lines 

      Boben, Marko; Grünbaum, Branko; Pisanski, Tomaz; Zitnik, Arjana (2006)
      In this paper we show that all combinatorial triangle-free configurations (v_3) for v (is less than or equal to) 8 are geometrically realizable. We also show that there is a unique smallest astral (18_3) triangle-free ...
    • Omittable lines 

      Grünbaum, Branko (2005)
      Every finite family of (straight) lines in the projective plane, not forming a pencil, is well know to have at least one "ordinary point" –– that is, a point common to precisely two of the lines. A line of a family is ...
    • Graphs of polyhedra; polyhedra as graphs 

      Grünbaum, Branko (2005)
      Relations between graph theory and polyhedra are presented in two contexts. In the first, the symbiotic dependence between 3-connected planar graphs and convex polyhedra is described in detail. In the second, a theory of ...
    • Configurations of points and lines 

      Grünbaum, Branko (2005)
      A vigorous study of geometric configurations started in the 1870's but was essentially abandoned early in the twentieth century. New approaches found during the last two decades prompted a renewed interest in the topic, ...
    • A catalogue of simplicial arrangements in the real projective plane 

      Grünbaum, Branko (2005)
      An arrangement is the complex generated in the real projective plane by a family of straight lines that do not form a pencil. The faces of an arrangement are the connected components of the complement of the set of ...
    • The level sets of iterated Brownian motion 

      Burdzy, Krzysztof; Khoshnevisan, Davar (Springer-Verlag, 1995)
      We show that the Hausdorff dimension of every level set of iterated Brownian motion is equal to 3/4.
    • An asymptotically 4-stable process 

      Burdzy, Krzysztof; Madrecki, Andrzej (CRC Press, 1995)
      An asymptotically 4-stable process is constructed. The model identifies the 4-stable process with a sequence of processes converging in a very weak sense. It is proved that the 4-th variation of the process is a linear ...
    • Excursion laws and exceptional points on Brownian paths 

      Burdzy, Krzysztof (Springer-Verlag, 1993)
      The purpose of this note is to present an example of a family of "exceptional points" on Brownian paths which cannot be constructed using an entrance law.
    • Variation of iterated Brownian motion 

      Burdzy, Krzysztof (American Mathematical Society, 1994)
      In this paper, we study higher order variations of iterated Brownian motion (IBM) with view towards possible applications to the construction of the stochastic integral with respect to IBM. We prove that the 4-th variation ...
    • Some path properties of iterated Brownian motion 

      Burdzy, Krzysztof (Birkhauser Boston, Inc., 1993)
      The present paper is devoted to studying path properties of iterated Brownian motion (IBM). We want to examine how the lack of independence of increments influences the results and estimates which are well understood in ...
    • Hitting a boundary point with reflected Brownian motion 

      Burdzy, Krzysztof; Marshall, Donald E. (Springer-Verlag, 1992)
      An explicit integral test involving the reflection angle is given for the reflected Brownian motion in a half-plane to hit a fixed boundary point.
    • A probabilistic proof of the boundary Harnack principle 

      Burdzy, Krzysztof; Bass, Richard F. (Birkhauser Boston, Inc., 1990)
      The main purpose of this paper is to give a probabilistic proof of Theorem 1.1, one using elementary properties of Brownian motion. We also obtain the fact that the Martin boundary equals the Euclidean boundary as an easy ...
    • On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions 

      Burdzy, Krzysztof; Toby, Ellen H.; Williams, Ruth J. (Birkhäuser Boston, Inc., 1989)
      In this paper, we continue the study initiated in Burdzy and Williams (1986) of the local properties of Brownian excursions in Lipschitz domains. The focus in part I was on local path properties of such excursions. In ...
    • Coalescence of skew Brownian motions 

      Burdzy, Krzysztof; Barlow, Martin T.; Kaspi, Haya; Mandelbaum, Avi (Springer-Verlag, 2001)
      The purpose of this short note is to prove almost sure coalescence of two skew Brownian motions starting from different initial points, assuming that they are driven by the same Brownian motion. The result is very simple ...
    • The supremum of Brownian local times on Holder curves 

      Burdzy, Krzysztof; Bass, Richard F. (Elsevier, 2001-11)
      For f : [maps the set] [0, 1] [into the set of real numbers] R, we consider L ([to the power of] f [subscript] t), the local time of spacetime Brownian motion on the curve f. Let S [subscript alpha] be the class of all ...
    • Uniqueness for reflecting Brownian motion in lip domains 

      Burdzy, Krzysztof; Bass, Richard F.; Chen, Zhen-Qing (Elsevier, 2005-03)
      A lip domain is a Lipschitz domain where the Lipschitz constant is strictly less than one. We prove strong existence and pathwise uniqueness for the solution X = {X [subscript] t, t [is less than or equal to] 0} to the ...
    • Lenses in skew Brownian flow 

      Burdzy, Krzysztof; Kaspi, Haya (Institute of Mathematical Statistics, 2004-10)
      We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding ...
    • The heat equation in time dependent domains with insulated boundaries 

      Burdzy, Krzysztof; Chen, Zhen-Qing; Sylvester, John (Academic Press (Elsevier), 2004-10)
      The paper studies, among other things, two types of possible singularities of the solution to the heat equation at the boundary of a moving domain. Several explicit results on "heat atoms" and "heat singularities" are given.