Browsing Mathematics, Department of by Title
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The Bilinski dodecahedron, and assorted parallelohedra, zonohedra, monohedra, isozonohedra and otherhedra.
(2010)Fifty years ago Stanko Bilinski showed that Fedorov's enumeration of convex polyhedra having congruent rhombi as faces is incomplete, although it had been accepted as valid for the previous 75 years. The dodecahedron he ... 
Bosonic Quantum Field Theory
(20080331)The purpose of these notes is to provide a systematic account of that part of Quantum Field Theory in which symplectic methods play a major role. 
The boundary Harnack principle for nondivergence form elliptic operators
(Cambridge University Press, 1994)If L is a uniformly elliptic operator in non–divergence form, the boundary Harnack principle for the ratio of positive L–harmonic functions holds in Hölder domains of order [alpha] if [alpha] > 1/2. A counterexample shows ... 
A boundary Harnack principle in twisted Hölder domains
(Annals of Mathematics, 199109)The boundary Harnack principle for the ratio of positive harmonic functions is shown to hold in twisted Hölder domains of order [alpha] for [alpha is an element of the set](1/2, 1]. For each [alpha is an element of the ... 
Brownian motion in a Brownian crack
(Institute of Mathematical Statistics, 199808)Let D be the Wiener sausage of width [epsilon] around twosided Brownian motion. The components of twodimensional reflected Brownian motion in D converge to onedimensional Brownian motion and iterated Brownian motion, ... 
Brownian motion reflected on Brownian motion
(SpringerVerlag GmbH, 200204)We study Brownian motion reflected on an "independent" Brownian path. We prove results on the joint distribution of both processes and the support of the parabolic measure in the spacetime domain bounded by a Brownian ... 
C*Algebras
(20101115)This book is addressed to those readers who are already familiar with the elements of the theory but wish to go further. While some aspects, e.g. tensor products, are summarized without proof, others are dealt with in all ... 
Can Every Face of a Polyhedron Have Many Sides?
(200811)The simple question of the title has many different answers, depending on the kinds of faces we are willing to consider, on the types of polyhedra we admit, and on the symmetries we require. Known results and open problems ... 
A catalogue of simplicial arrangements in the real projective plane
(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 ... 
Categorical Homotopy Theory
(201201)This book is an account of certain developments in categorical homotopy theory that have taken place since the year 2000. Some aspects have been given the complete treatment (i.e., proofs in all detail), while others are ... 
Censored stable processes
(SpringerVerlag GmbH, 200309)We present several constructions of a "censored stable process" in an open set D [is an element of the subset] R [to the power of] n, i.e., a symmetric stable process which is not allowed to jump outside D. We address ... 
Coalescence of skew Brownian motions
(SpringerVerlag, 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 ... 
Coalescence of synchronous couplings
(SpringerVerlag GmbH, 200208)We consider a pair of reflected Brownian motions in a Lipschitz planar domain starting from different points but driven by the same Brownian motion. First we construct such a pair of processes in a certain weak sense, since ... 
Comparison of potential theoretic properties of rough domains
(2005)We discuss the relationships between the notion of intrinsic ultracontractivity, parabolic Harnack principle, compactness of the 1resolvent of the Neumann Laplacian, and nontrap property for Euclidean domains with finite ... 
Conditioned Brownian motion in planar domains
(SpringerVerlag GmbH, 199504)We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains. 
Configurational transition in a FlemingViottype model and probabilistic interpretation of Laplacian eigenfunctions
(Institute of Physics, 19960607)We analyze and simulate a twodimensional Brownian multitype particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the twodimensional box, ... 
Configurations of points and lines
(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 counterexample to the "hot spots" conjecture
(Princeton University and Institute for Advanced Study, 199901)We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions ... 
A critical case for Brownian slow points
(SpringerVerlag GmbH, 199601)Let X [subscript] t be a Brownian motion and let S(c) be the set of reals r [is greather than or equal to] 0 such that X ([subscript] r+t) − X [subscript] r [is less than or equal to] c [square root of] t, 0 [is less ... 
Curvature of the convex hull of planar Brownian motion near its minimum point
(NorthHolland (Elsevier), 198910)Let f be a (random) realvalued function whose graph represents the boundary of the convex hull of planar Brownian motion run until time 1 near its lowest point in a coordinate system so that f is nonnegative and f(0) = ...