Browsing EPrint Collection  Mathematics by Title
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Labyrinth dimension of Brownian trace
(Institute of Mathematics, 1995)Suppose that X is a twodimensional Brownian motion. The trace X[0, 1] contains a selfavoiding continuous path whose Hausdorff dimension is equal to 2. 
Lagrangian Mechanics
(20090112)My original set of lectures on Mechanics was divided into three parts: Lagrangian Mechanics, Hamiltonian Mechanics, Equivariant Mechanics. The present text is an order of magnitude expansion of the first part and is ... 
Lectures on Arrangements
(1974) 
Lectures on Lost Mathematics
(2010) 
Lenses in skew Brownian flow
(Institute of Mathematical Statistics, 200410)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 level sets of iterated Brownian motion
(SpringerVerlag, 1995)We show that the Hausdorff dimension of every level set of iterated Brownian motion is equal to 3/4. 
Lifetimes of conditioned diffusions
(SpringerVerlag GmbH, 1992)We investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and nondivergence form can be found. The critical value of the parameter is found for ... 
Local time flow related to skew Brownian motion
(Institute of Mathematical Statistics, 200110)We define a local time flow of skew Brownian motions, i.e., a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian ... 
The Martin boundary in nonLipschitz domains
(American Mathematical Society, 1993)The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in C [to the power of gamma] domains, where [gamma](x) = ... 
Mathematical articles and bottled water
(American Mathematical Society, 200205)The system for publishing mathematical articles should be reformed and the new system should resemble, on the economic side, the bottled water industry. My main theses are: (i) the results of the mathematical research ... 
Mathematical Aspects of General Relativity
(20060908)These notes can serve as a mathematical supplement to the standard graduate level texts on general relativity and are suitable for selfstudy. The exposition is detailed and includes accounts of several topics of current ... 
Mechanisms for facilitated target location and the optimal number of molecules in the diffusion search process
(American Physical Society, 20010626)We investigate the number N of molecules needed to perform independent diffusions in order to achieve bonding of a single molecule to a specific site in time t [subscript] 0. For a certain range of values of t [subscript] ... 
Minimal Fine Derivatives and Brownian Excursions
(Nagoya University, 199009)Let f be an analytic function defined on D [is a subset of] [complex numbers] C. If [the derivative of the function f at the point x] has a limit when [the set] x [into the set] z [is an element of the set partial derivative] ... 
Neumann eigenfunctions and Brownian couplings
(Mathematical Society of Japan, 2004)This is a review of research on geometric properties of Neumann eigenfunctions related to the "hot spots" conjecture of Jeff Rauch. The paper also presents, in an informal way, some probabilistic techniques used in the proofs. 
No triple point of planar Brownian motion is accessible
(Institute of Mathematical Statistics, 199601)We show that the boundary of a connected component of the complement of a planar Brownian path on a fixed timeinterval contains almost surely no triple point of this Brownian path. 
Nonintersection exponents for Brownian paths. Part I: Existence and an invariance principle
(SpringerVerlag GmbH, 1990)Let X and Y be independent threedimensional Brownian motions, X(0) = (0; 0; 0), Y (0) = (1; 0; 0) and let p [subscript]r = P(X[0; r] [intersected with] Y [0; r] = [empty set]. Then the "non intersection exponent" [from] ... 
Nonintersection exponents for Brownian paths. Part II: Estimations and applications to a random fractal.
(Institute of Mathematical Statistics, 199007)Let X and Y be independent twodimensional Brownian motions, X(0) = (0; 0); Y(0) = ([epsilon]; 0), and let p([epsilon]) = P(X[0; 1] [intersected with] Y [0; 1] = [empty set], q([epsilon]) = {Y [0; 1] does not contain a ... 
Nonpolar points for reflected Brownian motion
(Elsevier, 1993)Our main results are (i) a new construction of reflected Brownian motion X in a halfplane with nonsmooth angle of oblique reflection and (ii) a theorem on existence of some "exceptional" points on the paths of the ... 
Omittable lines
(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 ...