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In previous work, a class of noninvertible topological dynamical systems $f: X \to X$ was introduced and studied; we called these {\em topologically coarse expanding conformal} systems. To such a sys...
Motivated by the rich geometry of conformal Riemannian manifolds and by the recent development of geometries modeled on homogeneous spaces $G/P$ with $G$ semisimple and $P$ parabolic, Weyl structures...
Representations of multidimensional linear process bridges
multidimensional linear process bridges math
2010/11/8
We derive bridges from general multidimensional linear non time-homogeneous processes using only the transition densities of the original process giving their integral representations (in terms of a s...
Looking for a Billiard Table which is not a Lattice Polygon but Satisfies Veech's Dichotomy
Billiard Table Lattice Polygon Satisfies Veech's Dichotomy
2010/11/19
Over the course of studying billiard dynamics, several questions were raised. One of the questions was, which surfaces satisfy the following property (which is called Veech's dichotomy): Any directio...
We give a geometric model for a tube category in terms of homotopy classes of oriented arcs in an annulus with marked points on its boundary. In particular, we interpret the dimensions of extension gr...
A complete unitary similarity invariant for unicellular matrices
invariant unicellular matrices
2010/11/8
Necessary and sufficient conditions for two n-by-n unicellular complex matrices to be unitarily equivalent are established.
Criterion of unitary similarity for upper triangular matrices in general position
upper triangular matrices general position
2010/11/8
Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A and B be upper triangular n-by-n matrices that (i) are not similar to...
A measure for the description of the chirality of triangles is introduced. The measure $X\delta$ is zero for triangles with at least one mirror axe, i.e. equilateral or isosceles triangles, and positi...
On Jiang's asymptotic distribution of the largest entry of a sample correlation matrix
On Jiang's asymptotic distribution correlation matrix
2010/11/19
Let $ \{X, X_{k,i}; i \geq 1, k \geq 1 \}$ be a double array of nondegenerate i.i.d. random variables and let $\{p_{n}; n \geq 1 \}$ be a sequence of positive integers such that $n/p_{n}$ is bounded a...
Direct Construction of Grassmann, Clifford and Geometric Algebras
Direct Construction of Grassmann Clifford and Geometric Algebras
2010/11/22
This is a simple way rigorously to construct Grassmann, Clifford and Geometric Algebras, allowing degenerate bilinear forms, infinite dimension, using fields or certain modules (characteristic 2 with ...
Existence and uniqueness theorem for convex polyhedral metrics on compact surfaces
uniqueness theorem convex polyhedral metrics compact surfaces
2010/11/19
We state that any constant curvature Riemannian metric with conical singularities of constant sign curvature on a compact (orientable) surface $S$ can be realized as a convex polyhedron in a Riemanni...
On the eigenvalue problem for a particular class of finite Jacobi matrices
the eigenvalue problem finite Jacobi matrices
2010/11/11
A function $\mathfrak{F}$ with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of $\mathfrak{F}$, first ...
We construct a spectral sequence converging to symplectic homology of a Lefschetz fibration whose E1 page is related to Floer homology of the monodromy symplectomorphism and its iterates. We use this ...
Let $E(k, \ell)$ denote the smallest integer such that any set of at least $E(k, \ell)$ points in the plane, no three on a line, contains either an empty convex polygon with $k$ vertices or an empty ...
A polyhedron in Euclidean 3-space is called a regular polyhedron of index 2 if it is combinatorially regular and its geometric symmetry group has index 2 in its combinatorial automorphism group; thus ...