Losing Hausdorff dimension while generating pseudogroups

Paweł Walczak

Displaying similar documents to “Losing Hausdorff dimension while generating pseudogroups”

A note on prediction for discrete time series

Gusztáv Morvai, Benjamin Weiss (2012)

Kybernetika

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Let ${X_{n}}$ be a stationary and ergodic time series taking values from a finite or countably infinite set $𝒳$ and that $f (X)$ is a function of the process with finite second moment. Assume that the distribution of the process is otherwise unknown. We construct a sequence of stopping times $λ_{n}$ along which we will be able to estimate the conditional expectation $E (f (X_{λ_{n} + 1}) | X_{0}, \dots, X_{λ_{n}})$ from the observations $(X_{0}, \dots, X_{λ_{n}})$ in a point wise consistent way for a restricted class of stationary and ergodic finite or countably infinite alphabet...

Totally reflexive modules with respect to a semidualizing bimodule

Zhen Zhang, Xiaosheng Zhu, Xiaoguang Yan (2013)

Czechoslovak Mathematical Journal

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Let $S$ and $R$ be two associative rings, let $_{S} C_{R}$ be a semidualizing $(S, R)$ -bimodule. We introduce and investigate properties of the totally reflexive module with respect to $_{S} C_{R}$ and we give a characterization of the class of the totally $C_{R}$ -reflexive modules over any ring $R$ . Moreover, we show that the totally $C_{R}$ -reflexive module with finite projective dimension is exactly the finitely generated projective right $R$ -module. We then study the relations between the class of totally reflexive modules and...

Generalized Thue-Morse words and palindromic richness

Štěpán Starosta (2012)

Kybernetika

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We prove that the generalized Thue-Morse word $𝐭_{b, m}$ defined for $b \geq 2$ and $m \geq 1$ as $𝐭_{b, m} = {(s_{b} (n) mod m)}_{n = 0}^{+ \infty}$ , where $s_{b} (n)$ denotes the sum of digits in the base- $b$ representation of the integer $n$ , has its language closed under all elements of a group $D_{m}$ isomorphic to the dihedral group of order $2 m$ consisting of morphisms and antimorphisms. Considering antimorphisms $Θ \in D_{m}$ , we show that $𝐭_{b, m}$ is saturated by $Θ$ -palindromes up to the highest possible level. Using the generalisation of palindromic richness recently introduced by the author...

Distances on the tropical line determined by two points

María Jesús de la Puente (2014)

Kybernetika

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Let $p^{'}$ and $q^{'}$ be points in $ℝ^{n}$ . Write $p^{'} \sim q^{'}$ if $p^{'} - q^{'}$ is a multiple of $(1, ..., 1)$ . Two different points $p$ and $q$ in $ℝ^{n} / \sim$ uniquely determine a tropical line $L (p, q)$ passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on $n$ leaves. It is also a metric graph. If some representatives $p^{'}$ and $q^{'}$ of $p$ and $q$ are the first and second columns of some real normal idempotent order $n$ matrix $A$ , we prove that the tree $L (p, q)$ is described by a matrix $F$ , easily obtained from $A$ . We also...

On the positivity of the number of t-core partitions

Ken Ono (1994)

Acta Arithmetica

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A partition of a positive integer n is a nonincreasing sequence of positive integers with sum $n .$ Here we define a special class of partitions. 1. Let $t \geq 1$ be a positive integer. Any partition of n whose Ferrers graph have no hook numbers divisible by t is known as a t- core partitionof $n .$ The hooks are important in the representation theory of finite symmetric groups and the theory of cranks associated with Ramanujan’s congruences for the ordinary partition function [3,4,6]. If $t \geq 1$ and $n \geq 0$ ,...