Results 21 to 30 of about 71,510 (217)

Exceptional families of measures on Carnot groups

Analysis and Geometry in Metric Spaces, 2023
We study the families of measures on Carnot groups that have vanishing pp-module, which we call Mp{M}_{p}-exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing through a common point to ...
Franchi Bruno, Markina Irina
doaj   +1 more source

Something About h - Measures of Sets in Plane

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2014
In this article we estimate the Hausdorff h-measures of the graphs of some functions, for different measure functions.
Bărbulescu Alina
doaj   +1 more source

Intersections of Projections and Slicing Theorems for the Isotropic Grassmannian and the Heisenberg group

Analysis and Geometry in Metric Spaces, 2020
This paper studies the Hausdorff dimension of the intersection of isotropic projections of subsets of ℝ2n, as well as dimension of intersections of sets with isotropic planes. It is shown that if A and B are Borel subsets of ℝ2n of dimension greater than
Román-García Fernando
doaj   +1 more source

Two Dimensional Yau-Hausdorff Distance with Applications on Comparison of DNA and Protein Sequences. [PDF]

PLoS ONE, 2015
Comparing DNA or protein sequences plays an important role in the functional analysis of genomes. Despite many methods available for sequences comparison, few methods retain the information content of sequences.
Kun Tian, Xiaoqian Yang, Qin Kong, Changchuan Yin, Rong L He, Stephen S-T Yau   +5 more
doaj   +1 more source

Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes [PDF]

, 2015
We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the ...
Falconer, Kenneth, Mattila, Pertti
core   +3 more sources

On the law of the iterated logarithm for continued fractions with sequentially restricted partial quotients

, 2021
We establish a law of the iterated logarithm (LIL) for the set of real numbers whose $n$-th partial quotient is bigger than $\alpha_n$, where $(\alpha_n)$ is a sequence such that $\sum 1/\alpha_n$ is finite. This set is shown to have Hausdorff dimension $
Stadlbauer, Manuel, Zhang, Xuan
core   +1 more source

The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping

International Journal of Mathematics and Mathematical Sciences, 2002
We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have ...
Hongwen Guo, Dihe Hu
doaj   +1 more source

Two Measures on Cantor Sets [PDF]

, 2014
We give an example of Cantor type set for which its equilibrium measure and the corresponding Hausdorff measure are mutually absolutely continuous.
Alpan, Gokalp, Goncharov, Alexander
core   +2 more sources

Geometrical properties of the space of idempotent probability measures

Applied General Topology, 2021
Although traditional and idempotent mathematics are "parallel'', by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be "parallel''.
Kholsaid Fayzullayevich Kholturayev
doaj   +1 more source

Some remarks on the Hausdorff measure of the Cantor set

SHS Web of Conferences, 2016
In this paper, the author further reveals some intrinsic properties of the Cantor set. By the properties, the author gives a new method for calculating the exact value of the Hausdorff measure of the Cantor set, and shows the facts that each covering ...
Wang Minghua
doaj   +1 more source