Search results for " Hausdorff"

Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces

2012

Abstract In this paper, we introduce the concept of a partial Hausdorff metric. We initiate study of fixed point theory for multi-valued mappings on partial metric space using the partial Hausdorff metric and prove an analogous to the well-known Nadlerʼs fixed point theorem. Moreover, we give a homotopy result as application of our main result.

Some fixed point results for multi-valued mappings in partial metric spaces

2013

Abstract In this paper, we obtain some fixed point results for multi-valued mappings in partial metric spaces. Our results unify, generalize and complement various known comparable results from the current literature. An example is also included to illustrate the main result in the paper. MSC:46S40, 47H10, 54H25.

Countably compact weakly Whyburn spaces

2015

The weak Whyburn property is a generalization of the classical sequential property that was studied by many authors. A space X is weakly Whyburn if for every non-closed set \({A \subset X}\) there is a subset \({B \subset A}\) such that \({\overline{B} \setminus A}\) is a singleton. We prove that every countably compact Urysohn space of cardinality smaller than the continuum is weakly Whyburn and show that, consistently, the Urysohn assumption is essential. We also give conditions for a (countably compact) weakly Whyburn space to be pseudoradial and construct a countably compact weakly Whyburn non-pseudoradial regular space, which solves a question asked by Angelo Bella in private communica…

Transformations by diagonal matrices in a normed space

1962

Hand Held 3D Scanning for Cultural Heritage: Experimenting Low Cost Structure Sensor Scan

2017

In the last years 3D scanning has become an important resource in many fields, in particular it has played a key role in study and preservation of Cultural Heritage. Moreover today, thanks to the miniaturization of electronic components, it has been possible produce a new category of 3D scanners, also known as handheld scanners. Handheld scanners combine a relatively low cost with the advantage of the portability. The aim of this chapter is two-fold: first, a survey about the most recent 3D handheld scanners is presented. As second, a study about the possibility to employ the handheld scanners in the field of Cultural Heritage is conducted. In this investigation, a doorway of the Benedictin…

The probability that $x$ and $y$ commute in a compact group

2010

We show that a compact group $G$ has finite conjugacy classes, i.e., is an FC-group if and only if its center $Z(G)$ is open if and only if its commutator subgroup $G'$ is finite. Let $d(G)$ denote the Haar measure of the set of all pairs $(x,y)$ in $G \times G$ for which $[x,y] = 1$; this, formally, is the probability that two randomly picked elements commute. We prove that $d(G)$ is always rational and that it is positive if and only if $G$ is an extension of an FC-group by a finite group. This entails that $G$ is abelian by finite. The proofs involve measure theory, transformation groups, Lie theory of arbitrary compact groups, and representation theory of compact groups. Examples and re…

Estimation of the elastic parameters of human liver biomechanical models by means of medical images and evolutionary computation.

2013

This paper presents a method to computationally estimate the elastic parameters of two biomechanical models proposed for the human liver. The method is aimed at avoiding the invasive measurement of its mechanical response. The chosen models are a second order Mooney–Rivlin model and an Ogden model. A novel error function, the geometric similarity function (GSF), is formulated using similarity coefficients widely applied in the field of medical imaging (Jaccard coefficient and Hausdorff coefficient). This function is used to compare two 3D images. One of them corresponds to a reference deformation carried out over a finite element (FE) mesh of a human liver from a computer tomography image, …

Area of intrinsic graphs and coarea formula in Carnot Groups

2020

AbstractWe consider submanifolds of sub-Riemannian Carnot groups with intrinsic $$C^1$$ C 1 regularity ($$C^1_H$$ C H 1 ). Our first main result is an area formula for $$C^1_H$$ C H 1 intrinsic graphs; as an application, we deduce density properties for Hausdorff measures on rectifiable sets. Our second main result is a coarea formula for slicing $$C^1_H$$ C H 1 submanifolds into level sets of a $$C^1_H$$ C H 1 function.

Convergence for varying measures in the topological case

2023

In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.

Planar Sobolev homeomorphisms and Hausdorff dimension distortion

2011

We investigate how planar Sobolev-Orlicz homeomorphisms map sets of Hausdorff dimension less than two. With the correct gauge functions the generalized Hausdorff measures of the image sets are shown to be zero.