Search results for " Topology"

Mappings of finite distortion : size of the branch set

2018

Abstract We study the branch set of a mapping between subsets of ℝ n {\mathbb{R}^{n}} , i.e., the set where a given mapping is not defining a local homeomorphism. We construct several sharp examples showing that the branch set or its image can have positive measure.

Extended Natural Numbers and Counters

2020

Summary This article introduces extended natural numbers, i.e. the set ℕ ∪ {+∞}, in Mizar [4], [3] and formalizes a way to list a cardinal numbers of cardinals. Both concepts have applications in graph theory.

Fixed point theorems on ordered metric spaces and applications to nonlinear elastic beam equations

2012

In this paper, we establish certain fixed point theorems in metric spaces with a partial ordering. Presented theorems extend and generalize several existing results in the literature. As application, we use the fixed point theorems obtained in this paper to study existence and uniqueness of solutions for fourth-order two-point boundary value problems for elastic beam equations.

Visible parts and dimensions

2003

We study the visible parts of subsets of n-dimensional Euclidean space: a point a of a compact set A is visible from an affine subspace K of n, if the line segment joining PK(a) to a only intersects A at a (here PK denotes projection onto K). The set of all such points visible from a given subspace K is called the visible part of A from K. We prove that if the Hausdorff dimension of a compact set is at most n−1, then the Hausdorff dimension of a visible part is almost surely equal to the Hausdorff dimension of the set. On the other hand, provided that the set has Hausdorff dimension larger than n−1, we have the almost sure lower bound n−1 for the Hausdorff dimensions of visible parts. We al…

Fixed point results for Gm-Meir-Keeler contractive and G-(α,ψ)-Meir-Keeler contractive mappings

Reduced complexity models in the identification of dynamical networks: Links with sparsification problems

2009

In many applicative scenarios it is important to derive information about the topology and the internal connections of more dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology. We cast the problem as the optimization of a cost function operating a trade-off between accuracy and complexity in the final model. We address the problem of reducing the complexity by fixing a certain degree of sparsity, and trying to find the solution that “better” satisfi…

Gas-liquid chromatographic analyses

1983

Abstract The gas chromatography of mixtures of n -alkyl acetates (CH 3 COOR, R = C 1 —C 8 ) and methyl esters of aliphatic n -carboxylic acids (R′COOCH 3 , R′ = C 1 —C 8 ) and certain of their monochlorinated derivatives has been studied on Carbowax 20M and SE-30 glass capillary columns under the same operating conditions. The separation of the isomeric monochlorinated esters was complete on Carbowax 20M, whereas on SE-30 the peaks of 6- and 7-chlorooctyl acetates and methyl (ω − 1)- and (ω − 2)-chlorooctanoates and -nonanoates partly overlapped. The complete separation of the mixtures could not be achieved, however, on Carbowax 20M, in spite of the use of various operating conditions. The …

Proton coordination by polyamine compounds in aqueous solution

1999

Abstract The present article is concerned with proton transfer reactions in aqueous solution of open-chain, macrocyclic and macropolycyclic or cage compounds having nitrogen atoms as protonation sites in the molecular framework, although several compounds with additional different donors will be considered. The main purpose of this review is to collect some significant examples of proton transfer processes in order to show how the electronic properties and molecular topology of polyamines affect the thermodynamic parameters of their protonation equilibria.

Pseudo-path connected homogeneous continua

2015

Abstract The main result of this paper states that every homogeneous pseudo-path connected continuum is weakly chainable, or equivalently, every homogeneous continuum connected by continuous images of the pseudo-arc is itself a continuous image of the pseudo-arc. We notice that even though there exist homogeneous path connected continua that are not continuous images of an arc (Prajs, 2002), they all are continuous images of the pseudo-arc.

Continuous images of arcs: Extensions of Cornette's Theorem

2015

In [J.L. Cornette “Image of a Hausdorff arc” is cyclically extensible and reducible Trans. Am. Math. Soc., 199 (1974), pp. 253–267], Cornette proved that a locally connected Hausdorff continuum X is the continuous image of an arc if and only if each of its cyclic elements is the continuous image of an arc. Cyclic elements form a closed null cover of X by retracts of X. We generalize Cornette's result to closed null covers of X with a dendritic structure. We give examples to show that some of our conditions are necessary and we pose some open questions.