Search results for "102"
showing 10 items of 2892 documents
PIP-Space Valued Reproducing Pairs of Measurable Functions
2019
We analyze the notion of reproducing pairs of weakly measurable functions, a generalization of continuous frames. The aim is to represent elements of an abstract space Y as superpositions of weakly measurable functions belonging to a space Z : = Z ( X , μ ), where ( X , μ ) is a measure space. Three cases are envisaged, with increasing generality: (i) Y and Z are both Hilbert spaces; (ii) Y is a Hilbert space, but Z is a pip-space; (iii) Y and Z are both pip-spaces. It is shown, in particular, that the requirement that a pair of measurable functions be reproducing strongly constrains the structure of the initial space Y. Examples are presented for each case.
On the representation of integers by indefinite binary Hermitian forms
2011
Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most s by f, as s tends to infinity.
Derivatives not first return integrable on a fractal set
2018
We extend to s-dimensional fractal sets the notion of first return integral (Definition 5) and we prove that there are s-derivatives not s-first return integrable.
Assouad dimension, Nagata dimension, and uniformly close metric tangents
2013
We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the dimensions of its metric tangents. Having uniformly close tangents is not sufficient. What is needed in addition is either that the tangents have dimension with uniform constants independent from the point and the tangent, or that the tangents are unique. We will apply our results to equiregular subRiemannian manifolds and show that locally their Nagata dimension equals the to…
Isometrically Homogeneous and Topologically Homogeneous Continua
2016
Based on the past study of homogeneous continua, this paper concludes that compact connected metric topological groups and isometrically homogeneous continua fall into the following three mutually disjoint classes: (1) indecomposable; (2) aposyndetic and semi-indecomposable; (3) mutually aposyndetic. Among all continua these are special classes with members having extremal properties. Indecomposable isometrically homogeneous continua are characterized as solenoids, and one-dimensional isometrically homogeneous continua are characterized as solenoids or circles. It is shown that path connected isometrically homogeneous continua are locally connected.
Mollusk carbonate thermal behaviour and its implications in understanding prehistoric fire events in shell middens
2018
Abstract Archaeological shell middens are particularly important for reconstructing prehistoric human subsistence strategies. However, very little is known about shellfish processing, especially when related to the use of fire for dietary and disposal purposes. To shed light on prehistoric food processing techniques, an experimental study was undertaken on modern gastropod shells (Phorcus lineatus). The shells were exposed to high temperatures (200–700 °C) to investigate subsequent mineralogy and macro- and microstructural changes. Afterwards, the three-pronged approach was applied to archaeological shells from Haua Fteah cave, Libya (Phorcus turbinatus) and from shell midden sites in the U…
Trace Operators on Regular Trees
2020
Abstract We consider different notions of boundary traces for functions in Sobolev spaces defined on regular trees and show that the almost everywhere existence of these traces is independent of the chosen definition of a trace.
On shortening u-cycles and u-words for permutations
2017
Abstract This paper initiates the study of shortening universal cycles (u-cycles) and universal words (u-words) for permutations either by using incomparable elements, or by using non-deterministic symbols. The latter approach is similar in nature to the recent relevant studies for the de Bruijn sequences. A particular result we obtain in this paper is that u-words for n -permutations exist of lengths n ! + ( 1 − k ) ( n − 1 ) for k = 0 , 1 , … , ( n − 2 ) ! .
Gray coding cubic planar maps
2016
International audience; The idea of (combinatorial) Gray codes is to list objects in question in such a way that two successive objects differ in some pre-specified small way. In this paper, we utilize beta-description trees to cyclicly Gray code three classes of cubic planar maps, namely, bicubic planar maps, 3-connected cubic planar maps, and cubic non-separable planar maps. (C) 2015 Elsevier B.V. All rights reserved.
The era of reference genomes in conservation genomics
2022
Progress in genome sequencing now enables the large-scale generation of reference genomes. Various international initiatives aim to generate reference genomes representing global biodiversity. These genomes provide unique insights into genomic diversity and architecture, thereby enabling comprehensive analyses of population and functional genomics, and are expected to revolutionize conservation genomics.