Search results for " spaces"
showing 10 items of 360 documents
Geometric Properties of Planar BV -Extension Domains
2009
We investigate geometric properties of those planar domains that are extension for functions with bounded variation.We start from a characterization of such domains given by Burago–Maz'ya and prove that a bounded, simply connected domain is a BV -extension domain if and only if its com- plement is quasiconvex. We further prove that the extension property is a bi-Lipschitz invariant and give applications to Sobolev extension domains.
Enumeration of L-convex polyominoes by rows and columns
2005
In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.
Caristi Type Selections of Multivalued Mappings
2015
Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems.
(p,q)-summing sequences
2002
Abstract A sequence (x j ) in a Banach space X is (p,q) -summing if for any weakly q -summable sequence (x j ∗ ) in the dual space we get a p -summable sequence of scalars (x j ∗ (x j )) . We consider the spaces formed by these sequences, relating them to the theory of (p,q) -summing operators. We give a characterization of the case p=1 in terms of integral operators, and show how these spaces are relevant for a general question on Banach spaces and their duals, in connection with Grothendieck theorem.
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…
On the continuity of discrete maximal operators in Sobolev spaces
2014
We investigate the continuity of discrete maximal operators in Sobolev space W 1;p (R n ). A counterexample is given as well as it is shown that the continuity follows under certain sucient assumptions. Especially, our research verifies that for the continuity in Sobolev spaces the role of the partition of the unity used in the construction of the maximal operator is very delicate.
Countable connected spaces and bunches of arcs in R3
2006
Abstract We investigate the images (also called quotients) of countable connected bunches of arcs in R 3 , obtained by shrinking the arcs to points (see Section 2 for definitions of new terms). First, we give an intrinsic description of such images among T 1 -spaces: they are precisely countable and weakly first countable spaces. Moreover, an image is first countable if and only if it can be represented as a quotient of another bunch with its projection hereditarily quotient (Theorem 2.7). Applying this result we see, for instance, that two classical countable connected T 2 -spaces—the Bing space [R.H. Bing, A connected countable Hausdorff space, Proc. Amer. Math. Soc. 4 (1953) 474], and th…
On Weakly Locally Uniformly Rotund Banach Spaces
1999
Abstract We show that every normed space E with a weakly locally uniformly rotund norm has an equivalent locally uniformly rotund norm. After obtaining a σ -discrete network of the unit sphere S E for the weak topology we deduce that the space E must have a countable cover by sets of small local diameter, which in turn implies the renorming conclusion. This solves a question posed by Deville, Godefroy, Haydon, and Zizler. For a weakly uniformly rotund norm we prove that the unit sphere is always metrizable for the weak topology despite the fact that it may not have the Kadec property. Moreover, Banach spaces having a countable cover by sets of small local diameter coincide with the descript…
The influence of agriculture on the structural economic vulnerability of small island spaces: Assessment using DEA based composite indicators
2020
Small island spaces are confronted with significant disadvantages that ultimately result in strong economic vulnerability. The conventional literature emphasizes the main role of agriculture in generating structural vulnerability. Specifically, the higher the weight of agriculture compared to other sectors is, the more structurally vulnerable an economy is. However, the recent food crises revealed that the economic dependence on agriculture is not a problem on its own, but the issue is rather the efficiency of this sector along with the orientation of domestic production towards diversification and food self-sufficiency. In this paper, we thus propose a new structural economic vulnerability…
Narrativas visuales de la Facultad de Magisterio mediadas por teléfonos móviles. Una mirada pedagógica y artística a la Investigación Basada en las A…
2020
[EN] This work focuses on the visual narratives generated from images captured by art education students, as a result of projects developed in the Teaching classrooms during different academic years. In them intervenes, at first, the gaze of the students as visual producers through portable devices, mainly mobile phones, in educational environments between 2011 and 2017. The images were captured at different chronological moments and materialized on the university campuses of Ontinyent and Dels Tarongers, from the Faculty of Education. The work theoretically approximates the method of Research Based on the Arts. The images produced by the students are composed by the author and researcher t…