1,720,976 research outputs found
Orientation preserving approximation
No full textIn this work we study the following problem on constrained approximation.
Let f be a continuous mapping defined on a bounded domain with piecewise smooth boundary in R^n and taking values in R^n. What are necessary and sufficient conditions for f to be uniformly approximable by C^1-smooth mappings with nonnegative Jacobian?
When the dimension is equal to one, this is just approximation by monotone smooth functions. Hence, the necessary and sufficient condition is: the function is monotone. On the other hand, for higher dimensions the description is not as clear. We give a simple necessary condition in terms of the topological degree of continuous mapping. We also give some sufficient conditions for dimension 2. It also turns out that if the dimension is greater than one, then there exist real-analytic mappings with nonnegative Jacobian that cannot be approximated by smooth mappings with positive Jacobian.
In our study of the above mentioned question we use topological degree theory, Schoenflies-type extension theorems, and Stoilow's topological characterization of complex analytic functions.October 201
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Polynomial approximation in weighted spaces
No full textOne of the most important problems in Approximation Theory is to connect the rate with which a function can be approximated and the smoothness of this function. The goal is to show direct and inverse estimates in terms of some measure of smoothness.
Typically, results are of the following type: ``a function can be approximated with a given order if and only if it belongs to a certain smoothness class".
We focus on the case of the weighted spaces with not rapidly changing bounded not vanishing inside interval weights. In order to describe
certain smoothness classes we will use moduli of smoothness and and prove their equivalence.
As a final result, we will prove direct theorems for monotone and convex approximation.October 201
Properties of extremal convex bodies
No full textIn 1948 Besicovitch proved that an affine image of a regular hexagon may be inscribed into an arbitrary planar convex body. We prove Besicovitch's result using a variational approach based on special approximation by triangles and generalize the Besicovitch theorem to a certain new class of hexagons.
We survey the results on the Banach-Mazur distance between different classes of convex bodies. We hope that our generalization of the Besicovitch theorem may become useful for estimation of the Banach-Mazur distance between planar convex bodies. We examined our special approximation by triangles in some specific cases, and it showed a noticeable improvement in comparison with known general methods.
We also consider the Banach-Mazur distance between a simplex and an arbitrary convex body in the three-dimensional case. Using the idea of an inscribed simplex of maximal volume, we obtain a certain related algebraic optimization problem that provides an upper estimate.October 201
Boundedly pseudo-amenable and boundedly pseudo-contractible Banach algebras
No full textIn this thesis we will study the notions of bounded pseudo-amenability and bounded pseudo-contractibility for a Banach algebra, where we require a Banach algebra to possess a multiplier bounded approximate diagonal or a multiplier bounded central approximate diagonal. We will investigate various properties of these types of Banach algebras, including: l^p-direct sums, relationships to unitizations, hereditary properties on ideal and quotient subalgebras, connections to other generalized notions of amenability, and projective tensor products of these Banach algebras. We will also provide some examples of boundedly pseudo-amenable and boundedly pseudo-contractible Banach algebras.May 202
On positive linear operators
No full textApproximation theory received much attention in the last century, and an intriguing area in this field is positive linear operators. This thesis is a literature survey on positive linear operators.
We discuss some of the well-known examples of positive linear operators. Preserving -monotonicity by positive linear operators is another interesting topic in this area. We are interested if is -monotone whenever function is -monotone. For a sequence of positive linear operators , it is a natural question if this sequence converges to and how fast is this convergence. We study the saturation of these operators. Usually, there is a relation between the rate of convergence and the smoothness of the function being approximated. If increasing smoothness of functions does not result in the increase of the degree of approximation, this phenomenon is called saturation. We discuss iteration of general positive linear operators and give numerical examples.February 201
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
On Hadwiger covering problem in five- and six-dimensional Euclidean spaces
No full textWe denote by the minimum number such that any convex body in can be covered by of its smaller homothets. Considering an -dimensional cube, one can easily see that . It is a well-known conjecture that for all . The main result of this thesis is the inequalities and . The previously known upper bounds were and . Specifically, we apply certain generalizations of an approach by Papadoperakis, which essentially reduces the problem to the study of covering of -dimensional faces of an -dimensional cube by parallelepipeds of a particular form. A step in the construction of the required covering uses computer assistance. We also study limitations of this technique and establish some lower bounds on performance of this method.May 202
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