1,720,957 research outputs found
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
Recommended from our members
Dynamics of bi-ordered groups
Get PDFIn this work, we investigate bi-ordered groups through the lens of topology and dynamics, with a particular emphasis on the structure of their spaces of orderings. Our central objective is to study the natural Chabauty-like topology on these spaces, especially for groups formed as free products of countable ordered groups. In particular, we show that the space of orderings on such groups is homeomorphic to the Cantor set. An important tool in the analysis of left-orderable groups is the dynamical realization, which provides a canonical faithful action of a countable group on the real line by orientation-preserving homeomorphisms. To address the bi-orderable setting, we construct an alternative dynamical realization for bi-ordered groups. This construction enables us to give a new proof of Vinogradov's classical result stating that the free product of two bi-orderable groups is again bi-orderable. We further extend this dynamical framework to left-orderable groups and explore its structural properties. As another application, we study the natural action of the automorphism group of the free group on the space of its bi-orderings, and we show that, in contrast to the left-orderable case, this action does not admit any dense orbits. Lastly, we examine the space of orderings on the group of orientation-preserving homeomorphisms of the real line. We show that the standard lexicographic orderings do not form a dense subset in this space.Mathematic
Topology of the space of bi-orderings of a free group on two generators
Get PDFLet be a group. We can topologize the spaces of left-orderings
and bi-orderings of with the product topology. These spaces may or
may not have isolated points. It is known that has no isolated
points, where is a free group on two generators. In this paper we show
that has no isolated points as well
On the topology of the space of bi-orderings of a free group on two generators
No full textLet be a group. We can topologize the spaces of left-orderings
and bi-orderings of with the product topology. These spaces may or
may not have isolated points. It is known that has no isolated
points, where is a free group on generators. In this paper, we
show that has no isolated points as well.Comment: duplicate of arXiv:1812.0605
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
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
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
- …
