1,720,971 research outputs found
On the discrepancy of some generalized Kakutani's sequences of partitions
Full text linkIn this paper we study a class of generalized Kakutani’s sequences of
partitions of [0,1], constructed by using the technique of successive refinements.
Our main focus is to derive bounds for the discrepancy of these sequences. The
approach that we use is based on a tree representation of the sequence of partitions
which is precisely the parsing tree generated by Khodak’s coding algorithm.
With the help of this technique we derive (partly up to a logarithmic factor)
optimal upper bound in the so-called rational case. The upper bounds in the irrational
case that we obtain are weaker, since they heavily depend on Diophantine
approximation properties of a certain irrational number. Finally, we present an
application of these results to a class of fractals
Uniform distribution on fractals
Full text linkIn this paper we introduce a general algorithm to produce u.d.
sequences of partitions and of points on fractals generated by an IFS consisting
of similarities which have the same ratio and which satisfy the open set condition
(OSC). Moreover we provide an estimate for the elementary discrepancy of van
der Corput type sequences constructed on this class of fractals
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The full infinite dimensional moment problem on semi-algebraic sets of generalized functions
Full text linkWe consider a generic basic semi-algebraic subset S of the space of generalized functions, that is a set given by (not necessarily countably many) polynomial constraints. We derive necessary and sufficient conditions for an infinite sequence of generalized functions to be realizable on S, namely to be the moment sequence of a finite measure concentrated on S. Our approach combines the classical results about the moment problem on nuclear spaces with the techniques recently developed to treat the moment problem on basic semi-algebraic sets of Rd. In this way, we determine realizability conditions that can be more easily verified than the well-known Haviland type conditions. Our result completely characterizes the support of the realizing measure in terms of its moments. As concrete examples of semi-algebraic sets of generalized functions, we consider the set of all Radon measures and the set of all the measures having bounded Radon–Nikodym density w.r.t. the Lebesgue measure
An intrinsic characterization of moment functionals in the compact case
Full text linkWe consider the class of all linear functionals on a unital commutative real algebra that can be represented as an integral w.r.t. to a Radon measure with compact support in the character space of . Exploiting a recent generalization of the classical Nussbaum theorem, we establish a new characterization of this class of moment functionals solely in terms of a growth condition intrinsic to the given linear functional. To the best of our knowledge, our result is the first to exactly identify the compact support of the representing Radon measure. We also describe the compact support in terms of the largest Archimedean quadratic module on which is non-negative and in terms of the smallest submultiplicative seminorm w.r.t. which is continuous. Moreover, we derive a formula for computing the measure of each singleton in the compact support, which in turn gives a necessary and sufficient condition for the support to be a finite set. Finally, some aspects related to our growth condition for topological algebras are also investigated.14 page
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
The Truncated Moment Problem for Unital Commutative R-Algebras
Full text linkWe investigate when a linear functional defined on a linear subspace
of a unital commutative real algebra admits an integral representation
w.r.t. a positive Radon measure supported on a closed subset of the
character space of . We provide a criterion for the existence of such a
representation for when is equipped with a submultiplicative seminorm.
We then build on this result to prove our main theorem for not necessarily
equipped with a topology. This allows us to extend well-known classical results
on truncated moment problems.Comment: 31 pages, 9 figures, minor corrections to the published version to
improve readabilit
Variations on the Author
Full text link“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
Full text linkWe 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
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Translation invariant realizability problem on the d-dimensional lattice: an explicit construction
Full text linkWe consider a particular instance of the truncated realizability problem on the d−dimensional lattice. Namely, given two functions ρ1(i) and ρ2(i,j) non-negative and symmetric on Zd, we ask whether they are the first two correlation functions of a translation invariant point process. We provide an explicit construction of such a realizing process for any d ≥ 2 when the radial distribution has a specific form. We also derive from this construction a lower bound for the maximal realizable density and compare it with the already known lower bounds
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