1,720,975 research outputs found
Relative Pfaffian closure for Definably Complete Baire Structures
Full text linkSpeissegger proved that the Pfaffian closure of an o-
minimal expansion of the real field is o-minimal. Here we give a
first order version of this result: having introduced the notion of
definably complete Baire structure, we define the relative Pfaf-
fian closure of an o-minimal structure inside a definably complete
Baire structure, and we prove its o-minimality. We derive effec-
tive bounds on some topological invariants of sets definable in
the Pfaffian closure of an o-minimal expansion of the real field
On the decidability of the real field with a generic power function
No full textWe show that the theory of the real field with a generic real power function is decidable,
relative to an oracle for the rational cut of the exponent of the power function. We also show the existence
of generic computable real numbers, hence providing an example of a decidable o-minimal proper expansion
of the real field by an analytic function
Theorems of the Complement
No full textThis is an expository paper on a Theorem of the Complement, due to
Wilkie, and its generalisations. Wilkie (Sel Math (NS) 5:397–421, 1999) gave
necessary and sufficient conditions for an expansion of the real field by C-infinity
functions to be o-minimal. Karpinski and Macintyre (Sel Math (NS) 5:507–516,
1999) weakened the original smoothness hypotheses of Wilkie’s theorem. Here
we exhibit the proof of a generalised Wilkie’s result, where we further weaken
the smoothness assumptions and show that the proof can be carried out not only
over the real numbers but more generally in a non-Archimedean context, i.e. for
definably complete Baire structures, which we introduced in 2008 and which form
an axiomatizable class. Furthermore we give necessary and sufficient conditions
for a definably complete Baire expansion of an o-minimal structure by C-infinity
functions to be o-minimal
An effective version of Wilkie's theorem of the complement and some effective o-minimality results
No full textWilkie (Selecta Math. (N.S.) 5 (1999) 397) proved a “theorem of the complement” which implies that in order to establish the o-minimality of an expansion of R with C ∞ functions it suffices to obtain uniform (in the parameters) bounds on the number of connected components of quantifier free definable sets. He deduced that any expansion of R with a family of Pfaffian functions is o-minimal. We prove an effective version of Wilkie’s theorem of the complement, so in particular given an expansion of the ordered field R with finitely many C^∞ functions, if there are uniform and computable upper bounds on the number of connected components of quantifier free definable sets, then there are uniform and computable bounds for all definable sets. In such a case the theory of the structure is effectively o-minimal: there is a recursively axiomatized subtheory such that each of its models is o-minimal. This implies the effective o-minimality of any expansion of R with Pfaffian functions. We apply our results to the open problem of the decidability of the theory of the real ÿeld with the exponential function. We show that the decidability is implied by a positive answer to the following problem (raised by van den Dries (in: Logic: From Foundations to applications, Oxford Science Publ., Oxford University Press, New York, 1996, p. 137)): given a language L expanding the language of ordered rings, if an L-sentence is true in every L-structure expanding the ordered field of real numbers, then it is true in every o-minimal L-structure expanding any real closed field
Definably Complete Baire Structures
No full textWe consider definably complete Baire expansions of ordered
fields: every definable subset of the domain of the structure has a
supremum and the domain can not be written as the union of a definable
increasing family of nowhere dense sets. Every expansion
of the real field is definably complete and Baire, and so is every
o-minimal expansion of a field. Moreover, unlike the o-minimal
case, the structures considered form an axiomatizable class. In
this context we prove the following version of Wilkie’s Theorem
of the Complement: given a definably complete Baire expansion
K of an ordered field with a family of smooth functions, if there
are uniform bounds on the number of definably connected components
of quantifier free definable sets, then K is o-minimal. We
further generalize the above result, along the line of Speissegger’s
theorem, and prove the o-minimality of the relative Pfaffian closure
of an o-minimal structure inside a definably complete Baire
structure
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
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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