1,720,977 research outputs found
A motivic zeta function to study real singularities
No full textNous nous intéressons à l'étude des singularités réelles à l'aide d'arguments provenant de l'intégration motivique. Une telle démarche a été initiée par S. Koike et A. Parusiński puis poursuivie par G. Fichou. Afin de donner une classification des singularités réelles, T.-C. Kuo a défini la notion d'équivalence blow-analytique. Il s'agit d'une relation d'équivalence pour les germes analytiques réels n'admettant pas de module continu pour les singularités isolées. Cette notion est étroitement liée à la notion d'applications analytiques par arcs définie par K. Kurdyka. Il est donc naturel d'adapter des arguments provenant de l'intégration motivique pour l'étude de l'équivalence blow-analytique. La difficulté réside désormais dans le fait de trouver des méthodes permettant de montrer que deux germes sont équivalents et de construire des invariants permettant de distinguer deux germes qui ne sont pas dans la même classe. Nous travaillons avec une variante plus algébrique de cette notion, l'équivalence blow-Nash introduite par G. Fichou. La première partie de la thèse consiste en un théorème d'inversion donnant des conditions pour que l'inverse d'un homéomorphisme blow-Nash soit encore blow-Nash. L'intérêt d'un tel énoncé est que de telles applications apparaissent dans la définition de l'équivalence blow-Nash. La seconde partie est consacrée à l'étude d'une nouvelle fonction zêta motivique. Il s'agit d'associer à un germe analytique une série formelle. Cette fonction zêta motivique généralise les fonctions zêta de Koike-Parusiński et de Fichou et admet une formule de convolution. Il s'agit d'un invariant pour l'équivalence blow-Nash.The main purpose of this thesis is to study real singularities using arguments from motivic integration as initiated by S. Koike and A. Parusiński and then continued by G. Fichou. In order to classify real singularities, T.-C. Kuo introduced the blow-analytic equivalence which is an equivalence relation on real analytic germs without moduli for isolated singularities. This notion is closely related to the notion of arc-analytic maps introduced by K. Kurdyka, thus it is natural to adapt arguments from motivic integration to the study of the relation. The difficulty lies in finding efficient ways to prove that two germs are equivalent and in constructing invariants that distinguish germs which are not in the same class. We focus on the blow-Nash equivalence, a more algebraic notion which was introduced by G. Fichou. The first part of this thesis consists in an inverse theorem for blow-Nash maps. Under certain assumptions, this ensures that the inverse of a homeomorphism which is blow-Nash is also blow-Nash. Such maps are involved in the definition of the blow-Nash equivalence. In the second part, we associate a power series to an analytic germ, called the zeta function of the germ. This construction generalizes the zeta functions of Koike-Parusiński and Fichou. Furthermore, it admits a convolution formula while being an invariant for the blow-Nash equivalence
Product structures on the weight filtration of real algebraic varieties
No full textOn associe à chaque variété algébrique définie sur R un complexe de cochaînes filtré, qui calcule la cohomologie à supports compacts et coefficients dans Z_2 de ses points réels. Ce complexe filtré est additif pour les inclusions fermées et acyclique pour la résolution des singularités, et est unique à quasi-isomorphisme filtré près. Il est représenté par la filtration duale de la filtration géométrique sur les chaînes semi-algébriques à supports fermés définie par McCrory and Parusiński, et induit une suite spectrale qui calcule la filtration par le poids sur la cohomologie à supports compacts. Cette suite spectrale est un invariant naturel qui contient les nombres de Betti virtuels. On montre que le produit cartésien de deux variétés nous permet de comparer le produit de leurs complexe de poids et suite spectrale respectifs avec ceux du produit, et on prouve que les produits cap et cup en cohomologie et homologie sont filtrés par rapport à ces filtrations par le poids réelles.We associate to each algebraic variety defined over R a filtered cochain complex, which computes the cohomology with compact supports and Z_2-coefficients of the set of its real points. This filtered complex is additive for closed inclusions and acyclic for resolution of singularities, and is unique up to filtered quasi-isomorphism. It is represented by the dual filtration of the geometric filtration on semialgebraic chains with closed supports defined by McCrory and Parusiński, and leads to a spectral sequence which computes the weight filtration on cohomology with compact supports. This spectral sequence is a natural invariant which contains the additive virtual Betti numbers. We then show that the cross product of two varieties allows us to compare the product of their respective weight complexes and spectral sequences with those of their product, and prove that the cup and cap products in cohomology and homology are filtered with respect to the real weight filtrations
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
A note on singularities at infinity of complex polynomials
No full textLet f be a complex polynomial. We relate the behaviour of f "at infinity" to the sheaf of vanishing cycles of the family of projective closures of fibres of f. We show that the absence of such cycles: (i) is equivalent to a condition on the asymptotic behaviour of gradient of f known as Malgrange's Condition, (ii) implies the -triviality of f. If the support of sheaf of vanishing cycles of is a finite set, then it detects precisely the change of the topology of the fibres of f. Moreover, in this case, the generic fibre of f has the homotopy type of a bouquet of spheres
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