1,720,963 research outputs found
FONCTIONS HARMONIQUES ET SOUSHARMONIQUES ASSOCIÉES A DES SYSTÈMES DE RACINES
Get PDFIn this thesis, we show that, for any root system in the Euclidean space and for any nonnegative multiplicity function on , we can develop in this geometric framework a Newtonian type or more generally a Riesz type potential theory which coincide with the classical theories when is the zero function.Dans cette th\`{e}se, nous montrons que pour tout syst\`{e}me de racines de l'espace euclidien et pour toute fonction de multiplicit\'{e} positive sur , on peut d\'{e}velopper dans ce cadre g\'{e}om\'{e}trique une th\'{e}orie du potentiel de type newtonien et plus g\'{e}n\'{e}ralement de type Riesz qui co\"{\i}ncident avec les th\'{e}ories classiques lorsque la fonction est identiquement nulle
Green function and Poisson kernel associated to root systems for annular regions
No full textLet ∆ k be the Dunkl Laplacian relative to a fixed root system R in R d , d ≥ 2, and to a nonnegative multiplicity function k on R. Our first purpose in this paper is to solve the ∆ k-Dirichlet problem for annular regions. Secondly, we introduce and study the ∆ k-Green function of the annulus and we prove that it can be expressed by means of ∆ k-spherical harmonics. As applications, we obtain a Poisson-Jensen formula for ∆ k-subharmonic functions and we study positive continuous solutions for a ∆ k-semilinear problem
Solutions aux équations WDVV associées aux variétés de Dubrovin-Frobenius sur les espaces de Hurwitz
Get PDFDans cette thèse, nous nous intéressons aux solutions des équations d’associativité de Witten-Dijkgraaf-
Verlinde-Verlinde (WDVV) et aux structures de variétés de Frobenius sur les espaces de Hurwitz. La
théorie des variétés de Frobenius, développée par Dubrovin, offre une reformulation géométrique des
équations WDVV. En particulier, chaque variété de Frobenius M donne naissance à une solution de ces
équations, connue sous le nom de prépotentiel de M.
Nous commençons par introduire, dans les trois premiers chapitres, certaines notions préalables essentielles
à la compréhension de la thèse. Ensuite, nous démontrons une nouvelle formule qui fournit les
prépotentiels pour les structures de variétés de Frobenius sur les espaces de Hurwitz. Cette approche est
appliquée pour construire divers nouveaux exemples explicites de solutions aux équations WDVV. En
particulier, pour tout espace de Hurwitz de dimension N en genre un, avec N arbitraire, nous exprimons
explicitement le prépotentiel associé à la différentielle holomorphe normalisée en termes de polynômes de
Bell, de séries d’Eisenstein et de fonctions de Weierstrass. Comme applications, nous discutons des liens
entre les prépotentiels obtenus en petites dimensions et certaines équations différentielles particulières,
y compris l’équation de Chazy et les équations différentielles de Ramanujan
Volume mean operator and differentiation results associated to root systems
No full textLet R be a root system in R d with Coxeter-Weyl group W and let k be a non-negative multiplicity function on R. The generalized volume mean of a function f ∈ L 1 loc (R d , m k), with m k the measure given by dm k (x) := ω k (x)dx := ∏ α∈R | ⟨α, x⟩ | k(α) dx, is defined by: ∀ x ∈ R d , ∀ r > 0, M r B (f)(x) := 1 m k [B(0,r)] ∫ R d f (y)h k (r, x, y)ω k (y)dy, where h k (r, x, .) is a compactly supported nonnegative explicit measurable function depending on R and k. In this paper, we prove that for almost every x ∈ R d , lim r→0 M r B (f)(x) = f (x). MSC (2010) primary: 42B25, 42B37, 43A32; secondary: 31B05, 33C52
New formula for the prepotentials associated with Hurwitz-Frobenius manifolds and generalized WDVV equations
Get PDFWe consider the Hurwitz spaces of ramified coverings of with
prescribed ramification profile over the point at infinity. By means of a
particular symmetric bidifferential on a compact Riemann surface, we introduce
quasi-homogeneous differentials. By following Dubrovin, we construct on Hurwitz
spaces a family of Frobenius manifold structures associated with the
quasi-homogeneous differentials. We explicitly derive new generating formulas
for the corresponding prepotentials. This produces quasi-homogeneous solutions
to the following generalized WDVV associativity equations:
, where the invertible constant matrix
is a linear combination of the matrices . In particular, our approach
provides another look at Dubrovin's construction of semi-simple
Hurwitz-Frobenius manifolds and establishes an alternative practical method to
calculate their primary free energy functions. As applications, we use our
formalism to obtain various explicit quasi-homogeneous solutions to the WDVV
equations in genus zero and one and give a new proof of Ramanujan's
differential equations for Eisenstein series
WDVV solutions associated with the genus one holomorphic differential
Get PDFConsider the genus one Hurwitz space of
ramified covering of fixed degree with prescribed poles of order
, respectively. Based on a recent formula proved in
\cite{Rejeb23}, we derive an explicit solution to the WDVV equations associated
with the genus one Dubrovin-Hurwitz-Frobenius manifold structure induced by the
normalized holomorphic differential. The obtained solution is written in terms
of Bell polynomials, Eisenstein series as well as the Weierstrass functions
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
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