1,720,968 research outputs found
Pairings between bounded divergence-measure vector fields and BV functions
Full text linkWe introduce a family of pairings between a bounded divergence-measure vector field and a function u of bounded variation, depending on the choice of the pointwise representative of u. We prove that these pairings inherit from the standard one, introduced in [G. Anzellotti, Pairings between measures and bounded functions and compensated compactness, Ann. Mat. Pura Appl. (4) 135 1983, 293-318], [G.-Q. Chen and H. Frid, Divergence-measure fields and hyperbolic conservation laws, Arch. Ration. Mech. Anal. 147 1999, 2, 89-118], all the main properties and features (e.g. coarea, Leibniz, and Gauss-Green formulas). We also characterize the pairings making the corresponding functionals semicontinuous with respect to the strict convergence in BV. We remark that the standard pairing in general does not share this property
A new model for suspension bridges involving the convexification of the cables
Full text linkThe final purpose of this paper is to show that, by inserting a convexity constraint on the cables of a suspension bridge, the torsional instability of the deck appears at lower energy thresholds. Since this constraint is suggested by the behavior of real cables, this model appears more reliable than the classical ones. Moreover, it has the advantage to reduce to two the number of degrees of freedom, avoiding to introduce the slackening mechanism of the hangers. The drawback is that the resulting energy functional is extremely complicated, involving the convexification of unknown functions. This paper is divided in two main parts. The first part is devoted to the study of these functionals, through classical methods of calculus of variations. The second part applies this study to the suspension bridge model with convexified cables
Bernoulli Free Boundary Problem for the Infinity Laplacian
Full text linkWe study the interior Bernoulli free boundary problem for the infinity Laplacian. Our results cover the existence, uniqueness, and characterization of solutions (above a threshold representing the ``infinity Bernoulli constant""), their regularity, and their relationship with the solutions to the interior Bernoulli problem for the p-Laplacian
On a geometric combination of functions related to Prekopa-Leindler inequality
Full text linkWe introduce a new operation between nonnegative integrable functions on Rn\mathbb {R}<^>n, that we call geometric combination; it is obtained via a mass transportation approach, playing with inverse distribution functions. The main feature of this operation is that the Lebesgue integral of the geometric combination equals the geometric mean of the two separate integrals; as a natural consequence, we derive a new functional inequality of Prekopa-Leindler type. When applied to the characteristic functions of two measurable sets, their geometric combination provides a set whose volume equals the geometric mean of the two separate volumes. In the framework of convex bodies, by comparing the geometric combination with the 0-sum, we get an alternative proof of the log-Brunn-Minkowski inequality for unconditional convex bodies and for convex bodies with n symmetries
The Brunn–Minkowski inequality for the principal eigenvalue of fully nonlinear homogeneous elliptic operators
Full text linkWe prove that the principal eigenvalue of any fully nonlinear homogeneous elliptic operator which fulfills a very simple convexity assumption satisfies a Brunn-Minkowski type inequality on the class of open bounded sets in satisfying a uniform exterior sphere condition. In particular the result applies to the (possibly normalized) p-Laplacian, and to the minimal Pucci operator. The proof is inspired by the approach introduced by Colesanti for the principal frequency of the Laplacian within the class of convex domains, and relies on a generalization of the convex envelope method by Alvarez-Lasry-Lions. We also deal with the existence and log-concavity of positive viscosity eigenfunctions
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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