1,720,980 research outputs found
Structure of Riemann solvers on networks (preliminary version 2)
No full textInternational audienceIn this paper we consider scalar Riemann solvers on networks, associated to scalar conservation laws. A junction is a particular network which is a finite set of half lines glued together at the origin. Riemann solvers solve uniquely the Riemann problem on the junction. We also assume that Riemann solutions are stable by passage to the limit.In part I of the paper, we only address fundamental questions concerning Riemann problems on junctions. We show a characterization of Riemann solvers either by their set of stationary solutions (the germ), or equivalently by their Godunov flux at the junction. Moreover, we show that the gluing of two junctions with Riemann solvers is well defined and leads to a new junction with a new Riemann solver. Because our theory is quite general, it encompasses in particular Kruzkov germs, Hamilton-Jacobi germs, monotone germs, conservative and non-conservative germs.In part II of the paper, we give an existence and uniqueness theory for conservation laws on networks in the special case where Riemann solvers are associated to Kruzkov germs
Strictly convex Hamilton-Jacobi equations: strong trace of the gradient
No full textWe consider Lipschitz continuous solutions to evolutive Hamilton-Jacobi equations. Under a condition of strict convexity of the Hamiltonian, we show that there exists a notion of strong trace of the gradient of the solution. This result is based on a Liouville-type result of classification of global solutions on the half space. Under zero Dirichlet boundary condition, we show that the solution only depends on the normal variable. As a consequence, we show that the existence of a pointwise tangential gradient implies existence of a pointwise normal gradient. For the Liouville-type result, and when the Hamiltonian is not convex, we give a counterexample with a solution which is not one-dimensional. We give two applications. On the one hand, for the classical stationary Dirichlet problem on a bounded domain, we show the existence of a closed subset of the boundary of the domain, where Taylor expansion of the solution is uniform. On the other hand, for Hamilton-Jacobi equations on a network, we show that the space derivative of the solution has a trace at each node, which satisfies a natural germ condition
Strictly convex Hamilton-Jacobi equations: strong trace of the derivatives in codimension ≥ 2
No full textWe consider Lipschitz continuous viscosity solutions to an evolutive Hamilton-Jacobi equation. The equation arises outside a closed set Γ. Under a condition of strict convexity of the Hamiltonian, we show that there exists a notion of strong trace of the derivatives of the solution on the Lipschitz boundary Γ of codimension d ≥ 2. The very special case d = 1 is done in a separated work. This result is based on a Liouville-type result of classification of global solutions with zero Dirichlet condition on the boundary Γ, where Γ is an affine subspace. We show in particular that such solutions only depend on the normal variable to Γ. As a consequence, we show more generally that the existence of a pointwise tangential gradient along Γ implies the existence of pointwise directional derivatives in all directions. This result also holds true for Hamiltonians depending on the time-space variables, under an additional Dini condition involving certain moduli of continuity. We also give a counterexample for d = 2 in the stationary case, where the Hamiltonian is only continuous in the space variable, and where the solution has no directional derivatives in any directions normal to Γ. Such phenomenon does not hold for d = 1
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
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe 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
Beyond uniqueness: Relaxation calculus of junction conditions for coercive Hamilton-Jacobi equations
No full textInternational audienceA junction is a particular network given by the collection of half lines glued together at the origin. On such a junction, we consider evolutive Hamilton-Jacobi equations with coercive Hamiltonians. Furthermore,we consider a general desired junction condition at the origin, given by some monotone function .There is existence and uniqueness of solutions which only satisfy weakly the junction condition (at the origin, they satisfy either the desired junction condition or the PDE).We show that those solutions satisfy strongly a relaxed junction condition (that we can recognize as an effective junction condition). It is remarkable that this relaxed condition can be computed in three different but equivalent ways: 1) using viscosity inequalities, 2) using Godunov fluxes, 3) using Riemann problems.Our result goes beyond uniqueness theory, in the following sense: solutions to two different desired junction conditions and do coincide if
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