1,720,959 research outputs found
Singular Perturbation and Homogenization Problems in Control Theory, Differential Games and fully nonlinear Partial Differential Equations
Full text linkIn this thesis we address different topics related to homogenization of first and second order fully nonlinear PDEs, essentially of Hamilton--Jacobi type, and more generally to singular perturbation in optimal control problems and differential games, in the light of the viscosity solution theory.
We take into account a singularly perturbed control systems (i.e. a system where the state variables evolve with two different time scales), both in the deterministic and in the stochastic setting, and the related first and second order Hamilton-Jacobi equations. A first part of the work is devoted to order reduction procedures: the goal of such procedures is to obtain, as the perturbation parameter tends to zero, a system where only the slow variables appear. The construction of the limit dynamics relies on the asymptotic behavior of the fast variables of the original system.
We use limiting relaxed controls, i.e. suitably defined Radon probability measures to average the fast part of the controlled dynamics. We give - both in the deterministic and in the stochastic framework - representation formulae for the effective Hamiltonian in terms of limiting relaxed controls. This allow a control interpretation of the limiting dynamics. As an application of these reduction procedures, we study the propagation of fronts moving with normal velocity depending on the position and undergoing fast oscillations.
In the second part of the work we study asymptotic controllability properties of a deterministic singularly perturbed systems and of the limit system. We prove first that, under suitable assumptions, the weak lower semilimit of Lyapunov functions of a singularly perturbed system is a lower semicontinuous Lyapunov function for the limiting system.
Furthermore, we also prove that the asymptotic controllability to the origin of the (smaller) limit system is enough to infer asymptotic controllability of the slow part of the (larger) perturbed system. More precisely, perturbing a Lyapunov pair for the limit dynamics, we construct a Lyapunov pair for the original system.
The third and last part of the thesis concerns homogenization of non-coercive Hamilton-Jacobi equations with oscillating Hamiltonian and initial data. We take into account a rather general class of Hamiltonians convex in some gradient variables and concave with respect to the others. In particular it is shown that for some of these equations homogenization does not take place, in contrast with the usual coercive case. Sufficient conditions for homogenization are provided involving the structure of the running cost and the initial data
On the Cauchy problem for a general fractional porous medium equation with variable density
No full textWe study the well-posedness of the Cauchy problem for a fractional porous medium equation with a varying density ρ>0. We establish existence of weak energy solutions; uniqueness and nonuniqueness is studied as well, according to the behavior of ρ at infinity. © 2013 Elsevier B.V. All rights reserved
Well-posedness for the cauchy problem for a fractional porous medium equation with variable density in one space dimension
No full textWe study the existence and uniqueness of the bounded solutions to a fractional nonlinear porous medium equation with a variable density in a one space dimension
On a fractional sublinear elliptic equation with a variable coefficient
No full textWe study the existence and uniqueness of bounded weak solutions to a fractional sublinear elliptic equation with a variable coefficient, in the whole space. Existence is investigated in connection to a certain fractional linear equation, whereas the proof of uniqueness relies on uniqueness of weak solutions to an associated fractional porous medium equation with variable density
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
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