1,720,981 research outputs found
Existence and uniqueness for the transport of currents by Lipschitz vector fields
No full textThis work establishes the existence and uniqueness of solutions to the initial-value problem for the geometric transport equationddtTt+LbTt=0 in the class of k-dimensional integral or normal currents Tt (t being the time variable) under the natural assumption of Lipschitz regularity of the driving vector field b. Our argument relies crucially on the notion of decomposability bundle introduced recently by Alberti and Marchese. In the particular case of 0-currents, this also yields a new proof of the uniqueness for the continuity equation in the class of signed measures
Characterization of generalized young measures generated by symmetric gradients
Full text linkThis work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer–Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The “local” proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti’s rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences
On the two-state problem for general differential operators
Full text linkIn this note we generalize the Ball-James rigidity theorem for gradient differential inclusions to the setting of a general linear differential constraint. In particular, we prove the rigidity for approximate solutions to the two-state inclusion with incompatible states for merely -bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting
Higher integrability for measures satisfying a PDE constraint
Full text linkWe establish higher integrability estimates for constant-coefficient systems of linear PDEs \Acal \mu = \sigma, where \mu \in \Mcal(\Omega;V) and \sigma\in \Mcal(\Omega;W) are vector measures and the polar \frac{\di \mu}{\di |\mu|} is uniformly close to a convex cone of intersecting the wave cone of \Acal only at the origin. More precisely, we prove local compensated compactness estimates of the form
\|\mu\|_{\Lrm^p(\Omega')} \lesssim |\mu|(\Omega) + |\sigma|(\Omega), \qquad \Omega' \Subset \Omega.
Here, the exponent belongs to the (optimal) range 1 \leq p < d/(d-k), is the dimension of , and is the order of \Acal. We also obtain the limiting case for canceling constant-rank operators. We consider applications to compensated compactness and {applications to the theory of} functions of bounded variation and bounded deformation
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
Calculus of variations
No full textThis textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix
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