1,720,958 research outputs found
Some remarks on the Sobolev inequality in Riemannian manifolds
No full textWe investigate Sobolev and Hardy inequalities, specifically weighted
Minerbe's type estimates, in noncompact complete connected
Riemannian manifolds whose geometry is described by an isoperimetric
profile. In particular, we assume that the manifold satisfies the
-hyperbolicity property, stated in terms of a necessary integral Dini
condition on the isoperimetric profile. Our method seems to us to
combine sharply the knowledge of the isoperimetric profile and the
optimal Bliss type Hardy inequality depending on the geometry of the
manifold. We recover the well known best Sobolev constant in the Euclidean
case
Large time behavior for the porous medium equation with convection
Full text linkWe consider the Cauchy problem for the porous medium
equation with nonlinear convection, when the nonlinearities are the
same in the convection and in the diffusion terms. We get a new
sharp bound of the solution for large times
Asymptotic behavior for the filtration equation in domains with noncompact boundary
Full text linkWe consider the initial value boundary problem with zero Neumann data for an equation modelled after the porous media equation, with variable coefficients. The spatial domain is unbounded and shaped like a (general) paraboloid, and the solution u is integrable in space and non-negative. We show that the asymptotic profile for large times of u is one-dimensional and given by an explicit function, which can be regarded as the fundamental solution of a one-dimensional differential equation with weights. In the case when the domain is a cone or the whole space (Cauchy problem) we obtain a genuine multi-dimensional profile given by the well known Barenblatt solution
Qualitative properties of solutions of degenerate parabolic equations via energy approaches
Full text linkWe consider several problems for degenerate parabolic equations exhibiting nonlinearities of various kinds. For
example the equations may contain superlinear sources, causing blow up of the solutions, or damping terms; the
principal part of the operator is also nonlinear. We mention as unifying features the fact that the spatial domains
have non-compact boundary, and the technical approach which is based on energy methods and a priori estimates.
The issues investigated include existence under optimal assumptions on the data, asymptotic behavior of solutions,
existence or non-existence of global in time solutions
Large time behavior of solutions to the Neumann problem for a quasilinear second order degenerate parabolic equation in domains with noncompact boundary
No full textAbstractWe investigate the optimal rate of stabilization at large time of a solution to the Neumann problemut=∑i=1N∂∂xi(ai(x, t, ∇u))−b(x, t, u),inΩ×(0, T),T>0∑i=1Nai(x, t, ∇u)ni=0,on∂Ω×(0, T)u(x, 0)=u0(x)x∈Ω,u0(x)⩾0inΩ,where Ω⊂RN, N⩾2, is an unbounded domain with sufficiently smooth noncompact boundary ∂Ω satisfying certain isoperimetrical inequality and n=(ni) is the outward normal to ∂Ω
Existence of solutions of degenerate parabolic equations with inhomogeneous density and growing data on manifolds
No full textWe consider doubly non-linear degenerate parabolic equations on Riemannian manifolds of infinite volume. The equation is inhomogeneous: indeed it contains a capacitary coefficient depending on the space variable, which we assume to decay at infinity. We prove existence of solutions for initial data growing at infinity in a suitable admissible class and some related estimates. We also prove, independently, a sup bound valid in the same geometrical setting for solutions which are a priori known to have compact support; the majorization depends on the size of the support
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
- …
