1,720,980 research outputs found
Morse theory for a fourth order elliptic equation with exponential nonlinearity
No full textGiven a Hilbert space (H, 〈.,.〉) and interval λ ⊂(0,+∞) and a map K ∈ C2(H,R) whose gradient is a compact mapping, we consider the family of functionals of the type: I(λ,u)=12;〈u,u〉 - λK(u), (λ,u) ∈ λ × H. As already observed by many authors, for the functionals we are dealing with the (PS) condition may fail under just this assumptions. Nevertheless, by using a recent deformation Lemma proven by Lucia (Topol Methods Nonlinear Anal 30(1):113-138, 2007), we prove a Poincaré-Hopf type theorem. Moreover by using this result, together with some quantitative results about the formal set of barycenters, we are able to establish a direct and geometrically clear degree counting formula for a fourth order nonlinear scalar field equation on a bounded and smooth C∞ region of the four dimensional Euclidean space in the flavor of (Malchiodi in Adv Differ Equ 13:1109-1129, 2008). We remark that this formula has been proven with complete different methods in (Lin and Wei Preprint, 2007) by using blow-up type estimates. © 2010 Springer Basel AG
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe 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
Get PDF“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
Get PDFWe 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
1. Sulla illegittimità costituzionale dei decreti legge adottati per fronteggiare l’emergenza Covid-19
No full textMorse index and bifurcation of p-geodesics on semi Riemannian manifolds.
No full textGiven a one-parameter family {gλ : λ ∈ [a, b]} of
semi Riemannian metrics on an ndimensional
manifold M, a family of time-dependent
potentials {Vλ : λ ∈ [a, b]} and a family {σλ : λ ∈ [a, b]} of trajectories connecting two points of the mechanical system defined by (gλ, Vλ), we show that there are trajectories bifurcating from the trivial branch σλ if the generalized Morse indices μ(σa) and μ(σb) are different. If the data are analytic we obtain estimates for the number of bifurcation points on the branch and, in particular, for the number of strictly conjugate points along a trajectory using an explicit computation of the Morse index in the case of locally symmetric spaces and a comparison principle of Morse Schoenberg type
Morse-Smale index theorems for elliptic boundary deformation problems
Get PDFAbstractMorse-type index theorems for self-adjoint elliptic second order boundary value problems arise as the second variation of an energy functional corresponding to some variational problem. The celebrated Morse index theorem establishes a precise relation between the Morse index of a geodesic (as critical point of the geodesic action functional) and the number of conjugate points along the curve. Generalization of this theorem to linear elliptic boundary value problems appeared since seventies. (See, for instance, Smale (1965) [12], Uhlenbeck (1973) [15] and Simons (1968) [11] among others.) The aim of this paper is to prove a Morse–Smale index theorem for a second order self-adjoint elliptic boundary value problem in divergence form on a star-shaped domain of the N-dimensional Euclidean space with Dirichlet and Neumann boundary conditions. This result will be achieved by generalizing a recent new idea introduced by authors in Deng and Jones (2011) [5], based on the idea of shrinking the boundary
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