1,720,958 research outputs found
Reducibility of Schrödinger Equation on the Sphere
No full textIn this article we prove a reducibility result for the linear Schrödinger equation on the sphere Sn with quasi-periodic in time perturbation. Our result includes the case of unbounded perturbation that we assume to be of order strictly less than 1/2 and satisfying some parity condition. As far as we know, this is one of the few reducibility results for an equation in more than one dimension with unbounded perturbations. Letus note that, surprisingly, our result does not require the use of the pseudodifferential calculus although the perturbation is unbounded
LONG TIME SOLUTIONS FOR QUASILINEAR HAMILTONIAN PERTURBATIONS OF SCHRÖDINGER AND KLEIN–GORDON EQUATIONS ON TORI
No full textWe consider quasilinear, Hamiltonian perturbations of the cubic Schrödinger and of the cubic (derivative) Klein–Gordon equations on the d-dimensional torus. If ε < 1 is the size of the initial datum, we prove that the lifespan of solutions is strictly larger than the local existence time ε-2. More precisely, concerning the Schrödinger equation we show that the lifespan is at least of order O(ε-4), and in the Klein–Gordon case we prove that the solutions exist at least for a time of order O(ε-8/3javax.xml.bind.JAXBElement@f17399) as soon as d ≥ 3. Regarding the Klein–Gordon equation, our result presents novelties also in the case of semilinear perturbations: we show that the lifespan is at least of order O(ε-10/3javax.xml.bind.JAXBElement@3095a7a6), improving, for cubic nonlinearities and d ≥ 4, the general results of Delort (J. Anal. Math. 107 (2009), 161–194) and Fang and Zhang (J. Differential Equations 249:1 (2010), 151–179)
Reducibility of Schrödinger equation on a Zoll manifold with unbounded potential
No full textIn this article, we prove a reducibility result for the linear Schrödinger equation on a Zoll manifold with quasi-periodic in time pseudo-differential perturbation of order less than or equal to 1/2. As far as we know, this is the first reducibility result for an unbounded perturbation on a compact manifold different from the torus
Long-Time Existence for Semi-linear Beam Equations on Irrational Tori
No full textWe consider the semi-linear beam equation on the d dimensional irrational torus with smooth nonlinearity of order n- 1 with n≥ 3 and d≥ 2. If ε≪ 1 is the size of the initial datum, we prove that the lifespan Tε of solutions is O(ε-A(n-2)-) where A≡A(d,n)=1+3d-1 when n is even and A=1+3d-1+max(4-dd-1,0) when n is odd. For instance for d= 2 and n= 3 (quadratic nonlinearity) we obtain Tε=O(ε-6-), much better than O(ε- 1) , the time given by the local existence theory. The irrationality of the torus makes the set of differences between two eigenvalues of Δ2+1 accumulate to zero, facilitating the exchange between the high Fourier modes and complicating the control of the solutions over long times. Our result is obtained by combining a Birkhoff normal form step and a modified energy step
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
Growth of Sobolev norms for abstract linear Schrodinger equations
Get PDFWe prove an abstract theorem giving a (t)ε bound (for all ε > 0) on the growth of the Sobolev norms in linear Schrodinger equations of the form i Ψ = H0ψ + V(t)ψ as t → ∞. The abstract theorem is applied to several cases, including the cases where (i) H0 is the Laplace operator on a Zoll manifold and V (t) a pseudodifferential operator of order smaller than 2; (ii) H0 is the (resonant or nonresonant) harmonic oscillator in Rd and V (t) a pseudodifferential operator of order smaller than that of H0 depending in a quasiperiodic way on time. The proof is obtained by first conjugating the system to some normal form in which the perturbation is a smoothing operator and then applying the results of [MR17]
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe 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
- …
