1,720,977 research outputs found
Lower bounds on the growth of Sobolev norms in some linear time dependent Schrödinger equations
Full text linkIn this paper we consider linear, time dependent Schrodinger equations of the form i partial derivative(t)psi = K-0 psi + V(t)psi, where K-0 is a positive selfadjoint operator with discrete spectrum and whose spectral gaps are asymptotically constant. We give a strategy to construct bounded perturbations V(t) such that the Hamiltonian K-0 + V(t) generates unbounded orbits. We apply our abstract construction to three cases: (i) the Har- monic oscillator on N, (ii) the half-wave equation on and (iii) the Dirac-Schrodinger equation on Zoll manifolds. In each case, V(t) is a smooth and periodic in time pseudodifferential operator and the Schrodinger equation has solutions fulfilling the optimal lower bound estimate parallel to psi(t)parallel to r greater than or similar to vertical bar t vertical bar as vertical bar t vertical bar >> 1
One smoothing property of the scattering map of the KDV on R
No full textIn this paper we prove that in appropriate weighted Sobolev spaces, in the case of no bound states, the scattering map of the Korteweg-de Vries (KdV) on R is a perturbation of the Fourier transform by a regularizing operator. As an application of this result, we show that the difference of the KdV ow and the corresponding Airy ow is 1-smoothing
Stokes Waves at the Critical Depth are Modulationally Unstable
Full text linkThe paper fully answers a long standing open question concerning the stability/instability of pure gravity periodic traveling water waves—called Stokes waves—at
the critical Whitham–Benjamin depth hWB = 1.363... and nearby values. We prove that
Stokes waves of small amplitude O() are, at the critical depth hWB, linearly unstable
under long wave perturbations. The same holds true for slightly smaller values of the
depth h > hWB − c2, c > 0, depending on the amplitude of the wave. This problem
was not rigorously solved in previous literature because the expansions degenerate at the
critical depth. To solve this degenerate case, and describe in a mathematically exhaustive
way how the eigenvalues change their stable-to-unstable nature along this shallow-todeep water transient, we Taylor-expand the computations of Berti et al. (Arch Ration
Mech Anal 247:91, 2023) at a higher degree of accuracy, starting from the fourth order
expansion of the Stokes waves. We prove that also in this transient regime a pair of
unstable eigenvalues depict a closed figure “8”, of smaller size than for h > hWB, as the
Floquet exponent varie
On the analyticity of the Dirichlet–Neumann operator and Stokes waves
Full text linkWe prove an analyticity result for the Dirichlet-Neumann operator under space periodic boundary conditions in any dimension in an unbounded domain with infinite depth. We derive an analytic bifurcation result of analytic Stokes waves-i.e., space periodic traveling solutions-of the water waves equations in deep water
Long time stability of small finite gap solutions of the cubic nonlinear Schrödinger equation on T2
Full text linkIn this paper we study long time stability of a class of nontrivial, quasi-periodic solutions depending on one spacial variable of the cubic defocusing non-linear Schrödinger equation on the two dimensional torus. We prove that these quasi-periodic solutions are orbitally stable for finite but long times, provided that their Fourier support and their frequency vector satisfy some complicated but explicit condition, which we show holds true for most solutions. The proof is based on a normal form result. More precisely we expand the Hamiltonian in a neighborhood of a quasi-periodic solution, we reduce its quadratic part to diagonal constant coefficients through a KAM scheme, and finally we remove its cubic terms with a step of nonlinear Birkhoff normal form. The main difficulty is to impose second and third order Melnikov conditions; this is done by combining the techniques of reduction in order of pseudo-differential operators with the algebraic analysis of resonant quadratic Hamiltonians
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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