1,721,280 research outputs found
Normalized eigenvectors of a perturbed linear operator via general bifurcation
No full textLet X be a real Banach space, A:X → X a bounded linear operator, and B:X → X a (possibly nonlinear) continuous operator. Assume that λ = 0 is an eigenvalue of A and consider the family of perturbed operators A + εB, where ε is a real parameter. Denote by S the unit sphere of X and let SA = S ∩ KerA be the set of unit 0-eigenvectors of A. We say that a vector x0 ∈ SA is a bifurcation point for the unit eigenvectors of A + εB if any neighborhood of (0, 0, x0) ∈ × × X contains a triple (ε, λ, x) with ε = 0 and x a unit λ-eigenvector of A + εB, i.e. x ∈ S and (A + εB)x = λx.
We give necessary as well as sufficient conditions for a unit 0-eigenvector of A to be a bifurcation point for the unit eigenvectors of A + εB. These conditions turn out to be particularly meaningful when the perturbing operator B is linear. Moreover, since our sufficient condition is trivially satisfied when KerA is one-dimensional, we extend a result of the first author, under the additional assumption that B is of class C
Treatment of spinal muscular atrophy
No full textPurpose of review The aim of the review was to provide an overview of safety and efficacy of the available treatments including information from both clinical trials and real-world data. Additional information form ongoing studies using other approaches than increasing SMN protein are also reported. Recent findings In the last 3years, there have been over 24 studies reporting safety and the impact of the available drugs on different aspects of function, including respiratory and bulbar function. These findings, obtained in a real-world setting, are extremely important to define the spectrum of responses in individuals with different age, weight, SMN2 copies, and other variables and will be of help to the families and the clinicians to set up the right expectations at the time of starting a new treatment. Summary The large number of studies that became available in the last few years support and expand the information on safety and efficacy provided by the clinical trials
A new theme in nonlinear analysis: continuation and bifurcation of the unit eigenvectors of a perturbed linear operator
No full textWe review some recent results concerning nonlinear eigenvalue problems of the form (*) Au + eB(u) =cu, where A is a linear Fredholm operator of index zero (with nontrivial kernel KerA) acting in a real Banach space X, and B from X to X is a (possibly) nonlinear perturbation term. We seek solutions u of (*) in the unit sphere S of X, and the emphasis is put on the existence - under appropriate conditions on B - of points u0 in S \ KerA (thus satisfying (*) for e = c = 0) which either can be continued as solutions of (*) for e different from 0 or - more generally - are bifurcation points for solutions of that kind
Topological persistence of the normalized eigenvectors of a perturbed self-adjoint operator
No full textLet T be a self-adjoint bounded operator acting in a real Hilbert space H, and denote by S the unit sphere of H. Assume that is an isolated eigenvalue of T of odd multiplicity greater than 1. Given an arbitrary operator B:H ! H of class C1, we prove that for any sufficiently small there exists such that Tx" C "B.x".
This result was conjectured, but not proved, in a previous article by the authors.We provide an example showing that the assumption that the multiplicity of 0 is odd
cannot be removed
A result on the existence of infinitely many solutions of a nonlinear elliptic boundary value problems at resonance
No full textGoing 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
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