1,721,060 research outputs found
Persistence of the normalized eigenvectors of a perturbed operator in the variational case
No full textLet H be a real Hilbert space and denote by S its unit sphere. Consider the nonlinear eigenvalue problem Ax+εB(x)=δx, where A:H→H is a bounded self-adjoint (linear) operator with nontrivial kernel KerA, and B:H→H is a (possibly) nonlinear perturbation term. A unit eigenvector x0∈S∩KerA of A (thus corresponding to the eigenvalue δ=0, which we assume to be isolated) is said to be persistent, or a bifurcation point (from the sphere S∩KerA), if it is close to solutions x∈S of the above equation for small values of the parameters δ∈R and ε≠0. In this paper, we prove that if B is a C1 gradient mapping and the eigenvalue δ=0 has finite multiplicity, then the sphere S∩KerA contains at least one bifurcation point, and at least two provided that a supplementary condition on the potential of B is satisfied. These results add to those already proved in the non-variational case, where the multiplicity of the eigenvalue is required to be odd
Topological persistence of the unit eigenvectors of a perturbed Fredholm operator of index zero
No full textLet A; C : E -> F be two bounded linear operators between real Banach spaces, and denote by S the unit sphere of E (or, more generally, let S = g(-1) (1), where g is any continuous norm in E). Assume that mu(0) is an eigenvalue of the problem Ax = mu Cx, that the operator L = A - mu C-0 is Fredholm of index zero, and that C satis fi es the transversality condition Img L + C (Ker L) = F, which implies that the eigenvalue mu(0) is isolated (and when F = E and C is the identity implies that the geometric and the algebraic multiplicities of mu(0) coincide).
We prove the following result about the persistence of the unit eigenvectors: Given an arbitrary C-1 map M : E -> F, if the (geometric) multiplicity of mu(0) is odd, then for any real epsilon sufficiently small there exists x(epsilon) is an element of S and mu(epsilon) near mu(0) such that Ax(epsilon) + epsilon M (x(epsilon)) = mu(epsilon)Cx(epsilon).
This result extends a previous one by the authors in which E is a real Hilbert space, F = E, A is selfadjoint and C is the identity. We provide an example showing that the assumption that the multiplicity of mu(0) is odd cannot be removed
On the persistence of the eigenvalues of a perturbed fredholm operator of index zero under nonsmooth perturbations
Full text linkOn general properties of n-th order retarded functional differential equations
Full text linkConsider the second order RFDE (retarded functional differential equation) x’’ (t) = f(t, xt), where f is a continuous realvalued function defined on the Banach space R x C1([−r, 0],R). The weak assumption of continuity on f (due to the strong topology of C1([−r, 0],R)) makes not convenient to transform this equation into a first order RFDE of the type z’ (t) = g(t, zt). In fact, in this case, the associated R2-valued function g could be discontinuous (with the C0- topology) and, in addition, not necessarily defined on the whole space R x C([−r, 0],R2). Consequently, in spite of what happens for ODEs, the classical results regarding existence, uniqueness, and continuous dependence on data for first order RFDEs could not apply. Motivated by this obstruction, we provide results regarding general properties, such as existence, uniqueness, continuous dependence on data and continuation of solutions of RFDEs of the type x(n)(t) = f(t, xt), where f is an Rk-valued continuous function on the Banach space R x C(n−1)([−r, 0],Rk). Actually, for the sake of generality, our investigation will be carried out in the case of infinite delay
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
- …
