1,721,027 research outputs found
Singular perturbation Dirichlet problem in a double-periodic perforated plane
No full textWe show that the spectrum of the Dirichlet problem for the Laplace operator -Δ in the plane R2 perforated by a double-periodic family of holes contains any a priori number of gaps, for sufficiently large holes. While this result was already known in the case of circular holes, we consider here a more general geometric setting with holes of the shape (Formula Presented.)
Spectral gaps for the linear water-wave problem in a channel with thin structures
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Embedded eigenvalues for water-waves in a three-dimensional channel with a thin screen
Full text linkWe construct asymptotic expansions as for an eigenvalue embedded
into the continuous spectrum of water-wave problem in a cylindrical three dimensional channel
with a thin screen of thickness . The screen may be either submerged or
surface-piercing. The channel and the screen are mirror symmetric so that imposing the
Dirichlet condition in the middle plane creates an artificial positive cut-off-value
of the modified spectrum. The wetted part of the screen has a
sharp edge. Depending on a certain integral characteristics of the screen profiles,
we find two types of asymptotics, and
in the cases and , respectively.
We prove that in the case there are no embedded eigenvalues in the
interval , while this interval contains
exactly one eigenvalue, if . For the justification of these
result, the main tools are a reduction to an abstract spectral equation and the
use of the max-min-principle
Asymptotic expansions of solutions to the Poisson equation with alternating boundary conditions on an open arc
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Heat equation in a periodic domain with special initial data
No full textWe consider the initial-boundary value problem with the Neumann boundary condition for the classical linear heat equation in unbounded domains ohm & subne; Rd which are periodic in all directions of the Cartesian coordinate system. Generalizing the results of a previous paper by the authors, we apply Floquet transform methods to obtain results on the large time decay rates of the solution in the sup-norm. We observe that for a general, integrable initial data, the solution decays at the same rate t-d/2 as in the case of the Cauchy problem in the entire Euclidean space. We also consider special initial data with vanishing x-integral and obtain a faster decay rate. In the main results of the paper we pose for the initial data certain more detailed conditions, which are related to the lowest eigenvalue and eigenfunction of the model problem coming from the Floquet transform. Faster decay rates are obtained for such initial data. (c) 2025 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe
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
The degree theory and the index of a critical point for mappings of the type (<em>S</em><sub>+</sub>)
No full textAbstractThe dissertation considers a degree theory and the index of a critical point of demi-continuous, everywhere defined mappings of the monotone type.A topological degree is derived for mappings from a Banach space to its dual space. The mappings satisfy the condition (S+), and it is shown that the derived degree has the classical properties of a degree function.A formula for the calculation of the index of a critical point of a mapping A : X→X* satisfying the condition (S+) is derived without the separability of X and the boundedness of A. For the calculation of the index, we need an everywhere defined linear mapping A' : X→X* that approximates A in a certain set. As in the earlier results, A' is quasi-monotone, but our situation differs from the earlier results because A' does not have to be the Frechet or Gateaux derivative of A at the critical point. The theorem for the calculation of the index requires a construction of a compact operator T = (A' + Γ)-1Γ with the aid of linear mappings Γ : X→X and A'. In earlier results, Γ is compact, but here it need only be quasi-monotone. Two counter-examples show that certain assumptions are essential for the calculation of the index of a critical point.Academic dissertation to be presented, with the assent of the Faculty of Science of the University of Oulu, for public defence in Raahensali (Auditorium L10), Linnanmaa, on June 9th, 2007, at 12 noonAbstract
The dissertation considers a degree theory and the index of a critical point of demi-continuous, everywhere defined mappings of the monotone type.
A topological degree is derived for mappings from a Banach space to its dual space. The mappings satisfy the condition (S+), and it is shown that the derived degree has the classical properties of a degree function.
A formula for the calculation of the index of a critical point of a mapping A : X→X* satisfying the condition (S+) is derived without the separability of X and the boundedness of A. For the calculation of the index, we need an everywhere defined linear mapping A' : X→X* that approximates A in a certain set. As in the earlier results, A' is quasi-monotone, but our situation differs from the earlier results because A' does not have to be the Frechet or Gateaux derivative of A at the critical point. The theorem for the calculation of the index requires a construction of a compact operator T = (A' + Γ)-1Γ with the aid of linear mappings Γ : X→X and A'. In earlier results, Γ is compact, but here it need only be quasi-monotone. Two counter-examples show that certain assumptions are essential for the calculation of the index of a critical point
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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