1,721,033 research outputs found
A criterion for the existence of the essential spectrum for beak-shaped elastic bodies
No full textWe establish a criterion for the existence of the essential spectrum for the elasticity problem in the case the traction-free surface of a finite elastic body has a beak-shaped irregularity (see Corollary 3.5 and Theorem 4.2). This boundary irregularity is angular in two dimensions and cuspidal in one dimension. We obtain further information on the spectral structure in some particular cases, and formulate open questions and hypotheses. (C) 2009 Elsevier Masson SAS. All rights reserved
Spectra of open waveguides in periodic media
No full textWe study the essential spectra of formally self-adjoint elliptic systems on doubly periodic planar domains perturbed by a semi-infinite periodic row of foreign inclusions. We show that the essential spectrum of the problem consists of the essential spectrum of the purely periodic problem and another component, which is the union of the discrete spectra of model problems in the infinite perturbation strip; these model problems arise by an application of the partial Floquet Bloch Gelfand transform. (C) 2015 Elsevier Inc. All rights reserved
Localization of eigenfunctions in the Dirichlet beaker
Full text linkWe construct the asymptotics of the eigenpairs of the Dirichlet problem for the Laplace operator in a thin-walled beaker and prove the localization effect for the functions near the bottom edge, a smooth closed contour, of the beaker. The main asymptotic terms are described by the eigenpairs of an ordinary differential equation on the edge and by the single eigenvalue belonging to the discrete spectrum of the Dirichlet Laplacian in an (Formula presented.) -shaped infinite waveguide. The corresponding eigenfunctions are shown to decay exponentially at some distance from the edge. Also, we find the asymptotics of eigenvalue sequences generated by planar Dirichlet problems on the bottom and walls of the limit beaker of zero thickness. Open questions related to other sequences of eigenvalues are discussed
A REAL ANALYTICITY RESULT FOR SYMMETRIC FUNCTIONS OF THE EIGENVALUES OF A QUASIPERIODIC SPECTRAL PROBLEM FOR THE DIRICHLET LAPLACIAN
Full text linkAs is well known, by the Floquet-Bloch theory for periodic problems, one can transform a spectral Laplace-Dirichlet problem in the plane with a set of periodic perforations into a family of “model problems” depending on a parameter n (Formula presented) [0,2π]2 for quasiperiodic functions in the unit cell with a single perforation. We prove real analyticity results for the eigenvalues of the model problems upon perturbation of the shape of the perforation of the unit cell
Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems
No full textWe give an example of a scalar second order differential operator in the plane with double periodic coefficients and describe its modification, which causes an additional spectral band in the essential spectrum. The modified operator is obtained by applying to the coefficients a mirror reflection with respect to a vertical or horizontal line. This change gives rise to Rayleigh type waves localized near the line. The results are proven using asymptotic analysis, and they are based on high contrast of the coefficient functions
Asymptotics of Neumann harmonics when a cavity is close to the exterior boundary of the domain
No full textWe construct the asymptotics (as epsilon -> 0) of solutions to the Neumann problem for the Laplace equation and of the corresponding Dirichlet integral. The problem concerns a three-dimensional domain having two connected components of the boundary at the distance epsilon > 0
Monomial basis in Korenblum type spaces of analytic functions
Full text link[EN] It is shown that the monomials A = (z(n))(n=0)(infinity) are a Schauder basis of the Frechet spaces A(+)(-gamma), gamma >= 0, that consists of all the analytic functions f on the unit disc such that (1 - vertical bar z vertical bar)(mu)vertical bar f(z)vertical bar is bounded for all mu > gamma. Lusky proved that A is not a Schauder basis for the closure of the polynomials in weighted Banach spaces of analytic functions of type H-infinity. A sequence space representation of the Frechet space A(+)(-gamma) is presented. The case of (LB)-spaces A(-)(-gamma), gamma > 0, that are defined as unions of weighted Banach spaces is also studied.Research of the third author was partially supported by the Vaisala Foundation of the Finnish Academy of Sciences and Letters.Bonet Solves, JA.; Lusky, W.; Taskinen, J. (2018). Monomial basis in Korenblum type spaces of analytic functions. Proceedings of the American Mathematical Society. 146(12):5269-5278. https://doi.org/10.1090/proc/14195S526952781461
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
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