Search results for "values."
showing 10 items of 1353 documents
Toeplitz band matrices with small random perturbations
2021
We study the spectra of $N\times N$ Toeplitz band matrices perturbed by small complex Gaussian random matrices, in the regime $N\gg 1$. We prove a probabilistic Weyl law, which provides an precise asymptotic formula for the number of eigenvalues in certain domains, which may depend on $N$, with probability sub-exponentially (in $N$) close to $1$. We show that most eigenvalues of the perturbed Toeplitz matrix are at a distance of at most $\mathcal{O}(N^{-1+\varepsilon})$, for all $\varepsilon >0$, to the curve in the complex plane given by the symbol of the unperturbed Toeplitz matrix.
Perturbed eigenvalue problems for the Robin p-Laplacian plus an indefinite potential
2020
AbstractWe consider a parametric nonlinear Robin problem driven by the negativep-Laplacian plus an indefinite potential. The equation can be thought as a perturbation of the usual eigenvalue problem. We consider the case where the perturbation$$f(z,\cdot )$$f(z,·)is$$(p-1)$$(p-1)-sublinear and then the case where it is$$(p-1)$$(p-1)-superlinear but without satisfying the Ambrosetti–Rabinowitz condition. We establish existence and uniqueness or multiplicity of positive solutions for certain admissible range for the parameter$$\lambda \in {\mathbb {R}}$$λ∈Rwhich we specify exactly in terms of principal eigenvalue of the differential operator.
Multiple solutions for nonlinear nonhomogeneous resonant coercive problems
2018
We consider a nonlinear, nonhomogeneous Dirichlet problem driven by the sum of a \begin{document}$p$\end{document} -Laplacian ( \begin{document}$2 ) and a Laplacian. The reaction term is a Caratheodory function \begin{document}$f(z,x)$\end{document} which is resonant with respect to the principal eigenvalue of ( \begin{document}$-\Delta_p,\, W^{1,p}_0(\Omega)$\end{document} ). Using variational methods combined with truncation and comparison techniques and Morse theory (critical groups) we prove the existence of three nontrivial smooth solutions all with sign information and under three different conditions concerning the behavior of \begin{document}$f(z,\cdot)$\end{document} near zero. By …
Infinitely many weak solutions for a mixed boundary value system with (p_1,…,p_m)-Laplacian
2014
The aim of this paper is to prove the existence of infinitely many weak solu- tions for a mixed boundary value system with (p1, . . . , pm)-Laplacian. The approach is based on variational methods.
Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model
2020
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix (Formula presented.). Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo-Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix (Formula presented.) and of its adjoint (Formula presented.). Then, we consider an extension of the so-called power method, for which we prove a fixed point theorem for (Formula presented.) useful in the determination of the eigenvalues of (Formula presented…
Optimal lower bounds for eigenvalues of linear and nonlinear Neumann problems
2013
In this paper we prove a sharp lower bound for the first non-trivial Neumann eigenvalue μ1(Ω) for the p-Laplace operator (p > 1) in a Lipschitz bounded domain Ω in ℝn. Our estimate does not require any convexity assumption on Ω and it involves the best isoperimetric constant relative to Ω. In a suitable class of convex planar domains, our bound turns out to be better than the one provided by the Payne—Weinberger inequality.
Determination of sugars in depilatory formulations: a green analytical method employing infrared detection and partial least squares regression.
2011
A green analytical method was developed for the analysis of sugar-based depilatories. Three independent partial least squares (PLS) regression models were built for the direct determination of glucose, fructose and maltose without any sample pretreatment based on their attenuated total reflectance - Fourier transform infrared (ATR-FTIR) spectra. The models showed adequate prediction capabilities with root-mean-square-errors of prediction ranging from 7.04 to 12.55 mg sugar g(-1) sample. As a reference procedure, gradient liquid chromatography with on-line infrared detection, employing background correction based on cubic smoothing splines, was used. The analysis revealed changes in the suga…
Evaluation of DR and CR digital mammography systems based on phantom and breast dosimetry.
2006
Digital mammography has been progressively introduced in screening centers, since recent evolution of CR and DR detectors. However, it is questionable which exposure conditions would be more suitable when these techniques are applied, in order to reduce the glandular breast doses, as they are related with induced carcinogenesis. Several exposures have been performed in CR and DR mammography units for comparing absorbed doses during quality control assessments and during screening, diagnosis and treatment. In the first case, the CIRS11A mammographic phantom has been used with standard exposure conditions (28 kV, AEC mode with blackening +0, 50:50 glandularity and 4.5 compressed breast thickn…
The course of fatigue in patients with gynecologic and breast cancer
2013
Objective: The objective of this study is to examine the course of fatigue in female cancer patients during the first months after treatment. Methods: We examined a sample of 110 patients suffering from gynecological or breast cancer. Fatigue was assessed with two questionnaires, the Multidimensional Fatigue Inventory (MFI) and the fatigue scale of the quality of life questionnaire European Organisation for Research and Treatment of Cancer (EORTC QLQ-C30). Participants were tested during their stay in the hospital (t1), two weeks after discharge (t2), and three months after discharge (t3). Results: Fatigue in the patients’ sample was markedly higher than the general population reference val…
Bond-based bilinear indices for computational discovery of novel trypanosomicidal drug-like compounds through virtual screening
2014
Two-dimensional bond-based bilinear indices and linear discriminant analysis are used in this report to perform a quantitative structure-activity relationship study to identify new trypanosomicidal compounds. A data set of 440 organic chemicals, 143 with antitrypanosomal activity and 297 having other clinical uses, is used to develop the theoretical models. Two discriminant models, computed using bond-based bilinear indices, are developed and both show accuracies higher than 86% for training and test sets. The stochastic model correctly indentifies nine out of eleven compounds of a set of organic chemicals obtained from our synthetic collaborators. The in vitro antitrypanosomal activity of …