Search results for "eigenvalue problem"
showing 10 items of 11 documents
On the mechanical stability and out-of-plane dynamics of a travelling panel submerged in axially flowing ideal fluid : a study into paper production …
2011
Using affinity perturbations to detect web traffic anomalies
2013
The initial training phase of machine learning algorithms is usually computationally expensive as it involves the processing of huge matrices. Evolving datasets are challenging from this point of view because changing behavior requires updating the training. We propose a method for updating the training profile efficiently and a sliding window algorithm for online processing of the data in smaller fractions. This assumes the data is modeled by a kernel method that includes spectral decomposition. We demonstrate the algorithm with a web server request log where an actual intrusion attack is known to happen. Updating the kernel dynamically using a sliding window technique, prevents the proble…
On the Fučík spectrum of the p-Laplacian with no-flux boundary condition
2023
In this paper, we study the quasilinear elliptic problem \begin{align*} \begin{aligned} -\Delta_{p} u&= a\l(u^+\r)^{p-1}-b\l(u^-\r)^{p-1} \quad && \text{in } \Omega,\\ u & = \text{constant} &&\text{on } \partial\Omega,\\ 0&=\int_{\partial \Omega}\left|\nabla u\right|^{p-2}\nabla u\cdot \nu \,\diff \sigma,&& \end{aligned} \end{align*} where the operator is the $p$-Laplacian and the boundary condition is of type no-flux. In particular, we consider the Fu\v{c}\'{\i}k spectrum of the $p$-Laplacian with no-flux boundary condition which is defined as the set $\fucik$ of all pairs $(a,b)\in\R^2$ such that the problem above has a nontrivial solution. It turns out…
Periodic solutions for a class of second-order Hamiltonian systems
2005
Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence result of two distinct periodic solutions is given.© 2005 Texas State University - San Marcos.
Inverse eigenvalue problem for normal J-hamiltonian matrices
2015
[EN] A complex square matrix A is called J-hamiltonian if AT is hermitian where J is a normal real matrix such that J(2) = -I-n. In this paper we solve the problem of finding J-hamiltonian normal solutions for the inverse eigenvalue problem. (C) 2015 Elsevier Ltd. All rights reserved.
A symmetrization result for Monge–Ampère type equations
2007
In this paper we prove some comparison results for Monge–Ampere type equations in dimension two. We also consider the case of eigenfunctions and we derive a kind of “reverse” inequalities. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Exact constants in Poincaré type inequalities for functions with zero mean boundary traces
2014
In this paper, we investigate Poincare type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We find exact and easily computable constants in these inequalities for some basic domains (rectangles, cubes, and right triangles) and discuss applications of the inequalities to quantitative analysis of partial differential equations. Copyright © 2014 John Wiley & Sons, Ltd.
Critical points for nondifferentiable functions in presence of splitting
2006
A classical critical point theorem in presence of splitting established by Brézis-Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational-hemivariational eigenvalue problems. © 2005 Elsevier Inc. All rights reserved.
A simple tool to forecast the natural frequencies of thin-walled cylinders
2023
Abstract. This paper presents an approximate method to predict the natural frequencies of thin-walled cylinders. By taking inspiration from a previous work of one of the authors, the starting point of the proposed approach is a proper construction of reasonable eigenfunctions. However, a new simple tool based on the principle of virtual work has been developed to estimate the natural frequencies and the amplitude of vibration without complex numerical resolution. Moreover, the applicability of the model is extended to all the most common constraint conditions. The identification of the natural frequencies of a continuous cylinder is reduced to an eigenvalue problem based on a matrix whose e…
Some remarks on nonlinear elliptic problems involving Hardy potentials
2007
In this note we prove an Hardy type inequality with a remainder term, where the potential depends only on a group of variables. Such a result allows us to show the existence of entropy solutions to a class of elliptic P.D.E.'s.