Search results for "Eigenvector"
showing 10 items of 303 documents
Evolution of Worldwide Stock Markets, Correlation Structure and Correlation Based Graphs
2011
We investigate the daily correlation present among market indices of stock exchanges located all over the world in the time period Jan 1996 - Jul 2009. We discover that the correlation among market indices presents both a fast and a slow dynamics. The slow dynamics reflects the development and consolidation of globalization. The fast dynamics is associated with critical events that originate in a specific country or region of the world and rapidly affect the global system. We provide evidence that the short term timescale of correlation among market indices is less than 3 trading months (about 60 trading days). The average values of the non diagonal elements of the correlation matrix, corre…
Numerical analysis of composite plates with multiple delaminations subjected to uniaxial buckling load
2006
Abstract In this paper the buckling and post-buckling behaviour of unidirectional and cross-ply composite laminated plates with multiple delaminations has been studied. Finite elements analyses have been performed, using a linear buckling model, based on the solution of the eigenvalues problem, and a non-linear one, based on an incremental-iterative method. With non-linear method large displacements have been taken into account and also contact constraints between sublaminates have been added to avoid their interpenetration. It has been found that both delamination length and position and stacking sequence of the plies influence the critical load of the plate; furthermore, linear and non-li…
Oscillator Strengths of Electronic Excitations with Response Theory using Phase Including Natural Orbital Functionals
2013
The key characteristics of electronic excitations of many-electron systems, the excitation energies ωα and the oscillator strengths fα, can be obtained from linear response theory. In one-electron models and within the adiabatic approximation, the zeros of the inverse response matrix, which occur at the excitation energies, can be obtained from a simple diagonalization. Particular cases are the eigenvalue equations of time-dependent density functional theory (TDDFT), time-dependent density matrix functional theory, and the recently developed phase-including natural orbital (PINO) functional theory. In this paper, an expression for the oscillator strengths fα of the electronic excitations is…
On the construction of lusternik-schnirelmann critical values with application to bifurcation problems
1987
An iterative method to construct Lusternik-Schnirelmann critical values is presented. Examples of its use to obtain numerical solutions to nonlinear eigenvalue problems and their bifurcation branches are given
Singular systems in dimension 3: Cuspidal case and tangent elliptic flat case
2007
We study two singular systems in R3. The first one is affine in control and we achieve weighted blowings-up to prove that singular trajectories exist and that they are not locally time optimal. The second one is linear in control. The characteristic vector field in sub-Riemannian geometry is generically singular at isolated points in dimension 3. We define a case with symmetries, which we call flat, and we parametrize the sub-Riemannian sphere. This sphere is subanalytic.
An eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities
2005
AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.
New isoperimetric estimates for solutions to Monge - Ampère equations
2009
Abstract We prove some sharp estimates for solutions to Dirichlet problems relative to Monge–Ampere equations. Among them we show that the eigenvalue of the Dirichlet problem, when computed on convex domains with fixed measure, is maximal on ellipsoids. This result falls in the class of affine isoperimetric inequalities and shows that the eigenvalue of the Monge–Ampere operator behaves just the contrary of the first eigenvalue of the Laplace operator.
A Note on Riesz Bases of Eigenvectors of Certain Holomorphic Operator-Functions
2001
Abstract Operator-valued functions of the form A (λ) ≔ A − λ + Q(λ) with λ ↦ Q(λ)(A − μ)− 1 compact-valued and holomorphic on certain domains Ω ⊂ C are considered in separable Hilbert space. Assuming that the resolvent of A is compact, its eigenvalues are simple and the corresponding eigenvectors form a Riesz basis for H of finite defect, it is shown that under certain growth conditions on ‖Q(λ)(A − λ)− 1‖ the eigenvectors of A corresponding to a part of its spectrum also form a Riesz basis of finite defect. Applications are given to operator-valued functions of the form A (λ) = A − λ + B(λ − D)− 1C and to spectral problems in L2(0, 1) of the form −f″(x) + p(x, λ)f′(x) + q(x, λ)f(x) = λf(x…
Planar maps whose second iterate has a unique fixed point
2007
Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is disjoint of the interval [1,1+a[, then Fix(F) has at most one element, where Fix(F) denotes the set of fixed points of F. (b) If Spec(F) is disjoint of the real line R, then Fix(F^2) has at most one element. (c) If F is a C^1 map and, for all p belonging to R^2, the derivative F'(p) is neither a homothety nor has simple real eigenvalues, then Fix(F^2) has at most one element, provided that Spec(F) is disjoint of either (c1) the union of the number 0 with the intervals ]-\infty, -1] and [1,\infty[, or (c2) t…
Some properties of [tr(Q2p)]12p with application to linear minimax estimation
1990
Abstract A nondifferentiable minimization problem is considered which occurs in linear minimax estimation. This problem is solved by replacing the nondifferentiable maximal eigenvalue of a real nonnegative definite matrix Q with [tr( Q 2 p )] 1/2 p . It is shown that any descent algorithm with inexact step-length rule can be used to obtain linear minimax estimators for the parameter vector of a parameter-restricted linear model.