Search results for "Linear"
showing 10 items of 7165 documents
Visible parts and dimensions
2003
We study the visible parts of subsets of n-dimensional Euclidean space: a point a of a compact set A is visible from an affine subspace K of n, if the line segment joining PK(a) to a only intersects A at a (here PK denotes projection onto K). The set of all such points visible from a given subspace K is called the visible part of A from K. We prove that if the Hausdorff dimension of a compact set is at most n−1, then the Hausdorff dimension of a visible part is almost surely equal to the Hausdorff dimension of the set. On the other hand, provided that the set has Hausdorff dimension larger than n−1, we have the almost sure lower bound n−1 for the Hausdorff dimensions of visible parts. We al…
On a global superconvergence of the gradient of linear triangular elements
1987
Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.
Multiple periodic solutions for Hamiltonian systems with not coercive potential
2010
Under an appropriate oscillating behavior of the nonlinear term, the existence of infinitely many periodic solutions for a class of second order Hamiltonian systems is established. Moreover, the existence of two non-trivial periodic solutions for Hamiltonian systems with not coercive potential is obtained, and the existence of three periodic solutions for Hamiltonian systems with coercive potential is pointed out. The approach is based on critical point theorems. © 2009 Elsevier Inc. All rights reserved.
Local behaviour of singular solutions for nonlinear elliptic equations in divergence form
2012
We consider the following class of nonlinear elliptic equations $$\begin{array}{ll}{-}{\rm div}(\mathcal{A}(|x|)\nabla u) +u^q=0\quad {\rm in}\; B_1(0)\setminus\{0\}, \end{array}$$ where q > 1 and $${\mathcal{A}}$$ is a positive C 1(0,1] function which is regularly varying at zero with index $${\vartheta}$$ in (2−N,2). We prove that all isolated singularities at zero for the positive solutions are removable if and only if $${\Phi\not\in L^q(B_1(0))}$$ , where $${\Phi}$$ denotes the fundamental solution of $${-{\rm div}(\mathcal{A}(|x|)\nabla u)=\delta_0}$$ in $${\mathcal D'(B_1(0))}$$ and δ0 is the Dirac mass at 0. Moreover, we give a complete classification of the behaviour near zero of al…
A geometrical criterion for nonexistence of constant-sign solutions for some third-order two-point boundary value problems
2020
We give a simple geometrical criterion for the nonexistence of constant-sign solutions for a certain type of third-order two-point boundary value problem in terms of the behavior of nonlinearity in the equation. We also provide examples to illustrate the applicability of our results.
Normal forms of hyperbolic logarithmic transseries
2021
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.
A strain-difference-based nonlocal elasticity model
2004
Abstract A two-component local/nonlocal constitutive model for (macroscopically) inhomogeneous linear elastic materials (but constant internal length) is proposed, in which the stress is the sum of the local stress and a nonlocal-type stress expressed in terms of the strain difference field, hence identically vanishing in the case of uniform strain. Attention is focused upon the particular case of piecewise homogeneous material. The proposed model is thermodynamically consistent with a suitable free energy potential. It constitutes an improved form of the Vermeer and Brinkgreve [A new effective nonlocal strain measure for softening plasticity. In: Chambon, R., Desrues, J., Vardulakis, I. (E…
Stochastic linearization of MDOF systems under parametric excitations
1992
Abstract The stochastic linearization approach is examined for non-linear systems subjected to parametric type excitations. It is shown that, for these systems too, stochastic linearization and Gaussian closure are two equivalent approaches if the former is applied to the coefficients of the Ito differential rule. A critical review of other stochastic linearization approaches is also presented and discussed by means of simple examples.
Non-linear oscillators under parametric and external poisson pulses
1994
The extended Ito calculus for non-normal excitations is applied in order to study the response behaviour of some non-linear oscillators subjected to Poisson pulses. The results obtained show that the non-normality of the input can strongly affect the response, so that, in general, it can not be neglected.
Internal fe approximation of spaces of divergence-free functions in three-dimensional domains
1986
SUMMARY The space of divergence-free vector functions with vanishing normal flux on the boundary is approximated by subspaces of finite elements having the same property. An easy way of generating basis functions in these subspaces is shown.