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Displaying 1201 –
1220 of
5449
We present a new method to compute normal forms, applied to the germs of reversible mappings. We translate the classification problem of these germs to the theory of ideals in the space of the coefficients of their jets. Integral factorization coupled with Gröbner basis constructionjs the key factor that makes the process efficient. We also show that a language with typed objects like AXIOM is very convenient to solve these kinds of problems.
On étudie le comportement des premières valeurs propres du laplacien agissant sur les formes différentielles lors d’un effondrement adiabatique d’un flot riemannien sur une variété compacte . Le nombre de petites valeurs propres peut alors se calculer en fonction de la cohomologie basique de , et on donne des critères spectraux pour l’annulation des classes d’Álvarez et d’Euler du flot. En outre, on définit un invariant de nature diophantienne du flot qui est lié au comportement asymptotique...
À courbure et diamètre bornés, les valeurs propres non nulles du laplacien de Hodge-de Rham agissant sur les formes différentielles d’une variété compacte ne sont pas uniformément minorées comme c’est le cas pour les fonctions, et si l’une d’elle tend vers zéro alors le volume de la variété tend aussi vers zéro, c’est-à-dire qu’elle s’effondre. On présente ici les résultats obtenus ces dernières années concernant le problème réciproque, à savoir déterminer le comportement asymptotique des premières...
We study stationary solutions of the damped wave equation on a compact and smooth Riemannian manifold without boundary. In the high frequency limit, we prove that a sequence of -damped stationary solutions cannot be completely concentrated in small neighborhoods of a small fixed hyperbolic subset made of -damped trajectories of the geodesic flow.The article also includes an appendix (by S. Nonnenmacher and the author) where we establish the existence of an inverse logarithmic strip without eigenvalues...
Asymptotics with sharp remainder estimates are recovered for number of eigenvalues of the generalized Maxwell problem and for related Laplacians which are similar to Neumann Laplacian. We consider domains with ultra-thin cusps (with ) width ; ) and recover eigenvalue asymptotics with sharp remainder estimates.
In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact manifolds
For compact hypersurfaces with constant mean curvature in the unit sphere, we give a comparison theorem between eigenvalues of the stability operator and that of the Hodge Laplacian on 1-forms. Furthermore, we also establish a comparison theorem between eigenvalues of the stability operator and that of the rough Laplacian.
We consider the nonlinear eigenvalue problem
in with . A condition on indefinite weight function is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in . A nonexistence result is also given for the case .
This is a readable review of recent work on non-Hermitian bound state problems with complex potentials. A particular example is the generalization of the harmonic oscillator with the potentials:
Other examples include complex generalizations of the Morse potential, the spiked radial harmonic potential, the Kratzer-Coulomb potential, the Rosen Morse oscillator and others. Instead of demanding Hermiticity the condition required is where changes the parity and transforms to .
Currently displaying 1201 –
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