this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

The objective of this work is to develop some tools for local instability analysis of multiple critical points, which can be computationally carried out. The Morse index can be used to measure local instability of a nondegenerate saddle point. However, it is very expensive to compute numerically and is ineffective for degenerate critical points. A local (weak) linking index can also be defined ...

In the last few years a number of works reported the appearance of thick branes with internal structure, induced by the parameter which controls the interaction between two scalar fields coupled to gravity in (4,1) dimensions in warped space-time with one extra dimension. Here we show that one can implement the control over the brane thickness without needing to change the potential parameter. ...

In this paper, we deal with the boundary controllability of a one-dimensional degenerate and singular wave equation degeneracy singularity occurring at spatial domain. Exact is proved in range both subcritical critical potentials for sufficiently large time, through controller acting away from degenerate/singular point. By duality argument, reduce problem to an observability estimate correspond...

We study critical and stationary, i.e., with respect to both inner outer variations, points of polyconvex functionals the form for . In particular, we show that a.e. have locally constant determinant except in a relatively closed set measure zero, stationary almost everywhere. This is deduced from more general result concerning solutions , linearized problem also present some generalization ori...

• To propose a direct and “elementary” proof of the main result of [3], nameley that the semi-classical spectrum near a global minimum of the classical Hamiltonian determines the whole semi-classical Birkhoff normal form (denoted the BNF) in the non-resonant case. I believe however that the method used in [3] (trace formulas) are more general and can be applied to any non degenerate non resonan...