Search results for " singularities."
showing 10 items of 27 documents
Discriminación indirecta por pertenencia a minoría nacional : denegación de prestación de viudedad en el caso de matrimonio celebrado según el rito g…
2021
The commented sentence rejects that the Muñoz Díaz doctrine is applicable to all cases of gypsy marriage. In addition, it considers that the denial of effects to the union celebrated according to said rite is not discriminatory. This conclusion is discussed, understanding that the analysis of the singularities of the gypsy people must lead to the conclusion of the existence of indirect discrimination.
MR3090050 Reviewed Belabbas, Mohamed Ali On global stability of planar formations. IEEE Trans. Automat. Control 58 (2013), no. 8, 2148–2153. (Reviewe…
2014
The focus of the paper is planar formation control, i.e. the design of control laws to stabilize agents at given distances from each other, under the constraint that the dynamics of each agent only depends on a subset of the other agents. The main contribution of the paper is the following: It is shown that a simple four-agent formation cannot be globally stabilized using twice differentiable control laws (this is not the case for three-agent formations), even up to sets of measure zero of initial conditions. This suggests that for four-agent formations one needs to look for control laws that are either not differentiable (or even not continuous) or of higher order in the dynamics. The appr…
Oscillatory integrals and fractal dimension
2021
Theory of singularities has been closely related with the study of oscillatory integrals. More precisely, the study of critical points is closely related to the study of asymptotic of oscillatory integrals. In our work we investigate the fractal properties of a geometrical representation of oscillatory integrals. We are motivated by a geometrical representation of Fresnel integrals by a spiral called the clothoid, and the idea to produce a classification of singularities using fractal dimension. Fresnel integrals are a well known class of oscillatory integrals. We consider oscillatory integral $$ I(\tau)=\int_{; ; \mathbb{; ; R}; ; ^n}; ; e^{; ; i\tau f(x)}; ; \phi(x) dx, $$ for large value…
Well-posedness and singularity formation for the Camassa-Holm equation
2006
We prove the well-posedness of Camassa--Holm equation in analytic function spaces both locally and globally in time, and we investigate numerically the phenomenon of singularity formation for particular initial data.
Quasianalytic Denjoy-Carleman classes and o-minimality
2003
We show that the expansion of the real field generated by the functions of a quasianalytic Denjoy-Carleman class is model complete and o-minimal, provided that the class satisfies certain closure conditions. Some of these structures do not admit analytic cell decomposition, and they show that there is no largest o-minimal expansion of the real field.
Complex singularities in KdV solutions
2016
In the small dispersion regime, the KdV solution exhibits rapid oscillations in its spatio-temporal dependence. We show that these oscillations are caused by the presence of complex singularities that approach the real axis. We give a numerical estimate of the asymptotic dynamics of the poles.
Removable singularities for div v=f in weighted Lebesgue spaces
2018
International audience; Let $w\in L^1_{loc}(\R^n)$ be apositive weight. Assuming that a doubling condition and an $L^1$ Poincar\'e inequality on balls for the measure $w(x)dx$, as well as a growth condition on $w$, we prove that the compact subsets of $\R^n$ which are removable for the distributional divergence in $L^{\infty}_{1/w}$ are exactly those with vanishing weighted Hausdorff measure. We also give such a characterization for $L^p_{1/w}$, $1<p<+\infty$, in terms of capacity. This generalizes results due to Phuc and Torres, Silhavy and the first author.
High-energy evolution to three loops
2018
The Balitsky-Kovchegov equation describes the high-energy growth of gauge theory scattering amplitudes as well as nonlinear saturation effects which stop it. We obtain the three-loop corrections to this equation in planar $\mathcal{N}=4$ super Yang-Mills theory. Our method exploits a recently established equivalence with the physics of soft wide-angle radiation, so-called non-global logarithms, and thus yields at the same time the three-loop evolution equation for non-global logarithms. As a by-product of our analysis, we develop a Lorentz-covariant method to subtract infrared and collinear divergences in cross-section calculations in the planar limit. We compare our result in the linear re…
Resolution of singularities for multi-loop integrals
2007
We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to terminate. The program can be used to compute numerically the Laurent expansion of divergent multi-loop integrals regulated by dimensional regularisation. The symbolic and the numerical steps of the algorithm are combined into one program.
About the role of hamiltonian singularities in controlled systems : applications in quantum mechanics and nonlinear optics
2012
This thesis has two goals: the first one is to improve the control techniques in quantum mechanics, and more specifically in NMR, by using the tools of geometric optimal control. The second one is the study of the influence of Hamiltonian singularities in controlled systems. The chapter about optimal control study three classical problems of NMR : the inversion problem, the influence of the radiation damping term, and the steady state technique. Then, we apply the geometric optimal control to the problem of the population transfert in a three levels quantum system to recover the STIRAP scheme.The two next chapters study Hamiltonian singularities. We show that they allow to control the polar…