Eigenvalues for radially symmetric non-variational fully nonlinear operators

In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear operators exists in the framework of viscosity solutions. Here we want to show that for the radially symmetric operators (and one dimensional) a much simpler theory can be established, and that the complete set of eigenvalues and eigenfuctions characterized by the number of zeroes can be obtained

Topological gravity and transgression holography

We show that Poincare-invariant topological gravity in even dimensions can be formulated as a transgression field theory in one higher dimension whose gauge connections are associated to linear and nonlinear realizations of the Poincare group ISO(d-1,1). The resulting theory is a gauged WZW model whereby the transition functions relating gauge fields live in the coset ISO(d-1,1)/SO(d-1,1). The coordinate parametrizing the coset space is identified with the scalar field in the adjoint representation of the gauge group of the even-dimensional topological gravity theory. The supersymmetric extension leads to topological supergravity in two dimensions starting from a transgression field theory which is invariant under the supersymmetric extension of the Poincare group in three dimensions. We also apply this construction to a three-dimensional Chern-Simons theory of gravity which is invariant under the Maxwell algebra and obtain the corresponding WZW model.Comment: 22 pages; v2: minor corrections, references added; v3: analysis involving Maxwell algebra expanded, references added; v4: referencing fixed; Final version to be published in Physical Review

Dynamic gating in the nucleus accumbens: Behavioral state-dependent synchrony with the prefrontal cortex and hippocampus

Contextual and sensory information, goals, and the motor plan to achieve them are integrated in the nucleus accumbens (NA). Although this integration needs flexibility to operate in a variety of environments, models of NA function rarely consider changing behavioral states. Here, intracellular recordings in anesthetized rats revealed rapid changes in the synchronization between NA up states and prefrontal cortical (PFC) local field potentials (LFPs). The synchronization of the NA with the PFC and ventral hippocampus also varied over time in awake rats, depending on the behavioral state of the animal: NA LFPs followed hippocampal theta rhythms during spatial exploration, but not during an operant task when they were instead synchronized with slower PFC rhythms. These data indicate that the ability of the NA to follow cortical inputs can rapidly change, allowing for a mechanism that could select an optimal response for a given behavioral condition

The photino sector and a confining potential in a supersymetric Lorentz-symmetry-violating model

We study the spectrum of the minimal supersymmetric extension of the Carroll-Field-Jackiw model for Electrodynamics with a topological Chern-Simons-like Lorentz-symmetry violating term. We identify a number of independent background fermion condensates, work out the gaugino dispersion relation and propose a photonic effective action to consider aspects of confinement induced by the SUSY background fermion condensates, which also appear to signal Lorentz-symmetry violation in the photino sector of the action. Our calculations of the static potential are carried out within the framework of the gauge-invariant but path-dependent variables formalism which are alternative to the Wilson loop approach. Our results show that the interaction energy contains a linear term leading to the confinement of static probe charges.Comment: 11 pages, photino dispersion relation is extended to included the case the photino acquires mass through spontaneous SUSY breakin

Un Fallo Del Tedh Que Denota Su Postura Acerca De La Gestación Por Sustitución: La Tarea De Enfrentar Los Conflictos Que Plantea Una Práctica “Sin Sustento Legal”, Priorizando Sus Efectos.

Desde una perspectiva realista se posiciona el Tribunal Europeo de Derechos Humanos en lo sucesivo TEDH encauzando el debate que se viene dando en la regi n en torno a la gestaci n por sustituci n 1 y tomando una postura determinada con respecto al tema Seguramente la tarea ha sido dificultosa ya que este pronunciamiento im plic romper con algunos esquemas cl sicos acerca de la filiaci n cuyo debate se presenta en varios puntos del mundo -inclusive en nuestro pa s2- De esta forma el Tribunal puso fin a un conflicto jur dico -con cuestiones ticas y morales de fondo- de gran complejidad abord ndolo sin abstracciones y posibilitando el asentamiento de las bases para futuras aperturas normativas As el 26 de junio de 2014 el TEDH ha dictado su sentencia declarando en los asuntos 65192 11 Mennesson c Francia y 65941 11 Labassee c Francia la violaci n del ar

Aspects of CPT-even Lorentz-symmetry violating physics in a supersymmetric scenario

Background fermion condensates in a landscape dominated by global SUSY are reassessed in connection with a scenario where Lorentz symmetry is violated in the bosonic sector (actually, the photon sector) by a $CPT$-even $k_F$-term. An effective photonic action is discussed that originates from the supersymmetric background fermion condensates. Also, the photino mass emerges in terms of a particular condensate contrary to what happens in the $k_{AF}$-violation. Finally, the interparticle potential induced by the effective photonic action is investigated and a confining profile is identified.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1102.3777 by other author