Lower bounds for the norms of decomposable symmetrized tensors

Lower bounds are given for the difference of two decomposable symmetrized tensors. The first bound uses a norm which makes the component vectors in a decomposable symmetrized tensor part of an orthonormal basis. The second bound holds only for decomposable elements of symmetry classes whose associated characters are linear.     

Selective Lanthanides Sequestration Based on a Self‐Assembled Organosilica

In this paper, we investigate the cation‐exchange properties of a self‐assembled hybrid material towards trivalent ions, lanthanides (La³⁺, Eu³⁺, Gd³⁺, Yb³⁺) and Fe³⁺. The bis‐zwitterionic lamellar material was prepared by sol–gel process from only 3‐aminopropyltriethoxysilane (APTES), succinic anhydride, and ethylenediamine. In ethanol heated under reflux, the exchange ethylenediammonium versus Ln³⁺ proved to be complete by complexometry measurements and elemental analyses, one Cl^? ion per one Ln^III remaining as expected for charge balance. In aqueous solution at 20 °C, the material was found to be selective towards lanthanide in spite of the similarity of their ionic radii. The cation uptake depends on the nature of the salt, the difference between two lanthanides reaching up to 20 % in some cases. Finally, ion‐exchange reaction with FeCl₃ was chosen as a probe to get more information on the material after incorporation of trivalent ions. Based on Mössbauer spectroscopic investigations on the resulting material in conjunction with the XRD analysis of materials containing trivalent ions, a structural model was proposed to describe the incorporation of trivalent ions by exchange reaction within the original zwitterionic material.     

Existence of Weak Solutions Up to Collision for Viscous Fluid‐Solid Systems with Slip

We study in this paper the movement of a rigid solid inside an incompressible Navier‐Stokes flow within a bounded domain. We consider the case where slip is allowed at the fluid/solid interface through a Navier condition. Taking into account slip at the interface is very natural within this model, as classical no‐slip conditions lead to unrealistic collisional behavior between the solid and the domain boundary. We prove for this model existence of weak solutions of Leray type, up to collision, in three dimensions. The key point is that, due to the slip condition, the velocity field is discontinuous across the fluid/solid interface. This prevents obtaining global H¹ bounds on the velocity, which makes many aspects of the theory of weak solutions for Dirichlet conditions inappropriate. © 2014 Wiley Periodicals, Inc.     

Metric Subregularity in Generalized Equations

In this article, we study the metric subregularity of generalized equations using a new tool of nonsmooth analysis. We obtain a sufficient condition for a generalized equation to be metrically subregular, which is not a necessary condition for metric regularity, using a subtle adjustment of the Mordukhovich coderivative. We apply these results to the study of the metric subregularity in a Cournot duopoly game.     

Constante de Bers en genre 2

We introduce a new tool, the contiguity graph, which enables us to determine the Bers’s constant in genus two.     

Rapid traveling waves in the nonlocal Fisher equation connect two unstable states

In this note, we give a positive answer to a question addressed in Nadin et al. (2011) [7]. To be precise, we prove that, for any kernel and any slope at the origin, there exist traveling wave solutions (actually those which are “rapid”) of the nonlocal Fisher equation that connect the two homogeneous steady states 0 (dynamically unstable) and 1. In particular, this allows situations where 1 is unstable in the sense of Turing. Our proof does not involve any maximum principle argument and applies to kernels with fat tails.     

Supersymmetry and its spontaneous breaking in the random field Ising model

We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group for the critical behavior of the random field Ising model in a superfield formalism, we are able to follow the associated supersymmetry and its spontaneous breaking along the functional renormalization group flow. Breaking is shown to occur below a critical dimension d(DR) ? 5.1 and leads to a breakdown of the "dimensional reduction" property. We compute the critical exponents as a function of dimension and give evidence that scaling is described by three independent exponents.