Liouville Results for <Emphasis Type="Italic">m</Emphasis>-Laplace Equations in Half-Space and Strips with Mixed Boundary Value Conditions and Finite Morse Index

We consider sign-changing solutions of the equation \(-\Delta _m u= |u|^{p-1}u\) where \(m\ge 2\) and \(p>1\) in half-space and strips with nonlinear mixed boundary value conditions. We prove Liouville type theorems for stable solutions or for solutions which are stable outside a compact set. The main methods used are the integral estimates, the Pohozaev-type identity and the monotonicity formula.     

Energy Scaling of Compressed Elastic Films –Three-Dimensional Elasticity¶and Reduced Theories

We derive an optimal scaling law for the energy of thin elastic films under isotropic compression, starting from three-dimensional nonlinear elasticity. As a consequence we show that any deformation with optimal energy scaling must exhibit fine-scale oscillations along the boundary, which coarsen in the interior. This agrees with experimental observations of folds which refine as they approach the boundary. We show that both for three-dimensional elasticity and for the geometrically nonlinear Föppl-von Kármán plate theory the energy of a compressed film scales quadratically in the film thickness. This is intermediate between the linear scaling of membrane theories which describe film stretching, and the cubic scaling of bending theories which describe unstretched plates, and indicates that the regime we are probing is characterized by the interplay of stretching and bending energies. Blistering of compressed thin films has previously been analyzed using the Föppl-von Kármán theory of plates linearized in the in-plane displacements, or with the scalar eikonal functional where in-plane displacements are completely neglected. The predictions of the linearized plate theory agree with our result, but the scalar approximation yields a different scaling.     

On the class of almost L-weakly and almost M-weakly compact operators

In this paper, we introduce and study new concepts of almost L-weakly and almost M-weakly compact operators.     

Synthese De (1,2a)Benzimidazolo-1,3,5,2-triazaphosphorine-2-oxides

The reaction of hexamethylphosphotriamide or methylphosphonic bis(dimethylamide) compounds with amidines derived from N-Benzimidazoyl imidates 1 leads to (1,2a)benzimidazolo-1,3,5,2-tiazaphosphorine-2-oxides 4 in good yields. If the condensation is realized at room temperature, N-phosphonic amidines 3 can be isolated as intermediates. The isolated compounds 2 , 3 , and 4 are identified by spectroscopic methods: IR, 1 H, 13 C, 31 P, NMR, and M.S.     

About b-weakly compact operators on Banach lattices

We characterize Banach lattices on which each positive operators is b-weakly compact and we derive some characterizations of KB-spaces.     

Uniqueness for an ill-posed parabolic system

The purpose is the uniqueness for an ill-posed parabolic system. This result enables us to state the identifiability for the problem of detecting pointwise organic pollution sources in surface waters.     

REACTION DES O,O-DIETHYL OXO-1 ALKANEPHOSPHONATES AVEC LES DERIVES DE L'HYDRAZINE: UNE VOIE DE SYNTHESE DES HYDRAZONES α-PHOSPHONATEES ET DES HYDRAZIDES

Abstract

Under the normal conditions, the reaction of hydrazine and methylhydrazine with OO-diethyl 1 oxoalkane phosphonates 1 proceeds by cleavage of the phosphorus-carbon bond and leads to the formation of diethylphosphite 2 and N-acylhydrazide 3 . A procedure has been developed for the synthesis of new primary hydrazone of OO-diethyl 1-oxoalkane phosphonates 4 . A mechanism is proposed. The structure of those compounds 4 was confirmed by NMR and IR spectroscopy.