On the Hong–Krahn–Szego inequality for the p-Laplace operator

Given an open set Ω, we consider the problem of providing sharp lower bounds for λ ₂(Ω), i.e. its second Dirichlet eigenvalue of the p-Laplace operator. After presenting the nonlinear analogue of the Hong–Krahn–Szego inequality, asserting that the disjoint unions of two equal balls minimize λ ₂ among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases p = 1 and p = ∞ are considered as well.     

Evidence for the flexo-electric effect in a nematic liquid crystal cell

Abstract

We present evidence for the flexo-electric effect in a hybrid aligned nematic cell containing 4-methoxybenzylidene-4'-n-butylaniline (MBBA) subject to d.c. excitation, by comparing the theoretical curve derived by including the flexo-electric term in the free energy with the experimental points. The agreement appears to be very good for MBBA doped with a small amount of an additive which shows reversible electrochemical reactions at very low redox potential; this allows us to determine the sum of the flexo-electric coefficients and the anchoring energy on the planar wall. For undoped MBBA the experimental results can be justified only by assuming a low voltage screening of the electric field, due to the presence of ionic impurities in the material.     

Synthetic Communication: Synthesis of Optically Pure Analogues of D-Arginine Methyl Ester with Antiarrhythmic Activity

The synthesis of the methyl esters of optically pure trans and cis 4-guanidinocyclohexylglycine as rigid analogues of D-arginine methyl ester are described.