On the Discrete Spectrum of a Spatial Quantum Waveguide with a Disc Window

In this study we investigate the bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width d. We impose the Neumann boundary condition on a disc window of radius a and Dirichlet boundary conditions on the remained part of the boundary of the strip. We prove that such system exhibits discrete eigenvalues below the essential spectrum for any a > 0. We give also a numeric estimation of the number of discrete eigenvalue as a function of \fracad\frac{a}{d}. When a tends to the infinity, the asymptotic of the eigenvalue is given.     

Decay rates of the solution of the Cauchy thermoelastic Bresse system

We consider two Cauchy problems for the one-dimensional thermoelastic Bresse model. Using the energy method in the Fourier space, we show that for the first model, the \({L^{2}}\)-norm of the solution decays with the rate \({(1+t)^{-1/12}}\). In addition, the same decay rate has been obtained for the second model.     

Reduced Jacobian Method

In this paper, we present the Wolfe’s reduced gradient method for multiobjective (multicriteria) optimization. We precisely deal with the problem of minimizing nonlinear objectives under linear constraints and propose a reduced Jacobian method, namely a reduced gradient-like method that does not scalarize those programs. As long as there are nondominated solutions, the principle is to determine a direction that decreases all goals at the same time to achieve one of them. Following the reduction strategy, only a reduced search direction is to be found. We show that this latter can be obtained by solving a simple differentiable and convex program at each iteration. Moreover, this method is conceived to recover both the discontinuous and continuous schemes of Wolfe for the single-objective programs. The resulting algorithm is proved to be (globally) convergent to a Pareto KKT-stationary (Pareto critical) point under classical hypotheses and a multiobjective Armijo line search condition. Finally, experiment results over test problems show a net performance of the proposed algorithm and its superiority against a classical scalarization approach, both in the quality of the approximated Pareto front and in the computational effort.     

Valeurs propres relatives à un cône convexe : caractérisation et résultats de cardinalité

Let A be an n×n real matrix, and $\text{K?}\text{R}{}^{\mathrm{n}}$ be a closed convex cone. The spectrum of A relative to K, denoted by σ(A,K), is the set of all $\text{λ∈}\text{R}$ for which the linear complementarity problem

$\text{x∈K,}\text{Ax?λx∈K}{}^{\mathrm{+}}\text{,}\text{〈x,Ax?λx〉=0}$

admits a nonzero solution $\text{x∈}\text{R}{}^{\mathrm{n}}$. The aim of this Note is to study the main properties of the set-valued mapping $\text{σ(·}\text{,K)}$, and discuss some structural differences existing between the polyhedral case (i.e., K is finitely generated) and the non-polyhedral case. To cite this article: A. Seeger, M. Torki, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Attenuation of Electromagnetic Waves by a Plasma Layer at Atmospheric Pressure

Plasma layers at atmospheric pressure, are good broad band absorbers of electromagnetic radiation. However, to get substantial attenuations, two parameters have to be optimized. These are the plasma number density, and the thickness of the plasma layer. It is found that in order to be an effective attenuator of microwave radiation, a plasma layer has to have a number density in the 10¹³ cm^–3 range, and a thickness equal or larger than the wavelength of the incident wave. However, as the frequency increases, the amount of attenuation tends to reach a limiting value directly proportional to the number density.     

Nanoemulsification Improves the Pharmaceutical Properties and Bioactivities of Niaouli Essential Oil (Melaleuca quinquenervia L.)

We develop a suitable delivery system for niaouli essential oil (NEO) using a nanoemulsification method for acne vulgaris. Prepared nanoemulsions (NEs) were characterized for droplet dimension, rheology, surface charge, and stability. The ability of NEO formulations against Propionibacterium acnes and Staphylococcus epidermidis was investigated and all formulations showed antiacne potential in vitro. Ex vivo permeation studies indicated significant improvement in drug permeations and steady state flux of all NEO-NEs compared to the neat NEO (p < 0.05). On the basis of the studied pharmaceutical parameters, enhanced ex vivo skin permeation, and marked effect on acne pathogens, formulation NEO-NE₄ was found to be the best (oil (NEO; 10% v/v); Kolliphor EL (9.25% v/v), Carbitol (27.75% v/v), and water (53% v/v)). Concisely, the in vitro and ex vivo results revealed that nanoemulsification improved the delivery as well as bioactivities of NEO significantly.     

Fluorous phase-switching of pyridyl-tagged substrates/products

A bis-monopyridyl Wang-type tag was prepared for application in the hydrocarbon/perfluorocarbon phase-switching of substrates/products. This "catch-and-release" strategy relies on the reversible coordination of the tag to a fluorous copper(II)-carboxylate complex. A hydantoin was prepared in high yield and purity by a four-step protocol where the intermediates were purified by the straightforward liquid/liquid phase-switching process. [reaction: see text]     

Sobolev Type Spaces on the Dual of the Laguerre Hypergroup

Sobolev type spaces E ^s,p (0, sR, p[1,+]) are defined on R×N by using the Fourier transform and its inverse on the Laguerre hypergroup. An analogue of H ^s (R ⁿ ), denoted by H ^s is investigated in this paper. Some properties including completeness and imbedding results for these spaces are given, Reillich-type theorem and Poincaré's inequality are proved. Also, global regularity results for certain differential operators are obtained.     

Positivity of the Shape Hessian and Instability of some Equilibrium Shapes

We study the positivity of the second shape derivative around an equilibrium for a 2-dimensional functional involving the perimeter of the shape and its the Dirichlet energy under volume constraint. We prove that, generally, convex equilibria lead to strictly positive second derivatives. We also exhibit some examples where strict positivity of the second order derivative holds at an equilibrium while existence of a minimum does not.     

Oxidative Effects during Irreversible Electroporation of Melanoma Cells—In Vitro Study

Irreversible electroporation (IRE) is today used as an alternative to surgery for the excision of cancer lesions. This study aimed to investigate the oxidative and cytotoxic effects the cells undergo during irreversible electroporation using IRE protocols. To do so, we used IRE-inducing pulsed electric fields (PEFs) (eight pulses of 0.1 ms duration and 2–4 kV/cm intensity) and compared their effects to those of PEFs of intensities below the electroporation threshold (eight pulses, 0.1 ms, 0.2–0.4 kV/cm) and the PEFs involving elongated pulses (eight pulses, 10 ms, 0.2–0.4 kV/cm). Next, to follow the morphology of the melanoma cell membranes after treatment with the PEFs, we analyzed the permeability and integrity of their membranes and analyzed the radical oxygen species (ROS) bursts and the membrane lipids’ oxidation. Our data showed that IRE-induced high cytotoxic effect is associated both with irreversible cell membrane disruption and ROS-associated oxidation, which is occurrent also in the low electric field range. It was shown that the viability of melanoma cells characterized by similar ROS content and lipid membrane oxidation after PEF treatment depends on the integrity of the membrane system. Namely, when the effects of the PEF on the membrane are reversible, aside from the high level of ROS and membrane oxidation, the cell does not undergo cell death.