用于电催化氧化甲醛的新型Ni(OH)2-X/CPE负载电极的制备

采用一种简易的方法制备了新型Ni(OH)2-X/CPE电极,并将其用于电催化氧化甲醛反应.采用扫描电镜和能量散射谱对所制Ni(OH)2-X/CPE电极进行了表征,并运用循环伏安法、电化学阻抗谱和计时电流法考察了该电极的电化学性能.结果表明,该Ni(OH)2-X/CPE电极对甲醛氧化表现出高电催化活性,这归功于X具有纳米孔结构和大的比表面积.电子传递系数和催化反应速率常数分别为0.7和6.1×104 cm3/(mol·s).该电极对甲醛氧化具有高而稳定的电催化活性,且制备重复性高,有望应用于燃料电池中.     

Large time behavior of solutions of a dissipative semilnear heat equation

We study the current of the Pauli operator in a strong constant magnetic field. We prove that in the semi-classical limit the persistent current and the current from the interaction of the spin with the magnetic field cancel, in the case where the magnetic field is very strong. Furthermore we calculate the next term in the asymptotics and estimate the error. Finally, we discuss the connection between this work and the semi-classical estimate of the energy in strong magnetic fields proved by Lieb, Solovej and Yngvason [8] Lieb, E., Solovej, J. P. and Yngvason, J. 1994. Asymptotics of heavy atoms in high magnetic fields: II. Semiclassical regions. Commun. Math. Phys., 161: 77–124. [Crossref], [Web of Science ®] , [Google Scholar].

     

An Analysis of the Dynamical Evolution of Experimental,Recreative and Abusive Marijuana Consumption in the States of Colorado and Washington Beyond the Implementation of I–502

We analyze the NERA model (N: Nonuser, E: Experimental Users, R: Recreational Users, A: Addicts), which describes the illicit drug usage dynamics in a population consisting of both drug users and nonusers. The model considers three categories of drug users: the experimental (E) category, the recreational (R) category and the addict(A) category. We prove the uniqueness and positivity of the solution to the model in time.

We extend the model by taking into account the unpredictability of person-to-person contacts and consider individuals susceptible to experience an illicit drug being subjected to a continuous spectrum of random factors. Based on the existence of such a randomness in the movement from nonuser to experimental users, we modify the model to set up a stochastic one. The latter model is also analyzed in the current work. We verify and validate our results by using the data available in Hanley (2013 Hanley, S. (2013). Legalization of recreational marijuana in Washington: Monitoring trends in use prior to the implementation of I–502. Retrieved from http://www.wsipp.wa.gov/ReportFile/1540/Wsipp Legalization-of-Recreational-Marijuana-in-Washington-Monitoring-Trends-in-Use-Prior-to-the-Implementation-of-I-502 Full-Report.pdf. [Google Scholar]), on the prevalence of marijuana in the population of 21+ in the states of Colorado and Washington. We simulate the evolution of the above mentioned categories of drug users within those two states from 2002, beyond the implementation of I–502 and until 2040. Our results show that the model can used as a policy decision mechanism in the problematic of illicit drug consumption by monitoring the respond of the different categories of drug users when subject to drug control interventions.     

Rate of decay to equilibrium in some semilinear parabolic equations

In this paper we prove, under various conditions, the so-called Lojasiewicz inequality $ \| E' (u + \varphi) \| \geq \gamma|E(u+\varphi) - E(\varphi)|^{1-\theta} $, where $ \theta \in (0,1/2] $, and > 0, while $ \| u \| $ is sufciently small and is a critical point of the energy functional E supposed to be only C⊃, instead of analytic in the classical settings. Here E can be for instance the energy associated to the semilinear heat equation $u_t = \Delta u - f(x,u) $ on a bounded domain $ \Omega \subset \mathbb{R}^N $. As a corollary of this inequality we give the rate of convergence of the solution u(t) to an equilibrium, and we exhibit examples showing that the given rate of convergence (which depends on the exponent and on the critical point through the nature of the kernel of the linear operator $ E' (\varphi)) $ is optimal.     

Régularité dans une équation de Schrödinger avec potentiel singulier à distance finie et à l'infini

In this Note we study the Schrödinger equation i?_tu+Δu+V₀u+V₁u=0 on $\text{R}{}^3\text{×(0,T)}$ with initial condition $\text{u}{}_0\text{∈{v∈H}{}^2\text{(}\text{R}{}^3\text{)}$, where V₀ is a coulombian potential, singular at finite distance and V₁ is an electric potential, possibly unbounded. Both of them may depend on space and time variables. We prove that this problem is well-posed and that the regularity of the initial data is conserved for the solution. The detailed proof will be given elsewhere (Baudouin et al., in press). To cite this article: L. Baudouin et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).