空间站快速充电事件的机理研究

空间站等大型航天器由于采用高压太阳电池阵而引发的 带电问题成为近年来航天器带电研究领域的热点问题. 近年来观测到国际空间站(ISS)在出地影瞬间产生的"快速带电"事件 (也称"异常带电") , 再度引起了对低轨道航天器充电效应的深入研究. "快速带电"事件的特征为, 集中出现在出地影的瞬间, 在几秒内快速上升到较高电位(30—70 V), 然后在几十秒时间内缓慢衰降, 相对高压电池阵本身引起的结构体带电(称为"正常带电", 一般在30 V以下)严重得多. 目前国际上对"快速带电"的研究尚不充分. 本文在Furguson等人机理研究工作的基础上, 首次建立了描述"快速带电"事件的物理模型, 定量揭示了其充电过程的主要机理. 根据该模型对国际空间站的"快速带电"进行计算, 结果与观测到的典型充电脉冲符合, 模型预测的快速带电事件的统计规律也与观测结果基本一致. 关键词： 表面充电 等离子体 空间站 高压太阳电池阵     

Friedrichs Method in a Lyapunov Problem

By using the well-known Friedrichs extension and some a priori inequality, we obtain weak solutions of a Lyapunov equation. In particular, we show that the Lyapunov functions satisfying necessary and sufficient conditions in the domain of asymptotic stability of a singular point some dynamical system must be absolutely continuous.     

The Pseudo-differential Operator hμ,a on Hankel Invariant Spaces

Using Hankel transform the symbol 'a' is defined and the pseudo-differential operator (p.d.o.) h_μ,a associated with the Bessel operator d ²/dx ² + (1 ? 4μ ²)/4x ² in terms of this symbol is defined. It is shown that the operator h_μ,a is a continuous linear map of a Hankel invariant space into itself. A special pseudo-differential operator called the Hankel potential is defined and some of its properties are investigated.     

Fixed point theorems for multivalued operators and application to discontinuous quasilinear BVP's

In this article, we prove an abstract fixed point theorem for increasing multivalued operators in ordered topological spaces, which provides an efficient tool to obtain qualitative results on the solution set of discontinuous quasilinear elliptic boundary value problems. In particular, we are able to show the existence of extremal solutions of such problems.     

On Groups with Finitely Many Conradian Orderings

We study the space of left-orderings on groups with (only) finitely many Conradian orderings. We show that, within this class of groups, having an isolated left-ordering is equivalent to having finitely many left-orderings.     

Approximation by Nonlinear Multivariate Sampling Kantorovich Type Operators and Applications to Image Processing

In this article, we study a nonlinear version of the sampling Kantorovich type operators in a multivariate setting and we show applications to image processing. By means of the above operators, we are able to reconstruct continuous and uniformly continuous signals/images (functions). Moreover, we study the modular convergence of these operators in the setting of Orlicz spaces L ^?(? ⁿ ) that allows us to deal the case of not necessarily continuous signals/images. The convergence theorems in L ^p (? ⁿ )-spaces, L ^αlog ^β L(? ⁿ )-spaces and exponential spaces follow as particular cases. Several graphical representations, for the various examples and image processing applications are included.     

Dynamics of Dislocation Densities in a Bounded Channel. Part II: Existence of Weak Solutions to a Singular Hamilton–Jacobi/Parabolic Strongly Coupled System

We study a strongly coupled system consisting of a parabolic equation and a singular Hamilton–Jacobi equation in one space dimension. This system describes the dynamics of dislocation densities in a material submitted to an exterior applied stress. Our system is a natural extension of that studied in [16 Ibrahim , H. ( 2009 ). Existence and uniqueness for a non-linear parabolic/Hamilton–Jacobi coupled system describing the dynamics of dislocation densities . Ann. Inst. H. Poincaré Anal. Non Linéaire 26 : 415 – 435 . [Google Scholar]] where the applied stress was set to be zero. The equations are written on a bounded interval with Dirichlet boundary conditions and require special attention to the boundary. We prove a result of global existence of a solution. The method of the proof consists in considering first a parabolic regularization of the full system, and then passing to the limit. For this regularized system, a result of global existence and uniqueness of a solution has been given in [17 Ibrahim , H. , Jazar , M. , Monneau , R. Dynamics of dislocation densities in a bounded channel. Part I: smooth solutions to a singular coupled parabolic system. Preprint . [Google Scholar]]. We show some uniform bounds on this solution which uses in particular an entropy estimate for the densities.