曲面平滑的自适应几何扩散

1.引 言 本文的目的是用求解偏微分方程（PDE）的方法来消除离散三角形曲面的噪声,所使用的方程是热传导方程到曲面的推广.热传导方程应用于图像处理已有二十余年的历史,有关参考文献相当丰富（见[1,11,12,19]）.众所周知,对于给定的初始图像ρ0,热传导方程　　在τ时刻的解与用Gauss滤波器Gσ（x）=　（当标准差σ=2τ,时）和ρ0作卷积的结果相同.容易看出Gρ和ρ0的卷积运算相当于对ρ0做加权平均,当标准离差σ变大时,该加权平均在一个较大的范围实现,这解释了热传导方程的滤波作用.近来热传导方程已推广到空间曲面[4,5]以及高维空间中的二维流形（见[3]）,对     

Fundamental processes in long air gap discharges

The development of atmospheric lightning is initiated and sustained by the formation in virgin air of ‘streamer corona’ and ‘leader’ discharges, very similar to those observed in laboratory long sparks. Therefore, the experimental and theoretical investigations of these laboratory discharges have become of large interest to improve the physical knowledge of the lightning process and to develop self-consistent models that could be applied to new protection concepts.In the present paper the fundamental processes of the subsequent phases of long air gap discharges are analyzed, from the first corona inception and development to the leader channel formation and propagation. For all these processes simulations models are discussed that have been essentially derived and simplified by the authors, in order to develop sequential time-dependent simulation of the laboratory breakdown, with both positive and negative voltages. The possibility of extending these models to the case of natural lightning is discussed in the companion paper, presented in this same volume. To cite this article: I. Gallimberti et al., C. R. Physique 3 (2002) 1335–1359.     

聚丙烯孔洞铁电驻极体膜的电极化及其电荷动态特性

根据栅控恒压电晕充电组合反极性电晕补偿充电法的实验结果计算出铁电驻极体的极化强度.结果说明，伴随着薄膜内孔洞气体的Paschen击穿，该铁电体的极化强度随栅压增加而显著上升.利用上述充电方法和热刺激放电(TSD)谱的分析讨论了这类空间电荷型宏观电偶极子，及与其补偿的空间电荷热退极化的电荷动态特性；阐明了这两类俘获电荷的能阱分布，即构成宏观电偶极子的位于孔洞上下介质层内的等值异号空间电荷分别被俘获在深、浅两种能值陷阱内，而位于薄膜表面层的注入空间电荷则被俘获在中等能值陷阱中. 关键词： 反极性电晕补偿充电法 铁电驻极体 充电电流 热刺激放电     

A Generalization of the Mean Size Formula of Wavelet Packets in Lp

The purpose of this paper is to investigate the mean size formula of wavelet packets in Lp for 0 〈 p ≤ ∞. We generalize a mean size formula of wavelet packets given in terms of the p-norm joint spectral radius and we also give some asymptotic formulas for the Lp-norm or quasi-norm on the subdivision trees. All results will be given in the general setting,     

Polynomial Reproduction in Subdivision

We study conditions on the matrix mask of a vector subdivision scheme ensuring that certain polynomial input vectors yield polynomial output again. The conditions are in terms of a recurrence formula for the vectors which determine the structure of polynomial input with this property. From this recurrence, we obtain an algorithm to determine polynomial input of maximal degree. The algorithm can be used in the design of masks to achieve a high order of polynomial reproduction.     

恒流电晕充电对聚四氟乙烯多孔薄膜驻极体驻极态的影响

利用常温下恒流和恒压电晕充电、充电后的等温表面电位衰减、热刺激放电和扫描电镜等实 验手段研究了恒流和恒压电晕充电技术对聚四氟乙烯多孔薄膜驻极体驻极态的影响.与恒压电晕充电相比较，恒流电晕充电时由于流过薄膜的电流恒定，增加了注入电荷在多孔结构厚度方向界面处的俘获概率，使沉积电荷密度上升，改善了驻极体的储电能力.然而，这些位于不同层深多孔界面处的俘获电荷在这类功能膜储存或使用过程中，经外激发从脱阱位置 以跳动（hopping）模式输运至背电极的路径相对缩短将导致脱阱电荷衰减较快. 关键词： 恒流电晕充电 聚四氟乙烯多孔膜 驻极体 电荷稳定性     

Regularity of multiwavelets

The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L _p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.     

A matricial corona theorem II

We extend the ``matricial corona theorem' of M. Andersson to general algebras of functions which satisfy a corona theorem.

     

On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

Effect of the subdivision strategy on convergence and efficiency of some global optimization algorithms

We investigate subdivision strategies that can improve the convergence and efficiency of some branch and bound algorithms of global optimization. In particular, a general class of so called weakly exhaustive simplicial subdivision processes is introduced that subsumes all previously known radial exhaustive processes. This result provides the basis for constructing flexible subdivision strategies that can be adapted to take advantage of various problem conditions.