Least-squares integration of one-dimensional codistributions with application to approximate feedback linearization

We study the problem of approximating one-dimensional nonintegrable codistributions by integrable ones and apply the resulting approximations to approximate feedback linearization of single-input systems. The approach derived in this paper allows a linearizable nonlinear system to be found that is close to the given system in a least-squares (L ₂) sense. A linearly controllable single-input affine nonlinear system is feedback linearizable if and only if its characteristic distribution is involutive (hence integrable) or, equivalently, any characteristic one-form (a one-form that annihilates the characteristic distribution) is integrable. We study the problem of finding (least-squares approximate) integrating factors that make a fixed characteristic one-form close to being exact in anL ₂ sense. A given one-form can be decomposed into exact and inexact parts using the Hodge decomposition. We derive an upper bound on the size of the inexact part of a scaled characteristic one-form and show that a least-squares integrating factor provides the minimum value for this upper bound. We also consider higher-order approximate integrating factors that scale a nonintegrable one-form in a way that the scaled form is closer to being integrable inL ₂ together with some derivatives and derive similar bounds for the inexact part. This allows a linearizable nonlinear system that is close to the given system in a least-squares (L ₂) sense together with some derivatives to be found. The Sobolev embedding techniques allow us to obtain an upper bound on the uniform (L _∞) distance between the nonlinear system and its linearizable approximation. This research was supported in part by NSF under Grant PYI ECS-9396296, by AFOSR under Grant AFOSR F49620-94-1-0183, and by a grant from the Hughes Aircraft Company.     

概率空间中的一个不等式

设｛Ｚ，（Ｗ）｝是定义在概率空间上的独立的随机变量序列，Ｚ（Ｗ）具有方差为期望Ｅ（Ｚｎ）＝０．本文证明了对任意算数序列｛ｂｎ｝及任意的存在充分大的整数Ｎ＞０使当Ｎ＇＞Ｎ″＞Ｎ时．有此不等式在随机级数研究中有重要作用．     

激光热源形成过程的定量描述

研究了热传导方程的通解，进而提出激光热源形成的微观机理和热源形成过程的三个理论计算式。对激光热效应的应用具有指导意义。     

多信道光纤环形网络结构分析

本文对多信道光纤环形网络结构进行了详细分析，推导出环网内平均路经长度和最大直径计算公式，并分析了最佳多信道光纤环网结构。     

薄Si膜对基底表面粗糙度的影响

利用ＺＹＧＯ光学干涉测量仪，散射积分测量法观测了光学元件表面均方根粗糙度．详细分析了薄Ｓｉ膜对基底均方根粗糙度的影响，由此认为薄膜并不总是复制基底表面的粗糙度，结果出现了薄膜降低表面粗糙度的现象．提出了一定厚度范围的薄Ｓｉ膜的表面粗糙度存在着一个稳定值的新设想．     

歧口凹陷及邻区上第三系油气藏形成条件和勘探前景分析

歧口凹陷及邻区上第三系发育两种类型油气藏:大断层下降盘被次级断层复杂化了的逆牵引构造油藏和披覆背斜油藏。大断层及与之伴生的次级断层的活动时期、活动强度、断距、断至层位、断至深度和断层间距等控制了上第三系油气运移和逆牵引型构造内油气富集程度。圈闭及运移途径控制了披覆型构造油气藏的形成和原油性质。歧口凹陷北区上第三系断层活动、油气运移及储盖组合特征与南区相似,是有利的勘探后备区。进一步勘探部署的关键是要查清断层组合及落实圈闭。     

On the computation of conjugacy classes of Chevalley groups

In this paper an algorithm is presented to determine the number of semisimple conjugacy classes for a given centralizertype for the Chevalley groupsSL _n(q) andSU _n(q). Moreover we give the exact number of regular semisimple classes of this groups and a summary of results on the generic classnumber of exceptional Chevalley groups of adjoint type.The first author acknowledges financial support by a grant of the Deutsche Forschungsgemeinschaft     

非线性隔振理论初探

本文以线必阻尼，立方刚度非线性系统为例，对非线性隔振理论进行了初步探讨，导出了系统的无量纲运动响应和传递率，并与线性隔振系统进行了比较，着重讨论了非线性对它们的影响，获得了一些有用的结论。     

钠化焙烧钒渣同时加碳氯化挥发镓的研究

考察了低温400℃和中温800℃条件下,添加活性碳及液体含碳物纸浆与钒渣、NaCl和Na_2CO_3混合焙烧时氯化挥发镓及钒转比为水溶性钒的情况。本实验得到的最高η_(Ga)为35.1％。焙烧料中不含Na_2CO_3和焙烧温度为400℃时,钒转比为水溶性钒的比率(ηv.t)较低。纸浆添加比L_(纸浆)为0.05mL/g、配料比W_(Na_2CO_3)/W_(Nacl)=2时,可望同时得到较高的η_(Ga)和(ηv.t)。     

Edge detection,three-dimensional cell boundary reconstruction and volume and surface area estimation from differential interference contrast images

Three-dimensional (3-D) cell morphology is important for the understanding of cell function and can by quantified in terms of volume and surface area. Differential interference contrast (DIC, or Nomarski) imaging can enable cell edges to be clearly visualized in unstained tissue due to the slight difference in refractive index between aqueous media and cytoplasm. DIC is affected in only one direction - the direction of the optical shear. A 1-D edge detector was used in that direction with a scale length equal to that of an in-focus edge to highlight cell boundaries. By comparison with the signal from the edge detector on an out-of-focus slice, the in-focus slices could be segmented and, after noise suppression, cell outlines obtained. A voxel paradigm was used to calculate cell volume and differential geometry was used for surface area estimation. We applied this approach to obtain 3-D dimensional information by optical sectioning of motile Amoeba proteus.