集合性的

In the last chapter,we study the control problems of the distributedparameter system governed by a class of higher order pseudohyperbolicequation related to the symmetric regularized long wave equation.we havediscussed the controllability and optimal control problems.we have obtainedcompatibility condition of the constraint when the state is controllable,therepresentation of the optimal control for both the time optimal control problemand the optimal control problem of minimum energy type,and the equationsatisfied by the minimum time.we have shown that the optimal control belongsto the boundary of the admissible control set.

在第六章中，我们研究了与对称正则长波方程相关的一类高阶拟双曲型方程支配的分布参数系统的控制问题。讨论了系统的状态能控性问题和最优控制问题，给出了状态能控时的约束相容性条件，给出了最速控制问题、最小能量型最优控制问题的最优控制表达式和最速时间所满足的方程式，证明了最优控制属于控制集合的边界。

This method represents the virtual objects in Euclidean space instead of in affine space, which is consistent with the popular graphics rendering tools such as OpenGL and is more common in practice. A new classification based local and global tracking strategy to match features between the reference image and the currently frame directly is presented, which enables the augmented reality system working effectively even under large changes of viewing angles. A novel affine coordinate system definition method based on a collection of feature points is also proposed, which makes the tracking method effective even when not all the reference points are detected during the whole process, as long as there are at least four pairs of reference points correspondences.

该方法以仿射变换为桥梁来建立欧氏空间下的摄像机坐标系与世界坐标系之间的变换关系，它与OpenGL等当前流行的图形渲染工具一致，具有更强的通用性；采用基于分类的自然特征匹配策略，能够在视角和视点发生大幅度变化情况下依然正常工作；提出基于特征点集合的仿射坐标系定义方法，使增强现实系统在最小配置下只需4点追踪成功即可完成注册，比需要6点的透视投影方法具有更好的健壮性和精确性。

First the math theory of machining simulation is studied, and the set structure of NC machining simulation system whose components, including time, input, output and so on, are defined. Hereby we set up the hierarchy structure, the logical structure, the static model and the dynamic model of simulation system. The construction method of sweep entity of cutter and rotation parts is researched, and their differential geometry invariants are calculated. NC code is unscrambled, and the recursion division arithmetic of time segment is put forward, which is the driven data of the movement or rotation parts. The CLDATA should be interference-free. To examine if there is interference between cutter flank and the work piece, an arithmetic that discussed the existence of intersecting curve between them is put forward. To examine if there is interference between two turrets, an arithmetic that discussed the existence of intersection set between two polygons is put forward.

首先研究加工过程仿真的数学基础，然后定义数控加工仿真系统的集合结构及时间集、输入集、输出集等概念，建立加工仿真的层次结构和逻辑结构，阐述双刀车削仿真系统的静态模型和动态模型建立方法，分析刀具扫描体和旋转部件扫描体的建立方法及其微分几何性质；研究NC代码解读技术和双刀加工时间段递归子分划技术，为驱动各仿真单元作数据准备；通过讨论后刀面和工件表面交线的存在性判断刀具后刀面与工件间是否干涉，通过求多边形的交集判断刀架与刀架是否干涉。

We introduce the general sigma point selection framework, and give two kinds of efficient methods: a reducing the computing complexity by decreasing the number of the sigma point; b scaling the sigma points to influence the effects of the higher order moments, then improve the accuracy of the UT; c Convergence analysis of the UKF, when used as an observer for nonlinear deterministic discrete-time system, is presented. Based on the UKF that captures the posterior mean and covariance accurately to the second or third order term (in terms of Taylor series expansion) for any form of nonlinearity, sufficient conditions to ensure local asymptotic convergence are established.

论文介绍了sigma点的一般选取规则，并给出了两种有效的方法：a通过减少sigma点集合的元素的数目来减少计算复杂度，b通过增加参数来逼近泰勒展开的高阶项，从而提高UT变换的精度；c论文研究了UKF算法应用于非线性确定性离散时间系统时的收敛性问题。

First we give the characterization of subsets on which every real-valued convex function bounded above is continuous on the space, and give the βperturbed optimization in Banach space by introducing new locally convex topology.

给出了广义实值凸函数在集合A上有上界则连续的一类子集的特征性刻画；并且通过引入新的局部凸拓扑的方法，给出任意Banach空间的β扰动优化。

First we give the characterization of subsets on which every real-valued convex function bounded above is continuous on the space, and give the fi-perturbed optimization in Banach space by introducing new locally convex topology.

给出了广义实值凸函数在集合A上有上界则连续的一类子集的特征性刻画；并且通过引入新的局部凸拓扑的方法，给出任意Banach空间的β扰动优化。

The soundness and completeness theorem of this method were proved at last. 5. The a-automated reasoning method based on the a-resolution principle of LP was discussed, the author given a method to describe the set of simple generalized clauses (veriables and non-subregular 1 - IBSFs are only contained) by using a matrix, and translated the a-resolution of two clauses to column operations of this matrix.

最后，证明了该方法的可靠性和完备性； 5、对格值命题逻辑系统LP中基于α-归结原理的α-自动推理方法进行了研究，给出了用符号矩阵表示一类简单的广义子句集合(只含命题变元和非正则1-IESF广义文字)的方法，把α-归结原理转换成矩阵的列变换。

The proposed model of the crystalline hydrocarbon p rotoorganism based on investigations of fibrous kerite crystals,eliminates the major discrepancies and blocks in the way to creating a unified concept of abiog enesis(structural organization,assembly of macromolecules,inheritance mechanisms ,chiral selection,etc.).

根据纤维状黄绿蛭石晶体的研究而提出的晶质原生有机体模型，消除了在创立统一的自然发生论概念(结构组织、大分子集合、继承机理、手性选择等等)方面的主要分歧和障碍。

From the above theorem,（1） compositional invariant security properties and constructive security properties are proved to exist, and （2） security properties are degraded under operators of process algebra, which is known as "bucket principle", i.e, a composed system cannot be securer than the weakest link of the system.

根据这一结果证明了复合不变性质和可构造安全性质在安全性质集上的存在性，并且在安全性质集合上证明了安全性质的"木桶原理"，即复合系统的整体安全性不强于系统中最弱的部分。

Through a new analysis on the essential relationship between Russell's Paradox and Cantor's proofs on the uncountability of real number set and the proof on the Cantor's Theorem of ,two mysterious errors were found: The very same idea was applied in both Russell and Cantor's work, but Cantor made wrong use of it with two logical mistakes.

分析了罗素悖论与康托的实数集合不可数证明及康托定理证明之间的本质性联系，发现康托的这两个非构造性证明与罗素悖论有完全相同的思路，但是康托犯了两个逻辑性错误而使他误用了这个悖论思路。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。