线性的

Then a new way was defined to prove that the unique set of sequences equivalent to context-free languages can be obtained by mixed self-assembly of mole-cules with 1-,2-,3- sticky ends,which is a supplement for Winfree's theory that the self-assem-bly of dendrimer nanostructures is equivalent to context-free language.

另一方面，文中定义了一种新的通过上下文无关语言通过自装配产生线性语言的方法，即证明了等价于上下文无关语言的特定序列集能通过1-，2-，3-粘头分子的混合自装配产生线性语言，同时，这是对Winfree关于树状纳米结构自装配等价于上下文无关语言理论的一个较好的补充。

In chapterⅡ, Firstly, we research the derivable mappings at unit and the anti-derivable mappings at zero point on Von Neumann algebra M.

证明了在单位可导和在单位反可导的范数连续的线性映射是M上的内导子，在零点反可导的范数连续的线性映射是M上的广义内导子。

The property of the algorithms on linear problems is studied and the Broyden's methods have been proved that they are not descant. More precisely, the distances between the sequences obtained by solving the linear problems and the solutions of the linear problems do not decrease under any vector norm.

笔者研究了将该方法用于求解线性方程组时的内在性质，否定了一个自然的推测，指出它在解线性方程组时不是一个下降的算法，即所得到的点列与方程组的解之间的距离在任何向量范数意义下都不具有单调下降性。

In this thesis,we study the existence and the regularity of positive classical solution and the existence of the large solutions for a singular semilinear elliptic Dirichlet problem and a semilinear elliptic value problem of second order with gradient terms.

本文研究一类奇异半线性椭圆型方程的Dirichlet问题正的古典解的局部存在性及其正则性以及一类含对流项的二阶半线性椭圆型方程爆破解的局部存在性。

Then the design of PID fuzzy control system based on T-S fuzzy controller is proposed. 5. The parallel distributed compensation method is proposed to devise fuzzy controller based on the existed fuzzy state equation model and its stability theory for continuous and discrete system. The stability of fuzzy closed-loop system is investigated using LMI.

在现有的连续和离散系统的模糊状态方程模型及其稳定性定理的基础上，用"并行分散补偿"方法设计出模糊控制器，利用线性矩阵不等式法对模糊闭环系统的稳定性进行了分析，并且在线性矩阵不等式的基础上设计出了稳定的模糊控制器。

For example,a generalization of linear algebra is developed in which "convex bifunctions" are the analogues of linear transformations,and "inner products" of convex sets and functions are defined in terms of the extremal values in Fenchel's Duality Theorem.

例如，一类线性代数的推广形式在凸双重函数中发展起来，而凸双重函数是线性变换的类似情况，凸集和凸函数的内积是根据 Fenchel 对偶理论的极值定义的。

In chapter 2 we propose a linear equality constraint optimization question , the new algorithm is combined with the new conjugate gradient method(HS-DY conjugate gradient method)and Rosen"s gradient projection method , and has proven it"s convergence under the Wolfe line search.In chapter 3 we have combined a descent algorithm of constraint question with Rosen"s gradient projection, and proposed a linear equality constraint optimization question"s new algorithm, and proposed a combining algorithm about this algorithm, then we have proven their convergence under the Wolfe line search, and has performed the numerical experimentation.

在第三章中我们将无约束问题的一类下降算法与Rosen投影梯度法相结合，将其推广到线性等式约束最优化问题，提出了线性等式约束最优化问题的一类投影下降算法，并提出了基于这类算法的混合算法，在Wolfe线搜索下证明了这两类算法的收敛性，并通过数值试验验证了算法的有效性。

In present, the discussions of EB estimation are almost all about to exponential distribution family and truncated distribution family, but linear exponential distribution is not exponential family and truncated family, thus, Empirical Bayes estimation for parameter of linear exponential distribution are studied in chapter 4 and chapter 7 that is new aspect.

当前对经验Bayes估计的讨论，大多是对指数分布族以及截断分布族的，线性指数分布即不属于指数分布族也不同于截断型分布族，因而在论文的第四章和第七章研究线性指数分布参数的EB估计是具有一定的新颖性的。

They are:1 design and implementation of nonlinear least Square Algorithm,2 design of general formula expositor,3 design and implementation of software encryption scheme and4 making of help files system.

数值实验表明：设计的算法具有极高的计算精度，也有较好的全局收敛性与稳定性，明显优于SPSS等软件，不仅可以处理小残量问题，而且能够处理大残量或非线性程度较高的问题，对于线性回归，可以一步达到精确的结果，使线性问题和非线性问题很好地统一起来。

We presents an accurate F method based on corresponding point adjustment.The method adjusts coresponding points according to the fixedness of projective transformed cross ratio,then calculates F matrix accurately through linear and non-linear methods. When computing intrinsic parameter,A matrix,we simplify the step,and stress on the two important parameters of A.The result will be getten through solving Kruppa equation based on SVD decomposition.In order to compute extrinsic parameters,we use linear method to get initial R and t,then apply non-linear method to accurate them.

提出了基于匹配点调整的F求精方法，先根据摄影交比不见性对手工选择的匹配点进行调整，再用线性、非线性结合的方法求精F矩阵；在计算内部参数A中，进行了一定的简化，把重心放在A中重要的两个参数上，用SVD分解法计算Kruppa方程；在计算外部参数时，首先用线性法求解R、t，然后再用非线性法迭代求精。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。