线性

Hamilton principle can be used in holonomic system and intrinsical linear nonholnomic system. The formulas of them are unified. Hamiltonian action is stability in intrinsical linear nonholnomic system.

本文将Hamilton原理应用到本质线性非完整系统，首次证明了在本质线性非完整系统中，Hamilton作用量为稳定的作用量；将完整系统和本质线性非完整系统的Hamilton原理从形式和本质上统一起来。

First of all,we have given some of the basic concepts of differential equations, described the constant coefficient linear ordinary differential equation solution, for a class of second-order variable coefficient linear ordinary differential equation initial value problem, an approximate solution, the method is first unknown function of a definition for N sub-interval, and then in between each district within a constant coefficient ordinary differential equations similar to the replacement, the solution has been the problem as similar to the original analytical solution, and then gives a detailed second-order change order coefficient of linear homogeneous ordinary differential equation solution examples, the examples of the approximate method proposed in this paper is valid.

首先给出了微分方程的一些基本概念，讲述了常系数线性常微分方程的解法，针对一类二阶变系数线性常微分方程初值问题，提出了一个近似解法，本方法是先对未知函数的一个定义区间作N等分，然后在每一个小区间内用一个常系数常微分方程近似替换，所得到的解作为原问题的近似解析解，随后详细给出了一个求二阶变系数齐次线性常微分方程的解的实例，该实例说明本文提出的近似方法是有效的。

To similinear hyperbolic system, we use interpolated coefficient FEM and get similar results as the linear one.

对于一阶半线性双曲组，我们对半线性项插值系数有限元方法，得到了和线性问题类似的结论。

Secondly, we discuss generalizedderivable mappings at unit and Jordan derivable mappings at unit on Von Neumannalgebra, and we prove that every norm continuous linear mapping generalized deriv- able at unit is a generalized inner derivation, every norm continuous linear mappingJordan derivable at unit is a inner derivation.

其次对Von Neumann代数M上的在单位广义可导和在单位Jordan可导的线性咉射进行了讨论，证明了在单位广义可导的范数连续的线性映射是M上的广义内导子，在单位Jordan可导的范数连续的线性映射是M上的内导子。

We make use of a normal element and circular permutations to construct polynomials over the intermediate extension field between F_q and F_ denoted by F_ where s divides t. The polynomials we constructed are F_q-linearly independent and return elements in F_q when they are evaluated at elements of the extension fields.

结合Reed-Solomon码的构造特点，我们将Chaoping Xing与San Ling所构造的线性码的方法推广到有限域的任意次扩张上，首先利用正规元和循环排列来构造系数属于F_q和F_q的任意次扩域F_之间的中间域的具有特殊性质的多项式，中间域记为F_，其中s为t的真因子，由正规元的选择可以保证所构造多项式的F_q-线性无关性，并且这些多项式在扩域F_中取值都属于F_q，从而构造出一类q元线性码。

It is proved that every Lie derivation of nest algebra is the sum of an associative derivation and a general trace. Every Lie isomorphism between nest subalgebras of a factor von Neumann algebra is the sum of an isomorphism and a general trace or the sum of a negative anti-isomorphism and a general trace. Lie invariant subspace of linear mappings on Banach algebras is introduced, and linear maps from nest subalgebra of a factor von Neumann algebra into itself which satisfy the property that the space of derivations is their Lie invariant subspaces are characterized. Simultaneously, it is shown that such maps are Lie derivations modulo the set of scalar multiple of the identity.

得到Lie导子的特征表示，即套代数上的任何一个Lie导子都是内导子与广义迹之和；给出了Lie同构和同构及反同构之间的关系，即因子von Neumann代数中套子代数之间的任何一个Lie同构要么是同构与广义迹之和要么是负反同构与广义迹之和；引入了Banach代数上线性映射的Lie不变子空间，并给出von Neumann代数中套子代数上以导子空间为Lie不变子空间的线性映射的一个刻画，同时也表明在模去数乘恒等映射的意义下，以导子空间为Lie不变子空间的线性映射就是Lie导子。

Establish integrated invertibility theory over it: By R〓R〓 transformation method, we solve the problem of deciding weakly invertibility and finding weak inverse, By founding the bijections between all quadratic form automata and input memory linear finite automata, we find a algorithm to produce all weak inverse quadratic form finite automata.

本文着眼于这些最基本问题，将有限域上的二次型和置换多项式理论引入有限自动机可逆性的研究，构造了一类由二次型构成的非线性有限自动机（3.6定义），称之为二次型有限自动机，我们在其上面建立了与线性有限自动机可逆性理论相对应的完整的可逆性理论：采用线性R〓R〓变换方法，解决了此类有限自动机的弱可逆性判定、求弱逆问题（3.10、3.12定理）、通过建立全体二次型有限自动机与全体输入存储线性有限自动机之间的保持弱逆性的一一对应，给出了产生全部可逆二次型有限自动机的方法。

This paper studies on weak invertibility of a linear finite automata based on its matrix model,gets a full and essential condition on which a linear finite automata weakly and invertibly delays finite steps,and also gives an algorithm whether or not a linear finite automata has weak invertibility .

主要讨论了基于矩阵模型表示的线性有限自动机的弱可逆性，利用矩阵模型得出了线性有限自动机延迟有限步弱可逆的充分必要条件，并且给出了线性有限自动机是否具有弱可逆的算法。

Summary: The concept of matrix and its determinant computing, matrix determinant, matrix sub-block with the elementary transformation, invertible matrix, rank of matrix; vector and its computation, the linear relationship between vector, vector group of rank; linear equations of the nature and structure of linear equations; matrix eigenvalue and eigenvector, similar to matrix and matrix diagonalization conditions, the standard quadratic form with the normal forms, quadratic and symmetric matrix There are qualitative.

内容提要：行列式矩阵的概念及其运算，方阵的行列式，矩阵的分块与初等变换，可逆矩阵，矩阵的秩；向量及其运算，向量间的线性关系，向量组的秩；线性方程组的性质与结构，线性方程组的求解；矩阵的特征值与特征向量，相似矩阵与矩阵可对角化条件，二次型的标准形与规范形，二次型和对称阵的有定性。

Three counter-examples of topological space are proposed in this study: There are two metric spaces, X and Y, in which and are isometric, whileand are not isometric; Non-metric tight regular space is a counter-example of the separation of topological space; No non-zero continuous linear functionals of the linear topological space is a counter-example of linear topological space.

这里给出三个反例，存在两个度量空间X与Y，使X^2与Y^2等距而X与Y并不等距是拓扑空间中的反例；存在不可度量化的紧的完全正规空间是拓扑空间分离性的反例；不存在非零连续线性泛函的线性拓扑空间是线性拓扑空间的反例。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。