极小元

The least norm solutions of symmetric and skew antisymmetric matrix equations (A~TXA, XA — YAD)=(D, 0)are also considered. 3. The least-squares solutions and the least norm solutions of the quaternion matrix equations AX = B and XD = E are studied by using

借助四元数的复表示方法，研究四元数矩阵方程组AX=B，XD=E的最小二乘问题和极小范数解的问题，并对主子阵约束下的方程组的解进行了讨论，得到了它们的显式表示。

Secondly, a finite element method is used to approximate the constrained minimization problem, both existence of minimizer for cost functional in finite demensional space and the convergence of minimizer are proven.

然后利用有限元方法对上述定解问题进行离散，并证明了有限维空间上泛函的极小元存在以及有限维空间上的极小元收敛到无限维空间上的极小元。

We prove that in every nonzero coset, there is a unique element with minimal Euclidean weight among the group of elements with minimal Mahattan weight.

证明了在每个非零陪集中，具有极小Hexagonal重量的元素集合里，具有极小欧氏重量的元是唯一的。

Let F=LF be a s-closed local formation such that every minimal non-F-groups is solvable. It is proved that 1 If every cyclic subgroup of of order 4 and every minimal subgroup of G are contained in, then G is a F-group. 2 If there exists a normal subgroup N of G such that G/N∈F and every cyclic subgroup of N of order 4 is weakly c-normal in G and every element of N of prime order is contained in Z(superscript f subscript ∞), then G is a F-group.

设F=LF是一个子群闭的局部群系，满足每个极小非F-群是可解群，证明了：1如果G的任意极小子群和任意4阶循环子群都含于Z中，那么G是F-群；2如果存在G的正规子群，使得G/N∈F，且N的任一4阶循环子群在G中弱c-正规，N的任一素数阶元含于Z中，那么G是F-群。

One reason is that the model is an algebra method and it is based on the theory of minimal element. It can give more credible proof. Another reason is that the model tries to prove security of protocols, rather than check them. Thirdly, the model is simple and easy to use, and proof can be finished by manual. Moreover, graphic description makes its proof more comprehensible. Fourthly, there is much research work related to the model, which gives me a good springboard.

首先，该模型是一种代数方法，以极小元等理论为基础，可以给出可信度较高的证明；其次，该模型不是验证协议，而是试图证明协议的安全性；第三，该模型简单、易用，可以手工的方式完成证明，而且图形表示使其证明更加直观；第四，关于该模型有许多相关的研究工作，这为进一步工作打下了良好的基础。

Bernstein type theorem; Quaternion Euclidean space; minimal Lagrangian graphs; Twisted special Lagrangian submanifold; twisted normal bundle; Austere submanifolds; Real space form; Complex space form; Hamiltonian minimal submanifold; A Lagrangian submanifold with conformal Maslov form

基础科学，数学，几何、拓扑伯恩斯坦型定理；四元数欧氏空间；极小拉格朗日图；扭曲特殊拉格朗日子流形；扭曲法丛； Austere子流形；实空间形式；复空间形式；哈密尔顿极小子流形；具有共形Maslov形式的拉格朗日子流形

If you are familiar with the article: Window Tray Minimizer

如果您熟悉的文章：窗口托盘极小元

In vector optimization one investigates optimal elements such as minimal, strongly minimal, properly minimal or weakly minimal elements of a nonempty subset of a partially ordered linear space.

前言在向量最优化中，人们研究偏序线性空间中非空子集的最优元，比如极小元，强极小元，真极小元或者弱极小元。

In the last of this dissertation, we give necessary and sufficient conditions for the existence of and the expressions of perpositive semidefinite solutions and bipositive semidefinite solutions to some systems of quaternion matrix equations.

给出了某些四元数矩阵方程组有广亚半正定解，双半正定解的充要条件及其表达公式；研究了矩阵方程组的最小二乘解，极小范数的最小二乘解，在某些约束条件下的最小二乘解和极小范数的最小二乘解，给出了其有这些解的充要条件及其表达公式。

For MU(1),a subclasses of minimal unsatisfiable formula s,we show the solvability in polynomial time.

公式的改名是将命题变元映到变元本身或变元的否定的一个映射，对于极小不可满足公式的子类MU( 1 )中的公式，我们证明了其改名判定问题在多项式时间内是可判定的。

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。