A necessary and sufficient condition of the existence of prime model is proved.
研究了主型的有关性质，证明了一个素模型存在的充分必要条件。
In this paper we give a necessary and sufficient condition on diagonalization matrix.
本文给出矩阵可对角化的一个充要条件。
In this note, a necessary and sufficient condition of diagonalization for square matrix is considering.
方阵是否可以对角化，是矩阵的一条很重要的性质。
It is obtained that a necessary and sufficient condition for a closed fuzzy set to be a convex fuzzy set.
引入线性拓扑空间中的凸闭模糊集概念，得到闭模糊集是凸模糊集的充分必要条件。
Firstly, a necessary and sufficient condition of regional stable for the closed-loop system is introduced.
首先，区域稳定的必要和充分条件闭环系统的介绍。
The question as to whether binarity is a necessary and sufficient condition to produce barium star is addressed.
讨论了双星是否是产生钡星的必要和充分条件，因为已知道的钡星系统全是双星。
A necessary and sufficient condition for an ideal of an integral table algebra being self-orthogonal is obtained.
本文给出了整表代数的单边理想是自正交理想的必要充分条件。
In this section, we also establish a necessary and sufficient condition for the algorithm of the mixed scheduling.
在这一部分里，我们同样得到了一个任务集可以用混合调度算法调度的一个充分必要条件。
In this paper, We give a necessary and sufficient condition that closed decomposable operator, is strongly decomposable.
本文给出了封闭可分解算子是强可分解的一个充分必要条件。
A necessary and sufficient condition for an inner set space with three critical sets which can be weighted is also given.
给出了具有三个临界集的内集空间可以赋权的一个充分和必要条件。
The results show that the overall energy consumption is a necessary and sufficient condition for China's industrialization;
结果表明，能源总体消费是中国工业化的充分必要条件；
In this short poper, the regularizability of descriptor decentralized systems is studied and a necessary and sufficient condition is given.
本文主要研究了广义分散控制系统的正则性，并给出了可以正则化的一个充要条件。
For global consistency judgment problem in AHP, a necessary and sufficient condition that the satisfy global consistency is true was provided.
针对层次分析法（AHP）中下层存在不满足满意一致性条件判断矩阵的整体一致性判别问题，提出了具有满意一致性的充要条件。
Based on Darboux theory, this paper discussed the integrability of the Riemann Integral and provides a necessary and sufficient condition for integrability.
文章利用达布和理论，讨论了黎曼积分的可积性问题，给出了一个可积的充分必要条件。
In this paper, we discuss when a quartic equation has no real roots, and obtain a necessary and sufficient condition on a quartic equation which has no real roots.
本文讨论了一元四次方程无实根的一些充分、必要条件，并得到了一元四次方程无实根的一个充要条件。
The paper presents a necessary and sufficient condition for topological dynamical system to be topologically conjugate with a generalized symbolic dynamical system.
本文证明了，拓扑动力系统与广义符号动力系统拓扑共轭的一个充分必要条件。
In this paper, we get the diameter of three kind of self-complementary and then give a necessary and sufficient condition from matrix adjacency when the diameter is 2 or 3.
本文给出了三种类型的自补图关于直径方面的结果，并从自补图的邻接矩阵给出了自补图直径为2或3的一个充要条件。
A necessary and sufficient condition for nonlinear systems to achieve optimal regulator is given by using the return difference condition and completion of the squares argument.
利用返回差条件，借助配方方法讨论非线性系统达到最优调节所必须满足的充要条件。
This paper examines port queuing system with single berth. For its imbedded Markov chain, the author gives a necessary and sufficient condition under which the system is ergodic.
港口系统排队模型由两个排队子系统构成。本文对单个泊位(服务台)的情形讨论了它的嵌入马氏链，给出了系统遍历的充分必要条件。
The concept of closed fuzzy set is introduced in topological linear space. It is obtained that a necessary and sufficient condition for a closed fuzzy set to be a convex fuzzy set.
引入线性拓扑空间中的凸闭模糊集概念，得到闭模糊集是凸模糊集的充分必要条件。
A necessary and sufficient condition is derived for the existence of monotone and convex interpolation by a cubic spline with an additional knot inserted between each pair of data points.
本文给出用三次样条在两两节点之间引进一个外加节点的条件下，存在凸而单调的插值的充分必要条件。
In this paper, the generalized vector composite formulas are proved by the mapping method of complex function, and a necessary and sufficient condition that can be used easily is proved too.
本文用复变函数论的映射方法证明了一个普遍意义的矢量性物理量的合成公式，并证明了一个易于判定的充要条件。
By lattice-theoretic methods we give a necessary and sufficient condition for a continuous mapping with the codomain T_3 to be extended continuously from a dense subspace to the whole space.
本文采用格论方法研究拓扑学中连续映射的扩充问题，给出陪域为T＿3空间时连续映射扩充的充要条件。
By discussing a class of the neutral difference equation with several delay arguments, the author deduces a necessary and sufficient condition for the existence of bounded positive solutions.
考虑一类含有多个滞量的中立型差分方程，获得了该方程存在有界正解的一个充分必要条件。
In this paper, we get a necessary and sufficient condition for a generalcodimensional submanifold with constant mean curvature in a Riemannian mani-fold to be a totally umbilical submanifold.
本文讨论黎曼流形里一般余维的常数平均曲率的子流形为全脐子流形的充要条件。
Wehave determind completely these representations. Using this result, we gave a necessary and sufficient condition about the problem of the isomorphism of two generalized quaternion algebras.
利用这一结果，给出了两个广义四元数代数同构的一个充分必要条件。
A necessary and sufficient condition for discriminating the independence of random variables directly from joint distribution instead of marginal probability distribution has been established.
本文建立了不需要求边缘概率分布而直接从联合分布判别独立性的一个充要条件。
Finally, an iterative learning algorithm was presented for a MIMO linear time-varying system in the paper and a necessary and sufficient condition for the existence of convergent algorithm was proved.
最后文章针对多输入多输出线性时变系统提出了一种迭代学习控制算法，证明了算法收敛的充分必要条件。
Finally, an iterative learning algorithm was presented for a MIMO linear time-varying system in the paper and a necessary and sufficient condition for the existence of convergent algorithm was proved.
最后文章针对多输入多输出线性时变系统提出了一种迭代学习控制算法，证明了算法收敛的充分必要条件。
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