必要条件

In this paper a new necessary and sufficient condition of graphic isomorphism is proved which is stated as following: two graphs are isomorphic if and only if their subgraphs are isomorphic and the new vertices as well as their adjancy edges are corresponding with the property of isomorphism.

提出了一个新的判定图同构的充分必要条件，即在子图同构的前提下，根据新增顶点及相应关联边的关系，判断母图同构的充分必要条件。

With the matrix direct product and straightening operator, the necessary and sufficient conditions of the linear matrix equations have solutions and have unique one solution are given.

本文介绍了矩阵直积的有关概念和性质，利用矩阵直积和拉直算子给出了线性矩阵方程有解的充分必要条件以及有惟1解的充分必要条件。

If ris also irreducible in Z_nand f~n~κ≡fmodn,r(xfor all f∈Z_nthen we call n a Carmichael number of orderκmodulo r.Denote the set of all such numbers by C_κ,r(x.Define C_κ=∪_r(xC_κ,r(x,where rpasses through all monic irreducible polynomials over Z of degreeκ.We call elements of the set C_κCarmichael numbers of orderκ.ZHU and SUN[Journal of Sichuan University,42;1(2005), 47-51]first gave a necessary condition for Carmichael numbers of order 3.Then they gave a sufficient condition for Carmichael numbers of order 3,but did not find any such numbers less than 10~8 satisfying the sufficient condition.At last,they asked three questions;1.is the necessary condition also sufficient?

f∈Z_n，就称n是模r的κ阶Carmichael数，用C_κ，r(x表示所有这种数的集合，定义C_κ=∪_r(xC_κ，r(x，这里r跑遍Z中所有κ次首一不可约多项式，C_κ里面的元素就称为κ阶Carmichael数，C_κ称为κ阶Carmichael数集，朱文余和孙琦[四川大学学报，42；1(2005)，47-51]首先给出了3阶Carmichael数的一个必要条件；然后又给出了这种数的一个充分条件，并发现10~8内没有满足此充分条件的这种数；最后他们提出三个问题；一、问必要条件是否也是充分的？

This paper is divided into two parts: The first part, mainly discussed the properties of unitary equivalence and the relation between unitary equivalence and similarity, introduced a unitary equivalent of the necessary and sufficient condition: Specht theorem; The second part of a major demonstration of the 11 normal matrix's necessary and sufficient conditions, given some important properties of normal matrix such as simultaneous diagonalization.

本文主要分为两部分：第一部分，主要讨论了酉等价的性质及酉等价与相似的关系，介绍了酉等价的充分必要条件Specht定理；第二部分，主要论证了正规矩阵的11条充分必要条件，给出了正规矩阵的一些重要性质

A prerequisite for positive or negative quadratic form was presented and it was proved by use of definition.

本文给出了二次型正定的1个必要条件，并对二次型正定、负定的必要条件给出了用定义证明的方法。

Once a dual unit commitment obtained within Lagrangian relaxation framework is judged by this feasibility condition to be infeasible, reselect the dynamic planning route with non ramp rate constraints by using the information of the dual solution, i.

当利用充分必要条件判断对偶机组组合不可行时，则利用对偶解的信息重新选择非爬升约束机组的动态规划的路径，即调整它们的启停序列，使之满足充分必要条件，最后以此解决经济分配问题。

In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.

在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。

In this paper,by the matrix method,a necessary and sufficient condition for two n-dimensional synclastic simplexes to be able embedded in the n-dimensional Euclidean space is obtained,as well as for two group finite point sets.

该文利用矩阵的方法，获得了两个同向的n维单形同时等距嵌入E~n维欧氏空间的一个充分必要条件是：对于预给(n+1)~2个距离，满足一组具有行列式形式的不等式组det，由此可以得到两组等数量的有限点集合到E~n维欧氏空间中等长嵌入的一个充分必要条件。

Finally, we discuss the compactness of operators products when a is a nonnegative integer, which is also similar to the case of the unweighted.

和H_fH_g~*的紧性，得到了它的充分必要条件，同样也得到了算子乘积T_fH_g~*和H_gT_是紧算子的充分必要条件。

Moreover, we proved a necessary and sufficient condition showing the relationship between the isomorphisms of semilattices and the isomorphisms of the lattices of the ideals of the semilattices.

此外，我们建立了一个充分必要条件。这一充分必要条件反映了两个半格之间的同构与这两个半格的理想格之间的关系。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。