必要条件

The paradigmatic sort of ontological entailment is necessitation: P necessitates Q when the material conditional PQ is metaphysically necessary, or when it is metaphysically impossible for P to hold without Q holding.

存有上推导的典型类型是'必要性'：当实质蕴涵PQ是形上学必要条件时，或当"持有P但不持有Q是形上学上不可能"时，P使得Q成为必要物。

By using the above conclusions the nondegeneracy condition of systems without steady errors is analyzed successfully.

利用上面的结果，成功地分析了结构无静差问题的非蜕化条件；证明了非蜕化条件不但是实现结构无静差的充分条件之一，而且还是实现结构无静差的必要条件。

The sufficient and necessary conditions of the nondegeneracy and struc- tural asymptotical stability for complex systems (parallel systems, series sys- tems and closed systems) are proved.

在这基础上，给出了系统在串联、并联及反馈时构成的复杂系统的非变阶条件和结构渐近稳定的充分必要条件。

In this article, based on one-dimension Heisenberg model, the unsymmetric bilayer ferromagnetic and antiferromagnetic thin films are investigated by using the interface rescaling approach under nonperiodic boundary condition.

本文以海森伯模型为基础，只考虑最近邻相互作用，在计入外磁场和非周期性边界条件下，应用界面重参数化方法，分别研究了由A、B两层组成的铁磁或反铁磁层间耦合薄膜中的自旋双链系统的界面自旋波及其存在的充分必要条件，重点讨论了体各向异性场和自旋链长度对界面自旋波存在条件的影响。

Missirlis in article [1]. At the same time, a sufficient condition for convergence of the PSD method is given to be compared when the coefficient matrix A of the linear system Ax = b is a symmetric, positively defective matrix. In §3.2, an example is given to state that the range of our sufficient condition is wider than theorem 3.3 of article [1]. On the other hand, following a.n analogous approach of [14] and starting the functional relationshipwe have a perfect analysis for the PSD method to converge and optimum valves for the involved parameters under different conditions.Under the assumptions that A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are real,we get necessary and sufficient conditions for the PSD method to convergence.The result is equal to theorem 1 of article [9].Under the same condition, we can see the optimal parameter and of corresponding spectral radius of thePSD method in [8]:(2)When A is a consistent ordered matrix with nonvanishing diagonal elements and the eigenvalues of the Jacobi matrix of A are imaginary or zero,we get necessary and sufficient conditions for the PSD method to convergence.In chapter 3, the optimal parameter and of corresponding spectral radius of the PSD method are given by table 3.3. Moreover, under the assumption 0

Missirlis在文献[1]中定理3.3的不准确，同时给出了当线性方程组Ax=b的系数矩阵A为对称正定阵时，PSD迭代法收敛的一个充分条件与之比较，并且在§2.3中用实例说明了对于一部分矩阵而言本文得到的充分条件广于[1]中定理3.3的充分条件；另一方面，按照文献[14]的方法，我们从PSD迭代法的特征值λ与其Jacobi迭代矩阵B的特征值μ的关系式：出发，在不同条件下对PSD迭代法的收敛性和最优参数以及最优谱半径进行了完整的分析：(1)在系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为实数的条件下，给出了PSD迭代法收敛的充分必要条件，此结果与[9]中的定理1等价，此时最优参数及最优谱半径由[8]得：(2)第三章表3.3中给出了，当系数矩阵A为(1，1)相容次序矩阵且对角元全不为零，其Jacobi迭代矩阵B的特征值全为纯虚数或零时的PSD迭代法的收敛范围和最优参数，并且我们可以得到当0

Then the necessary conditions of optimal control problem is obtained by the conception of normal cone.

由法锥概念得到了控制问题的最优必要条件。

The third chapter is about the optimal control for a class of age-dependent competitive population dynamics with diffusion, the continuity properties of the system solution in terms of the control variable is certificated, the Normal cone theory is applied and the necessary conditions of optimal control problem is obtained.

第三章研究了一类年龄相关的具有空间扩散的竞争种群系统最优控制问题，证明了最优解关于控制变量的连续依赖性，应用法锥理论，得到了最优解的必要条件。

Chet - Kolmogorov theorem,then obtains a necessary condition of the optimal solution to the nonlinear control problem according normal cone principle.

然后利用法锥理论得到了最优解存在的必要条件。

This paper discusses the necessary and sufficient conditions of normed linear spaces equading reflexive space and the relationship between reflexibility and weakly compact.

讨论了赋范线性空间为自反空间的充分条件和必要条件，并讨论了自反与弱紧的关系。

Moreover, some necessary conditions for a transitive non-minimal system to be null are obtained.

进一步地，我们给出了一个传递非极小系统为null系统的一些必要条件。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。