必要条件

The project involved:(1) Development of time and space resolved soft x-ray diagnostic instruments: a pinhole transmission grating streak spectrograph and a stigmatic grazing incidence grating flat-field streak spectrogrph, which are the most powerful in x-ray laser and laser plasma researches of our laboratory.

它们已成为我们实验室X射线激光和激光等离子体软X射线发射实验研究中最有力的诊断手段。（2）系统地研究了X射线激光增益介质—线状激光等离子体的均匀性。结果表明线聚焦激光照明的均匀性是实现均匀线性状激光等离子体的必要条件。

1St stage: a record high stock prices fell in one of the most obvious necessary conditions.

第一阶段：股价不创新高是下跌的最明显的必要条件之一。

Firstly, a necessary and sufficient condition for an uncertain multi-channel descriptor system to be robustly stabilizable with a specified disturbance attenuation level is derived in terms of a strict nonlinear matrix inequality.

主要考虑分散H输出反馈控制问题。推导出了使不确定多通道奇异系统能鲁棒稳定且满足一定的性能指标的充分必要条件，没有等式约束的非线性矩阵不等式条件。

The higher subduction velocity advantages the low temperature in the subduction belt. In addition, it takes less time for the crust rock to subduct the deep and then return to shallow. The low temperature and the short time are benefit to forming and reserve the ultrahigh\|pressure metamorphic rocks.

板块持续的高速俯冲，不仅可以使得俯冲带形成低温环境，而且在陆壳岩石俯冲到地幔经受超高压变质作用后返回地表浅部的过程中，超高压变质岩在地幔滞留的时间短，为超高压变质岩的形成提供了必要条件。

Furthermore,λ3 = 4 if and only if G contains K4 as its subgraph.

进一步，λ3=4的充分必要条件是图G含有子图K4。

In the present paper,a sharp inequality is obtained between the Ricci curvature and the squared mean curvature of semi-invariant submanifold s in cosymplectic space forms,and some conditions are reached to make the equality hold.

对余辛流形的半不变子流形进行研究，利用曲率的分量表示之间的简单的代数关系，得到了这类子流形的R icc i曲率与平均曲率平方之间的一个不等式，并讨论了等式成立的充分必要条件

Our results improve the former results. For periodic Jacobi matrix, some new spectral properties of periodic Jacobi matrix are given by studying the relationship of the eigenvalues of periodic Jacobi matrix and its n—1 principal submatrix. Applying these spectral properties, we present a necessary and sufficient condition for the solvability of an inverse problem of periodic Jacobi matrices and discuss the number and the relationship of its solutions. Furthermore, we propose a new algorithm to construct its solution and compare it with the former algorithms. As this inverse problem of periodic Jacobi matrix usually has multiple solutions as many other eigenvalue inverse problems, we study the uniqueness of this problem. And a necessary and sufficient condition is given to ensure its uniqueness, under which an algorithm is presented and the stability analysis is also given. Finally, we put forward a new inverse problem for periodic Jacobi matrix which has not been solved.

对周期Jacobi矩阵特征值反问题，通过研究周期Jacobi矩阵与其n-1阶主子阵特征值的关系，给出了周期Jacobi矩阵的一些新的谱性质；利用这些谱性质，研究了一类周期Jacobi矩阵特征值反问题，用新的方法推导出了该类特征值反问题有解的充分必要条件，并讨论了解的个数以及解与解之间的关系；此外，提出了一种新的构造周期Jacobi矩阵反问题解的数值算法，并与前人的算法做了一定比较；由于周期Jacobi矩阵特征值反问题和其他很多特征值反问题一样往往存在多个解，本论文给出了周期Jacobi矩阵反问题解唯一的充要条件，并发现周期Jacobi矩阵特征值反问题的解唯一当且仅当构造的矩阵满足一定的条件；在解唯一的情况下，给出了构造唯一解的数值算法，并做了相应的稳定性分析；最后，提出了一类新的有待于解决的周期Jacobi矩阵特征值反问题。

The Jacobi matrix rank one update problems, given either their mix-type eigenpairs or their pricinpal submatrix and defective eigenpairs(the eigenvalues of the matrix and some elements of the corresponding eigenvectors) are also discussed.

n阶对称箭形矩阵与n阶Jacobi矩阵一样只有2n-1个非零元素，类似Jacobi矩阵逆特征值问题的提法，本文提出并讨论了六类对称箭形矩阵逆特征值问题，研究了这类矩阵的结构性质，得到了问题有解的充分必要条件及求解的数值算法和数值算例。

It is the main precondition. It is both sufficient and prerequisite condition.

这是一个重要的前提，也是充分必要条件。

The author believes that the demand is only a necessary condition for high prices, not sufficient condition.

笔者认为，需求是唯一的一个必要条件高价格，而不是充分条件。

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。