查询词典 necessary condition

The results showed that during the 45 days experimental time the fresh weigh of Myriophyllum spicatum L, Hydrilla verticillata L and Cerato-phyllum demersum L were 0.92 g, 0.27 g, 1.11 g and 0.56 g, 0.41 g, 0.87 g in medium nutritional condition TN 1.86 mgL^(-1; TP0.087 mgL^(-1) and eutrophic condition TN 2.47 mgL^(-1; TP0.16 mgL^(-1), respectively. The largest single plant biomass of Myrio-phyllum spicatum L and Ceratophyllum demersum L in in middle nutritional condition were over 39% and 22% higher than those in eutrophicated condition, but that of Hydrilla verticillata L was less than 51%, which shown that Myriophyllum spicatum L and Ceratophyllum demersum L grow better than Hydrilla verticillata L in middle nutritional condition.

研究结果表明，在45 d的培养过程中，狐尾藻、轮叶黑藻和金鱼藻在中营养TN1.86 mgL^(-1； TP0.087 mgL^(-1)和富营养TN2.47 mgL^(-1； TP0.16 mgL^(-1)水平下的单株最大生物量分别是0.92、0.27、1.11、0.56、0.41和0.87 g，狐尾藻和金鱼藻在中营养水平下单株最大生物量分别较富营养水平下高出39%和22%，而黑藻在中营养水平下单株最大生物量较富营养水平下低了51%，表明狐尾藻和金鱼藻在中营养水平下的生长较黑藻好。

The positive region based on radix sorting is used to get the positive region condition attributes set of decision attributes and the condition attribute set which excludes one of the condition attributes of decision attribute positive region. Then the difference between the two radices of positive regions is calculated to judge whether the condition attribute is a core attribute, thereby all the condition attributes are judged and the required core is quickly acquired.

采用基数排序思想计算正区域，分别得到决策属性正区域的条件属性集和除决策属性正区域的一个条件属性之外的条件属性集，并且计算这2种属性集的基数之差，以判断该条件属性是否是核属性，依次判断所有条件属性，从而快速获得所需要的核。

Then it quotes a sufficient condition, the necessary conditions and necessary and sufficient conditions for integration, including the application of mathematical analysis, Real Variable Function-related content which is useful to sum up the necessary and sufficient conditions of the integrability.

然后引述了积分的充分条件、必要条件及充分必要条件，包括应用数学分析、实变函数相关内容总结的可积的充要条件，并作了翔实扼要的论述和证明，且给出针对性极强的应用例题，以便加深对可积条件的理解及加强应用能力。

In this project we obtain a sufficient and necessary condition for a finite group G has a p-block with a normal p-subgroup D as a defect group, a necessary and sufficient condition for a group which is an extension of a nilpotent group by an abelian group has a p-block of defect zero.

本项目中我们给出了正规p-子群是有限群G的亏群的一个充要条件和幂零群被交换群扩张的群有亏零块的充要条件。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

A necessary and sufficient condition for a fx + t(y + g to be a bent function is disscussed,on which basis a necessary and sufficient condition for a function F = fix + tq + g to be a bent function is given when q is not a balanced-function by use of cyclic walsh spectrum and decomposition formula of walsh spectrum.

讨论了形如fx+τ(y+g的布尔函数是Bent函数的充分必要条件，在此基础上利用Bent函数的循环Walsh谱及谱分解式，进一步给出了当q不是平衡函数时，形如F=fx+τ(yq+g布尔函数是Bent函数的充分必要条件。

In this paper,a necessary condition that a cut vertex belongs to every γ s set of G is discussed,and a necessary and sufficient condition of existing indepedent set dominating set in G is given.

本文讨论了割点属于G的任一最小集控制集的必要条件，并且给出了G有独立集控制集的充要条件。

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。

In this paper, the theoretical analysis of matrix's triangular decomposition is mainly discussed, including such as the necessary and sufficient condition of uniqueness of existence in matrix's triangular decomposition,the necessary and sufficient condition of existence and so on.

本文主要对矩阵的三角分解理论分析作了比较全面的统述，它包括矩阵三角分解存在唯一性的充要条件、存在性的充要条件、存在性的充分条件等。

An exceptional condition is a problem that divvents the continuation of the method or scope that you're in. It's important to distinguish an exceptional condition from a normal problem, in which you have enough information in the current context to somehow cope with the difficulty. With an exceptional condition, you cannot continue processing because you don't have the information necessary to deal with the problem in the current context .

异常条件是阻止你的方法正常运行的一个问题，在普通的问题当中分别出这些异常的条件是很重要的，对于普通的问题在当前的环境中你有足够的信息来应付这个难题，但是对于一个异常条件你则无法解决因为在当前的环境中你没有足够的信息来处理这个问题。

Mr. Putin said there were signs of genocide against the Ossetian people.

普京说，有迹象表明对南奥塞梯人进行了种族清洗。

What I'm trying to say, Tristan is...

特瑞斯坦。我想说的是。