查询词典 necessary and sufficient conditions

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。

It is proved in this paper that R/ is a principal ideal domain, where R=F+uF+…+u(superscript k-1)F, n is odd, and p is a prime number, and some necessary and sufficient conditions for the cyclic codes over R to be self-dual are given.

该文证明了R/是主理想环，其中R=F+uF+…+u(上标 k-1)F，n是奇数，p为素数，给出了环R上循环码是自对偶码的充要条件。

Analog to the discontinuous bifurcation analysis for classic elasto-plastic theory by Ottosen and Runesson et al, the sufficient and necessary conditions of weak discontinuity and strong discontinuity localization bifurcation for the strain-gradient-enhanced-damage model are obtained.

借鉴Ottosen和Runeson等的弹塑性模型不连续局部化分岔方法，对应变梯度损伤模型推导出与梯度相关的强不连续和弱不连续局部化分岔充要条件。

This Paper deals with problems of large number theorem in stochastic sense and obtains sufficient and necessary conditions,for weak law and strong law of large numbers in stochastic sense .

本文讨论随机大数定律，得到一个随机变量序列分别服从随机弱大数定律和随机强大数定律的充要条件。

We present necessary and sufficient conditions for which there exists A∨_G B and in this case we establish the explicit representation of A∧_G B, where A∨_G B denotes the supremum of A and B associated with the Gudder order.

对任意给定的自伴算子A和B，我们证明了存在A和B关于Gudder序的下(来源：ABC3c论文网www.abclunwen.com)确界A∧_G B并且我们具体地给出了A∧_G B。

Applying mechanics of partitioning of matrix and special structure, we have given the sufficient and necessary conditions for the matrix if it has bisymmetric and anti-bisymmetric solutions.

对于广义双对称与广义双反对称矩阵，首先结合矩阵的结构特点，应用广义逆的相关知识，给出了有解的充要条件以及有解时解的表达式，最后在一种特定的分解条件下，考虑了它的广义双反对称最小二乘解。

By using constructive methods and complicated techniques of matrices, necessary and sufficient conditions for the existence of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, skewbisymmetric solution and various interlaced solutions over a finite central algebra Ω to systems of generalized Sylvester matrix equations overΩ are presented.

利用构造方法和复杂的矩阵技巧，研究了有限维中心代数上的多项式环Ω上的广义Sylvester矩阵方程组在Ω上有自共轭解，斜自共轭解，广自共轭解，斜广自共轭解，中心对称解，斜中心对称解，双对称解，斜双对称解及其各种交错解的充要条件。

In the last of this dissertation, we give necessary and sufficient conditions for the existence of and the expressions of perpositive semidefinite solutions and bipositive semidefinite solutions to some systems of quaternion matrix equations.

给出了某些四元数矩阵方程组有广亚半正定解，双半正定解的充要条件及其表达公式；研究了矩阵方程组的最小二乘解，极小范数的最小二乘解，在某些约束条件下的最小二乘解和极小范数的最小二乘解，给出了其有这些解的充要条件及其表达公式。

In the second chapter, the stabilities of periodic regular gaits for six-legged robots walking longitudinally and laterally were systematically studied respectively, employing a hexpod's geometric model with outward extension of middle legs. Major progress and achievements reached are: a Both the necessary and the sufficient conditions for static walking of hexapods were established theoretically. b A generalized optimization method of gait stability was investigated. c For all feasible duty factor, stability-optimal gaits were obtained, with the expressions being of wide adaptation.

第二章系统分析研究了轴对称六足步行机器人在&中腿行程外置模型&下沿两个运动主方向运动时周期规则步态的稳定性及步态规划问题，主要取得以下三方面新的进展：（1）从理论上建立了六足步行机静态稳定的必要性定理和充分性定理；（2）探索了步态稳定性计算机择优的一般方法；（3）对于所有可能的有荷因数取值，从理论上证明静态稳定性最优步态的存在，并得到具有相当普遍意义的统一表达式。

By using the theory of linear algebra and that of groups,some sufficient and necessary conditions of isomorphic relation systems were found, and the degrees of the groups of these isomorphisms were obtained.

将线性代数及群论的有关知识应用到关系系统上，得到了两个关系系统同构的一些充要条件，并计算出这些同构所作成的群的阶数。

Looking to bounce back from defeat against Cesena last weekend, the Calabrian boss will be sticking to his tried and tested 4-3-3, with Lopez and Sedivic joined up front in Giampaolo's absence by either Nanni or Plasmati.

鉴于上周末对切塞纳的比赛中反败为胜，这支南方球队将会更坚持其一贯而有效的4-3-3阵型，洛佩斯和塞德维奇将取代受伤缺席的詹保罗，和纳尼或者帕斯马蒂中的一个搭档锋线。

Meanwhile, their exposure to the more freewheeling ways of the West broadened dramatically.

另外，西方较自由的生活方式对年轻人的影响增大。