查询词典 necessary and sufficient conditions

Under the conditions of compatibility or sub-compatibility between a single-valued mapping and a set-valued mapping,a necessary and sufficient condition for set-valued mapping pair and single-valued mapping which have the common fixed point in complete convex metric space are given.

在单值映象与集值映象相容或次相容的条件下，给出了完备凸度量空间中集值映象对与单值映象存在公共不动点的一个充要条件，改进和推广了某些已知结果。

On the basis of the differential game approach, necessary and sufficient solvable conditions for the hybrid estimation problem are provided in terms of solutions to a Riccati differential equation.

基于微分对策方法，混合估计问题有解的充要条件表达为 Riccati 微分方程的可解性。

Based on these and by the theories and methods of parametric programming, nonsmooth analysis and nonlinear analysis, the necessary and sufficient optimality conditions of cone efficient solutions for the model were obtained.

利用参数规划、非光滑分析和非线性分析的理论和方法，获得了模型锥有效解存在的最优必要条件和充分条件。

The necessary conditions and sufficient conditions for a set to be polar are listed.

具体内容如下：·研究了N指标d维广义Brownian Sheet的极集的性质，得到了其极集的必要条件与充分条件。

We next establish certain conditions which arc necessary and sufficient for a projective module over a cellular algebra to be injective.

给出了胞腔代数是标准分层代数的一个充分条件，利用这个条件我们介绍了一种归纳构造标准分层的胞腔代数的方法； 5。

A theorem of the alternative for the generalized subconvexlike set-valued maps is established using the separation theorem of convex sets in a Banach spaces, the concept of weak Benson proper efficient elements for a vector optimization problem is introduced, and the optimality necessary and sufficient Lagrange conditions for a vector set-valued map constrained optimization problem with the weak Benson proper efficiency is developed, with which the optimality Lagrange conditions for a nonconvex vector top-base constrained optimization of set-valued maps with the Benson proper efficiency are obtained.

刘莹 ，刘三阳，盛宝怀运用凸集分离定理对广义锥次类凸集值映射建立了一种择一性定理。引入向量优化弱Benson真有效元的概念，对带约束的非凸向量集值优化问题建立了在弱Benson真有效意义下有效元应满足Lagrange乘子型的必要及充分条件，并用这一结果建立了多目标主从非凸向量集值优化在弱Benson真有效意义下最优解的Lagrange乘子型充要条件。

Based on Pseudo-linearization and least square methods, the bearings-only target motion problem was studied under the conditions that the target takes uniform rectilinear motion in 2-dimensional space, the single observer takes uniform rectilinear motion first, and then takes rectilinear motion with constant acceleration. The necessary and sufficient observable conditions, some unobservable conditions are gained.

基于拟线性处理和最小二乘方法，在目标作匀速直线运动，单观测站作匀速直线运动，进而作匀加速直线运动的机动情形下，研究了二维纯方位系统的可观测性，得到了系统可观测性的充要条件以及系统的某些不可观测的条件。

In statistical analysis of ordinal data, we usually build up linear-by-linear association model and meet a trouble of choice of scores. Graubards et a1 (1987) proposed several methods for score choice in independence test in ordinal 2×κ contingency tables: equally spaced scores, midpoint scores and midrank scores. He also pointed out that the result of independence test may be different for the different choice of scores according to the same association model. Agresti et a1 (1987) treated the score vector in row effects and column effects model for two-way contingency tables as parameters and derived the necessary and sufficient condition of the solution under monotone order restriction by Kuhn- Tucker conditions.

在有序数据的统计分析中，通常要建立线线相关模型，其中得分的选取是一个棘手的问题，Graubard et a1（1987）给出了有序2×κ列联表中独立性检验的几种得分选取方法：等距离得分，中点得分和midrank得分等，同时指出，对于同一个相关模型，独立性的检验会由于得分选取的不同而得到不同的结论，Agresti et al（1987）把二维列联表中的行效应和列效应模型中的得分向量作为参数，在满足递增的序关系情况下，利用Kuhn-Tucker条件给出了解的充要条件。

Via basic and descriptor adverse transformation of matrix, an equivalent standard linear system is derived. Sufficient and necessary conditions are established for observers with disturbance decoupling and LTR in systems. Analysis showed that the necessary and sufficient condition for observers with LTR is disturbance decoupling to any undnown inputs. So it is con verted to the problem that observers are designed with disturbance decoupling.

通过矩阵的初等变换和广义逆变换，将非方广义系统等价地转化为正常状态空间的广义线性系统，并运用有关定理给出观测器具有干扰解耦和环路复现特性的充要条件，经分析可知，系统具有环路复现特性的充要条件是系统对于任何未知输入干扰解耦，则具有环路复现特性的干扰解耦观测器的设计问题转化为系统关于任何扰动都是解耦的。

Some necessary and sufficient conditions are introduced for the existence of the weighted Moore-Penrose inverse of the morphisms with universal factorization,and also given are some pertinent formulae.

文献[3]引进了广义Moore-Penrose逆，并讨论了交换环上具有秩分解的矩阵广义Moore-Penrose逆存在的充要条件。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。