查询词典 necessary and sufficient conditions

For a finite-security and finite- state financial market with three forms of friction: ask-bid spread, transaction costs and tax, by using the theory of convex analysis and some optimization techniques, a series of necessary and sufficient conditions are established to characterize weak and strong no-arbitrage respectively.

对存在买进卖出价差、交易费和税收三种摩擦和有限个可能的自然状态的金融市场，利用凸分析理论和最优化技术刻划出了强无套利和弱无套利的一系列充要条件，以往许多这方面的结果均是我们的特例。

Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

Further more, we get the necessary and sufficient conditions for the two-dimensional discrete system, where the permanence and extinction of the system are decided and only decided by the relationship of the non-delay coefficients in the system. Further, we for the first time find the equivalent permanence and extinction between the two-dimensional discrete Lotka-Volterra and its corresponding continuous system.

进一步，本得到了此类离散系统二维自治情形下，其持续生存和灭绝分别等价于系统非时滞系数构成的相应不等式；通过比较本文中二维自治Lotka-Volterra竞争系统的连续和离散两种情形的有关结论，首次发现这两类系统具有等价的持续生存和灭绝性质，建立了这两类系统之间的联系。

The exchange theorem of bases of closed regular fuzzy matroids is obtained with the help of "the exchange theorem of bases" of crisp matroids. Then,the relations between the fuzzy bases and the fuzzy circuits in closed regular fuzzy matroids are studied, and some necessary and sufficient conditions for some fuzzy independent set to be a fuzzy base; some fuzzy circuits from a fuzzy base, and some fuzzy bases from a fuzzy circuit are investigated.

根据传统拟阵的基交换定理，作者给出了闭正规模糊拟阵的基交换定理，得到了一系列结论，并在此基础上进一步研究了闭正规模糊拟阵的模糊基与模糊圈之间的关系，然后给出了闭正规模糊拟阵中某模糊独立集是模糊基、从一个模糊基得到一些模糊圈、以及从一个模糊圈得到一些模糊基的充要条件。

Meantime, the Namioka-Bauer's and Wong's positive extension theorem are generalized to ordered locally convex spaces (see Theorem 5.1) and hence some new necessary and sufficient conditions of positive extension in ordered locally convex spaces are obtained

同时Namioka-Bauer 定理和 Wong定理也被推广到半序局部凸空间中(定理5.1)，从而得到了一些新的关于半序局部凸空间中正延拓的充分必要条件

By generalized {1} inverse matrix,we obtain the necessary and sufficient conditions and general integral for a type of matrix equation having solution over regular ring with an identity,and generalize and complement some existing results in the literature.

借助矩阵的广义{1}逆，在含幺正则环上给出一类矩阵方程相容的充分必要条件及其通解表达式，推广和改进了已知的一些结果。

Both the infimum Vm of the Volume Vof M and the necessary and sufficient conditions of "V=Vm" are obtained under 2 cases of minimal M and pseudoumbilical M.

研究了复射影空间CP4中共形平坦的正曲率全实子流形M，分别在M极小与M 伪脐2种情况下，得到M的体积V的下确界Vm和达到下确界的充要条件。

With the matrix direct product and straightening operator, the necessary and sufficient conditions of the linear matrix equations have solutions and have unique one solution are given.

本文介绍了矩阵直积的有关概念和性质，利用矩阵直积和拉直算子给出了线性矩阵方程有解的充分必要条件以及有惟1解的充分必要条件。

Necessary and sufficient conditions for the existence and the expressions of selfconjugate solution, perselfconjugate solution, centrosymmetric solution, bisymmetric solution, skewselfconjugate solution, skewperselfconjugate solution, skewcentrosymmetric solution, and skewbisymmetric solution to 4 kinds of systems of linear matrix equations over a regular ring with an involutorial antiautomorphism are given.

利用矩阵技巧和所建立的矩阵理论，给出了正则环上五类矩阵方程组有解的若干充要条件和一般解的表达公式。这些矩阵方程组除了它们在理论上有重要的意义外，还有重要的应用价值。在具有对合反自同构的正则环上，给出了四类矩阵方程组有双对称解，中心对称解，斜中心对称解，广自共轭解，斜广自共轭解，自共轭解以及斜自共轭解的充要条件及其这些解的具体表达式。

The first section studies general inverse of morphism with generalfactorization, and gives some necessary and sufficient conditions for their existence and expression.

第一部分我们研究了具有广义分解的态射的广义逆，得到了他们存在的充分和必要条件以及他们的表达式。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。