查询词典 necessary and sufficient conditions

The fourth section studies general inverse of morphism sum. and obtains some necessary and sufficient conditions for their existence and expression.

第四部分我们研究了态射和的广义逆，得到了他们存在的充分和必要条件以及他们的表达式。

The second section studies general Moore-Penrose inverse of morphism with general factorization, and gives some necessary and sufficient conditions for their existence and expression.

第二部分我们研究了具有广义分解的态射的广义Moore-Penrose逆，得到了他们存在的充分和必要条件以及他们的表达式。

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。

In the first chapter, the one - to - one correspondence between mild solutions of an abstract deday equation and mild solutions of an associated abstract Cauchy problem is shown, and necessary and sufficient conditions for existence and uniqueness of mild solutions of the abstract delay equation are obtained.

全文共为三章，在第一章中，说明了抽象时滞方程的mild解与相应的抽象柯西问题的mild解一一对应，并且得到了抽象时滞方程的mild解存在唯一的充要条件。

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。

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。

This paper discusses singularities, inflection points and convexity of FB-spline curves in terms of their control polygons, and gives the necessary and sufficient conditions for testing when FB-spline curves have one or two inflection points, or a cusp, or a loop, or none of the above points by the envelope theory and the topological mapping method.

文章利用包络理论和拓扑映射的方法，讨论了FB-样条曲线的奇拐点和曲线性质，并给出了依据控制多边形判断FB-样条曲线出现1个或2个拐点、1个尖点、1个二重点以及处处为凸的充分必要条件；最后给出了FB-样条曲线的奇点、拐点以及二重点在λ-μ平面上的分布图。

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 view of the calculation of the start-up time difference of in-lake and out-lake pumping stations on the upper and lower lakes,this article researches on the following related contents,such as the necessary and sufficient conditions of start-up of out-lake pumping station,the relation between the start-up time of out-lake pumping station and rising velocity of lake water level.

针对南水北调南四湖上、下级湖各自调水的出、入湖口提水泵站开启时间差的计算问题，开展了调水出湖提水泵站开启的必要和充分条件、出湖提水泵站开启时间和湖内水位升高速率等相关内容的研究。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。