查询词典 sufficient condition

A necessary and sufficient condition is proved here for judging whetherthe ideal class group Hof a quadratic function field 〓has a cyclicsubgroup of order n for any given n.

给出了一般二次函数域的理想类群含有n阶循环子群的充分必要条件（其中〓是任意事先给定的正整数）。

In this paper, we present the sufficient and necessary condition for the sum of a identity matrix and a generalized cyclic matrix is nonsingular, and obtain the formal representation of the relative gain array of the sum matrix.

本文给出了单位矩阵与广义循环矩阵的和矩阵的非奇异的充要条件，得到了这样和矩阵的相对增益阵列的显示表达式。

Secondly, a conjecture about the stability for these systems is proposed based on the sufficient and necessary condition of the isolated transfer function being positive real. When the zeros and poles of the transfer functions lie in the imaginary axis, a known conclusion is derived from the conjecture; while the zeros and poles are on the real axis, a new result is obtained and is proved in this note. Finally, according to the conjecture, an example with poles existing on the complex plane is presented, which is not only interesting but also challenging.

然后， 基于所有孤立部分传递函数都正实的充分必要条件给出了上述系统为稳定的一个猜想，当传递函数的零极点都位于虚轴上时，由这一猜想得到了一个已知的结论；当传递函数的零极点都位于实轴上时，由这一猜想得到了一个新的结论，本文证明该结论是正确的；最后，根据这一猜想，给出了传递函数极点位于复平面的一个例子，它涉及到一类系数矩阵为时变正定矩阵的振动方程的稳定性问题，值得去深入研究。

The unique existence theorem for minimal determining set of completerational choice function is obtained,and the sufficient condition is used to show avery simple proof of Arrow Impossibility Theorem.

构造并证明了完全理性选择函数的最小决定集的存在惟一性定理，同时应用该定理的充分性条件给出了Arrow不可能性定理的一个简单证明。

In other words, basic science is a necessary but not sufficient condition for remaining industrially competitive.

换句话说，保持工业强大的竞争力，基础科学是必须的，但并不是全部。

The sufficient condition of the system stability is given in terms of linear matrix inequalities.

系统稳定性的充分条件以LMI的形式给出。

The sufficient and necessary condition for complete inertial force balancing of open-chain spatial linkages is derived and the concept of relative balancing is presented in this paper .

本文导出空间开链型机构惯性力完全平衡的充分必要条件，提出相对平衡的概念。

The necessary and sufficient condition for the existence of 2-dimensional minimal realization is given, which is described by the relation of elements of the infinite sequence and is easy to check.

给出了存在2维最小实现的充要条件，该条件是用无穷序列｛g｝(上标∞下标 0)元素之间的关系描述的，因而容易判断；同时，用涂奉生提出的结构标准形和最小实现算法给出了2维最小实现的构造方法，从而完全解决了2维最小实现问题。

Firstly,by using the estimating methodfor the compact embedding operators(from weighted Sobolev space to the weighted〓space),we obtain a necessary and sufficient condition for the discreteness of thespectrum of certain differential operators.Secondly,based on the property of thespectrum of difinitizable operators on the Krein space,we consider the left definitedifferential equations with middle deficiency indices,and give a completecharacterization for self-adjoint(J-self-adjoint)differential operators in theindefinite inner product space 〓.Especially,we prove that all the J-self-adjoint differential operators are definitizable.

我们首先运用加权Sobolev空间到加权〓空间嵌入算子紧性的判别方法，证明一类加权自伴微分算子具有离散谱的充要条件；然后，基于Krein空间上可定化算子谱的性质，对于具中间亏指数的左定型微分方程，建立其相应的微分算式在不定度规空间〓上所生成自伴算子的完备性刻画（特别证明了J-自伴微分算子具有可定化性）。

In this paper we have obtained the sufficient and necessary condition concerning the passage to the limit under the integral sign, and have given some examples of the problems which can be solved by the theorem of this paper but cannot be solved by the familiar Vitali's theorem.

关于积分号下取极限的问题，有著名的Lebesgue定理及Vitali定理。本文作者进一步研究了这一问题，得到了积分号下取极限的充分和必要条件，并给出了几个能用本文结果解决而不能用Vitali定理解决的例子。

Cable dampener cannot be rolled up but must be hung over the cable.

缆帆不能被卷起，必须保证处于展开状态

"This skylark is a present from my master," he says.

"这只云雀是我主人献上的礼物。"他说。