必要条件

Food is not only the prerequisite for maintaining human existence and reproduction of labor force but also an important criterion of people's daily life.

饮食作为维持人类生存和再生产的必要条件，是人们日常生活水准的重要指标，又是社会进步与经济发展的重要表现。

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）。

And finally we obtain the necessary and sufficient conditions for a fuzzy matrix to be idempotent.

得到了Fuzzy群矩阵是幂等矩阵的充分必要条件。

DOA identifiability issue for such arrays is discussed, and the corresponding Cramer-Rao Bound is derived also.

文中讨论了算法参数可辨识性的必要条件，并分析计算了多参数联合估计的克拉美-罗界。

For OFDM systems, necessary and sufficient conditions for blind channel identifiability based on the finite alphabet property of information symbols are established.

提出并证明了正交频分复用系统中基于信息符号有限字符集特性的信道盲可辨识的充分必要条件。

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。

Specially, in Hilbert spaces, some necessaryand sufficient conditions are given in terms of the uniformly square integrability anduniform boundness of the resolvent on the imaginary axis respectively. Furthermore,we consider this robustness fordifferential equations with unbounded operatorin the delay term.

我们进一步研究了时滞项含无界算子的抽象微分方程的小时滞鲁棒稳定性，获得了一些充分必要条件，并应用所得结论讨论了具解析半群生成元的时滞系统。

And all of these approaches are derived from the full rank decomposition technique for the incidence matrix.

讨论了Petri网系统状态方程存在整数解的条件，即可达性的一个必要条件。

It takes advantages of AR-quiver analysis and APR- tilting translation. We proved: if T_A is a tilting A-module over a path algebra of type A_n or a characteristic tilting A-module over a path algebra of type D_n,E_6,E_7, E_8,then there are points corresponding indecomposable direct summands of T_A in theτ- orbit of each edge.

通过对Dynkin型路代数的AR-箭图分析及利用APR-倾斜变换，证明了A_n型路代数倾斜模及D_n，E_6，E_7，E_8型路代数本性倾斜模T_A的一个必要条件是，在A的AR-箭图Γ_A的边缘的r-轨道都有T_A的不可分解直和项对应的点。

Mathematics is an organism for whose vital strength the indissoluble union of the parts is a necessary condition.

数学是一个有机体，它的生命力的一个必要条件是所有各部分的不可分离的结合。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。