查询词典 Stokes theorem

Using Taylor Theorem,we generalize the second sufficient conditions for extreme point and inflection point,and give the classification for a large class of stationary point .

利用泰勒定理，推广了极值的第二充分条件和拐点的第二充分条件，并对某一大类驻点进行了分类。

The stabilities of the stationary state solutions are studied with a linear stability theorem.

用线性稳定性定理分析了相对粒子数布居的定态解的稳定性。

By regarding the forest-sum growth-cutting rate as the control variable and judging its optimality by "norm minimum", we have given a existence theorem of the optimal control for the area distributing systems of forest trees by utilizing space L2(0,T)'s reflexivity, smoothness and strict convexity.

本文将林木总和长消率作为控制变量，以"范数最小"来衡量其最优性，利用空间L2（0，T），T＞0的自反、光滑和严格凸性，给出了森林面积分布系统最优控制的一个存在性定理。

The theorem seems to be so important and if we say that It has a very strong effect for almost 3-variable inequality, It's really incredible.

和definitally ，这是最大的关键，因为我们不需要使用任何中间阶段。上述两个例子可以证明了最小二乘分析方法，但在密闭的含义。

In the first part, we will first deal with the strong Bonnesen-style inequality (2.1.3) for closed convex curves in the plane (the numbers of formulae and references are those of them in the context below). Bonnesen had first proved the weaker inequality (2.1.2) in [12] and several years later, he outlined in his monograph [13] various Bonnesen-style inequalities including (2.1.3), he considered, however,(2.1.3) as a direct consequence of Kritikos theorem for convex bodies in higher dimensional Euclidean spaces,. Here, we will give an independent proof of the existence for inequality (2.1.3), and by the way, give an estimate on the width of the bi-enclosing annulus of closed convex curves in the plane.

具体地讲，在第一部分中，首先讨论平面上闭凸曲线的强Bonnesen型不等式(2.1.3)(公式的编号和参考文献的编号引自后面的正文)，Bonnesen在文[12]中先证明了较弱的不等式(2.1.2)，几年以后，在他的著作[13]中，讨论了多种Bonnesen型不等式，其中包括不等式(2.1.3)，不过，他把(2.1.3)作为高维欧氏空间中凸体的Kritikos定理的直接推论，我们这里对不等式(2.1.3)给出独立的存在性证明，并且还对平面闭凸曲线的bi-enclosing环的宽度给出了一个估计。

In the first part, we will first deal with the strong Bonnesen-style inequality (2.1.3) for closed convex curves in the plane (the numbers of formulae and references are those of them in the context below). Bonnesen had first proved the weaker inequality (2.1.2) in [12] and several years later, he outlined in his monograph [13] various Bonnesen-style inequalities including (2.1.3), he considered, however,(2.1.3) as a direct consequence of Kritikos\' theorem for convex bodies in higher dimensional Euclidean spaces,.

具体地讲，在第一部分中，首先讨论平面上闭凸曲线的强Bonnesen型不等式(2.1.3)(公式的编号和参考文献的编号引自后面的正文)，Bonnesen在文[12]中先证明了较弱的不等式(2.1.2)，几年以后，在他的著作[13]中，讨论了多种Bonnesen型不等式，其中包括不等式(2.1.3)，不过，他把(2.1.3)作为高维欧氏空间中凸体的Kritikos定理的直接推论，我们这里对不等式(2.1.3)给出独立的存在性证明，并且还对平面闭凸曲线的bi-enclosing环的宽度给出了一个估计。

This Paper deals with problems of large number theorem in stochastic sense and obtains sufficient and necessary conditions,for weak law and strong law of large numbers in stochastic sense .

本文讨论随机大数定律，得到一个随机变量序列分别服从随机弱大数定律和随机强大数定律的充要条件。

The strong law of large numbers for the state frequency and the strong limit theorem of arbitrary function for the Markov chain field on the arbitrary Cayley tree are investigated.

主要研究任意Cayley树上马尔可夫链场的状态出现频率的强大数定律以及Cayley树上任意函数的一类强大数定律。

Thirdly, proper probabilistic model is built for the bilateral stop-and-go generator and the probability properties of its output sequence are studied. It is proved that the output sequence obey strong law of large numbers and central limit theorem and that, however, the distributions of 0 and 1 in the output sequence are imbalanced, which implies that this generator cannot be used as keystream generator directly. The rate of coincidence between the output sequence and corresponding LFSR sequences, together with their first derivatives are obtained, which reveal the existence of correlation between these sequences.

最后，建立了双侧停走生成器的概率模型，研究了双侧停走生成器输出序列的概率分布性质和大数性质，证明了生成器输出序列服从强大数定律和中心极限定理，得到了生成器输出序列中0，1分布是不平衡的结论，由此指出不能将这种生成器直接作为密钥流生成器；给出了双侧停走生成器输出序列和相应的线性移位寄存器序列之间的符合率以及一阶差分序列之间的符合率，得到了符合率的表达式，揭示了这些序列的对应比特和对应序列段之间存在相关性。

Our results show that the rate of correlation among the random variables of those output sequences are low although they are not independent; in addition, the output sequences of those combined generators are homogeneous Markov chains which are strictly stationary processes with ergodicity; the output sequences of those combined generators are also proved to summit to the strong law of large numbers and the central limit theorem; finally the computation formula of the rate of the accordance between the output sequences and input sequences of those combined generators is given.

我们的研究结论表明：虽然这些序列中随机变量之间不具有相互独立性，但它们的相关程度却比较低；证明了"停走"生成器，KM_1M_2型组合生成器和加法型组合生成器的概率模型输出序列都是强平稳的和遍历的齐次马氏链；讨论了这些序列的概率极限性质，证明了它们均服从强大数定律和中心极限定理；还分别给出了各类生成器的输出序列与输入序列之间的符合率的计算公式。

This was not understood at the time, and therefore went unaddressed, until ascension became so distorted that we chose to stop ascending and wait for a time when all records would be revealed.

这在当时没有被了解，因此进行着无改编，直到提升变得如此扭曲，我们选择去停止提升并等待所有记录能被揭示的那一天。

The attack＇s nuisance value is increased because mobile phone networks also send notifications of new voicemail by sms,so an attacked phone may stop advising of new voice messages too,it warned.

它警告：这种攻击的危害增长是因为移动电话网络也会通过短信发送新语音邮件的通知。所以受到攻击的手机可也以停止新的语音信息的提示。