查询词典 differentiation theorem

When proving the differential mid-value theorem,"Higher Mathematics" does know to make the auxiliary function ф in order to apply Rolle Theorem.

在证明微分中值定理时，《高等数学》作辅助函数ф的目的是为了应用罗尔定理。

Equidistance point and difference theory in theory of function approximation are studied. Meanwhile, the relation among difference, difference quotient and derivate is revealed. By drawing Lagrange's and Cauchy's theorem of mean on difference and Taylor's formula into difference function, four theorems, such as Lagrange's theorem of mean on difference, are concluded in simple way. On the basis of these conclusions, the asymptotic property of middle point is studied, a series of new conclusions are drawn and the discussions on the asymptotic property of middle point in differential mid-value are summarized.

对函数逼近论中等距节点和差分理论进行了研究，揭示了差分、差商与导数之间的联系；将Lagrange中值定理、Cauchy中值定理、Taylor公式引入到差分函数中，简明地推导出Lagrange差分中值定理等4个定理，并在此基础上对&中间点&的渐近性进行了研究，得出了一系列&中间点&的渐近性的结果，概括了有关文献对微分中值公式的&中间点&的渐近性的讨论；给出的引理改进了函数逼近论的证明方法，精简了函数逼近论中的一些内容。

In chapter II,an extended strongly equivalent theorem forgerms with parameters is proved.The theorem is useful to constructthe factoring map between any unfoldings and universal unfolding.

在第二章中，对带有参数的核证明了一个推广的强等价性定理，这个定理在构造任意开折和普适开折因式相通的变换中有一定的应用。

Chapter 4 is devoted to the existence and multiplicity of homoclinic for self-adjoint nonlinear second order difference equations by using "Mountain Pass " theorem and "Symmetry Mountain Pass "theorem in critical point theory.

第四章应用临界点理论中的山路引理与对称山路引理研究了一类自共轭非线性二阶差分方程的同宿轨的存在性与多重性。

Based on the tree martingale decomposition theorem and the con-vergence of locally finite tree martingales,a tree martingale convergence theorem isverified.

再基于树鞅分解定理和局部有限树鞅收敛定理，证明了一个树鞅收敛定理。

In this paper, a fixed value theorem for direct areas of height triangle s in circular inscribed polygons is obtained, and some results, including the famous height theorem in a triangle, are deduced.

给出圆内接 2n +1边形中高线三角形有向面积的定值定理及其推论，其中包括著名的三角形的高线定

Differential Calculus: limits and continuity; derivatives; techniques of differentiation; mean value theorem; higher derivatives; maxima and minima; curve sketching.

微分学：极限与续性、导、微分的方法、值定理、阶导数、值、绘曲线。

In Chapter 4 we discuss the solvable theorem of adaptive inverse optimal control problems, and proceed with controller designs of global asymptotic stability in probability, adaptive inverse optimal stabilization in probability and output-feedback adaptive inverse optimal stabilization in probability for strict-feedback stochastic nonlinear continuous systems with additive standard Wiener noises and constant unknown parameters using It〓's differentiation rule and an adaptive backstepping algorithm. Control laws and adaptive laws can be obtained at one time by this design scheme. Many simulations have been performed to validate the properties of the proposed adaptive control scheme.

在第4章中，针对具有标准Wiener噪声扰动和未知定常参数的不确定随机非线性系统，提出并证明了自适应逆最优控制问题可解定理，构造了适当形式的四次型随机控制Lvapunov函数，基于It〓微分规则和自适应Backstepping算法，系统地设计了全局依概率渐近稳定控制器、自适应逆最优控制器、输出反馈逆最优控制器以及在设计中如何处理二阶Hessian矩阵函数的方法，这种方法可同时获得控制律和自适应律，通过实例仿真，表明该控制算法是有效性的。

In this study, the effect of nCDHA on chondrogenic differentiation of rat adipose-derived adult mesenchymal stem cells in alginate gel was evaluated. nCDHA/alginate composites containing different amounts of nCDHA were prepared and used to encapsulate rat ADAS. The chondrogenic differentiation of ADAS was enhanced after 7 days and the total collagen content increased after 14 days at 500 ppm of nCDHA.

中文摘要本研究先制备一系列nCDHA/alginate奈米复合材料以三维培养方式，探讨大鼠脂肪干细胞经过ㄧ周与二周培养后，软骨分化基因及软骨基质分泌(collagen，GAG)进行评估，结果发现500 ppm nCDHA可增加第7天软骨基因分化与第14天胶原蛋白增生。

In conclusion, we have conducted the in-depth analyses of HetR protein function in the molecular mechanism of heterocyst differentiation and pattern formation in Anabaena. Our results show that HetR/PatS interaction plays a key role in heterocyst differentiation and pattern formation.

综合以上内容，我们对HetR蛋白在蓝细菌异型胞分化与格式形成过程中的分子调控机制作了较为深入的研究，我们的研究显示HetR/PatS的相互作用在异型胞分化与格式形成中起重要作用。

But GST= 0.156, Nm=1. 588. As a result, the foundation of Youyongchi Avicennia marina population was the result of the migration of hypocotyles and human factors.

这项工作可以为海岸防护林中新引进种类的判定以及为研究种群建立者效应方法的确定提供科学依据。

The two-dimensional CDRC-ADI-FDTD update equations for collision unmagnetized plasma are induced. The unconditional stability of the CDRC-ADI-FDTD formulation for collision unmagnetized plasma is obtained by the examples.

推导了碰撞非磁化等离子体中的二维CDRC-ADI-FDTD迭代公式，并用算例验证了碰撞非磁化等离子体CDRC-ADI-FDTD算法也是无条件稳定的。