查询词典 extended mean value 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。

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

Based on the higher mathematics method proved inequalities are summarized, and the proposed using the function extreme value and the monotonicity and concave and convex function sex, and mean value theorem, Taylor formula, integral these common higher mathematics method, combining with concrete examples of each kind of method to solve the problems for type, and the key problem of the specific steps, and points out that the inequality proof of higher mathematics method used properly, improve the difficult easy to ability to solve problems.

本文对不等式证明中的高等数学方法作了归纳总结，提出了利用函数的单调性，极值与最值，函数凹凸性，中值定理，泰勒公式，积分这些常用的高等数学方法，并结合具体实例阐述了每一种方法的适用类型、解决问题的关键和证明问题的具体步骤，指出在不等式证明中恰当地运用高等数学方法可以化难为易，提高解题能力。

We proved the second mean value theorem of integral with intermediate value of continuous function and absolute continuity of integral, and determine that is true even in the infinity interval with same method.

用连续函数的介值性和积分的绝对连续性证明了积分第二中值定理，并用同样的方法证明了当区间为无穷区间时的积分第二中值定理。

Using nuclear DNA C-values for 539 angiosperms in China, we examined the variation of these values among growth forms and taxonomic groups and the relationship of these values with invasiveness. Mean DNA C-value of the 539 angiosperm species was 4.06 pg. Mean DNA C-value was(1) significantly lower for woody species (1.84 pg) than for herbaceous species(5.02 pg);(2) significantly lower for 360 dicots (2.20 pg) than for 179 monocots (7.80 pg);(3) significantly lower for annuals (2.78 pg) than for perennials(6.65 pg);(4) significantly lower for 134 weed species (1.93 pg) than for herbaceous non-weeds (6.75 pg) and for several families that have an unusually high proportion of weed species;(5) significantly lower for 47 exotic weed species (1.76 pg) than for 134 native weeds (1.93 pg), but significantly lower than that of "non-weedy" herbaceous species (6.75 pg);(6) lower for weeds than for "non-weedy" species in same genus or family; and (7) in herbaceous species, generally lower for weedy compared to "non-weedy" species, with some exceptions such as Avena fatua, whose DNA C-value is as high as 14.15 pg, contrarily, and some "non-weedy" herbaceous species in Cruciferae and Cucurbitaceae with very low values.

统计了中国境内有分布的539种被子植物的DNA C-值，分析了它们在不同分类群、生活型、倍性、生活史类型以及在杂草和非杂草类群中的分布情况，主要结果如下：(1)539种被子植物DNA C-值平均为4.06 pg，其中木本植物的DNA C-值平均为1.84 pg，低于草本植物的平均值(5.02 pg)；(2)双子叶植物(360种)的DNA C-值平均为2.20 pg，极明显地小于单子叶植物(179种)的平均值(7.80 pg)；(3)1年生植物的DNA C-值平均为2.78 pg，明显小于多年植物的平均DNA C-值(6.65 pg)；(4)134种杂草的DNA C-值平均为1.93 pg，明显小于非杂草草本植物的平均值(6.75 pg)，含杂草较多的科，平均DNA C-值相对较小；(5)统计的47种入侵杂草的DNA C-值平均为1.76 pg，略小于134种杂草的平均DNA C-值(1.93 pg)，极显著地小于非杂草性草本植物(6.75 pg)；(6)以科为单位，不同科的DNA C-值存在着极大的差异；(7)DNA C-值与染色体倍性的关系并不明显，但是，随着倍性的增加，基因组变小；(8)在同一科、属中，与非杂草相比，典型杂草的DNA C-值往往偏小；(9)总体上杂草或杂草性强的植物，它们的DNA C-值比非杂草性植物的要小。

In addition, MVD value was positively correlated with the expression level of MMP-9 and Integrin beta-3 mRNA (P＜0.05). The five year survival rate of patients with positive mRNA expression and mean MVD value≥39.5/mm2 were significantly lower than those of patients with negative mRNA expression and mean MVD value＜39.5/mm2; The expression of MMP-9 was significantly corelated with the expression of integrin β3 (P＜0.05). Conclusion The expression of MMP-9 and Integrin β3 can promote tumor angiogenesis and contributes to tumor invasion and metastasis in gastric carcinoma.

结果 MMP-9和Integrinβ3 mRNA 阳性表达率分别为58.10％和60.95％，其阳性表达与胃癌生长方式、浸润深度、脉管侵犯、淋巴结及远处转移均密切相关（P均＜0.01）； MMP-9、Integrin β3 mRNA 的阳性表达病例的平均血管数均高于阴性表达病例的平均血管数（P均＜0.05）；MVD值分别与MMP-9和Integrin β3 mRNA的表达水平呈正相关（P均＜0.05）； MMP-9和Integrinβ3 mRNA的阳性表达以及MVD值≥39.5病例的5年生存率显著低于阴性表达和MVD 值＜39.5的病例；MMP-9和Integrin β3 mRNA表达存在显著相关性（P＜0.05）。

Secondly, in view of the identification problem after the change of MRAPC structure, the research has been extended to a kind of continuous system with time delay, and the robust convergence analysis for this model reference adaptive identification algorithm has been given. Using the intermediate value theorem in this analysis, the approximate problem in original analysis has been solved partly.

2针对MRAPC算法结构改变后产生的自适应辨识问题，考虑一种更一般的具有实零极点的时滞连续系统的模型参考自适应辨识算法，作者分析了该算法的鲁棒收敛性，在运用微分中值定理的基础上，解决了原有的收敛性分析中存在的近似问题。

Using Extended Virial theorem , three recurrence relation of the average value of coordinate operator for linear harmonic oscillator, spherical harmonic oscillator and like-hydrogen ion were obtained respectively.

针对一维谐振子、类氢离子和三维各向同性谐振子三个量子体系，应用超维里定理，推导了幂坐标算符平均值的递推关系，方法较通常简洁明了。

Transforming the boundary value problem with p-Laplace operator into operator equation, giving propriety conditions for different value of p,and using an extension of Mawhin s continuation theorem,the existence of solution of a boundary value problem with p-Laplace operator is proved, and the sufficient conditions for solution existence are obtained.

将具p-Laplace算子的边值问题转化成算子方程，对于p的不同取值给出适当的条件。利用Mawhin连续引理的推广形式，证明了一类具p-Laplace算子的微分方程边值问题解的存在性，得到了一系列解存在的充分条件

On the basis of analyzing detailedly the correlative conclusions of the extreme value problem of two variable Function , this paper extends the essential condition and sufficient condition to multi-variable function by using the Taylor Formula 、Quadratic Form 、Hesse Matrix and so on,and gives a method to judge the extreme value of point whose vice-derivative doesn't exist by utilizing Lagranges theorem ,so that compensates for the blank above ,which turns idea that solve the extreme value of multi-variable function problem one by one into realities.

摘要本文在对二元函数极值问题的相关结论进行分析的基础上，用泰勒公式、二次型、海赛矩阵作为工具，将二元函数极值的必要条件和充分条件推广到多元函数的情形，而且还利用拉格朗日中值定理找到了一个判别不可导点处极值的方法，从而弥补了多元函数不可导点处极值无法判断的空缺。因而，使得用穷举判断的方法来解决多元函数的极值问题这一思路成为现实。

Methods Clinical data of 3 cases of bile duct injury during laparoscopic cholecystectomy were analyzed retrospectively.

回顾总结3例LC术中胆管损伤的临床资料，分析3例胆管损伤的原因及对策。

These techniques are applied to the gobang.

本文将这些技术用于五子棋中。