查询词典 extended mean value theorem

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。

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 recent years, along with the intensive study and extension of residue theorem, the residue theorem has been more intensively used, which illustrates the importance of residue theorem and its use value to a certain extent

近年来随着留数定理的深入研究与推广，留数定理得到了愈加广泛的运用，这在一定的程度上也说明了留数定理的重要性及其运用价值

For example, basic tools from calculus such as Fermat theorem, Rolle theorem and the intermediate value theorem may not necessarily hold and fundamental concepts such as chain and product rules and certain smoothness properties all need to be modified.

例如，微积分中的基本工具诸如Fermat定理、Rolle定理以及介值定理不再成立，一些基本的概念诸如链式法则、乘积公式以及某些光滑性都需要做适当的修正。

For example,basic tools from calculus such as Fermat theorem,Rolle theorem and the intermediate value theorem may not necessarily hold and it is difficult to find a universal program for simulation in a model with various timescales,which attract attention of great deal researchers.In this PhD thesis,we first consider classification schemes for positive solutions of the first and second order dynamic systems.

在探讨测度链上的动力方程的动力学行为时人们所熟悉的基本工具诸如Fermat定理，Rolle定理以及介值定理等不再成立，同时很难找到适应不同测度链的模拟程序，这些在给测度链理论研究带来诸多困难的同时，也更引起了广大学者的兴趣。

Meanwhile, deepen the research of socialism distribution theorem, clear out the kinds of mistiness view, comprehend the relation between labor value theorem and distribution theorem, between distribute with capital and eliminate the exploitation, between justice and efficiency.

与此同时，要深化对社会主义分配理论的研究，澄清各种模糊认识，正确理解劳动价值论与分配理论的关系，按资分配与消灭剥削的关系，公平与效率的关系。

As we all know,there is one Simson line at any point on the circumference of triangles,but in this paper, LHP theorem shows that the above conclusion is not correct for any quadrilateral pyramid in three-dimensional space and also during proving LHP theorem,fixed value theorem is proved,at the same time,one guess about the point H and point P on circumscribed sphere of tetrahedron has been concluded.

众所周知，三角形的外接圆周上任一点存在一条 simson 线，而 LHP 定理则指出对于正四面体该结论是不能推广到三维空间上的，并且在论证 LHP 定理的过程中得出了定值定理，同时作为一般四面体的外接球球面上的 H 点、P 点的分布，给出了一个猜想。

Differential intermediate value theorem commonly known as "Lagrange mean value theorem" is a differential study in one of the most important conclusion.

微分中值定理一般称为"Lagrange中值定理"，是微分学中最重要的结论之一。

Lagrange value theorem is an important one of the Mean Value Theorem.

拉格朗日中值定理是重要的微分中值定理之一。

In three separate studies, the investigators evaluated 105 adults with type 1 diabetes (mean age, 37 years; mean duration of diabetes, 20 years), 36 adults with type 2 diabetes (mean age, 50 years; mean duration of diabetes, 10 years), and 91 adults with type 1 diabetes (mean age, 39 years; mean duration of diabetes, 20 years). During a four-week period, participants used a hand-held computer to complete 70 trials of cognitive-motor tasks and to enter their current blood glucose reading after each test. Hyperglycemia was defined as blood glucose level higher than 15 mmol/L.

在3个不同的试验中，研究人员评估105位第1型糖尿病患者（平均年龄为37岁；患糖尿病平均时间为20年），36位第2型糖尿病患者（平均年龄为50岁；患糖尿病平均时间为10年），以及91位第1型糖尿病患者（平均年龄为39岁；患糖尿病平均时间为20岁）；在4周期间，受试者使用一种掌上型电脑来完成70种认知运动任务的试验，以及在每次测试后，输入他们目前的血糖读数，血糖高於15 mmolL被定义为高血糖。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？