公式

In this paper, the asymptotic state of mean value of generalized Taylor formule is studied.

本文研究广义Taylor公式的中值的变化趋势，使文[1—4]的相应结果成为本文的特例。

Results Two new asymptotic formulae on their mean value are given.

结果 给出两个新的数论函数均值的渐近公式。

Number theory function; Smarandache function; Mean value; Asymptotic formula

基础科学，数学，代数、数论、组合理论数论函数； Smarandache函数；均值；渐近公式

By using the limit theory,we discuss and prove the asymptotic properties of mean point in integral mean value formula for a complex function.

利用极限理论，给出了复函数积分中值公式的"中值点"的渐近性的简洁证明。

The authors intend to discuss and prove the asymptotic properties of mean point in integral mean value formula for a copmplex function.

给出了复函数积分中值公式的"中值点"的渐近性，相信在复函数中有着很重要的作

The authors intend to discuss and prove the asymptotic properties of the intermediate point in integral mean value formula for a copmplex function,and meanwhile to improve and popularize the previous conclusions.

给出了复函数积分中值公式"中值点"的渐近性质，改进和推广了已有的结论。

The authors intend to discuss and prove the asymptotic properties of the intermediate point in integral mean value formula for a copmplex function, and meanwhile to improve and popularize the previous conclusions.

摘要给出了复函数积分中值公式"中值点"的渐近性质，改进和推广了已有的结论。

It is proved that, when the value of critical threshold less than 1, the disease free equilibrium point is globally asymptotically stable. Further more, Bursaphelenchtis Xylophilus is used to construct the Lyapunov function, and the stability theory of Lyapunov function is used to prove that the equilibrium point is Global asymptotic stable. It explains that the Bursaphelenchus Xylophilus wiil eventually disappear.

证明了当临界阈值小于1时，无病平衡点是局部渐近稳定的，进一步利用巴尔巴欣公式构造Lyapunov函数，运用Lyapunov稳定性理论证明了该平衡点的全局渐近稳定性，说明松材线虫病会最终消失；当临界阈值大于1时，病虫害平衡点是局部渐近稳定的。

This particular formula involves a special function,which is the uniformly bounded solution to a scalar Riemann-Hilbert problem,and which is asymptotically equal to the constant "1" except at the origin.

这个特殊的公式包含了一个特殊函数，这个特殊函数实际上是一个一维Riemann-Hilbert问题的一致有界的解，并且除了在原点，它的取值都渐近地等于常数"1"。

It was, in view of the actual state of the controversy, a colourless, or what at the present day would be called a comprehensive, formula.

这是，鉴於实际状况的争议，一种无色，或用什麼，在现今社会，将所谓全面，公式。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。