查询词典 theorem of alternative

This article discusses the use of the theorem of the residues to calculate Cauchy's Principal values of the improper integral, where auxiliary function has poles of higher order on the real axis and proposes a new theorem of culcuation.

在复函中应用留数定理计算广义积分的科希主值时，许多著作仅讨论了辅助函数在实轴上有一阶极点的情形[1-3]，有的则认为：辅助函数"在实轴上的奇点不能是二阶或二阶以上的极点["4，5]。

Applying this new theorem, one can easily find the auxiliary function and solve many problems of Cauchy's principal values of improper integral as well, the original theorem being unable to do so.

由于这个条件的限制，在寻找辅助函数时往往碰到困难，甚至找不到在实轴上只有一阶极点的辅助函数。

In the first chapter (1.1.1)-(1.1.4) is studied by means of fixed point index theorem, not only the existence theorem is obtained, but the multiplicity is also obtained.

本文第一章利用这一理论研究方程(1.1.1)-(1.1.4)的正周期解问题，与已有研究成果相比，本章不仅获得了该类方程的正周期解的存在性定理又获得了正周期解的多解性定理，并将所取得的结论应用于一些具有实际背景的方程。

Motivated by this, we consider the global behavior of positive solutions of three-point boundary-value problems for second-order differential equations, under two different kinds of boundary-value problems, using fixed point theorem, fixed point index theorem and cone theory.

本文受到文献[7]的启发，运用不动点定理、不动点指数定理以及锥理论，分别研究了两种不同边值条件下二阶微分方程三点边值问题正解的整体性。

Based on the minimizing vector theorem of the fuzzy inner product space ,the pseudo fuzzy orthogonal vector is defined and the projected theorem of the fuzzy inner product space is testified.

在模糊内积空间的极小化向量定理基础上，给出了向量拟模糊正交定义，并在模糊内积空间中证明了投影定理。

In this paper we have obtained the sufficient and necessary condition concerning the passage to the limit under the integral sign, and have given some examples of the problems which can be solved by the theorem of this paper but cannot be solved by the familiar Vitali's theorem.

关于积分号下取极限的问题，有著名的Lebesgue定理及Vitali定理。本文作者进一步研究了这一问题，得到了积分号下取极限的充分和必要条件，并给出了几个能用本文结果解决而不能用Vitali定理解决的例子。

Third, the use of Lagrange's theorem proving the points of the study on some conclusions, that the Lagrange theorem in the integral study also has a wide range of applications.

再次，利用拉格朗日定理证明了积分学上的几个结论，说明拉格朗日定理在积分学中也有广泛的应用。

Although it is easy to prove the result of the integral mean value theorem in advanced mathematics, the application of the theorem is thus limited.

摘要高等数学中的积分中值定理，其结论易于证明，但限制了定理的应用。

In the second chapter, we consider a kind of Kolmogorov system. The sufficient condition for nonexistence of the closed orbit and existence of the unique and stable limit cycle are obtained by using divergence integral, Poincare-Bendixson theorem and Zhang Zhifenunique theorem.

第二章讨论了一类Kolmogorov系统，利用发散量积分、环域定理和张芷芬唯一性定理，得到了该系统无闭轨的充分条件和存在唯一极限环的条件。

What is discussed in this paper is on the applications of the integral upper limit function in proving the equality, proving the inequality, calculating the repeated integral , the theorem of integratl mean value , prove the theorem of differention mean value .

给出了积分上限函数在证明等式和不等式、算累次积分、明微分中值定理和积分中值定理中的应用。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。