查询词典 limit theorem

In thisthesis, we first extend the vanishing theorem due to Lawson, Simons and Xinto the case of compact submanifolds of a hyperbolic space. Thus, by using thenew vanishing theorem for homology groups, we prove the topological spheretheorem for complete submanifolds in a hyperbolic space. Hence we generalizethe Shiohama-Xu topological sphere theorem.

本文进一步将Lawson-Simons-Xin同调群消没定理拓广到双曲空间中紧致子流形的情形，并运用这一新的同调群消没定理证明了双曲空间中完备子流形的拓扑球面定理，从而推广了Shiohama-Xu的拓扑球面定理。

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simon\'s nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

Simons [30] proved the non-existence theorem for stable integral current in acompact Riemannian submanifold isometrically immersed into a unit sphere andvanishing theorem for homology groups. In 1984, Y. L. Xin [47] generalized theLawson-Simons nonexistence theorem for stable integral current and vanishingtheorem for homology groups to the case of compact submanifolds in Euclideanspace, and gave several important applications.

Simons运用Federer-Fleming存在性定理[19]和几何测度论中变分技巧证明了单位球面中紧致黎曼子流形上稳定积分流的不存在性定理和同调群消没定理[30]。1984年，忻元龙将Lawson-Simons稳定积分流的不存在性定理和同调群消没定理拓广到了欧氏空间中紧致子流形的情形，并给出了若干重要的应用[47]。1997年，K。

In chapter 4, we first discussed the existence of multiple positive solutions of the second order nonsingular Dirichlet boundary value problem for impulsive differential equations by using the fixed point index theorem in cones . Next, we presented some new existence results for singular boundary value problems for second order impulsive differential equations by using fixed point theorem in cones and Leray-Schauder nonlinear alternative theorem.

第四章我们首先利用锥不动点定理讨论了非奇异二阶脉冲微分方程狄利克莱边值问题多个正解的存在性；其次我们用锥不动点定理和Leray-Schauder型非线性抉择定理，讨论了奇异二阶脉冲微分方程狄利克莱边值问题一个及多个正解的存在性。

The general form of the triple I solution of FMP is given. The monotonity theorem, the infimum theorem, and the existence theorem have been proved.

给出了FMP的三Ⅰ解的一般形式，证明了关于区间值模糊推理的单调性定理、下确界定理以及存在性定理。

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。

Moreover, the semiopen mapping theorem, the semiclosed graph theorem and the semibounded inverse theorem are established under some conditions of weaker t-norms.

对MengerPN空间上的线性算子引入β-半有界，β-半开及β-半闭等概念，讨论了它们间的关系，并在较弱的t-模条件下建立了半开射定理，半闭图定理和半有界逆定理。

At the beginning of this paper, we briefly introduced the fundamental knowledge of the Newton iterative methods , and the local convergence theorem which extended the classical Newton method, because of the local convergence, the theorem had its certain restrict. Large-scale convergence theorem was proved under the condition that matrix M is irreducible diagonally dominant by Newton's method with line search.At the last part of this paper, we present the method for solving linear complementarity problems arising from journal bearings.

本文首先介绍了Newton型迭代法的基础知识，然后着重介绍了B-可微方程的Newton法，给出B-可微法的局部收敛结论，推广了古典的Newton法，但由于收敛的局部性，该算法仍有一定的不足之处；文章在证明大范围收敛定理时，假设M是不可约对角优势矩阵，采用一维Newton寻查的方法，保证算法的收敛性。

The theorem of mean has the Lagrange theorem of mean and the Cauchy theorem of mean, they are prove the inequality the powerful tool.

中值定理有Lagrange中值定理和Cauchy中值定理，它们都是证明不等式的有力工具。

Theorem of mean significance: The application derivative research function's nature wants directly or indirectly with the aid of Yu Zhongzhi,Specially Lagrange theorem of mean,Here is mainly from the equality proof, the inequality proof, existence asks some limits, the determination equation root and so on five aspects to carry on the discussion,so, The theorem of mean is transforms as the function in the sector research important tool, Must bring to the enough attention in the middle of ours study and the teaching.

中值定理意义：应用导数研究函数的性质都要直接或间接地借助于中值，特别是拉格朗日中值定理，这里主要是从等式的证明、不等式的证明、求一些极限、判定方程根的存在性等五个方面来进行讨论，因此，中值定理是转化为函数在区间上的研究的重要工具。在我们的学习与教学当中要引起足够的注意。

Putt your way through 36 fun-filled holes of minigolf on 3D designed courses with elevated greens, bunkers, bridges and water hazards, among other crazy obstacles.

您的推杆方式，通过36个有趣的填孔迷你的三维设计的课程，以提升绿党，掩体，桥梁和水的危害，除其他疯狂的障碍。

Some participles can be used either as attributes or as predicatives.

有些分词既可当定语用，也可当表语用。