查询词典 weierstrass approximation theorem

The Fundamental Theorem of Calculus in Higher Dimensions; Additive Measures, Stokes Theorem and the Divergence Theorem

微积分在多维中的基本定理：加性测度，斯托克斯定理以及散度定理

Those questions about " Gauss theorem" of electro - magnetic field arecleared up, and the difference between " Gauss theorem" of electro - magnetic field and" Gauss theorem"of vector field is pointed.

本文旨在澄清有关电磁学中"高斯定理"的诸多疑问，并指出它与高等数学中的"高斯定理"的区别。

Consequently, Divergence theorem, Green's theorem and Stokes' theorem those very important and active applications in applied engineering are our main goals of this course.

譬如说，Divergence Theorem、Green's Theorem、Stokes' Theorem等，这些在物理学、流体力学、应用力学以及电磁场学上被广泛应用的重要定理。

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。

The father that if work,mad father, love annoys, disposition is too indrawn the be short ofing that the father of Mu Ne, resign oneself to adversity causes father easily to love is broken; Communicate time effectively between father and son, Mu Zizhi to be less than a hour on average to wait a moment every week, it is the cause that causes the child to become addiction.

如工作狂的父亲、爱愤怒的父亲、性格过于内向木讷、逆来顺受的父亲都易造成父爱的缺失；父子、母子之间的有效沟通时间每周平均小于一小时等等，都是造成孩子成瘾的原因。

These are vandal proof and they come with a locking mechanism.

这是野蛮的证据，他们来到了锁机制。