查询词典 incompleteness theorem

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。

The last chapter talks about the H"yashenko"s two-side cycle theorem, that is, every two-side cycle of an analytic vector field in the real plane is the finite polycycle. The quadratic finiteness theorem is a direct corollary of this theorem.

最后一章介绍了Il'yashenko两边形定理，即实平面上解析向量场的任一两边形均为有限多边环，这个定理的直接推论便是二次系统的有限性定理。

Using variable upper limit integration and Lagrange mean value theorem,this article proves the first mean value theorem under the same condition and give several spread of the first integral mean value theorem .

在条件完全相同的情况下改进积分第一中值定理，并利用变上限积分函数和拉格郎日中值定理证明该定理，并给出积分第一中值定理的几个推广

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 small blue capacitor has very high chances to go fully shorted compare to electrolytic capacitor which is very rare.

小蓝电容器具有很高的机会去充分地缩短了比较电解电容器，这是非常罕见的。

In the Italian campaigns of 1513 and 1515, when the Swiss won the victories of Novara and Marignan, he acted as army chaplain.

在意大利的运动， 1513年和1515年，当瑞士赢得了胜利，诺瓦拉和marignan ，他担任军队的牧师。