椭圆空间

Some geometric data of ellipse in hyperbolic space are considered, such as set inclusion, arc length, geodesic curvature, curvature, area and total curvature.

摘要在双曲空间中，考察椭圆的包含关系，对弧长元素、测地曲率、曲率、面积及全曲率等几何量做出细致考察。

First, we introduce the concept of polarizable Carnot group and give some new properties of its homogeneous norm. Then we construct a class of non-divergence equations as well as their nontrivial solutions. The failure of corresponding A-B-P type estimate and uniqueness to the Dirichlet problems in space~ follow.

首先引入可极化Carnot群的概念，给出了可极化Carnot群上齐次模的若干性质，然后构造了一类非散度型次椭圆方程及其非平凡解，由此证明此类方程Dirichlet问题的解在函数空间L~中不唯一，进而证明相应的Alexandrov-Bakelman-Pucci型估计不成立。

Two types of the mathematical models of Spatial Variogram are inferred based on the elliptic distribution function.

基于椭圆分布函数可导出两类空间变异函数的数学模型。

The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry Beginning at the introductory level with curves in Euclidean space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book:transformation groups, the geometry of differential equations,geometric structures, the equivalence problem the geometry of elliptic operators, G-structures and contact geometry.

这本书是结构，以便读者可以选择部分文本阅读，还带了一个完整的画面，有些地区的微分几何开始入门级和曲线的部分，在欧氏空间变得更有挑战性，终于到达了高级的主题，形成了最大的一部分书：变换团体、几何的微分方程、几何结构、等价问题的几何形状，G-structures椭圆算子和接触几何。

Under the assumption that the Earth is a triaxial rigid body which is rotating freely in the Euclidian space, the elliptic integral solution of the Euler dynamic equation is provided, and then the numerical solutions of the Euler dynamic as well as kinetic equation are realized.

在Euclid空间中，假定地球是一个作自由旋转的3个主惯性矩互不相等的刚体，给出了Euler动力学方程的椭圆积分解，并实现了Euler动力学方程和运动学方程的数值解。

Making use of the space vector method, this article sets up two coordinate numeric control grinding motion model of elliptic taper piston, and researches on the law of error compensation for the systematic motion after dressing grinding wheel.

用空间矢量方法建立了椭圆锥体活塞的两坐标数控磨削运动模型，研究了砂轮修整后应对系统运动进行的误差补偿规律。

The existence of weak solution for quasilinear elliptic system in the whole space is studied.

讨论了在全空间上拟线性椭圆型方程组的非平凡解的存在性。

A class of elliptic problems in Orlicz-Sobolev space with Neumann boundary conditions are studied. The sublinear case and the superlinear case are discussed, and using the classical critical point theory with the Cerami compactness condition two existence theorems are given.

研究一类在Orlicz-Sobolev空间上具有Neumann边界条件的椭圆问题，分别讨论了次线性和超线性情形，利用满足Cerami紧性条件的经典临界点理论给出两个解的存在性定理。

In part III by using capacity theory and extension theorem of Lip-schitz functions we first discuss the uniqueness of weak solution ofnonhomogeneous quasilinear elliptic equations〓in space〓,which is bigger then〓.

第三部分首先用容量理论、Lipschitz函数延拓定理讨论了一类非齐次拟线性椭圆型方程〓在比〓更大的空间〓中弱解的唯一性。

In the theory part, based on the rate-equation theory of four-level system, the expressions of output power and slope efficiency under the conditions of near-threshold and deeply pumping have been given. The effects of space distribution variables(the position of focusing point, dimension of pumping light and laser light and ellipticity)on the output characteristics were also discussed.

在理论部分，首先从四能级系统的理论出发，得到了近阈值条件和强泵浦条件下的输出功率和斜效率的表达式，并详细讨论了泵光聚焦位置，泵浦光和振荡光的光斑大小、椭圆度等空间变量对输出特性的影响。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。