查询词典 curvature of a curve

We get some results about the scalar curvature of 2 and n(n≥3)dimensions Einstein manifold :ρ Maybe is constant and ρ is constant, the relation between Einstein Manifold and Riemannian Manifold with constant sectional curvature.

本文对其有关性质进行了讨论，得到了2维和n(n≥3)维爱因斯坦流形的数曲率的一些结果：ρ可能为常数和ρ为常数，以及爱因斯坦流形与常曲率黎曼流形之间的关系

Using the mathematical tool"DifferenceGeometry",it is possible to define the discrete geometric metrics such as discretefirst fundamental form,discrete second fundamental form,discrete unit mainnormal vector,discrete Gauss curvature,discrete mean curvature and discreteLaplacian.

首先，运用"差分几何"这一工具，可以构造离散第一、第二基本形式，离散单位主法向，离散高斯曲率，离散中曲率等离散几何量和离散Laplace算子。

In chapter 4,we consider the existence of harmonic function in negative sectional curvature manifolds.we get that,if Ricci ≥-C(1 + r~2)r =ρ(O.x, then there have non-canstant bounded harmnic function in negative sectional curvature manifolds.

第四章考虑负曲率流形上调和函数，得到了在Ricci≥-C(1+r~2)其中r=ρ的负曲率流形的调和函数的存在性。

Theorem 4 There is no compact totally real 2-harmonic submanifold with non-zero parallel mean curvature and positive sectional curvature in a locally symmetric Bochner -Kaehler manifold.

定理4局部对称Bochner-Kaehler流形中不存在具有非零平行平均曲率向量且截面曲率大于零的紧致全实2-调和子流形。

Theorem 3 Let M~n be a compact totally real 2-harmonic submanifold in M~n which is a locally symmetric Bochner-Kaehler manifold.If Ricci curvature of M~n is nonegative and positive at a point at least,then the holomorphic sectional curvature of M~n is a postive constant number.

定理3设M~n是局部对称Bochner-Kaehler流形M~n的紧致全实2-调和子流形，若M~n的Ricci曲率非负且至少在一点为正，则M~n具有正常数全纯截面曲率。

The effect from transverse webs and frames and the effect from collision velocity on ship bow collision properties are also studied in this paper. 7. The idea of buffer bow is put forward from aspects of the overall situation of environmental protection and reducing the damage of struck shipside caused by striking bow. The influence of curvature of bow shape on mode of distortion, collision force, collision force density and energy absorption of bulbous bow is described detailedly through a series of collision numerical simulation for bulbous bows that have different curvature.

发现横向框架对于船艏结构的变形形态，碰撞力及能量吸收都有一定的影响，在进行碰撞分析时不能忽略，在较低的速度范围内碰撞速度对碰撞力及能量吸收没有太大影响，所以可以从较高速度撞击后得到的能量吸收曲线中得到较低速的碰撞能量吸收曲线，从而可以得到低速碰撞时的撞深，然后通过这个撞深在较高速碰撞的碰撞力曲线中可以获得低速碰撞的碰撞力曲线。

High-precision spherical components have been widely used in precision machinery and aerospace industry, and spherical curvature is one of determinant to the capability of optical components, and the measure of it is an important matter in the optical component manufacture. So the research of the high precision measurement of spherical curvature has important significance.

中文摘要高精度球面元件在精密机械和航天工业中的应用越来越广泛，在光学生产的加工制造过程中也大量需要对具有球面形状的透镜的曲率半径进行高精密测量的情况，因此，球面元件曲率半径的精密测量对高质量球面样板，光学系统的质量控制等方面具有重要的意义。

The curvature radius of optical sphere is an important parameter to determine the properties of an optical sphere. The measurement result of the spherical curvature radius can be used to assess the quality of an optical component.

光学球面曲率半径是决定光学球面光学特性的重要参量，通过测量光学球面的曲率半径，可以审核光学元件设计制造质量。

In this thesis, several kinds of spherical curvature measurement methods are introduced, and the "arch-high and chord-length method" is selected after introduction of the existing methods, and then the novel type of instrument for measuring spherical curvature with the variable ring is developed. In research, the grating sensor, integrated circuits and other new technologies are adopted and integrated. As a result of this, Its specific technical indicator is 0.1um in absolute accuracy, 0.01% in relative accuracy, and 0.001% in repeat accuracy.

本文首先对几种球面曲率半径的测量系统进行了深入的理论分析，在分析了各个测量方法优缺点的基础上，选用了"弓高弦长法"的测量原理，并从理论上推导了本文所述系统的可行性，采用光栅传感器、集成电路等新技术成果，将机械、电子技术、计算机技术以及传感器技术有机结合，研制出一种新型的可变径球面曲率测量仪器。

In the present paper,a sharp inequality is obtained between the Ricci curvature and the squared mean curvature of semi-invariant submanifold s in cosymplectic space forms,and some conditions are reached to make the equality hold.

对余辛流形的半不变子流形进行研究，利用曲率的分量表示之间的简单的代数关系，得到了这类子流形的R icc i曲率与平均曲率平方之间的一个不等式，并讨论了等式成立的充分必要条件

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。