曲率是黎曼几何中的热门研究课题。
Positive curvature has been a frequent subject in Riemannian geometry.
同时，它还可处理定积分和黎曼积分。
It will also be capable of evaluating definite integrals and Riemann sums.
数学家可以证明黎曼猜想吗？
设m是紧致连通的黎曼流形。
黎曼流形运动群的研究是微分几何中一个重要问题。
Research of the group of motions in Riemann manifold is an important question of the differential geometry.
研究一类解耦非线性双曲守恒律系统的广义黎曼问题。
The generalized Riemann problem for a class of decoupled nonlinear hyperbolic system of conservation laws is studied.
所以，不要哭，没有黎曼假设依然能够有健康的生活。
So, do not cry, there is healthy life without the Riemann hypothesis.
在黎曼位形空间中研究了约束多体系统的动力学问题。
The dynamic problem of constrained multibody systems in Riemannian configuration space is researched.
黎曼解涉及的经典基本波包括疏散波、激波和接触间断。
The classical elementary waves in Riemann solutions include rarefaction wave, shock wave and contact discontinuity.
估计了一般黎曼流形上的布朗运动关于球面击中时的各阶矩。
Estimations of the moments of the hitting time by Brownian motions on general Riemannian manifolds are also obtained.
研究拟常曲率黎曼流形中具有平行平均曲率向量的紧致子流形。
The compact submanifolds in quasi constant curvature Riemannian manifolds with Parallel Mean Curature Vector were studied.
文章先介绍了黎曼积分的产生以及黎曼积分的定义性质与应用。
The article first introduced the production of Riemann Integration and by the way tell the nature, definition and application of Riemann Integration.
模型在有限体积法框架下应用黎曼近似解求得耦合方程的数值解。
Under the framework of finite volume method, the Riemann approximate solver is applied to obtain the numerical solution of the equation.
解析数论非常幸运还有一个最为有名的未解决的问题，即黎曼假设。
Analytic number theory is fortunate to have one of the most famous unsolved problems, the Riemann hypothesis.
而由于黎曼积分具有局限性，黎曼积分只能用于连续函数类的积分。
And because of the limitations of Riemann Integration, it can only be used for continuous function.
在黎曼流形上分别给出了伪不变凸函数和弱向量似变分不等式的概念。
The definitions of pseudo-invex function and weak vector variation-like inequality on Riemannian manifolds are presented.
并由此讨论了紧致的非单连通黎曼流形上无穷多的闭测地线存在性问题。
Also, the paper discuss the existence of the infinite closed geodesics of a compact no-simply connected Riemannian manifold.
用积分和的极限定义的黎曼积分对于初学者来说是一个很难理解的概念。
It is difficult for learner to understand the concept of Riemann integral which is defined by using the limit of Riemann sum.
讨论特殊半对称联络的黎曼流形，给出了该流形曲率张量的一个代数结构。
In the present paper, the algebra property of Riemannian manifold which is contained some special semi symmetric connection is given.
最后，应用近似化方法和黎曼度量方法，研究了机器人最优轨迹规划的问题。
In the end, the problem of robot trajectory planning is investigated by the linearization method and Riemannian metric.
本文对牛顿万有引力定律提出了一种非黎曼几何的相对论性的可能修正公式。
In this paper, a possible Correction of non-Riemannian geometric relativity is made for Newton's Law of Gravitation.
它进一步说明一个四元流形的截面曲率的估计对许多对称黎曼空间都是有效的。
It proves that the estimate sectional curvature of a quaternion manifold is very useful for Riemann symmetric space.
在已知空间物体表面区域方程的前提下，利用黎曼和可以方便地求出被测物体的体积。
It is very convenient to calculate the object volume to use Riemann sum after obtained the object surface region equation.
本文采用求解非齐次方程组的广义黎曼问题解，对模型数值通量计算格式进行了修改。
In hydrodynamics, however, the scheme for numerical flux is constructed from the solution of the generalized Riemann problem in the present research.
爱因斯坦流形是特殊的一种黎曼流形，它有很好的特征，其定义弱于常曲率黎曼流形。
Einstein manifold is a particular kind of Riemannian manifold, it has good characters, its definition is weaker than Riemannian manifold with constant sectional curvature.
文章利用达布和理论，讨论了黎曼积分的可积性问题，给出了一个可积的充分必要条件。
Based on Darboux theory, this paper discussed the integrability of the Riemann Integral and provides a necessary and sufficient condition for integrability.
对于黎曼流形的浸没建立了垂直能量泛函的二阶变分公式，研究强垂直调和映射的稳定性。
The second variation formula of vertical energy functional for a submersion between Riemannian manifolds is calculated with a simple and direct manner.
对于黎曼流形的浸没建立了垂直能量泛函的二阶变分公式，研究强垂直调和映射的稳定性。
The second variation formula of vertical energy functional for a submersion between Riemannian manifolds is calculated with a simple and direct manner.
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