Can mathematicians prove the Riemann hypothesis?

数学家可以证明黎曼猜想吗？

In his lecture Riemann covered an enormous variety of topics.

里曼的演讲涵盖了各种各样的主题。

So, do not cry, there is healthy life without the Riemann hypothesis.

所以，不要哭，没有黎曼假设依然能够有健康的生活。

It will also be capable of evaluating definite integrals and Riemann sums.

同时，它还可处理定积分和黎曼积分。

These two airfoils lie on different Riemann sheets in the hodograph plane.

该两个翼型处在不同的黎曼面内。

Riemann treats the basic element of music as the basic kernel of musical art.

里曼将音乐的基本要素，看作是音乐艺术实现的基本内核。

And because of the limitations of Riemann Integration, it can only be used for continuous function.

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。

Research of the group of motions in Riemann manifold is an important question of the differential geometry.

黎曼流形运动群的研究是微分几何中一个重要问题。

Analytic number theory is fortunate to have one of the most famous unsolved problems, the Riemann hypothesis.

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。

Furthermore, we compute the Riemann solution by using a bisection method combined with the phase-plane analysis.

进一步地，我们采用二分法与相平面分析结合的方法计算压差方程的数值解。

The classical elementary waves in Riemann solutions include rarefaction wave, shock wave and contact discontinuity.

黎曼解涉及的经典基本波包括疏散波、激波和接触间断。

It proves that the estimate sectional curvature of a quaternion manifold is very useful for Riemann symmetric space.

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。

The generalized Riemann problem for a class of decoupled nonlinear hyperbolic system of conservation laws is studied.

研究一类解耦非线性双曲守恒律系统的广义黎曼问题。

It is very convenient to calculate the object volume to use Riemann sum after obtained the object surface region equation.

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 difficult for learner to understand the concept of Riemann integral which is defined by using the limit of Riemann sum.

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。

This paper has drawn and proved the conclusion that continuous function of Riemann integrable function is certainly Riemann integrable.

但是，本文指出并论证了下述结论：黎曼可积函数的连续函数必定黎曼可积。

Under the framework of finite volume method, the Riemann approximate solver is applied to obtain the numerical solution of the equation.

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。

We combine Riemann globe with it by Mobius transformation, thus it is developed that the connotation and the extension of aberration effect.

本文对光行差效应进行了较为深入的探讨，通过麦比乌斯变换将其与黎曼球联系了起来，从而极大地拓展了光行差效应的内涵与外。

In this paper we give some simpler definitions of definite integral, and show that they are all equivalent to the definition of Riemann integral.

本文给出了定积分的几个较简单的定义，并证明这些定义均与黎曼积分定义等价。

In this paper, we get a method to solve a non-linear RH problem by the Cauchy-Riemann conditions and the theories of partial differential equation.

利用柯西黎曼条件和偏微分方程理论，得到了一类非线性RH问题的求解方法，并通过实例表明该方法是可行的。

In hydrodynamics, however, the scheme for numerical flux is constructed from the solution of the generalized Riemann problem in the present research.

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。

The article first introduced the production of Riemann Integration and by the way tell the nature, definition and application of Riemann Integration.

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。

Under the Euclidean measure, the analytical solutions to the above problem are obtained by employing the Riemann Liouville fractional calculus theory.

在欧氏测度下 ，应用R L分数阶微积分算子理论给出了上述问题的精确解 。

The problems discussed can be transformed into Riemann-Hilbert problems by this method, then analytical solutions are obtained by self-similar functions.

采用自相似函数的方法可以获得解析解的一般表达式。

Based on Darboux theory, this paper discussed the integrability of the Riemann Integral and provides a necessary and sufficient condition for integrability.

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。

In concluding this talk I wish to emphasize my advocacy for analytic number theory by saying again that the theory flourishes with or without the Riemann hypothesis.

在结束这次讲话时，我愿通过再次说明，数论将在无论有还是没有黎曼假设的情况下继续繁荣，来强调我对于解析数论的拥护。