查询词典 Riemann function

By getting Lebesgue characteristic of integrable function of Riemann from the definition of Gather zero measure, discussing the relation between almost continuous everywhere and existent of limit, it gets the theory which is from the function integrability to the consecution and from consecution to the limit existence .i.e. the almost limit existence is equal to the almost continuous everywhere in the integrable function of Riemann. It also gets a unified condition which has a wider range than regulated function and comes to the conclusion that the function of bounded variation is the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征，讨论了其几乎处处连续与极限存在的关系，从而得到了从函数可积性到连续性，从连续性到极限存在性的函数特性理论，即可积函数中极限的几乎处处存在与几乎处处连续是等价的，得出比正规函数更加宽泛的统一条件，得出了有界变差函数是可积函数的结论。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

Under some reasonable assumptions of the'Distribution Matrix', the Riemann Problem with piecewise constant initial data is proved to have a unique Riemann Solver; furthermore, using'Wave Front Tracking Method'and properties of the'Generalized Characteristics', we prove the existence of weak entropy solution to the Riemann Problem with arbitrary initial data of bounded Total Variation.

在"分布矩阵"满足合理的假设前提下，证明了具有分片常值初始条件的黎曼问题的黎曼解算子的存在唯一性；并进一步运用"波前追踪法"和"广义特征"等得到了具有任意有界全变差初值条件的广义黎曼问题的弱熵解的存在性。

This paper discusses the integrability of Riemann integral systematically: By analyzing the common characters of a lot of integral calculus, it abstracts the concept of Riemann integral and discusses its integrability of Riemann integral and then gets integrable functions.

摘要本文较为系统地讨论了积分的可积性：通过分析诸多积分概念的共性，抽象定义了积分并详细讨论了其可积性，得出了可积函数类。

This paper discusses the integrability of Riemann's integral theory systematically: By analyzing the common characters of a lot of integral calculus, it abstracts the concept of Riemann integral and discusses its integrability of Riemann's integral theory and then gets integrable functions.

摘要本文较为系统地讨论了积分可积性理论：通过分析诸多积分概念的共性，抽象定义了积分，详细讨论了其可积性理论，得出了可积函数类。

Secondly, based on the different structure characteristics and additional conditions, we study several kinds of inverse problems of pseudoparabolic equations. One is a kind of pseudoparabolic inverse problem of identifying a constant coefficient solved by combining the formal solution of the problem and the additional condition properly. The second is the pseudoparabolic inverse problems of identifying an unknown boundary function and an unknown source term solved by using the Riemann function method to get the formal solution of the problem and then using the additional condition to transform the problem into a Volterra integral equation of the second kind. The third is a kind of backward heat flow problem of nonlinear pseudoparabolic equation solved by combining the Riemann function method and the fixed point theory properly.

其次，根据不同模型的结构特点和附加条件，研究了几类伪抛物型方程的反问题：一是利用问题的形式解并结合附加条件，解决了一类伪抛物型方程常数系数的反问题；二是利用Riemann函数方法获得问题的形式解，利用附加条件将问题转化成求解第二类Volterra积分方程问题，解决了一类伪抛物型方程未知边界值的反问题和未知源项的反问题；三是将Riemann函数方法和不动点定理相结合，解决了一类非线性伪抛物型方程的后向热流问题。

By getting Lebesgue characteristic of integrable function of Riemann from the definition of gather zero measure, it discusses the relation between almost continuous everywhere and existent of limit, and gets that the almost continuous everywhere is equal to the almost limit existence everywhere in the integrable function of Riemann.

通过定义零测度集给出了可积函数的特征，讨论了其几乎处处连续与极限存在的关系，即可积函数中几乎处处连续与极限的几乎处处存在是等价的，得出了比正规函数更加广泛的统一条件，得出了有界变差函数是可积函数的结论。

The second chapter is the main part of this paper, in which the formulation of the Riemann boundary value problem of non-normal type on the real axis, the solution method of homogeneous problem, the relation between the two kinds of different derivatives and the inhomogeneous problem will be thoroughly given. In this paper, the solution and the solvability of the Riemann boundary value problem of non-normal type on the real axis will be given. Furthermore, it is shown that the twokinds of derivatives of the function Ψ are existing and equivalent in the case ofthe solution about the original problem, therefore, we get uniformly Hermite interpolatory polynomial. The relation between the two kinds of different derivativesof the function Ψ are similar for smooth closed contours by means of the same proof.

第二章是本文的主要部分，分别给出了实轴上一类非正则型Riemann边值问题的提法、齐次问题的解法、两种导数的关系及非齐次问题的求解，本文运用杜金元教授[11]的方法获得了实轴上非正则型Riemann边值问题的封闭解及可解性条件，且在问题可解的情况下论证了函数Ψ的非切向极限导数和Peano导数存在且相等，从而获得了统一的Hermite插值多项式，同样关于封闭曲线上非正则型Riemann边值问题，采用本文论证方法证得了函数Ψ的非切向极限导数和Peano导数存在且相等，从而较好地统一了[10]、[11]中的Hermite插值多项式。

The Riemann- Jacobi inversion is discussed to yield the final expression of explicit solution by means of the Riemann theta function, which is directly related to algebraic geometry.

为了最终生成由θ函数所给出的显式解，我们讨论了Riemann-Jacobi反演，这一过程直接关系到代数几何。

A hybrid rotated Riemann solver is employed to form an economical numeric flux function and base Riemann solvers employ HLL and Roe FDS.

为减小计算量，采用HLL和Roe FDS混合旋转格式。

Continuously improve the production mechanism, to provide customers with better quality products and services.

不断的完善生产机制，给客户提供更优质的产品及服务。

B:Yes, he was the very prize-winner in the court tennis ten years ago?

是的，他是十年前的世界网球冠军。