查询词典 Riemann function

Thirdly,we study certain Riemann boundary value problems and Singularintegral equations with values in a universal Clifford algebra 〓,by com-bining the classical methods of solving Riemann boundary value problems andsingular integral equations with the Taylor's expansion of regular function in Clif-ford analysis,proving a lemma which is similar to the Painleve theorem in theclassical complex analysis,and the Plemelj formula in Clifford analysis,we obtainthe better results under weaker condition than before.

第三，本文第一次借助于用来解决经典的Riemann边值问题与奇异积分方程的方法来研究Clifford分析中的某些Riemann边值问题与奇异积分方程，获得了在比以前文献中条件更弱的情况下，结论更广的结果，并且，它为更进一步地解决在Clifford分析中一般的Riemann边值问题与奇异积分方程提供了基本的解决思想，为这一新的研究领域奠定了基础。

In more formal language, the set of all left-hand Riemann sums and the set of all right-hand Riemann sums is cofinal in the set of all tagged partitions.

积分是线性定义的，即如果，则。特别地，由于复数是实数向量空间，故值为复数的函数也可定义积分。

In this paper,at first we transformed the nonlinear elliptic system of 2m first order equations into the complex form, then by use the results on the Riemann-Hilbert problem for nonlinear elliptic complex equation of first order, the method of continuity, the Schauder fixed-point theorem and the Leray-Schauder theorem, we proved that the modified Riemann-Hilbert boundary value problem for the complex system with some conditions is solvable.

本文先将较一般的多个未知函数的一阶椭圆型实方程组化为复方程组，然后讨论这些复方程组在某些条件下的一些边值问题的可解性。这里所考虑的方程组既包含线性的，也包含非线性的，比广义超解析函数所满足的方程组还要广，又本文主要研究较一般的Riemann-Hilbert边值问题，先给出这种边值问题解的先验估计式，然后用参数开拓法及Leray-Schauder定理证明这种边值问题的可解性结果。

We generalize the concept of the set of variability defined in the unit diskby K.Strebel to general Riemann surfaces and prove that the set of variablity withrespect to the modulo homotopic class of a quasiconformal mapping between twoRiemann surfaces is a compact and connected subset.Consequently the num-ber of the extremal mappings in the modulo homotopic class of a quasiconformalmapping between two general Riemann surfaces is either one or infinity.

Strebel的定义在单位圆上的可变性集合的概念推广到一般Riemann曲面上去，并且证明了Riemann曲面之间的拟共形映射的模边同伦类所确定的可变性集合是一个连通的紧子集，从而得出一般Riemann曲面之间拟共形映射的模边同伦类中的极值映射要么唯一，要么有无穷多个。

Mathematic proof of the hypertonicity for this model is given using two different cases. Furthermore, the Riemann invariants for the multi-class traffic flow LWR model are studied by using characteristic line method, and the physical interpret of the Riemann invariants are also pointed out. The information in transfer is obtained, that is, the total density and the relative density hold the same.

用两种方法给出了该模型在不同情形下双曲性的数学证明，运用特征线方法研究并计算了任意等级MCLWR交通流模型的Riemann不变量，得到了其传递的交通信息，给出了Riemann不变量物理意义的解释，即总密度保持不变和相对密度保持不变，最后又从形式上指出了在多等级车流并行时，MCLWR与LWR两种交通流模型实际上是等价的。

Therefore, it is not every Newton indefinite integral that can carry on Riemann integral, and not every Riemann integral has Newton Indefinite integral.

牛顿所积分的函数都是连续的，可分为牛顿不定积分和牛顿定积分，而黎曼所积分的函数又是有界的。

By the research of metric tensor and Riemann tensor on Riemann manifold, we getthe inherent curvature of configuration space belonging to parallel mechanism.

通过对度量张量和Riemann张量的研究，得出并联机构运动可达子空间的内在"弯曲"性质，指出使用相对坐标系和广义坐标是研究并联机构运动学和动力学问题的必然选择。

It introduces partial fractions of meromorphic functions, product developments of entire functions, Hadamard's theorem, Riemann Zeta functions, Poisson-Jensen's formula; elliptic functions, including simply periodic functions and doubly periodic functions; algebraic functions and algebroid functions, Riemann surface, Nevanlinna theory, including characteristic functions, the first and second fundamental theorems, growth orders, etc; complex differential equations and complex functional equations, etc.

具体为：亚纯函数的部分分式、整函数的无穷乘积展开、Hadamard定理、Riemann Zeta函数、Poisson-Jensen公式；椭圆函数，包括单周期函数、双周期函数；代数函数和代数体函数、Riemann曲面简介；Nevanlinna理论简介，包括特征函数、第一和第二基本定理、增长级等；复微分方程和复函数方程，等等。在教学内容上充分体现基础性、新颖性。

The most researches on Riemann boundary value problem are confined to normal type. The Riemann boundary value problem of non-normal type on smooth closed contours first arised in the book [1] written by F.D.

Riemann边值问题的研究大多限于正则型Riemann边值问题，封闭曲线上非正则型Riemann边值问题的研究最早始于F.D。

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

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。