查询词典 Riemann function

Since the early work of Gauss and Riemann, differential geometry has grown into a vast network of ideas and approaches, encompassing local considerations such as differential invariants and jets as well as global ideas, such as Morse theory and characteristic classes.

~ 90年代初以来的工作、微分几何和黎曼高斯已经发展成一个巨大的网络的思想和方法，包括当地的因素，例如差不变量与喷气机以及全局观念，例如莫尔斯班原理和特点。

Of or relating to Riemann's non-Euclidean geometry.

属于或关于黎曼几何学而非欧几里得几何学的。

It was this concept that Riemann generalized, thereby opening up new vistas in non-Euclidean geometry.

这个概念嗣后为Riemann所推广，从而在非欧几里德几何学中开辟了新前景。

Get in torch with.of or relating to Riemann's non-Euclidean geometry.

属于或关于黎曼几何学而非欧几里得几何学的。

It can be translated into a Riemann-Hilbert problem by means of self-similar functions, and the universal representations of analytical solution were obtained when there is $Pt / x$ or $Px^3 / t^2$ load at the origin of the crack coordinates.

采用自相似函数的方法可以轻易地将所论问题转化为Riemann-Hilbert问题，并求得了裂纹坐标原点分别受到变载荷$Pt/ x$，$Px^3 /t^2$作用下的解析解的一般表达式。

The results show that using the theory of complex functions, the problems discussed can be easily translated into Riemann-Hilbert problems. Analytical solutions of the displacements, stresses and dynamic stress intensity factors under the action of increasing loads Px/t and Pt^3/x^2 situated at the origin of the coordinates of propagation crack, are gained by self-similar approaches.

研究结果表明：利用复变函数论方法，将所讨论的问题转化为Riemann-Hilbert问题；通过自相似方法，求得纤维增强混凝土的动态扩展裂纹的坐标原点分别在增加载荷Px/t和Pt^3/x^2作用下的位移、应力和动态应力强度因子的解析解。

The problems dealt with can be readily transformed into Riemann-Hilbert problems by this technique, and general expressions of analytical solutions are given considering the action of pulse loads and unit-step loads located at the origin of the coordinates respectively.

应用该法可以迅速地将所论问题转化为Riemann-Hilbert问题，并给出了坐标原点分别受到脉冲载荷、阶越载荷作用下解析解的一般表达式。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

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。

Based on this and the relations between integral and integral, integral and Riemann integral are established.

在此基础上讨论了非紧模糊数值函数的积分与积分之间的关系，以及积分与Riemann积分的关系。

The teacher likes the honeymouthed little girl very much.

老师很喜欢这个嘴甜的小姑娘。

Mr. Notker Bien's interests are traveling, spending quality time with the family and long-distance-running.

诺特卡·柏恩先生热爱旅游，长跑，以及和家人一起共度美好时光。