Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

库仑加线性位基态解析解

应用新发展的单一轨迹积分方法求解库仑加线性位的基态量子波函数,得到基态能量和波函数的一般解析表达式,并讨论了解的收敛性.应用此方法讨论了重夸克偶素系统.     

高速摄影与光子学

第三讲 高速电影术和针定位间歇式相机 高速电影摄影机是一种记录记时仪,它对物理学家来说,如同显微镜对生物学家,望远镜对天文学家,示波器对电子学工程师一样,是一个无价之宝。高速电影术,实际上已被广泛地用于每个科技和工程技术领域,都取得了不同程度的成功。 应用高速电影术来研究运动是根据这样一种基本原理,即,以高的重复频率拍摄图象,却以较低的频率放映它,用这种方法使图象的运动速度变慢,变慢的速度正比于拍摄和放映速度之比。     

An analysis of residual stress patterns resulting from hole expansion in an infinite plate, a thick cylinder, and an asymmetric lug

Residual stresses were induced in three specimen geometries: a quasiinfinite plate, a thick cylinder and an asymmetric lug. In each case, a hole expansion process was used, whereby the bore was expanded into the plastic regime; this in effect left residual compression at the bore and residual tension in the far field. In view of the symmetry, the stress patterns in the quasi-infinite plate were measured by a hole drilling method, using an interferometric moiré method to measure the resulting strain patterns. In the case of the thick cylinder and the asymmetric lug, the residual stresses were evidenced by a dissection method. A comparison with theoretical treatments shows that the theory predicts an approximate upper bound to the actual stress levels in the quasi-infinite plate. In the lug geometry, there was a similar systematic difference between theory and experiment.