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.     

Control of laser high-harmonic generation with counterpropagating light

Relatively weak counterpropagating light is shown to disrupt the emission of laser high-harmonic generation. Harmonic orders ranging from the teens to the low thirties produced by a 30-femtosecond pulse in a narrow argon jet are "shut down" with a contrast as high as 2 orders of magnitude by a chirped 1-picosecond counterpropagating laser pulse (60 times less intense). Alternatively, under poor phase-matching conditions, the counterpropagating light boosts harmonic production by similar contrast through quasiphase matching where out-of-phase emission is suppressed.     

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.     

Probe of high-order harmonic generation in a hollow waveguide geometry using counterpropagating light

We use counterpropagating light to directly observe the coherent buildup of high harmonic generation in a hollow waveguide geometry. We measure, for the first time, coherence lengths for high photon energies that cannot be phase matched using conventional approaches. We also probe the transition through phase matching, the ionization level at which different harmonic orders are generated, and the change in the coherence length as the driving laser is depleted. These results directly prescribe the optimal structures or pulse trains required for implementing quasiphase matching.