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.     

Optimization of sequencing conditions using near-infrared lifetime identification methods in capillary gel electrophoresis

We have investigated the sample preparation and electrophoresis conditions necessary to prepare DNA sequencing samples appropriate for use with near-infrared (IR) fluorescent labels with dye identification accomplished via lifetime techniques. It was found that several sample preparation protocols required attention to maximize the fluorescence yields of the labeling dyes, such as thermal cycling conditions, choice of counter ion used for the ethanol precipitation step and also, dye-primer versus dye-terminator chemistries. In addition, several different sieving matrices were investigated for their effects on both the fluorescence properties of the labeling dyes and electrophoretic resolution. Extended times used for the high temperature denaturing of duplexed DNA fragments during cycle sequencing produced cleavage products, in which the covalently attached dye to the sequencing primer was released through attack by dithiothreitol (DTT). Even under optimized thermal cycling conditions, free dye was generated that masked readable data from the sequencing traces. Ethanol precipitation was necessary to remove this free dye with the proper choice of counter ion (sodium). The results using different sieving matrices indicated that linear polyacrylamides (LPAs) were appropriate for any fluorescence measurement, since they could readily be replaced between runs minimizing deleterious memory effects associated with cross-linked polyacrylamide gels. After investigation of several different sieving LPAs, the commercially available POP6 was found to be particularly attractive, since it produced good electrophoretic resolution, single exponential behavior for the near-IR dye series investigated herein, and also, discernible lifetime differences within the dye set. Finally, dye-terminator chemistry was also found to minimize bleeding in the gel matrix produced by large amounts of unextended dye-primer within the gel lane.