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.     

Thermionic emission properties of LaB6 and CeB6 in connection with their surface states,examination by XPS,Auger spectroscopy and the Kelvin method

The surface of the thermionic emitters LaB₆ and CeB₆ was investigated as a function of temperature by means of XPS, Auger electron spectrosopy and the Kelvin method. The hexaborides are sensitive to oxidation at room temperature, a thin layer of rare earth oxide and boron oxide having been detected at their surfaces. This study has shown the influence of surface carbon on the Auger line intensities of lanthanum and boron in the case of LaB₆. A surface cleaning by ionic bombardment leads to a preferential erosion of the rare earth with respect to boron. One may conclude that the emission mechanism in hexaborides is an intrinsic property of the material. The hypothesis previously proposed by other authors, that the low work function may be due to the presence of a layer of rare earth metal on the LaB₆ substrate was not confirmed.     

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.