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.     

Two-dimensional pseudo-Riemannian metrics reconstructed by a given curvature

The problem of reconstruction of a two-dimensional, pseudo-Riemannian metric in isotropic coordinates by a given Gaussian curvature is considered. In particular, we present sufficient conditions for the possibility of reconstruction of such a metric in a coordinate quadrant. Possible applications of results obtained are discussed. __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.     

Pinning of the Peierls-Frohlich state by weak random impurities and “giant conductivity” induced by large electric fields in TTF-TCNQ and K2Pt(CN)4Br0.3 · 3H2O

It is argued that a macroscopically ordered charge density wave sliding in a one dimensional crystal will not be pinned by weak random non-substitutional impurities. This implies that the metal-insulator transition in pseudo-one-dimensional conductors might be due to other sources of pinning, such as three dimensional ordering or commensurability energy. Random impurities do, however, pin charge density wave fluctuations for weak externally applied electric fields.     

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.