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.     

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.     

Self-assembled growth of nanostructural Ge islands on bromine-passivated Si(111) surfaces at room temperature

We have deposited relatively thick (∼60 nm) Ge layers on Br-passivated Si(111) substrates by thermal evaporation under high vacuum conditions at room temperature. Ge has grown in a layer-plus-island mode although it is different from the Stranski-Krastanov growth mode observed in epitaxial growth. Both the islands and the layer are nanocrystalline. This appears to be a consequence of reduction of surface free energy of the Si(111) substrate by Br-passivation. The size distribution of the Ge nanoislands has been determined. The Br-Si(111) substrates were prepared by a liquid treatment, which may not produce exactly reproducible surfaces. Nevertheless, some basic features of the nanostructural island growth are reasonably reproducible, while there are variations in the details of the island size distribution.     

Biomolecular interaction monitoring of autoantibodies by scanning surface plasmon resonance microarray imaging

A new commercial surface plasmon resonance (SPR) imaging analysis system with a novel SPR dip angle scanning principle allows the measurement, without the need for labeling, of the exact SPR dip angle. With this system hundreds of biomolecular interactions can be monitored on microarrays simultaneously and with great precision. The potency of this system is demonstrated by automatically monitoring the interactions between citrullinated peptides and serum autoantibodies of 50 rheumatoid arthritis (RA) patients and 29 controls in a single step. The smallest antibody concentration that could be measured in this experimental setup was 0.5 pM.     

Negative refraction

Light bends the wrong way in materials where both ε and μ are negative as was pointed out in 1968, but the absence of natural materials with this property led to neglect of the subject until 1999 when it was shown how to make artificial materials, metamaterials, with negative μ. The rapid advance of the subject since that date, both in theory and experiment, is reflected in the exponential growth of publications now at the 200 per year level and still growing. This interest is explained by the sudden availability of a qualitatively different class of electromagnetic materials combined with the quite startling properties which these materials appear to have; all of which provokes debate as each new facet of their behaviour is revealed. Experiment has been vital to resolution of controversy and has chiefly been in the microwave region of the spectrum though there is potential in the optical region currently being explored by several groups.