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Simple Zeros of the Riemann Zeta-Function 总被引:1,自引:0,他引:1
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. 相似文献
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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.
- b the existence of strictly positive IPDs,and
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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. 相似文献
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Thomsen MH Holm-Nielsen JB Oleskowicz-Popiel P Thomsen AB 《Applied biochemistry and biotechnology》2008,148(1-3):23-33
To have all-year-round available feedstock, whole-crop maize is harvested premature, when it still contains enough moisture
for the anaerobic ensiling process. Silage preparation is a well-known procedure for preserving plant material. At first,
this method was applied to obtain high-quality animal feed. However, it was found that such ensiled crops are very suitable
for bioenergy production. Maize silage, which consists of hardly degradable lignocellulosic material, hemicellulosic material,
and starch, was evaluated for its potential as a feedstock in the production of bioethanol. It was pretreated at low severity
(185 °C, 15 min) giving very high glucan (∼100%) and hemicellulose recoveries (<80%)—as well as very high ethanol yield in
simultaneous saccharification and fermentation experiments (98% of the theoretical production based on available glucan in
the medium). The theoretical ethanol production of maize silage pretreated at 185 °C for 15 min without oxygen or catalyst
was 392 kg ethanol per ton of dry maize silage. 相似文献
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Pablo V. Holm-Nielsen Nan Chi Jianfeng Zhang Christophe Peucheret Idelfonso Tafur Monroy Palle Jeppesen 《光学学报》2003,23(Z1)
Optically labeled IM/FSK signal saretran smitte dover 50km of SMF under different compensation schemes.All-opticallabel swapping based on MZ-SOA and EAM is presented. Transmission followed by label swapping shows a 2dB overall power penalty. 相似文献
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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. 相似文献