Higher moments of certain <Emphasis Type="Italic">L</Emphasis>-functions on the critical line

We study the sixth-power moments of certain L-functions belonging to a sub-class of the Selberg’s class on the critical line and, using this, we conclude an upper bound for the fourth-power moments of certain L-functions related to GL ₃ on the critical line. This is an analogue of the upper bound for the twelfth-power moment of the Riemann zeta-function on the critical line. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 341–380, July–September, 2007.     

Characterization of the Zwitterionic Intermediate in 1,1-Carboboration of Alkynes

The reaction of a Lewis acidic borane with an alkyne is a key step in a diverse range of main group transformations. Alkyne 1,1-carboboration, the Wrackmeyer reaction, is an archetypal transformation of this kind. 1,1-Carboboration has been proposed to proceed through a zwitterionic intermediate. We report the isolation and spectroscopic, structural and computational characterization of the zwitterionic intermediates generated by reaction of B(C₆F₅)₃ with alkynes. The stepwise reactivity of the zwitterion provides new mechanistic insight for 1,1-carboboration and wider B(C₆F₅)₃ catalysis. Making use of intramolecular stabilization by a ferrocene substituent, we have characterized the zwitterionic intermediate in the solid state and diverted reactivity towards alkyne cyclotrimerization.     

Finite-reductive dual pairs in G2

This paper classifies dual pairs (F,G^′) in complex G₂ where F is finite and G^′ is infinite complex reductive.     

1-乙酰基-2,3-吲哚二酮的光诱导氢转移反应的CIDNP研究

采用CIDNP方法对UV光照条件下的1-乙酰基-2, 3-吲哚二酮与几类氢给体的光诱导氢转移反应进行了研究.     

用正常色散的双折射光纤所作的暗孤子开关的开关条件

在正常色散的双折射光纤中传输的暗孤子对之间由于耦合周期性交换能量，一个暗孤子可把能量完全转给另一暗孤子，因此双折射光纤可作光开关。本文讨论了椭圆角为３５°的双折射光纤的开关条件，发现脉冲只有以特定的极化角入射才有开关现象产生，而且建立了光纤长度与孤子对相差、初始能量差的解释关系     

Isospectral polygons, planar graphs and heat content

Given a pair of planar isospectral, nonisometric polygons constructed as a quotient of the plane by a finite group, we construct an associated pair of planar isospectral, nonisometric weighted graphs. Using the natural heat operators on the weighted graphs, we associate to each graph a heat content. We prove that the coefficients in the small time asymptotic expansion of the heat content distinguish our isospectral pairs. As a corollary, we prove that the sequence of exit time moments for the natural Markov chains associated to each graph, averaged over starting points in the interior of the graph, provides a collection of invariants that distinguish isospectral pairs in general.

     

AC-PDP中等离子体电场的实验研究

用激光荧光技术直接测量了AC-PDP单元高气压He和He／Xe0．1％放电中的电场行为，估算了由放电电场产生的AC—PDP单元上的壁电压。选用高气压下寿命较长的氦的亚稳态2s^3S，比较主量子数n＝8和n＝9的Stark分裂谱，使电场的测量精度提高到10％。电场和壁电压的时间分布描述了PDP单元的放电行为。     

Yb：Er共掺杂对掺铒光纤激光器中自脉冲行为的抑制作用

为了进一步提高镱铒共掺杂光纤激光器的实用性，对镱铒掺杂光纤激光器的自脉冲现象进行了理论分析。利用掺杂光纤中铒离子对的可饱和吸收的作用而引起自脉冲运转及离子对互作用模型作为理论基础建立系统模型，通过理论计算分析了共掺杂镱后掺铒光纤的有效抽运速率，证明了镱铒共掺杂可以提高有效抽运速率。使用这种光纤，可以使抑制光纤激光器中离子对导致的自脉冲效应所需的抽运功率水平大大降低。半导体激光器输出的抽运功率足以抑制由离子对导致的自脉冲，提供稳定激光运转。在研制稳定单频或高重复频率锁模光纤激光器方面，这种可用激光二极管抽运的镱铒共掺光纤具有很大的潜力。