On Rapidly Convergent Series Expressions for Zeta- and L-Values,and Log Sine Integrals

Regarding the rapidly convergent series expansion for special values of - and L-functions for integer points, there are two approaches.One approach starts from Euler's 1772 formula for (3) and culminates in Srivastava's very recent results via many intermediate results, and the other is due to Wilton's investigation, which was shown by us (Aeq. Math. 59, 2000, 1–19) to be a consequence of Ramanujan's work (Collected Papers of Srinivasa Ramanujan, CUP 1927, reprint Chelsea, 1962, pp. 163–168).More recently, Katsurada (Acta Arith. 90, 1999, 79–89.) has generalized all existing formulas into a rather wide framework of Dirichlet L-functions.Our purpose is to show that even the most general Katsurada's formulas are easy consequences of our fundamental summation formulas for the series with Hurwitz zeta-function coefficients.We give a three-line proof of Katsurada's main theorem, and also we make some remarks on the recent paper of Bradley (The Ramanujan J. 3, 1999, 159–173).     

Hardy's theorem for the -dimensional Euclidean motion group

An uncertainty principle, due to Hardy, for Fourier transform pairs on says that if the function is ``very rapidly decreasing', then the Fourier transform cannot also be ``very rapidly decreasing' unless is identically zero. In this paper we state and prove an analogue of Hardy's theorem for the -dimensional Euclidean motion group.

     

New rapidly convergent series representations for

We give three series representations for the values of the Riemann zeta function at positive odd integers. One representation extends Ewell's result for [Amer. Math. Monthly 97 (1990), 219-220] and is considerably simpler than the two generalisations proposed earlier. The second representation is even simpler:

where the coefficients for a fixed are rational in and are explicitly given by the finite sum involving the Bernoulli numbers. The third representation is obtained from the second by the Kummer transformation. We demonstrate the rapid convergence of this series using several examples.

     

具有快速振荡外力的拟地转运动的平均原理

一类大尺度的地球物理流体流可以用拟地转方程来描述．有限、但是大时间区间和整个时间轴上在快速振荡外力下的拟地转运动的平均原理被得到了．其中包括比较估计,稳定性估计和拟地转运动及其平均运动之间的收敛性．进一步,几乎周期拟地转运动的存在性和吸引子的收敛性也被得到了．     

快速声表面波气相色谱技术检测水中苯系物*

建立了便携式声表面波气相色谱快速检测水中苯系物的方法。实验条件:检测器温度25℃,DB-5毛细管色谱柱:初始温度40℃,10℃/s程序升温至180℃。结果表明,氯苯、间二甲苯、苯乙烯、异丙苯保留时间分别为1.72 s、1.86 s、2.00 s、2.22 s,检出限分别为1.34μg/L、0.55μg/L、0.50μg/L、0.39μg/L,测得相对标准偏差值为4.08%~5.98%,回收率为82.7%~103.8%,且线性良好,线性相关系数为0.9946~0.9993。因此,该方法适用于水中苯系物的快速应急监测。     

闪锌矿结构AlSb空位缺陷性质的第一性原理研究

采用基于密度泛函理论(DFT)第一性原理的平面波超软赝势方法,计算含有锑空位和铝空位的AlSb电子结构,发现空位引起周围原子弛豫,晶体结构发生畸变.在此基础上研究了空位缺陷对闪锌矿型AlSb体系电子结构的影响,结果表明,铝空位缺陷使锑化铝费米能级降低,带隙变窄;而锑空位缺陷则使锑化铝费米能级升高,带隙变窄,同时,锑化铝的半导体类型由p型变为n型.对光学性质的研究发现,由于空位的引入使其邻近原子电子结构发生变化,使得空位缺陷系统光学性质的变化主要集中在低能量区域.     

RT-PCR技术在凡纳滨对虾健康苗种培育中的应用

应用PCR和RT-PCR技术对WSSV、IHHNV和TSV这3种对虾病毒在凡纳滨对虾育苗过程中各个环节进行了检测，防止亲虾、卵、无节幼体、仔虾、亲虾饵料、丰年虫、水体等诸环节受到以上3种病毒携带或感染，保证培育出的凡纳滨对虾仔虾是高健康的虾苗，为凡纳滨对虾健康养殖的可持续发展提供一条可行的途径．     

闪锌矿结构AlSb空位缺陷性质的第一性原理研究

采用基于密度泛函理论(DFT)第一性原理的平面波超软赝势方法，计算含有锑空位和铝空位的电子结构，发现空位引起周围原子弛豫，晶体结构发生畸变。在此基础上研究了空位缺陷对闪锌矿型AlSb体系电子结构的影响，结果表明，铝空位缺陷使锑化铝费米能级降低，带隙变窄；而锑空位缺陷则使锑化铝费米能级升高，带隙变窄，同时，锑化铝的半导体类型由p型变为n型。对光学性质的研究发现，由于空位的引入使其邻近原子电子结构发生变化，使得空位缺陷系统光学性质的变化主要集中在低能量区域。     

Hybridizing rapidly exploring random trees and basin hopping yields an improved exploration of energy landscapes

The number of local minima of the potential energy landscape (PEL) of molecular systems generally grows exponentially with the number of degrees of freedom, so that a crucial property of PEL exploration algorithms is their ability to identify local minima, which are low lying and diverse. In this work, we present a new exploration algorithm, retaining the ability of basin hopping (BH) to identify local minima, and that of transition based rapidly exploring random trees (T‐RRT) to foster the exploration of yet unexplored regions. This ability is obtained by interleaving calls to the extension procedures of BH and T‐RRT, and we show tuning the balance between these two types of calls allows the algorithm to focus on low lying regions. Computational efficiency is obtained using state‐of‐the art data structures, in particular for searching approximate nearest neighbors in metric spaces. We present results for the BLN69, a protein model whose conformational space has dimension 207 and whose PEL has been studied exhaustively. On this system, we show that the propensity of our algorithm to explore low lying regions of the landscape significantly outperforms those of BH and T‐RRT. © 2015 Wiley Periodicals, Inc.     

On the rate of convergence of solutions in domain with periodic multilevel oscillating boundary

In this paper we deal with the homogenization problem for the Poisson equation in a singularly perturbed domain with multilevel periodically oscillating boundary. This domain consists of the body, a large number of thin cylinders joining to the body through the thin transmission zone with rapidly oscillating boundary. Inhomogeneous Fourier boundary conditions with perturbed coefficients are set on the boundaries of the thin cylinders and on the boundary of the transmission zone. We prove the homogenization theorems and derive the estimates for the convergence of the solutions. Copyright © 2010 John Wiley & Sons, Ltd.