富里叶级数的收敛速度

对正弦和余弦富立叶级数,通过合并相邻同号项,使其重排成交错级数.讨论了重排形成的交错级数的敛散性.指出根据自变量x的不同取值,该交错级数可能是单调递减或周期递减的级数.按照莱布尼茨判定法提出了不同精度要求的级数项数的计算公式.选取一到三阶收敛的富立叶级数计算了不同比值精度及差值精度要求的级数项数.计算表明,在x的取值为2π的等分点时,富立叶级数的部分和随项数的增加单调地逼近其收敛值.在x的取值为其它点时,富立叶级数的部分和随项数的增加围绕收敛值上下变动,周期地逼近其收敛值.低收敛阶富立叶级数的收敛速度较慢.要达到0.01%的精度,一收敛阶富立叶级数需要数万项,二收敛阶富立叶级数也需要数百项.在不同计算点处,要达到相同的计算精度,需要的级数项数差别较大.     

A semidefinite programming approach to the hypergraph minimum bisection problem

The hypergraph minimum bisection (HMB) problem is the problem of partitioning the vertices of a hypergraph into two sets of equal size so that the total weight of hyperedges crossing the sets is minimized. HMB is an NP-hard problem that arises in numerous applications – for example, in digital circuit design. Although many heuristics have been proposed for HMB, there has been no known mathematical program that is equivalent to HMB. As a means of shedding light on HMB, we study the equivalent, complement problem of HMB (called CHMB), which attempts to maximize the total weight of non-crossing hyperedges. We formulate CHMB as a quadratically constrained quadratic program, considering its semidefinite programming relaxation and providing computational results on digital circuit partitioning benchmark problems. We also provide results towards an approximation guarantee for CHMB.     

Realization of superposition and entanglement of coherent and squeezed states in circuit quantum electrodynamics

We propose a new scheme for generating the superposition and entanglement of the coherent states and squeezed states by considering N superconducting charge qubits (or artificial two-level atoms) interacting with photons in a high finesse cavity on a chip, assisted by a strong driving field. By virtue of the parameters of this system, we can generate novel quantum states, for example, multiparty entangled states and Schro¨dinger cat states among the superconducting qubits, coherent states and squeezed state...     

On the free vibration response of rectangular plates,partially supported on elastic foundation

Rectangular plates on distributed elastic foundations are widely employed in footings and raft foundations of variety of structures. In particular, mounted columns and single footings may partially occupy the rectangular plate of any kind.     

Further bounds for waiting time distributions and their means in the case ρ<1

In the paper exponential bounds for the instationary and stationary waiting time d.f.'s in GI/GI/1/∞, derived by several authors partly using martingale theory arguments, are improved with the help of monotonicity properties. Further it is shown that Ne?eptjrenko's bound for the rate of convergence of the mean waiting time in single server queues Is also valid for many server queues with ρ < 1.     

不同磁路下微型ECR中和器电子引出的模拟研究

电子回旋共振(ECR)中和器是微型ECR离子推力器的重要组成部分,其引出的电子用于中和ECR离子源的离子束流,避免了航天器表面电荷堆积,并且电子引出性能对推力器的整体性能起着重要作用.为了分析影响微型ECR中和器电子引出的因素,本文建立了二维轴对称PIC/MCC计算模型,通过数值模拟研究不同磁路结构对中和器的电子引出,及不同腔体长度对壁面电流损失的影响.计算结果表明, ECR区位置和引出孔附近磁场构型对中和器的电子引出性能至关重要.当ECR区位于天线上游,电子在迁移扩散中易损失,并且电子跨过引出孔前电势阱所需的能量更高.如果更多磁力线平行通过引出孔,中和器引出相同电子电流所需电压较小.当ECR区被天线切割或位于下游时,电子更易沿磁力线迁移到引出孔附近,从而降低了收集板电压.研究了同一磁路结构下不同腔体长度对电子引出的影响,发现增加腔体长度,使得更多平行轴线的磁力线通过引出孔从而避免电子损失在引出板表面,增加了引出电子电流.研究结果有助于设计合理的中和器磁路和腔体尺寸.     

n阶不等距常系数线性差分方程的解

利用Mikusinski的算符演算理论和移动算符的幂级数表示,给出了n阶不等距常系数线性差分方程的解法.     

The side chain effects on TPD-based copolymers: the linear chain leads to a higher jsc

Abstract

Alkyl substituents appended to polymers play the determining role on self-assembly and film-forming properties, and on device performance. In this work, we highlight the effects of the linear and branched flexible chains appended to the acceptor moiety (A) in D-A type copolymers. Two thieno[3,4-c]-pyrrole-4,6-dione (TPD) based copolymers PT1 and PT2 with different alkyl chains, were designed and synthesized. By comparison their UV-vis absorptions, HOMO/LUMO energy levels, as well as the characters in polymer solar cells, the influences of alkyl chains were investigated. Both copolymers showed molecular weights of 21?kDa and similar optical properties with a medium band gap of 1.93?eV, while PT2 with the branched chain exhibited a lower HOMO than that of PT1 (?5.43 vs???5.37?eV). In bulk heterojunction (BHJ) solar cells, PT1 with a linear chain presented a short circuit current (J_sc) of 6.76?mA cm^?2, open circuit voltage (V_oc) of 0.89?V and power conversion efficiency (PCE) of 2.92%. To the contrary, PT2 showed a J_sc of 3.53?mA cm^?2, V_oc of 0.99?V, delivering a relatively lower PCE of 2.05%. The result indicates that appending a linear alkyl chain to the TPD unit could sufficient enhance the J_sc value of the related polymer.