The Order of Automorphisms of Quasigroups

We prove quadratic upper bounds on the order of any autotopism of a quasigroup or Latin square, and hence also on the order of any automorphism of a Steiner triple system or 1‐factorization of a complete graph. A corollary is that a permutation σ chosen uniformly at random from the symmetric group will almost surely not be an automorphism of a Steiner triple system of order n, a quasigroup of order n or a 1‐factorization of the complete graph . Nor will σ be one component of an autotopism for any Latin square of order n. For groups of order n it is known that automorphisms must have order less than n, but we show that quasigroups of order n can have automorphisms of order greater than n. The smallest such quasigroup has order 7034. We also show that quasigroups of prime order can possess autotopisms that consist of three permutations with different cycle structures. Our results answer three questions originally posed by D.  Stones.     

Classification of Graeco‐Latin Cubes

A q‐ary code of length n, size M, and minimum distance d is called an code. An code with is said to be maximum distance separable (MDS). Here one‐error‐correcting () MDS codes are classified for small alphabets. In particular, it is shown that there are unique (5, 5³, 3)₅ and (5, 7³, 3)₇ codes and equivalence classes of (5, 8³, 3)₈ codes. The codes are equivalent to certain pairs of mutually orthogonal Latin cubes of order q, called Graeco‐Latin cubes.     

Adaptive RAKE receiver in chaos based pilot-added DS-CDMA system

This paper presents the theoretical analysis of adaptive multiuser RAKE receiver scheme in frequency selective fading channel for direct-sequence code division multiple access (DS-CDMA) system. Least mean square (LMS) algorithm is used to estimate the channel coefficients. Chaotic sequences are used as spreading sequence and corresponding bit error rate (BER) in closed form is derived for imperfect channel estimation conditions. Performances of chaotic sequences are compared with pseudorandom noise (PN) sequences. Under perfect synchronization assumption, various simulation results are shown to investigate the performance of the proposed system.     

应用极化水分子模型研究单分子层受限水的介电性质

受限条件下水的介电性质因测量极具挑战,其在诸多电化学过程与反应输运过程中如何扮演关键角色从未被定量地澄清.本工作利用平衡态分子动力学模拟和受限体系介电性质计算方法,系统性地探索了0.65 nm限域尺寸、5×10⁸ Pa限域压强、不同温度条件下单分子受限冰和受限水的介电性质.详细比较了恒定偶极矩SPC/E水分子模型和可极化的SWM4-NDP水分子模型在描述受限冰、水结构与介电性质上的优劣势,包括统计分析SWM4-NDP模型模拟的单分子层受限水和受限冰的瞬时分子偶极矩概率密度分布,计算每个模拟体系的静态结构因子、静态偶极空间关联函数、静态介电常数、体系偶极时间关联函数和德拜弛豫时间.首次发现了极化水分子模型描述的低维度受限水和受限冰的奇异分子极性变化,并观察到两种模型描述静态结构性质的效果相当,SWM4-NDP模型对于静态介电常数描述的优势会因受限条件的增强而被大幅削减.但在受限水介电极化弛豫动力学性质描述上SWM4-NDP模型明显优于SPC/E模型.我们推断SWM4-NDP模型在探索受限水结构相变动力学以及受限体系离子输运和溶剂化动力学等过程的模拟研究中是比SPC/E模型更好的选择.本工作将在进一步开展基于受限水系统储能、传感、输运的设计工作中提供一定的理论指导意义.     

Effect of Ionic Liquid Structure on the Electrochemical Response of Dopamine at Room Temperature Ionic Liquid‐modified Carbon Paste Electrodes (IL–CPE)

In this work 12 different ionic liquids (ILs) have been used added as co‐binders in the preparation of modified carbon paste electrodes (IL–CPEs) used for the voltammetric analysis of dopamine in Britton‐Robinson buffer. The ionic liquids studied were selected based on three main criteria: (1) increasing chain length of alkyl substituents (studying 1‐ethylimidazolium and ethyl, propyl, butyl, hexyl and decylmethylimidazolium bis(trifluoromethylsulfonyl)imide ionic liquids); (2) nature of the counter ion (dicyanamide, bis(trifluoromethylsulfonyl)imide and hexafluorophosphate) in 1‐butyl‐3‐methylimidazolium ionic liquids; and (3) cation ring structures (1‐butyl‐3‐methylimidazolium, 1‐butyl‐1‐methylpiperidinium, 1‐butyl‐1‐methylpyrrolidinium and 1‐butyl‐3‐methylpyridinium) in bis(trifluoromethylsulfonyl)imide or hexafluorophosphate (1‐butyl‐3‐methylimidazolium or 1‐butyl‐3‐methylpyridinium as cations) ionic liquids. The use of IL as co‐binders in IL–CPE results in a general enhancement of both the sensitivity and the reversibility of dopamine oxidation. In square wave voltammetry experiments, the peak current increased up to a 400 % when 1‐ethyl‐3‐methylimidazolium bis(trifluoromethylsulfonyl)imide was used as co‐binder, as compared to the response found with the unmodified CPE. Experimental data provide evidence that electrostatic and steric effects are the most important ones vis‐à‐vis these electrocatalytic effects on the anodic oxidation of dopamine on IL–CPE. The relative hydrophilicity of dicyanamide anions reduced the electrocatalytic effects of the corresponding ionic liquids, while the use of 1‐ethyl‐3‐methylimidazolium hexafluorophosphate or 1‐ethyl‐3‐methylimidazolium bis(trifluoromethylsulfonyl)imide (two relatively small and highly hydrophobic ionic liquids) as co‐binders in IL–CPE resulted in the highest electrocatalytic activity among all of the IL–CPE studied.     

用转移矩阵法数值研究二维正方介质柱光子晶体的传输特性

利用转移矩阵方法对二维正方介质柱光子晶体的传输特性进行了研究,数值计算研究了不同晶格、同一晶格柱体截面面积不同、放置方位角不同时光子晶体的传输特性。数值结果表明光子禁带的宽度与中心频率和晶格结构有很大关系,正方晶格更易形成平坦光子禁带,柱体截面面积大,则形成的禁带较宽,在其他因素相同的条件下柱体放置的方位角对光子禁带有重要影响。数值研究表明在正方介质柱下设计宽平坦光子禁带时,可以首先考虑正方晶格结构,其次设法使柱体截面尽量大一些,最后可通过柱体放置方位角来微调光子禁带的宽度与中心频率以达到设计要求。     

一组新氨基酸描述子用于肽定量构效关系研究

用主成分分析从20种天然氨基酸0D～3D结构信息中收集到的共1369个描述子变量得到了一组新氨基酸描述子(SZOTT), 将其用于血管紧张素转化酶抑制剂和苦味二肽结构表征并以偏最小二乘法建立定量构效关系模型, 得复相关系数R_CU²分别为0.894和0.908, 留一法交互检验的复相关系数R_CV²分别为0.828和0.736, 估计均方根误差RMS分别为0.331和0.195. 研究结果表明, SZOTT描述子含信息量大, 操作简便, 结构表达能力强, 有望在多肽定量构效关系研究中得到进一步推广.     

一种计算复合材料等效弹性性能的有限元方法

在最小二乘意义下提出了一种计算复合材料等效弹性性能的有限元方法.这种方法由于考虑了等效弹性张量各分量之间的耦合关系,所求得的等效弹性常数比传统方法更可靠,可适用于求解含任意形状的夹杂和夹杂物问题.通过算例计算了在不同弹性模量对比度下两相复合材料的等效弹性性能,并与相关的理论及数值结果进行了比较,结果表明,利用该方法计算含夹杂复合材料等效弹性常数是可行的.     

深空光通信中的图像信标捕获技术

为实现深空光通信链路建立过程中精确的对准,提出了一种深空光通信系统扩展信标的捕获方案。该方案以可视地球图像作为信标,在航天器上存储一幅信标图像作为参考图像,采用天线扫描的方式在各点对所瞄准的区域成像,利用像素扫描的方式,使参考图像和实际探测图像进行相关,在天线扫描完成以后,找出相关性最大的位置,即可认为在该点捕获到地球图像。在计算两图像相关系数的过程中,由于傅里叶梅林变换幅度谱具有伸缩及旋转不变性,因此利用傅里叶梅林变换即可消除两图像相关系数因为旋转和伸缩的影响。利用蒙特卡罗方法随机产生1000个视场,仿真结果表明,3σ内正确捕获到信标图像的概率为99.6%,表明这是一种可行的方法。     

受限亚音速气流中倒置悬臂壁板静气弹稳定性的理论及实验研究

板壳结构在航空航天、高速列车、能量采集等诸多工程领域已经得到了广泛应用. 将悬臂壁板倒置于轴向气流中并在壁板周围流场中设置刚性壁面可有效地调控壁板的失稳速度, 是俘能器优化设计的重要措施之一. 但针对刚性壁面作用下亚音速气流中倒置悬臂壁板的失稳机制仍需要开展深入研究. 本文以受限亚音速气流中倒置的二维悬臂壁板为对象, 以理论分析及风洞实验为手段, 研究了单侧刚性壁面效应对倒置悬臂壁板静态失稳特性的影响规律. 在理论分析中, 首先应用镜像函数法来处理壁面约束条件, 基于算子理论研究获得了以Possio积分方程为表征的壁板气动力, 壁面效应实际表征为一包含移位Tricomi算子的复合算子; 然后将壁板失稳方程的求解问题转化为定区间上的函数逼近问题; 最后, 依据Wererstrass定理并利用最小二乘法求解该最优函数, 以获得系统的失稳临界参数. 在试验研究中依据压杆稳定原理设计了壁板静态失稳的测试方法并完成了风洞实验. 理论分析结果表明, 壁板会发生发散(静气动弹性)失稳, 临界动压随壁板与壁面间距的增加而增大并最终趋于稳定(无壁面情况); 通过理论与风洞实验结果的对比分析, 验证了本文气动力及理论分析的适用性及准确性. 针对倒置悬臂壁板结构的气动弹性失稳问题, 本文提出的方法不涉及系统方程的离散及特征值求解问题, 而是将其转化为了定区间上的函数逼近问题进行求解, 这为弹性结构静气动弹性失稳问题的研究提供了一个可行的新思路.