非负交换整半环上矩阵的正/负行列式保持问题

设R为非负交换整半环,用M_n(R)表示R上所有n×n矩阵构成的矩阵半环.令T是M_n(R)到其自身的线性变换,若T满足|T(X)|~+=|X|~+,■X∈M_n(R)(或|T(X)|~-=|X|~-,(?)X∈Mn(R)),称T为M_n(R)上保持正行列式(负行列式)的线性变换.刻画了n≥4时,M_n(R)上保持正行列式/负行列式的线性满射形式.     

正负折射率的一维圆形受限光子晶体特性研究

对正负折射率材料构成的一维光子晶体,在横向圆形受限的条件下,推出了光波在其中传播时模式所满足的条件,并利用特征矩阵法研究了正负折射率绝对值相同时,光波在不同模式和不同介质厚度可见光能实现透射波和零反射。正负折射率绝对值不等时,得出介质厚度为半波长时透射波出现在中心波长处;随着模式数即入射角增大,透射波曲线向短波方向移动;介质折射率差的绝对值越大、周期数增加都使透射波谱宽度变窄。     

偏压及测试环境对离子束DLC膜摩擦学行为的影响

采用线性阳极层离子束技术制备了类金刚石薄膜(DLC膜),研究了不同衬底负偏压和测试环境对DLC薄膜摩擦学性能的影响.结果表明:在-50V偏压下,薄膜硬度和弹性模量最大,这主要与薄膜中高的sp³含量相关;衬底负偏压对薄膜在室温大气条件下的摩擦学性能影响不显著,薄膜总体呈现较低的摩擦系数和磨损率,显示出优异的抗磨损性能;线性离子束制备的含氢DLC薄膜的摩擦学行为受湿度及环境气氛影响较大,归因于环境中的氧气和水分造成的摩擦化学反应.     

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Let $X_1,X_2,\ldots,X_n$ be a sequence of extended negatively dependent random variables with distributions $F_1,F_2,\ldots,F_n$,respectively. Denote by $S_n=X_1+X_2+\cdots+X_n$. This paper establishes the asymptotic relationship for the quantities $\pr(S_n>x)$, $\pr(\max\{X_1,X_2, \ldots,X_n\}>x)$, $\pr(\max\{S_1,S_2$, $\ldots,S_n\}>x)$ and $\tsm_{k=1}^n\pr(X_k>x)$ in the three heavy-tailed cases. Based on this, this paper also investigates the asymptotics for the tail probability of the maximum of randomly weighted sums, and checks its accuracy via Monte Carlo simulations. Finally, as an application to the discrete-time risk model with insurance and financial risks, the asymptotic estimate for the finite-time ruin probability is derived.     

基于永磁体间的磁性负刚度的分析与优化

为了有效地降低磁性负刚度结构的非线性程度,从简单三磁体结构出发,引入新型负刚度结构模型——五磁体对称结构,运用MATLAB建立新型负刚度结构的磁力学模型并应用Ansoft Maxwell进行仿真验证。研究永磁体间的相对位置参数对五磁体对称结构的负刚度曲线走势的影响,在微幅振动下对基于磁引力的负刚度曲线拟合后使用谐波平衡法求解动力学方程。最终得出结论:在给定的条件下,五磁体负刚度结构的负刚度曲线的非线性相较于简单三磁体结构,一定程度上得到了改善,且其隔振性能相较于传统线性隔振系统有了大幅提高,为磁性负刚度结构的负刚度曲线非线性的优化和应用提供了理论上的参考。     

Vibrational spectra obtained from high quality potential energy surfaces spanned by low level normal coordinates: application to CHFClI and CDFClI

The impact of approximate normal coordinates for spanning high level potential energy surfaces on vibrational frequencies is studied within the framework of vibrational SCF and configuration interaction calculations (VCI). The use of low level normal coordinates avoids expensive geometry optimizations and harmonic frequency calculations and thus allows for a significant reduction in CPU time. Benchmark calculations are provided for a set of molecules ranging from 5 to 7 atoms. An application to CHFClI and CDFClI shows that this approximation still allows for very accurate results. These molecules are of particular interest for studying parity violation effects.     

Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

少节点基因调控网络的控制

近年来,自组织振荡网络受到越来越多科学家的关注,对生物体的生长、发育起调控作用的基因调控网络即是其中的一种.本文研究了少节点基因调控网络的控制问题.运用多相位超前驱动方法对该种网络进行调控,可以有效地提高对网络的控制效率.通过数值模拟,发现对于少节点基因调控网络,当系统参数确定时,网络的有效控制率可以达到95％以上(10节点网络);当系统参数不确定时,控制的效率也非常高.     

非高斯噪声对惯性棘轮中粒子负迁移率的影响

利用随机模拟方法研究了惯性棘轮中非高斯噪声对负迁移率的影响. 分别模拟了绝对负迁移率(ANM), 非线性迁移率(NNM) 和负微分迁移率(NDM) 等三种反常输运现象. 计算结果表明: 1) 在不同的参数空间里, 非高斯噪声参数q 能够增强或者削弱ANM, 诱导NNM 和NDM; 2) 当q 较大时, 反常输运现象转化为正常输运; 3) 随着q 逐渐增大, 平均速度- 关联时间特性曲线朝着关联时间较小的方向移动并且其峰值逐渐减小. 关键词： 反常输运 负迁移率 非高斯噪声