An expectation formula with applications

In this paper, we derive an expectation formula of a random variable having distribution W(x;q). As applications of the expectation formula, we give a transformation formula and an expansion of Sears? transformation formula.     

Condensed Cramer rule for some restricted quaternion linear equations

In this paper, we derive an alternative more condensed Cramer rule for the unique solution of some restricted left and right systems of quaternion linear equations. The findings of this paper extend some known results in the literature.     

The rotational dimension of a graph

Given a connected graph G = (N, E) with node weights s∈? and nonnegative edge lengths, we study the following embedding problem related to an eigenvalue optimization problem over the second smallest eigenvalue of the (scaled) Laplacian of G: Find v_i∈?^|N|, i∈N so that distances between adjacent nodes do not exceed prescribed edge lengths, the weighted barycenter of all points is at the origin, and is maximized. In the case of a two‐dimensional optimal solution this corresponds to the equilibrium position of a quickly rotating net consisting of weighted mass points that are linked by massless cables of given lengths. We define the rotational dimension of G to be the minimal dimension k so that for all choices of lengths and weights an optimal solution can be found in ?^k and show that this is a minor monotone graph parameter. We give forbidden minor characterizations up to rotational dimension 2 and prove that the rotational dimension is always bounded above by the tree‐width of G plus one. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:283‐302, 2011     

Trigonometric Widths and Best N-Term Approximations of the Generalized Periodic Besov Classes BΩp,θ

In this paper,we determine the estimates exact in order for the trigonometric widths and the best n-term trigonometric approximations of the generalized classes of periodic functions BΩp,θ in the space Lq for some values of parameters p,q.     

An accurate theory for the square-well potential: from long to short well width

Density function theory (DFT) is combined with the first-order mean spherical approximation (FMSA) to study the radial distribution function (RDF) of the square-well (SW) potential. The combination (DFT + FMSA) is based on the direct correlation function (DCF) of the FMSA. Upon comparison with computer simulation data, DFT + FMSA is shown to give better performance than FMSA for mid- and long-range attractions. For short-range and very short-range attractions, the theory successfully corrects the deficiencies of the original FMSA. Comparisons include the evaluation of contact values, gap height at a discontinuity and profiles of the RDF. This work provides an accurate and consistent way to handle the SW potential.     

200 kV闪光照相测试系统

介绍了一种基于Marx发生器原理设计的200 kV闪光照相测试系统,该系统具有延时功能,可按照实验要求,在预定时刻产生脉冲X射线进行闪光照相测试。设计了一台10级同轴结构的Marx发生器,采用了正负极充电,极间电容耦合为Z形回路的Marx发生器线路,利用开关与屏蔽外筒间的结构电容来锐化高压脉冲的输出,同时采用紧凑性、低电感设计获得窄脉冲的输出。在充电电压为25 kV的情况下,75 的负载上获得了脉宽小于100 ns、幅度大于200 kV的高压脉冲,通过高压电缆驱动闪光X射线二极管, 在距光源25 cm处获得了剂量大于910-6 C/kg、脉冲宽度约为70 ns的闪光X射线。     

Yb:YAG晶体性能实验测量

为了测量脉冲时间宽度小于20 ns时的射线时间分辨图像,发展了新型无机闪烁体Yb:YAG,并实验测量了晶体的发光衰减时间、X射线激发发光光谱、相对发光效率和空间分辨等性能,研究了Yb:YAG晶体的发光性能。实验表明,Yb:YAG发光有三种衰减成分,快成分衰减常数为1.2 ns,慢成分衰减常数与射线种类有关;X射线激发发光光谱在250~800 nm范围,有三个发光峰,分别为320,380和500 nm,且320 nm处强度最大;相对发光效率为1900 ph/MeV;使用钨分辨卡测得Yb: YAG空间分辨能力为2 lp/m,使用刀口法测得空间调制传递函数为0.5时的频率为0.7 lp/mm。结果说明Yb:YAG晶体性能能够满足所需测量要求。     

闪烁体衰减常数对辐射源边界测量影响数值模拟

在辐射成像系统测量辐射源边界中,有闪烁体时间弥散效应得到的边界值与没有闪烁体时的真实边界值存在差别,影响辐射源尺寸变化计算。研究构建了一类辐射源强时间宽度、半径扩散速率与边界相对强度不同的辐射源,应用卷积和图像强度梯度法,对选用BC408,LaBr3和LSO闪烁体得到的边界与真实边界的偏差进行了数值模拟计算。结果表明,拍摄时间为20 ns时,由BC408闪烁体得到的边界值偏差最小;若偏差小于1 mm认为闪烁体适合测量,BC408,LaBr3和LSO测量的强度时间宽度最小值分别为33 ns,133 ns和266 ns; 拍摄全积分图像时偏差大小不受闪烁体不同的影响;最终得出的偏差计算公式较好地反映了真实偏差的变化趋势。     

基于PIC单片机的种子源设计

对种子源结构进行了优化设计,为了缩短充电时间,在现有的电容和DC变换器基础之上,选用单片机作为控制芯片,利用其脉冲宽度调制(PWM）输出功能产生用于控制DC变换器的线性电压。对单片机PWM输出转化为线性控制电压的性能以及控制DC变换器恒流充电的可行性开展了实验研究。实验结果表明,基于PIC单片机的种子源储能可以达到250 J,充电时间缩短到6 min以内,满足实验要求。