选择题试编

选择题作为一种新颖的试题形式,目前在国内外已普遍采用,这类试题能较好地考查学生的思维能力。现行中学数学教材,这类习题极其欠缺,为了使学生能适应这种试题,我在教学过程中,根据教学内容,给学生平时练习中出现的错误,编拟了一些选择题给学生练习,现抄录一部分供同行们参考。     

Luminescence Properties of Sr2SnO4：Sm^3＋ Afterglow Phosphor

A new long-lasting phosphorescence （LLP） phosphor, Sr2SnO4：Sm3＋ which emits reddish-orange LLP upon UV-excitation, is prepared by a conventional high-temperature solid-state method. After irradiation under 247-nm UV light, Sr2SnO4：Sm3＋ emits an intense reddish-orange emission afterglow from the 4G5/2 to 6HJ （J = 5/2,7/2,9/2） transitions. The afterglow decay curve of the Sm3＋-doped Sr2SnO4 phosphor contains a fast decay component and another slow decay one. Due to the presence of the slow decay component, the afterglow can be seen with the naked eye in the dark clearly for more than 1 h after removal of the excitation source.     

求解均衡问题的内部束方法

结合logarithmic二次函数和Lemar6chal和Wolfe(1975)提出的束方法,本文提出了一个求解非光滑均衡问题的束方法.一方面,我们算法推广了Nguyen等在文[1]中的束方法,并且保证了算法生成的序列在集合的内部.另一方面,将内部束方法应用到求解均衡问题.     

具有奇异非线性项的抛物系统的非同时熄灭与同时熄灭[英文]

本文研究具有奇异非线性项的一维拟线性抛物系统解的熄灭性质. 首先, 利用标准正则化方法得到该系统弱解的局部存在性. 然后对解的同时熄灭和非同时熄灭进行区分, 并按照熄灭速率参数进行了详细分类.     

多线性Marcinkiewicz积分在Campanato空间上的存在性与有界性

设n≥2, m≥1,y=(y1,..., ym).μ(f)是如下定义的多线性Marcinkiewicz积分:μ(f)(x)=(∫∞01/tm∫(B(0,t))~m?(y)|y|m(n-1)m∏i=1f_i(x-y_i)|2dt/t)~(1/2),其中dy=dy1···dym.本文考虑了μ(f)在Campanato空间上的存在性与有界性,证明了若m-线性Marcinkiewicz积分μ(f)在一点处有限,则它几乎处处有限,而且,如下范数不等式成立:||μ(f)||Eα,p≤C m∏j=1||fj||Eαj,pj,其中E~(α,p)是经典的Campanato空间,1/p=1/_p1+···+1/p_m,α=α_1+···+α_m.     

改进的三维电磁PIC系统模拟并行算法

为了更好地实现对大尺度器件的模拟,以及更系统地验证和解决高功率微波系统在设计和实验中负载变化等影响,在进一步深入研究电磁PIC并行算法的基础上,运用MPI消息传递函数做出了改进。提出了一种整体建模、分段解析的并行算法,并从并行时序算法入手,通过减少一次同步提高了计算的效率。最后经过一个磁绝缘线振荡器进行验证,改进的算法正确,并且当计算进程数4个增加到16个时,计算速度能提高2.5倍左右。     

一类具有无穷边界值的二次奇摄动边值问题

研究一类具有无穷边界值的二次奇摄动Robin边值问题解的存在性与解的渐进行为,重点关注边界值的奇异程度对解的边界层行为的影响;同时将所得的结果与Chang及Howes的结果(带正常边界值)进行比较.研究表明:(1)当边界值大小为O(1/)时,得到的边界层大小为O( ln ),这比Chang及Howes带正常边界值的情形提高了O(ln )量级;(2)增大边界值的奇性至O(1/ r),这里r >1,边界层大小的量级不变,依然为O( ln );(3)若要使得边界层大小为O(1),则边界值的大小需为O(e?1/).最后给出一个算例验证得到的结果.     

Totally asymmetric exclusion processes at constrained m-input n-output junction points

Totally asymmetric exclusion processes at constrained m-input n-output junction points under random update are studied by theoretical calculation and computer simulation in this paper. At the junction points, the hopping rate of particles from m-input parallel lattices to n-output parallel lattices is assumed to be equal to r/n （0 〈 r 〈 1 ）. The mean-field approach and Monte Carlo simulations show that the phase diagram can be classified into three regions at any value of r. More interestingly, there is a threshold rc = n（ 1 - √1 - m/n）/m. In the cases of r 〉 re and r 〈 rc, qualitatively different phases exist in the system. With the increase of the value of m/n, the regions of （LD, LD） and （MC, LD） or （HD, LD） decrease, and the （HD, HD） is the only phase that increases in the region （LD stands for low density, HD stands for high density, and MC for maximal current）. Stationary current and density profiles are calculated, showing that they are in good agreement with Monte Carlo simulations.     

Statistical distribution based detector response function of a Si(PIN) detector for K_α and K_β X-ray

A semi-empirical detector response function (DRF) model of a Si (PIN) detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on the statistical distribution analytic (SDA) method. The model for each single peak contains a step function, a Gaussian function, and an exponential tail function. Parameters in the model are obtained by the weighted nonlinear least-squares fitting method. In the application, six kinds of elements’ characteristic X-ray spectra are obtained by using the Si (PIN) detector, and fitted by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.     

Cross-section measurement for Ni（n,x）^58（m＋g）Co, Ni（n, x）^60mCo, Ni（n,x）^61Co and Ni（n,x）^62mCo reactions induced by neutrons around 14 MeV

The cross sections of Ni(n,x)~(58(m g))Co,Ni(n,x)~(60m)Co,Ni(n,x)~(61)Co and Ni(n,x)~(62m)Co reactions induced by neutrons around 14 MeV were measured in this work and calculated by a previously developed formula in this work.The neutron flux was determined using the monitor reaction ~(27)Al(n,α)~(24)Na and the neutron energies were measured with the method of cross-section ratios for ~(90)Zr(n,2n)~(89)Zr to ~(93)Nb(n,2n)~(92m)Nb reactions.