对《关于〈一维圆环上双原子链的马德隆常数〉的解析解》的讨论

本文绘制了一维等距离子晶体的累加法、埃夫琴法和平均值法的各级马德隆常数的曲线.本文推导了二聚化直线离子晶体马德隆常数的求和式,比较了两种解析式的优劣.本文详细地推导了圆环上等距和二聚化离子晶体的马德隆常数的解析式,使读者更易于理解.本文修正了《关于〈一维圆环上双原子链的马德隆常数〉的解析解》的两个笔误,还建议修正二聚化马德隆常数的定义式,使其物理意义更明显.     

算术观点下的林氏微积分与传统教科书中微积分比较分析

微积分是大学里普及程度非常高的一门学科,数学系学生、理工科学生、文科学生都需要学习,传统教科书中的微积分复杂度较高,使很多学生望而生畏.而算术观点下的林氏微积分复杂度保持在乘法表的水平,大大降低了微积分的门槛,且直击微积分的核心:牛顿—莱布尼茨公式.以《数学分析》中的微积分部分为例,与林群的微积分做对比,以期为大学微积分的教学改革提供思考.     

基于几何均值的惩罚型状态变权向量的构造及应用

依据惩罚型状态变权向量的定义和对各因素间的均衡性要求,构造了含有几何平均值的惩罚型状态变权向量.给出了各因素的几何平均值相等和几何平均值不相等两种情况的构造方法,对多因素的变权综合提供了有效的理论支持.最后,用一个实例验证了该方法的可行性和有效性.     

Stochastic Hopf bifurcation in quasi-integrable-Hamiltonian systems

A new procedure is developed to study the stochastic Hopf bifurcation in quasiintegrable-Hamiltonian systems under the Gaussian white noise excitation. Firstly, the singular boundaries of the first-class and their asymptotic stable conditions in probability are given for the averaged Ito differential equations about all the sub-system‘s energy levels with respect to the stochastic averaging method. Secondly, the stochastic Hopf bifurcation for the coupled sub-systems are discussed by defining a suitable bounded torus region in the space of the energy levels and employing the theory of the torus region when the singular boundaries turn into the unstable ones. Lastly, a quasi-integrable-Hamiltonian system with two degrees of freedom is studied in detail to illustrate the above procedure.Moreover, simulations by the Monte-Carlo method are performed for the illustrative example to verify the proposed procedure. It is shown that the attenuation motions and the stochastic Hopf bifurcation of two oscillators and the stochastic Hopf bifurcation of a single oscillator may occur in the system for some system‘s parameters. Therefore, one can see that the numerical results are consistent with the theoretical predictions.     

追问引渡 演绎精彩

提问是课堂教学中不可或缺的交流手段,是开启学生心智的钥匙,是引起思考的策动力.陶行知先生云:“发明千千万,起点是一问.智者问得巧,愚者问得笨.”已经形象地道出了问的重要性.“问得巧”能使得师生思维产生“同频共振”,增进师生间的信息与情感交流,从而有效驱动学生积极参与.而适时适地、一语深中肯綮地追问(即追根究底地问,是课堂教学中普遍运用的一种方式,它是针对某一内容或某一问题,为了使学生弄懂弄通,在已提出问题、学生也有了一定的理解之后,再次补充或深化的“二度提问”),能有效扩充学生的思维张力,培养学生思维的深刻性品质,收获生成的硕果.     

阈算术代数系统及电流型CMOS电路设计

根据电流信号易于实现算术运算的特点，定义了阈算术运算、非负运算和阈算术函数，提出了和图为阈算术函数的图形表示，从而建立了阈算术代数系统.并通过具体的电流型CMOS电路的设计实例，阐述了算术意义明确的电流型电路设计方法及基于和图的电流型电路设计方法，实现了阈算术代数在二值电流型CMOS电路中的应用.计算机模拟结果表明，所设计的电路具有正确的逻辑.提出的阈算术代数系统为电流型电路的设计提供了一种新的简单有效的方法.     

再谈Minc-Sathre不等式的上下界

用调和平均值、均值不等式之间的关系及对数平均不等式,对Minc-Sathre不等式的上下界进行改进,使结论更精确.     

平均值不等式的证明及其应用

n n n设 a1，a2，…，an为正数，若∏i＝1 ai ＝1或∑i＝1 ai ＝1，借助数学归纳法可相应地证明∑ai ≥ n或i＝1 n nn∏ai ≤1．这两个不等式可用于证明平均值不等式，并由此得出三者相互等价．实例说明平均值不等式在求数列极限方面的应用． i＝1     

Projectile fragment emission in the fragmentation of 56Fe on C,Al and CH2 targets at 471 A MeV

The emission angle and the transverse momentum distributions of projectile fragments produced in the fragmentation of 56Fe on CHs, C and A1 targets at 471 A MeV are measured. It is found that for the same target, the average value and width of the angular distribution decrease with an increase of the projectile fragment charge; for the same projectile fragment, the average value of the distribution increases and the width of the distribution decreases with increasing the target charge number. The transverse momentum distribution of a projectile fragment can be explained by a single Gaussian distribution and the averaged transverse momentum per nucleon decreases with the increase of the charge of projectile fragment. The cumulated squared transverse momentum distribution of a projectile fragment can be explained well by a single Rayleigh distribution. The temperature parameter of the emission source of the projectile fragment, calculated from the cumulated squared transverse momentum distribution, decreases with the increase of the size of the projectile fragment.     

基于加权可能性均值的亚式期权模糊定价

主要探讨不确定环境下用模糊集理论处理亚式期权的定价问题.运用梯形模糊数来表示标的资产价格、无风险利率、红利率和波动率,建立了亚式期权的加权可能性均值模糊定价模型,得到连续几何和算术亚式期权的模糊价格公式.最后通过数值例子表明:亚式期权的加权可能性均值模糊定价模型具有很大的灵活性,更符合现实的不确定情况,具有较强的实用价值.