微积分的再思考

基于代数和显式一致估计的微积分思想可以追溯到前牛顿时代,或者欧拉和拉格朗日.由于所涉及的数学非常简单,新的方法可以从一些简单的例子出发,直接、自然却严格地建立微分和积分的流线型理论,并不需要连续性、极限和紧性的概念.     

碳纳米管的近边吸收谱研究

用X射线近边吸收谱研究了单壁, 双壁和多壁碳纳米管在超高真空系统中不同温度下退火处理后的行为.碳的K边吸收谱表明, 多壁管上吸附的杂质将在热处理过程中最先被去除, 其次是双壁管, 最后是单壁管.这种热处理下杂质去除的顺序说明了曲率越小杂质吸附得越牢靠, 即越容易吸附杂质.另外, 结果中显示, 经退火处理后3种碳纳米管在多重散射区域的峰结构呈现规律性的移动,由单壁管到多壁管, 谱峰向低能方向移动; 这是由于碳纳米管的层数不同造成的, 证明这部分谱峰结构直接受到碳纳米管层数的调制, 有利于鉴别3种碳纳米管.     

对苯醌二亚胺与吡啶共聚物的金属配合物催化法合成及性能

在二氯-1,3-双(二苯基磷)丙烷基镍(Ⅱ)存在下,通过N,N′-二氯苯醌二亚胺和2,5-二甲基-N,N′-二氯苯醌二亚胺与2,5-二溴吡啶的格氏(Grignard)试剂共聚,得到了两种新型共轭聚合物。采用FT-IR1、H-NMR、UV-Vis、XRD、循环伏安、充放电对共聚物进行结构与性能测试。结果表明:该类共聚物具有一定的电化学活性,每种聚合物均在-1.0~2.0 V出现一对氧化-还原峰。聚(N,N′-二氯苯醌二亚胺-吡啶)和聚(2,5-二甲基-N,N′-二氯苯醌二亚胺-吡啶)的比电容分别为126 F/g和63 F/g。     

猜一猜，算一算--估计

1.要是我问你：“你们班上有几个小朋友？”你会先数一数。然后才告诉我正确的数字。如果我再问你：“你住的城市或小镇有多少人？”这次你可没办法一个个去数了。怎么办呢？你可以说一个大概的数字．也就是说。你可以估计你住的城市或小镇有多少人。     

可否走停

你有没有注意到,我们周围的许多事物,只出现两种情形？ 电灯不是开的,就是关的; 婴儿不是睡着的,就是醒着的; 门不是开的,就是关的; 吊桥不是升起的,就是放下的。     

FUNCTIONAL ANALYSIS METHOD FOR THE M/G/1 QUEUEING MODEL WITH OPTIONAL SECOND SERVICE

By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point.     

Gauss白噪声激励下分数阶导数系统的非平稳响应

研究了Gauss(高斯)白噪声激励下具有分数阶导数阻尼的非线性随机动力系统的非平稳响应.应用等价线性化方法将非线性系统转化为等价的线性系统,之后采用随机平均法获得系统响应满足的FPK(Fokker-Planck-Kolmogorov)方程,其中分数阶导数近似为一个周期函数.使用Galerkin方法求解FPK方程进而得到系统的近似非平稳响应.数值结果验证了方法的正确性和有效性.     

NONCOMMUTATIVE ORLICZ-HARDY SPACES

Let(Φ, Ψ) be a pair of complementary N-functions and HΦ(A) and HΨ(A) be the associated noncommutative Orlicz-Hardy spaces. We extend the Riesz, Szeg and innerouter type factorization theorems of Hp(A) to this case.     

Analytical and experimental studies on nonlinear characteristics of an L-shape beam structure

This paper focuses on theoretical and experimental investigations of planar nonlinear vibrations and chaotic dynamics of an L-shape beam structure subjected to fundamental harmonic excitation,which is composed of two beams with right-angled L-shape.The ordinary differential governing equation of motion for the L-shape beam structure with two-degree-of-freedom is firstly derived by applying the substructure synthesis method and the Lagrangian equation.Then,the method of multiple scales is utilized to obtain a four-dimensional averaged equation of the L-shape beam structure.Numerical simulations,based on the mathematical model,are presented to analyze the nonlinear responses and chaotic dynamics of the L-shape beam structure.The bifurcation diagram,phase portrait,amplitude spectrum and Poincare map are plotted to illustrate the periodic and chaotic motions of the L-shape beam structure.The existence of the Shilnikov type multi-pulse chaotic motion is also observed from the numerical results.Furthermore, experimental investigations of the L-shape beam structure are performed,and there is a qualitative agreement between the numerical and experimental results.It is also shown that out-of-plane motion may appear intuitively.     

Achievement of chaotic synchronization trajectories of master-slave manipulators with feedback control strategy

This paper addresses a master-slave synchronization strategy for complex dynamic systems based on feedback control.This strategy is applied to 3-DOF planar manipulators in order to obtain synchronization in such complicated as chaotic motions of end-effectors.A chaotic curve is selected from Duffing equation as the trajectory of master end-effector and a piecewise approximation method is proposed to accurately represent this chaotic trajectory of end-effectors.The dynamical equations of master-slave mani...