利用杨辉三角形对称性推导高阶运动微分方程

利用Mathematica数学软件计算函数r=r(q(t),t)各变量之间偏导和高阶导数的关系，发现具有杨辉三角形对称性.结合杨辉三角形的对称性规律和牛顿第二定律推导出了高阶运动微分方程，并讨论了理想约束系统下的高阶运动微分方程. 关键词： 杨辉三角形 牛顿第二定律 高阶运动微分方程 高阶力变率 高阶速度能量 理想约束     

二氧化钒薄膜的低温制备及其性能研究

针对VO₂薄膜在微测辐射热计上的应用，采用射频反应溅射法，在室温下制备氧化钒薄膜；研究了氧分压对薄膜沉积速率、电学性质及成分的影响.通过调节氧分压，先获得成分接近VO₂的非晶化薄膜，再在400℃空气中氧化退火，便可制得高电阻温度系数，低电阻率的VO₂薄膜，电阻温度系数约为-4%/℃，薄膜方块电阻为R_□为100—300kΩ；薄膜在室温下沉积，400℃下退火的制备方法与微机电加工(micro electromechanic 关键词： 二氧化钒 电阻温度系数 氧分压 射频反应溅射法     

High index of refraction via quantum interference in a three-level system of Er^3＋-doped yttrium aluminium garnet crystal

A simple three-level system is proposed to produce high index of refraction with zero absorption in an Er^3＋-doped yttrium aluminium garnet （YAG） crystal, which is achieved for a probe field between the excited state 4I13/2 and ground state 4I15/2 by adjusting a strong coherent driving field between the upper excited state 4I11/2 and 4I15/2. It is found that the changes of the frequency of the coherent driving field and the concentration of Er^3＋ ions in the YAG crystal can maximize the index of refraction accompanied by vanishing absorption. This result could be useful for the dispersion compensation in fibre communication, laser particle acceleration, high precision magnetometry and so on.     

Dominant modes of submerged thin cylindrical shells

The relationship between the dominant mode of the submerged thin cylindrical shell and the flexural wave velocity is investigated. The natural frequency corresponding to the vibration mode is obtained as the solution of characteristic equation of thin cylindrical shell. However, it is difficult to estimate the dominant mode, especially if two or more vibration modes are involved. To estimate the dominant mode of a thin shell in vacuo, the concept of “modified bending stiffness” has been introduced. In this paper, the concept of modified bending stiffness is extended to estimate the dominant mode of a submerged thin cylindrical shell. The dominant mode of a submerged thin cylindrical shell is theoretically discriminated from the other mode based on the smallness of the modified bending stiffness of the submerged shell. The validity of our theory is confirmed by a good agreement between theoretical and experimental results on flexural wave velocity.     

Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys

Abstract In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor. * Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis of Free Boundary Problems”.     

EXISTENCE OF PERIODIC SOLUTIONS OF SYSTEM OF DIFFERENCE EQUATIONS

This paper studies the nonautonomous nonlinear system of difference equationsΔx(n)=A(n)x(n)+f(n,x(n)),n∈Z,(*) where x(n)∈R~N,A(n)=(a_(ij)(n))N×N is an N×N matrix,with a-(ij)∈C(R,R) for i,j= 1,2,3,...,N,and f=(f_1,f_2,...,f_N)~T∈C(R×R~N,R~N),satisfying A(t+ω)=A(t),f(t+ω,z)=f(t,z) for any t∈R,(t,z)∈R×R~N andωis a positive integer.Sufficient conditions for the existence ofω-periodic solutions to equations (*) are obtained.     

FORMATION OF SINGULARITIES FOR A KIND OF QUASILINEAR NON－STRICTLY HYPERBOLIC SYSTEM

The author gets a blow-up result of C1 solution to the Cauchy problem for a first order quasilinear non-strictly hyperbolic system in one space dimension.     

用Riccati变换求解同调谐振子

利用Riccati变换求解同谐谐振子的定态薛定谔方程,求得了能谱及态函数 关键词： 同调谐振子 本征值谱 Riccati变换法     

安装偏差对光纤布喇格光栅应变测量的影响

通过理论推导和试验分析研究了安装偏差对光纤应变测量的影响，得到安装误差所带来测量误差的计算公式.发现光纤的轴向与预定安装方向的角偏差越大，测量误差也越大.用光纤光栅进行应变测量时，必须考虑光纤的安装偏差，它直接关系到测量结果的准确性.实际测量中要尽量确保传感器安装方位的准确.     

显微动态图像分析技术及其在生物物理中的应用

介绍了一种可实时监测细胞生命活动的显微动态图像分析技术。该技术把显微光学成像技术、数字处理技术和动态图像分析技术结合为一体,可实现对活细胞的结构功能、生长过程和环境变化的影响等进行非侵入性连续监测。通过在细胞膜弹性模量测量中的应用表明,该技术不仅原理可靠,实现容易,应用方便,而且检测速度快,测量精度高,稳定性能好。此项技术可望在生物物理学的实验研究中获得广泛的应用。