Holder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

A Hilbert transform for H?lder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in ?²ⁿ , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the H?lder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the H?lder exponents, the diameter of Γ and a specific d-sum (d > d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.     

“对数与对数运算（一）”的教学设计

一、教材分析 “对数与对数运算”作为高一新教材的内容,被安排在第一册第二章“基本初等函数”的第二节,共分三个课时完成,对数概念为第一课时．对数概念对于高一的学生来讲是一个全新的概念．此前,学生已学习了指数及指数函数,明白了指数运算是已知底数和指数求幂值,而对数则是已知底数和幂值求指数,二者是互逆的关系．对数概念的引入,以凸显高中数学新课程理念中的“运算思想”和“函数思想”,对数概念的学习,既加深了学生对指数的理解,又为后面对数的运算性质及对数函数的学习做了充分准备,起到了承上启下的作用．     

基于代表性频率的介电谱解析形式

基于电介质复折射率的实验数据,采用晟小二乘法结合选取的代表频率拟合得到了电介质的介电谱解析表达式,可以得到电介质在全频段的光频常数和介电常数．研究了三个典型液态电介质,水、乙醇和甲苯的介电谱．在实验数据可以获取的频率范围内,采用解析表达式得到的光频常数与采用Kramers—Kronig转换得到的折射率实部和实验得到的折射率虚部吻合得很好．基于介电谱解析表达式可以预测目前实验无法测量的区域的介电谱．     

Wavelength-dependent Photodissociation Dynamics of Benzaldehyde

The ultrafast dynamics of benzaldehyde upon 260, 271, 284, and 287 nm excitations have been studied by femtosecond pinup-probe time-of-flight mass spectrometry. A bi-exponential decay component model was applied to fit the transient profiles of benzaldehyde ions and fragment ions. At the S2 origin, the first decay of the component was attributed to the internal conversion to the high vibrational levels of S1 state. Lifetimes of the first component decreased with increasing vibrational energy, due to the influence of high density of the vibrational levels. The second decay was assigned to the vibrational relaxation of the S1 whose lifetime was about 600 fs. Upon 287 nm excitation, the first decay became ultra-short （-56 fs） which was taken for the intersystem cross from S1 to T2, while the second decay component was attributed to the vibrational relaxation. The pump-probe transient of fragment was also studied with the different probe intensity at 284 nm pump.     

边界元法计算切口多重应力奇性指数

提出采用边界元法直接计算V形切口的多重应力奇性指数。首先在切口尖端挖出一微小扇形域,在该域边界列常规边界积分方程,后将扇形域内的位移场和应力场表示成关于切口尖端距离ρ的渐近级数展开式,回代入切口边界积分方程,离散后得到关于切口奇性指数的代数特征方程,从而求解获得V形切口的应力奇性指数。该法避免了常规边界元法和有限元法在切口尖端附近布置细密单元的缺陷,并可同时求得多阶应力奇性指数。     

具有指数型弱耦合时滞系统的同步分支周期解

利用F loquet指数理论,研究了一类弱耦合时滞系统的参数在不同情况下同步分支周期解的稳定性。分别讨论了非耦合时滞系统分支周期解的存在性,稳定性及其近似表达式。通过实例利用MATLAB给出模型分支周期解的仿真图形,并分析了各参数对图形的影响。     

Vibrations of FGM thin cylindrical shells with exponential volume fraction law

In this paper, the influence of an exponential volume fraction law on the vibration frequencies of thin functionally graded cylindrical shells is studied. Material properties in the shell thickness direction are graded in accordance with the exponential law. Expressions for the strain-displacement and curvature-displacement relationships are taken from Love＇s thin shell theory. The Rayleigh-Ritz approach is used to derive the shell eigenfrequency equation. Axial modal dependence is assumed in the characteristic beam functions. Natural frequencies of the shells are observed to be dependent on the constituent volume fractions. The results are compared with those available in the literature for the validity of the present methodology.     

V形切口应力强度因子的一种边界元分析方法

将V形切口结构分成围绕切口尖端的小扇形和剩余结构两部分. 尖端处扇形域应力场表示成关于尖端距离$\rho$的渐近级数展开式,从线弹性理论方程推导出了一组分析平面V形切口奇异性的常微分方程特征值问题,通过求解特征方程,得到前若干个奇性指数和相应的特征向量. 再将切口尖端的位移和应力表示为有限个奇性阶和特征向量的组合. 然后用边界元法分析挖去小扇形后的剩余结构. 将位移和应力的线性组合与边界积分方程联立,求解获得切口根部区域的应力场、应力幅值系数和整体结构的位移和应力. 从而准确计算出平面V形切口的奇异应力场和应力强度因子.      

互相关DPIV亚像素匹配方法研究

使用传统互相关法对DPIV粒子图像进行粗匹配,取得整像素匹配结果,在此基础上开展亚像素定位方法研究.将最小二乘匹配法应用到DPIV技术中,获得比经典的高斯曲面、二次多项式拟合法更高的估算精度,弱化算法对粗匹配相关测度的依赖性.通过控制初始位置和匹配精度降低最小二乘算法的时间开销.标准图像仿真实验以及在氧化沟模型实验中的成功应用,验证了最小二乘匹配法在DPIV技术中的有效性和可靠性.     

A new control law based on characteristic exponent assignment for libration point orbit maintenance

A new method is developed for stabilizing motion on collinear libration point orbits using the formalism of the circular restricted three body problem. Linearization about the collinear libration point orbits yields an unstable linear parameter-varying system with periodic coefficients. Given the variational equations, an innovative control law based on characteristic exponent assignment is introduced for libration point orbit maintenance. A numerical simulation choosing the Richardson＇s third order approximation for a halo orbit as a nominal orbit is conducted, and the results demonstrate the effectiveness of this control law.