CM⁃Phos配体在钯催化交叉偶联反应中的应用

本文综合评述了近年来2-[2-(二环己膦基)苯基]-1-甲基-1H-吲哚(CM-Phos)膦配体及其衍生物在钯催化的交叉偶联反应中的应用, 主要根据不同种类的交叉偶联反应进行系统性分述, 并对该领域的发展前景进行了展望.     

具有性质cr+1=3,ar+1=3a+1或 4a的(a+1,3)型距离正则图

设г是直径为d且型为(a 1,3)的距离正则图,其中a≥2.用l(c,a,b)表示交叉阵列ι(г)中列(c,a,6)t的个数,记r=r(г)=l(c1,a1,b1),8=8(г)=l(Cr 1,ar 1,br 1)及t=t(г)=l(cr s 1,ar s 1,br s 1).那末,若Cr 1=3,ar 1=4a或3a 1,则d=r t 2.     

带有相依重尾冲击的Poisson噪音过程尾的一致渐近性质

本文考虑了带有某种相依重尾冲击的Poisson噪音过程尾的一致渐近性质.当冲击是二元上尾渐近独立的非负随机变量具有长尾和控制变化尾分布且噪音函数具有正的上下界时,得到了过程尾概率的一致渐近公式.进而,当冲击具有连续的一致变化尾分布时,去除了噪音函数具有正的下界的限制.对于噪音函数不一定具有正的上界的情形,当冲击具有两两负象限相依结构时,也得到了一致渐近性结果.     

Nonlinear Exact Solutions of the 2-Dimensional Rotational Euler Equations for the Incompressible Fluid

In this paper, the Clarkson–Kruskal direct approach is employed to investigate the exact solutions of the2-dimensional rotational Euler equations for the incompressible fluid. The application of the method leads to a system of completely solvable ordinary differential equations. Several special cases are discussed and novel nonlinear exact solutions with respect to variables x and y are obtained. It is of interest to notice that the pressure p is obtained by the second kind of curvilinear integral and the coefficients of the nonlinear solutions are solitary wave type functions like tanh(kt/2)and sech(kt/2) due to the rotational parameter k = 0. Such phenomenon never appear in the classical Euler equations wherein the Coriolis force arising from the gravity and Earth's rotation is ignored. Finally, illustrative numerical figures are attached to show the behaviors that the exact solutions may exhibit.     

通识化学:有机物燃烧方程式的简易配平法

在通识化学的教学层面上,面向不同背景的学生,以简单有机物完全燃烧的化学方程式的配平为主题,梳理数学方法在化学方程式配平中的应用和特点,采用跨学科的方式,让学生能从不同的角度进行思考和学习,以掌握数学方法在化学中的应用。     

圆孔的菲涅耳衍射

得到了圆孔菲涅耳衍射光强分布的表达式,此式由贝塞尔函数的数列(或Lommel函数)给出,因此很容易利用普及的数学软件算出结果.并且利用CCD照相机量度了衍射光强分布,与运算的结果作了比较,也与Burch在1985报导的结果作了比较.     

Study of Defect-Layers Effect in Ferroelectric Thin Film with TransverseIsing Model

By taking into account the two-spin interaction in the transverse Ising model (TIM), the influence of the defect layers (including J_B andΩ_B on the polarization and Curie temperature are calculated numerically, within the framework of the decoupling approximation under Green's function. The numerical results show that the polarization and Curie temperature will both become large sensitively due to the large values ofJ_B and the small value of Ω_B of the defect layers. Meanwhile, the dependence of the crossover values of the exchange interaction J_A, the transverse field Ω_Aof the bulk material on the exchange
interaction J_B and the transverse fieldΩ_B of the defect layers are shown in 3-Dimensional (3-D) figures for the first time. Moreover, the transition features of the ferroelectric thin film with defect layers are presented.     

Bivariational Methods for Hammerstein Integral Equations

Bivariational methods are presented for nonlinear integral equationsof Ham-merstein type = Kf(). With appropriate conditions onK and f, various upper and lower bounding functionals are derivedfor inner products and associated with the solution . Inthe latter case, suitable choices for g lead to point wise boundson both and its derivative. The methods are tested on a pendulumequation, and encouraging accuracy is obtained using simpletrial vectors.