自由微观粒子相对论

给出自由微观粒子的时空变换理论和自由微观粒子的相对论能量表示.     

一个1+1维Boussinesq系统的Darboux变换及其应用

主要考虑1+1维Boussinesq系统的一个Darboux变换,反复利用该Darboux变换,可以从该系统的一个已知解出发,通过代数运算和求导运算得到系统的新解.     

6×n阶矩形网络等效电阻猜想的证明

任意k×n阶电阻网络等效电阻的公式研究属于科学难题,到目前为止已经获得了当k=1,2,…,5时的5种情形下的等效电阻公式,但对k≥6时的等效电阻的普适公式仅仅作为猜想给出.本文根据建立的任意k×n阶电阻网络等效电阻研究的方法,证明了k=6时的等效电阻公式的正确性,并且给出了其无穷网络的等效电阻公式,在对比验证时得到了一些新的三角恒等式.     

一道三角题解法的探讨

题目在△ABC中,已知sinA/cosB＋sinB/cosA=2,判断△ABC的形状,并给出证明（以下简称＂题＂）.这是一道传统老题,因涉及三角的方方面面而深得高三师生的心仪.在高考复习中本人亦情有独钟地选择了她,作为训练学生三角恒等变换与解三角形的代表＂作＂.分析直觉思维显示：A与B是互为余     

New method to solve electromagnetic parabolic equation

This paper puts forward a new method to solve the electromagnetic parabolic equation （EMPE） by taking the vertically-layered inhomogeneous characteristics of the atmospheric refractive index into account. First, the Fourier transform and the convo- lution theorem are employed, and the second-order partial differential equation, i.e., the EMPE, in the height space is transformed into first-order constant coefficient differential equations in the frequency space. Then, by use of the lower triangular characteristics of the coefficient matrix, the numerical solutions are designed. Through constructing ana- lytical solutions to the EMPE, the feasibility of the new method is validated. Finally, the numerical solutions to the new method are compared with those of the commonly used split-step Fourier algorithm.     

图的移边变换与原子键连通性指数的关系

设G是简单图,对G中任意顶点v,d_v表示v的度数.图G的ABC指数定义为ABC(G)=∑_(uv∈E(G))((d_u+d_v-2)/(d_ud_v))^(1/2).讨论了对图进行移边变换后其ABC指数的变化情况.     

A Novel Mixed-valence and Capped-keggin Structural Polyoxometal Complex： {[Co（dien）]4- [（PO4）MoVs（WVI0.56 noVI0.44）4033（OH）3]}.nH2O （n ≈ 1）

A novel inorganic-organic hybrid compound, {[Co（dien）]4[0aO4）MoV8（wV10.56MoV10.44）4- O33（OH）3]}＇nH20 （1, n = 1, dien = diethylenetriamine）, has been synthesized hydrothermally and characterized by single-crystal X-ray diffraction. Compound 1 crystallizes in the triclinic system with a = 11.927（2）, b = 13.328（3）, c = 19.306（4）A, a = 93.76（3）, β = 94.14（3）, γ = 109.99（3）°, V= 2863.2（12） A3, space group P1 and Z = 2 at 173 K. The final full-matrix least-squares refinement converged to R = 0.049 for 9621 observed reflections with 1 〉 2σ（I） and wR = 0.139 for all data （9871） and S = 1.073. Crystal structure analysis shows that 1 contains a kind of the first reported mixed-valence and molybdenum-tungsten mixed-distributed e-Keggin structural polyanion capped by four Co（dien） fragments with the main group element P occupying the center site. These results were further confirmed by energy-dispersive X-ray spectroscopy （EDS）, X-ray powder diffraction （XRD）, Fourier transform infrared spectroscopy （FTIR）, Raman spectroscopy, Thermogravimetry （TG） and X-ray photoelectron spectroscopy （XPS） analyses.     

涉及周期函数积分的变换公式

受到一则积分计算的启发,提出了能应用于周期函数积分的变换公式,包括其等价形式,建立起周期函数在半周期内的积分与相应的无穷积分之间的变换公式,给出了计算这类积分的新途径.