Fixed points of smoothing transformation in random environment

At each time n\in \mathbb{N},\mathrm{l}\mathrm{e}\mathrm{t}{\overline{Y}}^{(n)}(\xi )=(y_1^{(n)}(\xi ),y_2^{(n)}(\xi ),\cdots ) be a random sequence of non-negative numbers that are ultimately zero in a random environment\xi \text{=}（{\xi }_n{）}_{n\in \mathbb{N}}. The existence and uniqueness of the nonnegative fixed points of the associated smoothing transformation in random environment are considered. These fixed points are solutions to the distributional equation for a.e.\xi ,Z(\xi )\stackrel{\text{d}}{=}{\sum }_{i\in \mathbb{N}+}{y}_i^{(\mathrm{0})}(\xi )Z_i^{(\mathrm{1})}(\xi ),where ｛Z_i^{(\mathrm{1})}:i\in {\mathbb{N}}_{+}｝ are random variables in random environment which satisfy that for any environment\xi; under P_{\xi }; ｛Z_i^{(\mathrm{1})}:i\in {\mathbb{N}}_{+}｝are independent of each other and {\bar{Y}}^{(\mathrm{0})}(\xi ), and have the same conditional distribution P_{\xi }(Z_i^{(1)}(\xi )\in \cdot )=P_{T\xi }(Z(T\xi )\in \cdot ) where T is the shift operator. This extends the classical results of J. D. Biggins [J. Appl. Probab., 1977, 14: 25-37] to the random environment case. As an application, the martingale convergence of the branching random walk in random environment is given as well.     

Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

量子体系的相空间规范变换

外尔于1918年引入的规范变换实际上是相位变换而非真正的尺度变换,但规范不变性、规范理论等概念都沿袭了下来.我们发现,针对由量子化条件[x,p]=i(h)而来的量子体系之本征值问题存在规范变换,或者说尺度变换,x→x/α,p→αp,该变换保体系的能量谱不变.量子谐振子、氢原子问题及一类多体问题的精确解析解证实了这一点....     

非牛顿幂律流体有界双重介质渗流模型实空间解析解与样版曲线

在前人工作的基础上,建立了非牛顿幂律流体有界双重介质试井模型.根据模型的特点,提出了相应的特征值问题,求出了特征值和特征函数.定义了油层压力关于空间变量的正交积分变换.根据特征函数系的完备正交性和矩阵微分方程理论,获得了油层压力分布以及井底压力,压力导数的实空间解析解(无穷级数形式).首次直接根据实空间解析解绘制了样版曲线,并在同一张双对数坐标纸上描出拉普拉斯方法制作的样版曲线,同时给出二者间的误差走势图.通过对比分析发现,随着级数项数的增大,根据解析解制作的样版曲线逐渐逼近拉普拉斯方法制作的样版曲线.新疆油田实例证实了该方法的有效性.研究结果进一步补充,完善了试井分析理论.     

磁单极与磁洛伦兹力

概述了磁单极概念的历史发展,从洛伦兹变换出发,利用电磁场张量和四维力的协变性以及电荷相对论不变,直接证明了运动磁单极受磁洛伦兹力,建议了一个磁洛伦兹力的验证方案,并用磁洛伦兹力公式导出狄拉克电荷量子化条件．证明了磁洛伦兹力公式具有与库仑定律相同的精确度．     

一类矩阵多项式的秩特征

给出了一类矩阵多项式的秩特征定理及它的多种证法.     

Supramolecular Coordination Cages Based on N-Heterocyclic Carbene-Gold(I) Ligands and Their Precursors: Self-Assembly,Structural Transformation and Guest-Binding Properties

The incorporation of functional groups into the cavity of discrete supramolecular coordination cages (SCCs) will bring unique functions and applications. Here, three dicarboxylate ligands (H₂ L1 Cl, H₂ L2 Cl and H₂ L3 Cl) containing N-heterocyclic carbene (NHC) precursors as linkers were introduced to construct SCCs by combining with two C₃-symmertic (CpZr)₃(μ₃-O)(μ₂-OH)₃ clusters as three-connect vertices, resulted in a series of rugby-like V₂E₃ (V=vertex, E=edge) type homoleptic cages ( SCC-1 , SCC-2 and SCC-3 ). However, V₄E₆-type tetrahedral cages ( SCC-4 and SCC-5 ), incorporating six Au-NHC moieties, were obtained when the corresponding NHC-gold(I) functionalized ligands (H₂ L1 ^Au, H₂ L2 ^Au) were applied. For the first time, we present a trackable CpZr-involved cage to cage conversion to generate a heteroleptic V₂E₃ cage ( SCC-6 ) from two homoleptic cages ( SCC-2 and SCC-5 ) with different geometries of V₂E₃ and V₄E₆. The heteroleptic assembly SCC-6 can also be formed upon a subcomponent displacement strategy. The structural transformation and reassembly processes were detected and monitored by ¹H NMR spectroscopy and electrospray-ionization mass spectrometry. The formation of heteroleptic assembly was further supported by single crystal X-ray diffraction analysis. Moreover, homoleptic cage SCC-2 possesses a trigonal bipyramidal cationic cavity allowing the encapsulation of a series of sulfonate anionic guests.     

Thermally induced structural transformation of polytriazoleimide to polyindoleimide

A new kind of polytriazoleimide containing bisphenyl-l,2,3-triazole（BPT） was synthesized by copper-catalyzed 1,3-dipolar cycloaddition of azides and alkynes（CuAAC） and polycondensation.The thermal stability and degradation mechanism of the polytriazoleimide were investigated.The results show that the structure of BPT in polytriazoleimide transforms to phenylindole after thermal treatment,accompanying the release of N₂.     

优化MGM(1,n)模型及其应用研究

从最小二乘估计的适用条件出发,在建立MGM(1,n)模型前,先采用BoxCox变换对原始数据进行变换,以解决或缓解误差项的正态性偏离问题.首先,以模型拟合平均误差最小化为目标,建立非线性优化模型,在参数的置信区间内,应用PSO(Particle Swarm Optimization)算法求最优解.然后,应用求解得到的参数,建立优化MGM(1,n)模型.在实例分析中,将优化MGM(1,n)模型应用于深基坑围护结构变形预测,实验结果表明通过对原始数据做合适的Box-Cox变换,能够有效提高模型的拟合及预测精度,拓广多变量灰色预测模型的适用范围.     

组合发电仪的制作

仪器应用生活中常见的材料,仅仅围绕物理学科知识,通过巧妙设计,组装出一系列发电机。旨在让学生明白各种发电机的工作原理,以及能量之间是如何相互转化的,培养学生节约能源,保护环境利用清洁能源的意识。此外本仪器制作简单,便于学生亲手制作,锻炼动手能力的同时,又可提高学习兴趣。