计算富勒烯结构的新方法:曲率定理*

介绍了利用曲率定理计算富勒烯结构的方法,证明了富勒烯结构中五元环数恒为12,与传统的欧拉定理法进行了对比,凸显了曲率定理法在研究多面体结构时直观形象的特点,强调了数学方法对解决化学问题和认识化学模型的重要性。     

Weak Euler Approximation for Itô Diffusion and Jump Processes

This article studies the rate of convergence of the weak Euler approximation for Itô diffusion and jump processes with Hölder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in Hölder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.     

Euler方程的解在Besov空间上的存在性和惟一性

利用交换子及不可压缩流的性质,得到了Eu ler方程在Besov空间的端点情形时存在性和惟一性.     

带次线性中立项的二阶广义Emden-Fowler微分方程的Philos型振动准则

研究一类带次线性中立项的二阶非线性广义Emden-Fowler时滞微分方程的振动性.利用Riccati变换和不等式技巧,在非正则条件下建立了该类方程多个简便的Philos型和Kamenev型新振动准则.所得定理也适应于包括经典Euler方程等线性非中立型方程,推广和改进了已有文献中的相应结果.最后还给出应用实例展示了所...     

Aeroelastic analysis of cantilever plates using Peters’ aerodynamic model,and the influence of choosing beam or plate theories as the structural model

In this paper, the aeroelastic analyses of a rectangular cantilever plate of varying aspect ratio is presented. The classical plate theory has been selected as the structural model. The main point that distinguishes this study from previously reported research is employing Peters’ theory to model aerodynamic effect which is not straightforward. The Peters’ aerodynamic model was originally developed to provide lift and moment, which is only applicable to the structural model based on the beam theories. In this study, using the basic concept of the Peters’ aerodynamic model in addition to utilizing the Fourier series, the pressure distribution is derived, which makes Peters’ model applicable to structural models based on plate theory. This combination provides a much simpler state–space aeroelastic model for plates in comparison to the prevalent panel methods, which could lead to a significant reduction in computational time. In addition, the aeroelastic response of the plate with respect to changes in the structural model from the beam theory to the plate theory is evaluated. By using data from an experiment carried out at Duke University, the theoretical results are evaluated. Furthermore, the differences in structural models obtained from the plate and beam theories can be divided into two distinct parts, which are responsible for differences in bending and torsional behaviors of the structure, separately. This approach enables us to measure the effects of differences of each behavior separately, which could provide with a new insight into the problem. It has been determined that the flutter speeds obtained from the beam and plate aeroelastic models are little affected by the difference in bending behavior, but rather is mainly caused by the difference in torsional frequencies.     

非线性双曲型守恒律的高精度MmB差分格式

构造了一维非线性双曲型守恒律方程的一个高精度、高分辨率的广义G odunov型差分格式。其构造思想是:首先将计算区间划分为若干个互不相交的小区间,再根据精度要求等分小区间,通过各细小区间上的单元平均状态变量,重构各等分小区间交界面上的状态变量,并加以校正;其次,利用近似R iem ann解算子求解细小区间交界面上的数值通量,并结合高阶R unge-K u tta TVD方法进行时间离散,得到了高精度的全离散方法。证明了该格式的Mm B特性。然后,将格式推广到一、二维双曲型守恒方程组情形。最后给出了一、二维Eu ler方程组的几个典型的数值算例,验证了格式的高效性。     

Pole placement controllers for linear time-delay systems with commensurate point delays

This paper investigates the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled diophantine equations of polynomials. An extra complexity is incorporated to the above design to cancel extra unsuitable dynamics being generated when solving the above diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delaydependent) closed-loop spectrum. However, if the controller is simplified by deleting the above mentioned extra complexity, then the robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is maintained. In the current approach, the finite spectrum assignment is only considered as a particular case to the designer‘s choice of a (delay-dependent) arbitrary spectrum assignment objective.     

图的倍图与补倍图

计算机科学数据库的关系中遇到了可归为倍图或补倍图的参数和哈密顿圈的问题．对简单图C,如果V（D（G））：V（G）∪V（G′）E（D（G））=E（C）∪E（C″）U{vivj′｜vi∈V（G）,Vj′∈V（G′）且vivj∈E（G））那么,称D（C）是C的倍图,如果V（D（G））=V（C）∪V（G′）,E（D（C））：E（C）∪E（G′）∪{vivj′}vi∈V（G）,vj′∈V（G’）and vivj∈（G））,称D（C）是G的补倍图,这里G′是G的拷贝．本文研究了D（G）和D的色数,边色数,欧拉性,哈密顿性和提出了D（G） 的边色数是D（G）的最大度等公开问题．     

待定系数法在三角函数积分计算中的应用

运用复分析方法,首次给出了一类由三角函数、指数函数与幂函数乘积的线性组合产生的函数在某个区间上恒为零的充分必要条件证明,建立了此类函数积分计算的理论基础,结合微分和线性代数思想,系统讨论了待定系数法在一类含有三角函数的积分计算中的应用.