Exact solutions using symmetry methods and conservation laws for the viscous flow through expanding–contracting channels

We present a range of definitions and methods dealing with the reduction of partial differential equations on the basis of the underlying symmetry structure, conservation laws and a combination of these. The method is used to reduce a complex system to an easy-to-handle second-order ordinary differential equation system independent of restrictions on any physical parameters. In particular, we construct exact solutions of a system modelling viscous flow between slowly expanding and contracting walls.     

Generalized mix functions and orthogonal equitable rectangles

Ristenpart and Rogaway defined “mix” functions, which are used to mix inputs from two sets of equal size, and produce outputs from the same two sets, in an optimal way. These functions have a cryptographic application in the context of extending the domain of a block cipher. It was observed that mix functions could be constructed from orthogonal latin squares. In this article, we give a simple, scalable construction for mix functions. We also consider a generalization of mix functions, in which the two sets need not be of equal size. These generalized mix functions turn out to be equivalent to an interesting type of combinatorial design which has not previously been studied. We term these “orthogonal equitable rectangles” and we construct them for all possible parameter situations, with a small number of exceptions and possible exceptions. Research supported by NSERC discovery grant 203114-06.     

基于模拟退火算法的矩形优化排样问题的研究

考虑了一种矩形优化排样系统中遗传算法和模拟退火算法的结合算法.首先建立了该系统的通用数学模型.然后给出了求解该问题的遗传模拟退火算法.最后用VC++6.0模拟算例的结果表明该算法是一种行之有效的方法.     

平行光斜入射光栅(矩孔)的衍射光场

在"衍射光栅光栅常量的测定"实验中用矩孔代替光栅,利用菲涅尔-基尔霍夫积分公式,计算出平行光以任意倾斜角度入射后的光场分布公式,当平行光斜入射且接收屏与矩孔平面平行时,光斑分布图形为双曲线,并结合实验图像和计算机模拟,很好地验证了公式的正确性,解释了实验中观察到的现象.     

Hardness of approximation for orthogonal rectangle packing and covering problems

Bansal and Sviridenko [N. Bansal, M. Sviridenko, New approximability and inapproximability results for 2-dimensional bin packing, in: Proceedings of the 15th Annual ACM–SIAM Symposium on Discrete Algorithms, SODA, 2004, pp. 189–196] proved that there is no asymptotic PTAS for 2-dimensional Orthogonal Bin Packing (without rotations), unless P=NP. We show that similar approximation hardness results hold for several 2- and 3-dimensional rectangle packing and covering problems even if rotations by ninety degrees are allowed. Moreover, for some of these problems we provide explicit lower bounds on asymptotic approximation ratio of any polynomial time approximation algorithm. Our hardness results apply to the most studied case of 2-dimensional problems with unit square bins, and for 3-dimensional strip packing and covering problems with a strip of unit square base.     

Ca-Tb4O7-Fe体系中生成TbFe2的动力学研究

高纯TbFe2 可以作为生产 (TbDy)Fe2 的一种中间合金原料。开发低成本、无污染、直接从氧化铽还原制备高纯TbFe2 的方法具有非常重要的实际意义。本文在已有关于Ca Tb4O7 Fe体系 ,还原扩散法制备TbFe2 合金在热力学上可能的基础上 ,进一步研究了其动力学可行性。XRD物相鉴定证明生成物是TbFe2 ;应用收缩核模型得知 :扩散是反应的控制步骤 ,表观活化能Ea=39kJ·mol- 1 。     

股价崩盘风险、投资者保护与银行贷款契约

本文使用2013~2017年中国非金融上市公司数据,考察股价崩盘风险、投资者保护与银行贷款契约之间的关系。研究发现,股价崩盘风险越高,贷款利率越高,贷款期限越短,更不可能使用信用贷款担保。此外,良好的投资者保护会缓解股价崩盘风险对银行贷款契约的负面影响。进一步研究发现,投资者保护对股价崩盘风险与银行贷款契约之间关系的影响在非国有企业和非主板市场中更加明显。     

一维矩形受限光量子阱光传输特性的研究

结合分离变量法和薄膜光学理论推导了一维矩形受限光量子阱的传输矩阵,并分析了一维矩形受限光量子阱结构的传输特性.计算结果表明:相对于非受限光量子阱结构来说,受限光量子阱的带隙和束缚态向高频方向移动,且束缚态的数目也与阱光子晶体的周期数相同.束缚态的频率随模式量子数的增加而线性增加,随矩形边长参量的增加而呈Lorentz函...     

磁场力作用下胀缩可渗透壁面管道非稳态流动摄动解

分析了磁场力作用下胀缩可渗透管道中的不可压缩流动．应用相似变换,控制方程被转换成非线性常微分方程,得到不同的膨胀率和Hartmann数下的奇异摄动解,并对相关的流动特征进行了详细的分析．