抓好数学建模竞赛 推动数学教学改革

本文通过近几年组织数学建模教学和指导学生参加竞赛的实践 ,探索抓好数学建模竞赛 ,促进数学教学改革 ,推动数学素质教育 ,提高人才培养质量的途径、措施和方法     

A complete global solution to the pressure gradient equation

We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Z. Dai, T. Zhang, Existence of a global smooth solution for a degenerate Goursat problem of gas dynamics, Arch. Ration. Mech. Anal. 155 (2000) 277-298] up to the free boundary of vacuum. We prove that the vacuum boundary is the coordinate axes.     

新型噻吩基取代卟啉的合成及其荧光光谱研究

合成了两种新型噻吩基卟啉－5，15－二（2－噻吩基）－2，8，12，18－四乙基－3，7，13，17－四甲基卟啉7a（45．1％）和5，15－二（2－联噻吩基）－2，8，12，18－四乙基－3，7，13，17－四甲基卟啉7b(61.2%),并研究了它们的光谱性质，其中荧光光谱的最大发射峰蜂都在631nm处，量子产率分别为4．1％（7a)和1．4％（7b)。     

Sn-C60薄膜的紫外吸收光谱和X-射线衍射谱分析

对Sn-C60薄膜进行紫外可见光吸收，X-射线衍射和扫描电镜的测定结果显示，薄膜样品紫外可见光吸收的两个短波段吸收峰比纯C60薄膜的吸收峰显著下降，说明Sn-C60薄膜的电子光吸收跃迁为间接跃迁，能带中有杂质能级的存在；样品的X射线衍射峰则对应于面心立方结构；扫描电镜结果显示薄膜为纳米级颗粒组成。     

介质极化的瞬时相位与振幅

求解电子运动的二阶微分方程，在旋转波近似下，介质在外场突然变化时产生的瞬态感应极化与外场同频，但相位总是落后，最大落后为π/2；振幅大小与初态有关，随时间按指数规律衰减，衰减快慢由介质的阻尼系数决定。     

基于VAGUE集多准则决策的模糊TOPSIS方法

给出了V AGUE集之间距离的新定义,在此基础上,提出一个基于V AGUE集多准则决策的模糊TOP-S IS方法,它为决策系统提供了一个有用的工具,并通过例子阐明本文方法的有效性.     

19F+27Al耗散反应中双核系统的转动与形变

测量了¹⁹F+²⁷Al耗散反应产物B,C,N,O,F和Ne的激发函数,入射束流的能量从110.25MeV到118.75MeV, 能量步长为250keV. 从产物的 能量自关联函数中提取了反应中所形成的中间双核系统的转动惯量, 与相粘模型计算的刚体转动惯量相比较, 结果表明形成的双核系统有大的形变.     

量子卡诺循环

以经典理想气体为工质的卡诺热机循环由两个等温和两个绝热过程构成，热机可逆时，它的效率为最大。本文建立一种量子卡诺热机循环模型，该量子卡诺热机循环以一维无限深势阱中极端相对论粒子系统为工质。通过分析，发现该量子卡诺热机循环中的等温和绝热过程和经典卡诺热机的等温和绝热过程具有相似之处，它的效率表达式和经典热力学的可逆卡诺热机的效率表达式也类似，只是用系统的哈密顿量的期望值即系统的能量平均值代替经典热力学中的温度。     

Formation of Interfacial Layers in LaAlO3/Silicon during Film Deposition

We have studied the interracial reactions between amorphous LaAlO3 thin films and Si substrates, using high- resolution transmission electron microscopy and x-ray photoelectron spectroscopy. It has been shown that the interracial layer between LaAlO3 film and Si substrate chemical states show that the ratio of La 4d3/2 to Al 2p is SiLaxAlyOz. The depth distributions of La, Si and Al of the interfacial layer remains unchanged with the depth compared to that of the LaAlO3 film. Moreover, the Si content, in the interracial layer gradually decreases with increasing thickness of the interracial layer. These results strongly suggest that the Al element is not deficient in the interracial layer, as previously believed, and the formation of a SiLaxAlyOz interracial layer is mainly due to the diffusion of Si from the substrate during the LaAlO3 film deposition. With the understanding of the interracial layer formation, ones can control the interface characteristics to ensure the desired performances of devices using high-k oxides as gate dielectrics.     

Paper-like Microfibrous Nickel Catalyst for Hydrogen Production via NH3 Decomposition in Fuel Cell Applications

Recently, miniature H2 generator to power fuel cells for portable/micro electronic devices and passenger propulsion has been the focus of intense research activities1-3. One of the strategies is to find simple CO-free H2 production with novel microreactor…