THE COLLOCATION METHODS FOR SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNELS

1 Introduction Singular integral equations (SIEs) with Cauchy kernels Of the formoften arise in mathematical models of physical phenomena. Since closed-form solutions to SIEsare generally not available, much att.ntion has been focused on numerical methods of solution.In the past twenty years, various collocation methods for SIEs have been the topic of a greatmany of papers, most of which can be found in two surveys[213]. The early works in the fieldis to study tile numerical solutions for…     

弹塑性损伤结构耦合分析的虚功原理和线性互补解法

从弹塑性损伤力学的瞬态边值问题的虚位移原理出发,利用有限元技术,导出了弹塑性损伤结构分析的线性互补方程,并给出了有限元算法.这一方法适用于解决硬化、软化及非关联流动等非线性材料的损伤结构分析.     

高精度隐式参差光滑格式的构造

参照Lax-Wendroff格式的构造方法,就双曲型方程、抛物型方程和双曲-抛物型方程,构造了一种新的IRS(implicit residual smoothing)格式。该IRS格式有二阶或三阶时间精度且大大地拓宽了解的稳定区域和CFL数。这种新的IRS格式有中心加权型和迎风偏向型两种,并用von-Neumann分析方法分析了格式的稳定范围。讨论了在透平机械中广泛应用的Dawes方法的局限性,发现该方法对稳态问题得出的解与时间步长的选取有关,对粘性问题求解时,时间步长受严格限制。最后,结合TVD(total variation diminishing)格式和四阶Runge-Kutta技术,用IRS格式和Dawes方法对二维反射激波场进行了数值模拟,数值结果支持本文的分析结论。     

Banach空间二阶常微分方程两点边值问题迭代求解

本文利用一些新的微分和积分不等式研究Ｂａｎａｃｈ究竟中二阶常微分方程两点边值问题解的存在唯一性,给出了解的迭代序列和误差估计式。     

Characteristics of selective oxidation during the fabrication of vertical cavity surface emitting laser

Taking into account oxidation temperature, N₂ carrier gas flow, and the geometry of the mesa structures this paper investigates the characteristics of selective oxidation during the fabrication of the vertical cavity surface emitting laser (VCSEL) in detail. Results show that the selective oxidation follows a law which differs from any reported in the literature. Below 435℃ selective oxidation of Al_0.98Ga_0.02As follows a linear growth law for the two mesa structures employed in VCSEL. Above 435℃ approximately increasing parabolic growth is found, which is influenced by the geometry of the mesa structures. Theoretical analysis on the difference between the two structures for the initial oxidation has been performed, which demonstrates that the geometry of the mesa structures does influence on the growth rate of oxide at higher temperatures.     

利用H3PO4液层侧面红外热像研究YBCO高温超导薄膜的激光辅助刻蚀特性

利用红外热像实时监测系统,获取钇钡铜氧激光辅助化学刻蚀中H₃PO₄液层的侧面红外热像,研究了其溶液温度分布与热对流特性,并对红外监测数据与钇钡铜氧薄膜激光化学刻蚀特性的关系进行了分析.主要实验结论包括:红外灰度图可真实反映溶液的温度分布和热对流情况,为激光化学刻蚀的热环境分析提供有价值的红外监测数据;通过任意时刻钇钡铜氧表面生成热流所到达高度的分布情况和该时刻的红外灰度图,分析出钇钡铜氧薄膜表面各区域的腐蚀启动先后和刻蚀程度差异等重要信息,为钇钡铜氧及其它材料的激光化学刻蚀特性的实时监测提供了一种新的技术手段.     

New Operator Identities and Combinatorics Studied by Virtue of IWOP Technique

Using the coherent state representation we derive some new operator identities and study some mathematical relations in combinatorics. The technique of integral within an ordered product (IWOP) of operators plays an essential role in realizing our goal.     

General Formalism for Setting Up Unitary Transform Operators from Classical Transforms via IWOP Technique

We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too.     

香豆素分子模板聚合物的合成与性能研究

以香豆素为模板分子, α-甲基丙烯酸(MAA)、丙烯酰胺(MA)、2-乙烯基吡啶(2-VP)和4-乙烯基吡啶(4-VP)为功能单体, 二甲基丙烯酸乙二醇酯(EGDMA)为交联剂, 利用分子模板技术分别在甲苯、甲醇、氯仿和乙腈溶剂中合成了一系列香豆素分子模板聚合物(MTP), 研究了聚合体系组成对模板聚合物吸附特性的影响. 结果表明, 在所合成的模板聚合物中, 以MAA为功能单体, 乙腈为致孔溶剂, 以1∶4∶30的摩尔比加入模板分子、MAA及EGDMA时制备的模板聚合物吸附容量高、印迹效果和选择性好. 此模板聚合物有作为白芷样品中香豆素吸附分离材料的应用前景.     

红外光谱技术对广东博罗横岭山商周时期墓地出土古玉器上蜡工艺的揭示及其意义

广东博罗横岭山商周时期墓地是广东省目前所发现的最重要的商周时期墓葬群,该墓地出土的玉器样品通过一系列的科学鉴定研究后发现,玉器的红外光谱在2 960 cm-1(相对较弱)、2 920和2 853 cm-1附近出现了2～3个明显的特征性吸收峰,结合对纯蜡样品、现代上蜡玉器样品的测试比较,认为博罗横岭山墓地出土玉器在加工过程中曾经经过上蜡处理,首次揭示出商周时期岭南先民掌握了在加工中利用蜡来增加玉器美观技术的事实。