溃坝问题的间断有限元方法

本文研究90年代初提出的Runge-Kutta间断Galerkin有限元方法，给出该方法的精度分析，通过经典算例验证该方法处理间断问题、捕捉锐利波形的能力，并将其推广到求解浅水问题．针对坝底无摩擦，无坡度的理想情形进行讨论，给出方溃坝和圆溃坝问题的数值模拟结果．     

Effects of electron-interface-phonon interactions on interactions between electrons in double-heterostructures

Effects of electron-interface-phonon interaction on the interaction between electrons in double heterostructures are considered. It is found that the interaction potential between electrons caused by each of four interface-phonon modes is different. For electrons moving at the two interfaces of double heterostructure, the interaction energies of the electrons produced by the interaction with antisymmetric modes are positive which indicate that the forces between electrons are repulsive. The interaction energies caused by interaction with symmetric modes are negative and the forces are attractive. The resultant of the forces are attractive and become larger when the width of potential barrier decreases for InAs/GaSb/InAs double heterostructure.     

Relations among eigenvalues of Sturm-Liouville problems with different types of leading coefficient functions

For any Sturm-Liouville problem with a separable boundary condition and whose leading coefficient function changes sign (exactly once), we first give a geometric characterization of its eigenvalues λn using the eigenvalues of some corresponding problems with a definite leading coefficient function. Consequences of this characterization include simple proofs of the existence of the λn's, their Prüfer angle characterization, and a way for determining their indices from the zeros of their eigenfunctions. Then, interlacing relations among the λn's and the eigenvalues of the corresponding problems are obtained. Using these relations, a simple proof of asymptotic formulas for the λn's is given.     

A new auxiliary equation and exact travelling wave solutions of nonlinear equations

A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein–Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham–Broer–Kaup equations.     

Equation of state of the hard-disk fluid on a sphere from Percus–Yevick equation

The Percus–Yevick equation is solved numerically for hard disks on a sphere. The effect of curvature of the hosting surface is calculated, and an empirical correction to the equation of state is proposed.     

可溶性汞化苯乙烯－丙烯酸甲酯共聚物的合成

用自由基溶液降合方法制备一系列苯乙烯－丙烯酸甲酯线型共聚物，用核磁共振测定了苯基在共聚物中的百分比，在该共聚物的四氢呋喃溶液中，用三氟乙酸汞在共聚物的苯环上进行亲电取代反应，得到可溶性汞化共聚物，由于这类泵化共的可溶于四氢呋喃，二氯甲烷等溶剂，用重沉淀法多次提纯，得到了纯度很高，溶解性较好的含重金属二价汞的共聚物，用红外光谱仪测定共聚物上的汞基团，用原子吸收定量测试共聚中的汞的百分聚代率，结果表明     

钙钛矿型LaNiO3、LaMnO3的形成条件

用混合硝酸盐分解法和柠檬酸络合法分别制取了单一钙铁矿型多晶粉末LaNiO_3和LaMnO_3. XRD分析表明LaNiO_3的形成经历了混合氧化物转化为LaNiO_3的同相反应; 而LaMnO_3晶相直接由无定形相转化而来。根据DTA、TG、IR分析两者的形成, NO_3~-离子都起了重要作用. 同时讨论了络合剂柠檬酸的作用.     

四核钴羰基簇合物Co4(CO)8(μ-CO)2(μ4-PSR)2的合成和晶体结构

The title compounds Co4(CO)8(μ-CO)2 (μ4-PSR) [R=-CH3, -C2H5, -C(CH3)3,-(CHa)4CH3] were synthesized by the reaction of Co2(CO)8 with RSPCl2. They were characterized by IR, 1HNMR, elemental analysis. The crystal and molecular structure of Co4(Co)8(μ-CO)2 (μ4-PSC2H5) has been determined by single crystal diffraction method. Crystal data: monoclinic, space group P21 /c, with a=8-445(3), 6=8.562(3), c= 17.125(6)Å, β=104.26 (3)' 9 V=1200.1Å3, Z=2, Dc=1.937gcm-3. Its molecular structure contains an octahedral Co4P2 skeleton which consists of a rectangular four cobalt atoms core and the Co4 core is capped above and below by two quadruply bridging PSR ligands.     

SinH/SinH-(n=3～8)的结构和电子亲合能的研究

选用四种不同的密度泛函理论方法(B3LYP，B3P86，BLYP，BP86)，在全电子的双ξ加极化加弥散函数基组(DZP )下，对SinH／SinH^-(n=3～8)体系进行研究，获得它们的基态结构和电子亲合能。预测Si3H／Si3H^-,Si4H／Si4H^-,Si5H／Si5H^-,Si6H／Si6H^-，Si7H／Si7H^-和Si8H／Si8H^-的基态结构分别为C2v(^2B2)／C2v(1^A1)氢桥结构，Cs(^2A’)／C(^1A’)，C2v(^2B2)／C2v(^1A1)，C2v(^2B2或^2B1)／C4v(^1A1)，C5v(^2A1)／C5v(^1A1)和C5(^2A‘‘)／C3v(^1A1)。在电子亲合能方面，B3LYP方法预测的电子亲合能是最可靠的，预测Si3H，Si4H，Si5H，Si6H，Si7H和Si8H的电子亲合能分别为2．56，2．59，2．84，2．86，3．19和3．14eV。     

Lanthanide MOFs for inducing molecular chirality of achiral stilbazolium with strong circularly polarized luminescence and efficient energy transfer for color tuning

We present herein an innovative host–guest method to achieve induced molecular chirality from an achiral stilbazolium dye (DSM). The host–guest system is exquisitely designed by encapsulating the dye molecule in the molecule-sized chiral channel of homochiral lanthanide metal–organic frameworks (P-(+)/M-(−)-TbBTC), in which the P- or M-configuration of the dye is unidirectionally generated via a spatial confinement effect of the MOF and solidified by the dangling water molecules in the channel. Induced chirality of DSM is characterized by solid-state circularly polarized luminescence (CPL) and micro-area polarized emission of DSM@TbTBC, both excited with 514 nm light. A luminescence dissymmetry factor of 10⁻³ is obtained and the photoluminescence quantum yield (PLQY) of the encapsulated DSM in DSM@TbTBC is ∼10%, which is close to the PLQY value of DSM in dilute dichloromethane. Color-tuning from green to red is achieved, owing to efficient energy transfer (up to 56%) from Ln³⁺ to the dye. Therefore, this study for the first time exhibits an elegant host–guest system that shows induced strong CPL emission and enables efficient energy transfer from the host chiral Ln-MOF to the achiral guest DSM with the emission color tuned from green to red.

Homochiral Ln-MOFs are synthesized to encapsulate achiral dyes to induce strong circularly polarized luminescence with a luminescence dissymmetry factor of 10⁻³.