关于2-Hessian方程解的全局C2估计的一个注记

采用2-Hessian方程C~2估计的检验函数方法,研究了一般2-Hessian型方程σ_2(λ(D~2 u+B))=f(x,u,Du)的Dirichlet问题解的全局C~2估计.所得结果在形式上对关于2-Hessian方程C~2估计的结果做了一般化的发展,建立了该方程解的全局C~2估计,进而得到了该方程Dirichlet问题解的存在性.     

非球谐环形振子势的Schrdinger方程的解析解

量子力学中除了无限深势阱、一维线性谐振子、库仑势和三维各向同性谐振子势外,绝大部分Schrdinger方程是没有精确解的,这给具体问题的深入研究带来了很大的障碍。本文从求解Schrdinger方程的NU Method方法出发,求解了非球谐环形振子势V(r,θ)=μω2r2/2 h-2α/(2μr2) -h2βcosθ/(2μr2sin2θ)的本征方程的角向方程,获得解析解,将求解的过程大大简化;同时用特殊函数的方法求解了非球谐环形振子势的Schrdinger方程的径向方程,借以拓宽对Schrdinger方程求解方法的研究。     

关于一类二次丢番图方程的解

二次方程是一类基本的丢番图方程．本文指出了参考文献中的错误,利用Pell方程的解的一般结论,研究了一类二次丢番图方程x^2＋（x＋1）^2=Dy^2,并求出了该方程的所有正整数解．     

N-维无限深球势阱中Klein-Gordon方程和Dirac方程的解

精确求解了N-维无限深球势阱中的Klein-Gordon方程和Dirac方程,结果表明:在N-维无限深球势阱中,Klein-Gordon方程和Dirac方程的径向方程在形式上与非相对论中的三维中心场的径向方程一致,均为贝塞尔方程。通过求解Bessel方程,任意束缚态的本征函数已被获得,其解可用通常的球贝塞尔函数表示。利用径向波函数在r=a处的连续性条件,其相应的能谱公式也被发现.对于Klein-Gordon方程:En2r,l′=m2 xn2r,l′/a2,而对于Dirac方程,则En2r,l′=-m2 m2a2 xn2,l′/a2.     

Pell方程x~2-Dy~2=±2的解的递推性质

在各类不定方程中,Pell方程x2-Dy2=N是一类基础而重要的Diophantine方程,其正整数解与实二次域的基本单位以及其它代数数论理论有密切联系,对解高次丢翻图方程以及有关递推数列问题有广泛且深入的应用.利用Pell方程的基本解的性质,对方程x2-Dy2=±2的通解进行了讨论,获得了该方程解的一个三阶递推性质,证明了文献(A.Tekcan.Irish.Math.Soc.Bulletin,2004,54(1):73-89.)提出的一个猜想.最后,提出了关于Pell方程x2-Dy2=-2可解性的一些待解决的问题.     

拟线性扩散方程的不变集

目的 构造拟线性扩散方程的2个不变集和精确解.方法 利用方程和微分约束的相容性导出了方程适应集合应满足的条件.结果与结论 构造了拟线性扩散方程的2个不变集,继而讨论了几种情况,同时给出了几类导出方程及其精确解.     

矩阵Sato理论的注记

本文从2×2矩阵Sato理论导出多分量的KP方程族,讨论了这方程族的新的达布变换,并考虑从这方程族的约束而引出的1 1维的可积方程。     

打开物质微观世界大门的金钥匙--薛定谔方程

介绍了薛定谔方程的表述形式,分析了不同体系的薛定谔方程的建立方法,并介绍了求解复杂体系的薛定谔方程的近似模型和方法.针对求解薛定谔方程的Hartree-Fock近似自洽场模型,借助Gaussian98W量子化学计算软件,以H2O和C2H4分子的量子化学从头算为实例,分析了薛定谔方程在揭示物质微观世界的实际应用价值,从而有助于更好地认识薛定谔方程的重要意义.     

非球谐环形振子势的Schrdinger方程的解析解

量子力学中除了无限深势阱、一维线性谐振子、库仑势和三维各向同性谐振子势外，绝大部分Schrodinger方程是没有精确解的，这给具体问题的深入研究带来了很大的障碍。本文从求解Schrodinger方程的NU Method方法出发，求解了非球谐环形振子势V（r，θ）=μω^2r^2／2＋h^2α／（2μr^2）＋h^2βcosθ／（2μr^2sinθ）的本征方程的角向方程，获得解析解，将求解的过程大大简化；同时用特殊函数的方法求解了非球谐环形振子势的Schodinger方程的径向方程，借以拓宽对Schrodinger方程求解方法的研究。     

一类新型浅水波方程的2-孤子解

研究了一类含线性和非线性色散项的新型浅水波方程即Dullin-Gottwald-Holm方程(简称为DGH方程)的2-孤子解。利用反散射方法建立了DGH方程的反散射求解方程,在不考虑反射的情况下,利用方程的散射数据,借助于Matlab数学软件,以参数形式给出了DGH方程的2-孤子解。最后给出了几个取特殊值时解的波形图,从而清楚地显示了孤波之间的相互作用。     

F修饰对SiO2@TiO2亲疏水性及光催化性能的影响

采用两步法制备了氟修饰疏水性F-SiO_2@TiO_2材料.以三乙氧基氟硅烷(TEFS)为硅源,采用后嫁接的方法在短孔道MCM-41小球表面引入F原子,再利用醇热法在F-MCM-41小球表面生长TiO_2纳米晶颗粒.利用透射电子显微镜(TEM)、X射线粉末散射(XRD)、X射线光电子能谱(XPS)、N_2气吸脱附等手段表征了材料的物相组成和表面结构.研究表明:所制备的氟修饰F-SiO_2@TiO_2纳米复合材料为核壳结构,具有较大的比表面积、较好的介孔结构及较佳的热稳定性.同时,TiO_2纳米颗粒在F-MCM-41小球表面分散均匀、结晶度高、颗粒尺寸小且均一、与F-SiO_2结合牢固.重量吸附实验和光催化实验进一步证实F修饰可抑制水的吸附有利于提高F-SiO_2@TiO_2材料的疏水性和对气相有机污染物的光催化性能.     

稀土金属与IVA族的金属酞菁配合物的热分析

用差示扫描量热仪与热重分析仪对常用稀土金属与ⅣA族的金属酞菁配合物进行系统的热分析,找出它们的热稳定性 顺序为CePc_2>HTmFe_2>HLaPc_2>HNdPc_2>HSmPc_2;PbPc>SiPcCl_2>GeFeCl_2>SnPc_2>SnPcCl_2,同时还发现了镧、钕、钐、铥、锗、锡与钼等金属酞等配合物在加热中产生了晶型转变,并找出其转变温度。     

氧化吸收法同步脱除燃烧烟气中SO2，NOx和CO2的化学热力学及其评价

湿化学法同步脱除烟气中气态污染物是燃烧源大气污染控制的重要方法之一,为探究采用不同氧化吸收策略同时脱除燃烧烟气中SO_2,NO_x和CO_2的可行性,基于化学热力学原理,分析了9种联合氧化吸收策略的性能,具体的氧化吸收策略包括:H_2O_2-NH_3·H_2O,H_2O_2-MDEA,H_2O_2-NaOH,O3-NH_3·H_2O,O3-MDEA,O3-NaOH,NaClO_2-NH_3·H_2O,NaClO_2-MDEA和NaClO_2-NaOH,并提出新的动态加权法对其性能进行综合评价。结果表明:上述所有策略均具有SO_2,NO_x和CO_2捕获的可行性。O3-NaOH,NaClO_2-MDEA和NaOH做吸收剂的氧化吸收溶液分别对单一脱硫、脱硝和脱碳效果最好。当综合考虑同步脱除SO_2,NO_x和CO_2时,NaClO_2-MDEA优于其他策略,其结果可为燃烧烟气中的气体污染物的联合脱除提供参考。     

微波辐射下苯氧乙酸锌、甘氨酸锌的固相合成及表征

研究了乙酸锌与苯氧乙酸,甘氨酸在微波辐射及这曙条件下的固－固相配位化学反应,通过固相反应一步合成了苯氧乙酸锌和甘氨酸锌。经电导率,ＩＲ,ＵＶ及元素分析表征了产物。     

Effects of acetylene at low concentrations on nitrification, mineralization and microbial biomass nitrogen concentrations in forest soils

Temperate forest surface soils at the varying distances from main trunks (e.g., Pinus koraiensis and Quercus mongolica) were used to study the effects of acetylene (C₂H₂) at low concentrations on nitrification, mineralization and microbial biomass N concentrations of the soils, and to assess the contribution of heterotrophic nitrification to nitrous oxide (N₂O) emissions from soils. The use of acetylene at partial pressures within a range from 10 to 100 Pa C₂H₂ in headspace gas gave a significant decrease in N₂O emission at soil moisture of c. 45% water-filled porosity space, and the decrease was almost the same in each soil after exposure of C₂H₂ at low concentrations. Heterotrophic nitrification could account for 21%―48% of total N₂O emission from each soil; the contribution would increase with increasing distances from the Pinus koraiensis trunks rather than from the Quercus mongolica trunks. Under the experimental conditions, the use of C₂H₂ at low concentrations showed no significant influence on soil microbial biomass N, net N mineralization and microbial respiration. However, 100 Pa C₂H₂ in headspace gas could reduce carbon dioxide (CO₂) emissions from soils. According to the rapid consumption of 10 Pa C₂H₂ by forest soils and convenience for laboratory incubations, 50 Pa C₂H₂ in headspace gas can be used to study the origin of N₂O emissions from forest soils under aerobic conditions and the key associated driving mechanisms. The N₂O and CO₂ emissions from the soils at the same distances from the Quercus mongolica trunks were larger than those from the Pinus koraiensis trunks, and both emissions decreased as the distances from trunks increased. The stepwise regression analysis showed that 95% of the variability in soil CO₂ emissions could be accounted for by the concentrations of soil total C and water soluble organic C and soil pH, and that 72% of the variability in soil N₂O emissions could be accounted for by the concentrations of soil total N, exchangeable NH⁺₄-N and microbial biomass N and 25% of the variability in heterotrophic nitrification by the soil microbial biomass N concentration. The emissions of N₂O and CO₂ from forest soils after exposure of C₂H₂ at low concentrations were positively related to the net nitrification of the soils.     

Synthesis,structure and catalytic behavior of yttrium complexes bearing a diaminobis（phenolate） ligand

Yttrium complexes stabilized by a diaminobis（phenolate） ligand were synthesized and their catalytic behavior was explored. Reaction of YCI3 with 1 equiv of LNa2 [L= Me2NCH2CH2N{CH2-（2-O-C6H2-^1Bu2-3,5）}2] gave the yttrium chloride LYCI（THF） （1） in 92% yield. Complex I can be used as starting material to prepare the yttrium amido derivative. Complex 1 reacted with 1 equiv of LiNPh2 in THF to afford the expected yttrium amido complex LYNPh2 （2） in high yield. Both of complexes 1 and 2 have been well detected by elemental analysis, NMR spectra and single-crystal X-ray analysis. It was found that complex 2 can efficiently initiate the ring-opening polymerization of L-lactide and ε-caprolactone, and a controlled manner is observed in the former case.     

Biosorption of Cu（Ⅱ） and Pb（Ⅱ） by Auricularia polytricha

For searching biological material for heavy metal removal of waste-water, using macrofungus Auricularia polytricha as biosorbent for Cu^2＋ and Pb^2＋ removal was investigated. After shaking and biosorbing Cu^2＋ and Pb^2＋ in solution by biosorbents, the filtrates were tested by AAS and the adsorbed quantity of Cu^2＋ and Pb^2＋ was calculated. The biosorbents were effective in removal of Cu^2＋ and Pb^2＋ on the biosorbents that showed a high- est value around pH 5-6. The biosorption rate of Cu^2＋ and Pb^2＋ on A. polytricha biomass decreased with increasing the initial concentration of Cu^2＋ and Pb^2＋ in the medium. The biosorption of Cu^2＋ and Pb^2＋ on the biomasses follows pseudo-second order kinetics. The determined maximum biosorption capacities presented by the fungus biomass were 3.34 and 13.03 mg·g^-1 dry weight for Cu^2＋ and Pb^2＋, respectively by the biosorption equilibrium with Langmuir adsorption isotherm. According to the whole data analysis in each experiment of studying Cu^2＋ and Pb^2＋ biosorption including condition factors and adsorption isotherm, the adsorbed capacity of Pb^2＋ by A. polytricha biomass was bigger than Cu^2＋. The biosorption by A. polytricha was most effective when pH 5-6. The biosorbents are suitable for low Cu^2＋ and Pb^2＋ concentration waste-water, especially for Pb^2＋ removal.     

Degradation of 2, 4-D acid using Mn2+ as catalyst under UV irradiation

In this paper, the oxidative degradation of 2, 4-dichlorophenoxyacetic acid (2, 4-D) using Mn²⁺/H₂O₂ reagent under UV irradiation was studied. The results show that 2, 4-D was degraded more completely in Mn²⁺/H₂O₂ solution than traditional Fenton solutions. The effects of the concentration of Mn²⁺, H₂O₂ and pH were also investigated. And under the optimal condition of 1.48×10⁻⁴ mol/L, 8.99×10⁻⁵ mol/L and pH 3.38, the formation of ·OH was the most, both the decomposition rate of H₂O₂ and the degradation rate of 2, 4-D were the fastest. In addition, the photoreaction process was monitored using spin-trapping electron paramagnetic resonance (EPR), and the results indicated that the oxidative process was predominated mainly by the hydroxyl radical (·OH) gennerated in the system. Biography: HUANG Yingping (1964–), Professor, Ph. D., research direction: pollution ecology and water pollution control.     

两种三维无机-有机杂化材料的溶剂热法合成及反射光谱研究

文中采用溶剂热法合成了两种三维网状无机-有机杂化材料Co(C₄H₄N₂)(VO₃)₂(Ⅰ)和Ni₂(C₄H₄N₂)V₄O₁₂(H₂O)₂(Ⅱ)。分别以n(CoCl₂·6H₂O)∶n(吡嗪)∶n(NH₄VO₃)=1∶2∶2和n(NiCl₂·6H₂O)∶n(吡嗪)∶n(NH₄VO₃)=1∶2∶2的摩尔比、纯水为溶剂,在140℃下反应3d,分别得到了紫黑色块状晶体Ⅰ和绿色块状晶体Ⅱ。对影响溶剂热反应的主要因素如反应温度、pH值、反应物摩尔比等进行了系统研究,确定了合成这两种化合物的最佳反应条件。并对产物晶体进行了UV-VIS-NIR漫反射光谱分析和热重分析(TG)。漫反射光谱研究表明,这两种晶体的光学能隙分别为2.13eV和2.56eV,都属于半导体,对太阳辐射具有选择吸收特性,它们在温度分别低于410℃和210℃时是稳定的。     

In situ time-resolved FTIR investigation on the reaction mechanism of partial oxidation of methane to syngas over supported Rh and Ru catalysts

In situ time-resolved FTIR spectroscopy was used to study the reaction mechanism of partial oxidation of methane (POM) to synthesis gas and the reaction of CH₄/O₂/He (2/1/45, molar ratio) gas mixture with adsorbed CO species over Rh/SiO₂, Ru/γ-Al₂O₃ and Ru/SiO₂ catalysts at 500—600℃. It was found that CO is the primary product of POM reaction over reduced and working state Rh/SiO₂ catalysts. Direct oxidation of CH₄ is the main pathway of synthesis gas formation over Rh/SiO₂ catalyst. CO₂ is the primary product of POM over Ru/γ-Al₂O₃ and Ru/SiO₂ catalysts. The dominant reaction pathway for synthesis gas formation over Ru/γ-Al₂O₃ catalyst is via the reforming reactions of CH₄ with CO₂ and H₂O. For the POM reaction over Rh/SiO₂ and Ru/γ-Al₂O₃ catalysts, consecutive oxidation of surface CO species is an important pathway of CO₂ formation.