THE EXACT SOLUTIONS OF THE BURGERS EQUATION AND HIGHER-ORDER BURGERS EQUATION IN (2+1) DIMENSIONS

Some exact solutions of the Burgers equation and higher-order Burgers equation in (2+1) dimensions are obtained by using the extended homogeneous balance method. In these solutions there are solitary wave solutions, close formal solutions for the initial value problems of the Burgers equation and higher-order Burgers equation, and also infinitely many rational function solutions. All of the solutions contain some arbitrary functions that may be related to the symmetry properties of the Burgers equation and the higher-order Burgers equation in (2+1) dimensions.     

拓扑向量空间中实齐性连续函数的延拓定理

得到如下结果,在有限维具To公理的拓扑向量空间中,其内任意不含原点的有界闭集上定义的齐性连续函数均可延拓为全空间上的齐性连续函数。     

Photocatalytic Effects of Rutile Phase TiO2 Ultrafine Powder with High Specific Surface Area Obtained by a Homogeneous Precipitation Process at Low Temperatures

The photocatalytic characteristics of nanostructured TiO₂ ultrafine powder with rutile phase produced using the homogeneous precipitation process at low temperatures (HPPLT) were compared with those of commercial P-25 TiO₂ powder by flame hydrolysis. The TiO₂ powder by the HPPLT showed much higher photoactivity in the removal rate, showing lower pH values in the solution than the P-25 powder when eliminating metal ions such as Pb and Cu from the aqueous metal-EDTA solutions. This can be inferred as the more rapid photo-oxidation or -reduction of metal ions from the aqueous solution, together with relatively higher efficiencies in the use of an electron-hole pair formed on the surface of the TiO₂ particles under UV light irradiation. Also, in the view of the TiO₂ particle morphology, compared to the well-dispersed spherical P-25 particles, the agglomerated TiO₂ secondary particles by the HPPLT consist of acicular typed primary particles with a thickness in the range of 3–7 nm and the primary particles radialize in all directions, which would be more effective to photocatalytic reactions without the large electron-hole recombination on the surface of the TiO₂ particle under UV light irradiation. It can be, therefore, thought that the higher photoactivity of the rutile TiO₂ powder by the HPPLT in the aqueous solutions results mainly from having a larger surface area by the acicular shaped primary particles with very thin thickness and radialization in all directions.     

过渡金属络合物催化乙烯齐聚

综述了乙烯齐聚的最新成果,重点阐述了用于乙烯齐聚的新型催化剂,讨论了烯烃高聚与齐聚催化剂的关系,烯烃高聚与齐聚的反应机理相同,。差别主要在于烯烃插入与β－H消除反应的速率,第IV副族金属络合物主要催化乙烯齐聚,第Ⅲ副族金属主要催化乙烯高聚,改变茂金属催化体系的助催化剂和反应条件可得到齐聚产物,选择体积较小配体的第Ⅷ族金属络合物,有利于β－H消除得到齐聚产物。     

沉淀法制备CeO_2纳米晶与表征

采用乙醇为分散剂和保护剂 ,用反向沉淀法制备了不同粒径的CeO2 纳米晶。XRD分析表明 ,当焙烧温度为 2 5 0～ 80 0℃时 ,所合成的CeO2 纳米粒子属于立方晶系 ,空间群为O5 H FM 3M。TEM分析表明 ,CeO2 纳米粒子呈球形 ,粒度随焙烧温度的增加而增大。热失重分析表明 ,样品的热失重主要受温度的影响 ,而焙烧时间的影响不大。相对密度分析表明 ,随CeO2 纳米晶粒度的增大 ,粉末的密度增加。     

低温液相合成甲醇及甲酸甲酯用Cu-Cr-M-O催化剂的制备与表征

采用共沉淀法和配合物沉淀法制备了分别添加Ｂａ, Ｍｎ,Ｖ,Ｂｉ,Ｎｉ 和Ｚｎ 的ＣｕＣｒＭＯ三组分催化剂,采用ＢＥＴ,ＸＲＤ和ＴＥＭ 对催化剂进行了表征,并考察了其对合成甲醇及甲酸甲酯反应的活性及选择性． 结果表明,添加第三种金属使催化剂的稳定性及甲酸甲酯选择性有所提高,但使催化活性有所下降． 配合物沉淀法制备的催化剂的比表面积较大,粒径较小． 热分解温度越高,催化剂的比表面积越小． 除ＣｕＣｒＶＯ 催化剂为纳米非晶态之外,其它催化剂均呈晶态． 催化剂的最小平均粒径为３８ ｎｍ , 最大平均粒径为６８ ｎｍ , 属纳米级催化剂．     

水解法制备的掺铁二氧化钛超微粉的热分析、晶粒生长和结构相变

研究了用四氯化钛水解制备的纯二氧化钛和分步沉淀,共沉淀方式制备的掺铁二氧化钛的热分解状况,品化过程。采用Ｘ射线衍射和Ｖｏｉｇｔ单峰分析法计算了这三种样品在各个燃烧温度下的晶体晶粒度。结果表明,四氯化钛水争方法得到的二氧化钛粉为无定形,无定形博物经钛加热晶化过程是一个持续的过程,并没有以往文献中所报道的明显的晶化温度和晶化放热峰。应用非晶物质晶化晶核生长速率方程了晶粒生长活化能并且进行了讨论。     

Protein—Protein Interactions in Aqueous Ammonium Sulfate Solutions. Lysozyme and Bovine Serum Albumin (BSA)

Osmotic pressures have been measured to determine lysozyme—lysozyme,BSA—BSA, and lysosyme—BSA interactions for protein concentrations to 100 g-L^–1in an aqueous solution of ammonium sulfate at ambient temperature, as a functionof ionic strength and pH. Osmotic second virial coefficients for lysozyme, forBSA, and for a mixture of BSA and lysozyme were calculated from theosmotic-pressure data for protein concentrations to 40 g-L^–1. The osmotic second virialcoefficient of lysozyme is slightly negative and becomes more negative withrising ionic strength and pH. The osmotic second virial coefficient for BSA isslightly positive, increasing with ionic strength and pH. The osmotic second virialcross coefficient of the mixture lies between the coefficients for lysozyme andBSA, indicating that the attractive forces for a lysozyme—BSA pair areintermediate between those for the lysozyme—lysozyme and BSA—BSA pairs. For proteinconcentrations less than 100 g-L^–1, experimental osmotic-pressure data comparefavorably with results from an adhesive hard-sphere model, which has previouslybeen shown to fit osmotic compressibilities of lysozyme solutions.     

Espaces homogènes d'Einstein non-compacts

In this text, we consider the solvmanifolds obtained by an abelian extension of two-step nilmanifolds and obtain Einstein metrics (with negative scalar curvature) near to the symmetric spaces.     

奇异积分算子在实与复分析中的应用

本文是一份综合报告,它基于作者的一部份研究工作和他在北京师范大学的五次讲演稿,以奇异分算子作为桥梁联结函数空间的结果和偏微分方程的结果作了阐述,它包括奇次空间上的调和分析,并应用到多复变函数论上,综述了右的结果并提出未解决的问题。