关于不定方程组x-1=3py^2，x^2＋x＋1=3z^2

设P为素数，利用同余及高次丢番图方程的一些结果证明了不定方程组x-1=3py^2，x^2＋x＋1=3z^2仅有正整数解（p，x，y，z）=（7，22，1，13）。     

Evolution of TiO2 coating layers on lamellar sericite in the presence of La and the pigmentary properties

TiO₂-coated sericite powders were prepared by the chemical deposition method starting from lamellar sericite and TiCl₄ in the presence or absence of La³⁺ cations. After calcination at 900 °C for 1 h, the resultant TiO₂ nanoparticles on the sericite surfaces existed in anatase phase. The light scattering indexes of the TiO₂-coated lamellar sericite powders were dozens of times higher than that of the naked lamellar sericite powders. The presence of La³⁺ in the deposition solution was beneficial to the formation of the small-sized anatase TiO₂ nanoparticles, resulting in the formation of the dense and uniform island-like TiO₂ coating layers in a large range of the weight ratios of TiO₂ to sericite from 5% to 20%. The TiO₂-coated lamellar sericite powders prepared in the presence of La³⁺ had higher light scattering index than that prepared in the absence of La³⁺. XPS analysis shows that when La³⁺ cations were absent in the reaction solution, TiO₂ coating layers anchored at the sericite surface via the Ti-O-Si and Ti-O-Al bonds. The presence of La³⁺ cations caused the formation of Si-O-La and Al-O-La bonds at the sericite surface and Ti-O-La bond at the surface of TiO₂ coating layers. After coating TiO₂ on the sericite surface, the yellowness of the TiO₂-coated sericite powders obviously increased and the brightness slightly decreased.     

厚尾相依序列的均值变点估计

本文研究了厚尾相依序列的均值变点估计. 证明了变点的CUSUM估计的一致性并得到了收敛速度.在方差无穷的情况下推广了H\'{a}jek--R\'{e}nyi不等式.     

Influence of substituents in the salicylaldehyde‐derived Schiff bases on vanadium‐catalyzed asymmetric oxidation of sulfides

A series of chiral Schiff bases ( L ¹ – L ⁵ ) with different substituents in the salicylidenyl unit were prepared from condensation of 3‐aryl‐5‐ tert ‐butylsalicylaldehyde derivatives and optically active amino alcohols. Bromination of 3‐phenyl‐5‐ tert ‐butylsalicylaldehyde gave an unexpected product 3‐(4‐bromophenyl)‐5‐bromosalicylaldehyde, from which the corresponding Schiff base ligands L ⁶ and L ⁷ , derived from (S)‐valinol and (S)‐ tert ‐leucinol, respectively, were prepared. Ligands L ¹ – L ⁷ were applied to the vanadium‐catalyzed asymmetric oxidation of aryl methyl sulfides. Under the optimal conditions, the oxidation of the thioanisole with H₂O₂ as oxidant in CH₂Cl₂ catalyzed by VO(acac)₂‐ L ¹ – L ⁷ gives good yields (74–83%) with moderate enantioselectivity (58–77% ee). Ligand L ⁷ , containing a 4‐bromophenyl group on the 3‐position and a Br atom on the 5‐position of the salicylidenyl moiety, displays an 80–90% ee for vanadium‐catalyzed oxidation of methyl 4‐bromophenyl sulfide and methyl 2‐naphthyl sulfide. Copyright © 2008 John Wiley & Sons, Ltd.     

Synthesis,crystal structure and properties of di-μ2-alkoxo bridged binuclear manganese(III) Schiff base complexes

Transition Metal Chemistry - Preparation and isolation of the dimeric manganese(III) complex, [Mn2(Salpa)2(H2O)2Cl2] · 2DMF, (1), was accomplished by air oxidation of a solution containing...     

一种新的结合NCP函数的SQP滤子算法

对于SQP滤子算法,本文提出了一种新方法来构造滤子,目的是为了使滤子的接受条件更宽松,降低进行可行性恢复的机率.另外,本文通过一些数值例子对这种新算法进行了检验,事实证明这种算法是有效的.最后还证明这种算法具有超线性收敛性.     

图K(r,2)的邻强边色数

本文给出了每部有2个点的完全r-部图(r≥2)的邻强边色数.     

Dielectric Response of Graded Spherical Composites

We investigate the effective dielectric responses of graded spherical composites under an external uniform electric field by taking the dielectric function of spherical inclusion, εi = cr^ke^βr, where r is the inner distance of a point inside the particle from the centre of the spherical particle in the coordination. In the dilute limit, our exact result is used to test the validity of differential effective dipole approximation （DEDA） for estimating the effective response of graded spherical composites and it is shown that the DEDA is in excellent agreement with the exact result.     

本体聚合反应过程中聚甲基丙烯酸甲酯增长自由基的ESR研究

采用TM₁₁₀谐振腔和φ2mm样品管,在17℃室温条件下成功地记录了MMA本体聚合反应过程中增长自由基的ESR谱。当把DMA加入到MMA和BPO中后,立即抽取0.17ml混合液到φ2mm样品管并记谱。以后每隔2分钟记谱一次,波谱从13(5+8)条线逐渐变成9(5+4)条线。我们用阻碍振荡模型和构象重叠模型作了模拟。从全部谱图看,前者似更合理些。ESR实验表明:在聚合过程前期,自由基浓度基本保持不变,但从聚合中期的某一时刻开始,浓度剧增,它正好同步地与本体聚合反应的自加速效应相对应,而且其变化规律和单体转化率相平行。最后,我们用微波功率饱和方法观测到9线谱的协同自旋跳跃所产生的卫线,证明了主导的电子自旋晶格弛豫机理来自电子一核自旋间的偶极偶合角调制。