To Define Or Not To Define: The Case Of (-8)1/3

This paper discusses two possible approaches to (-8)^1/3. The first is that (-8)^1/3 = ³(-8) = -2. The second is that (-8)^1/3 is undefined. The pros and cons of each of these approaches are considered and some implications to teacher education are specified.This revised version was published online in September 2005 with corrections to the Cover Date.     

关于丢番图方程(x~m-1)(x~(mn)-1)=y~2

找出了方程 (xm - 1) (xmn - 1) =y2 适合x>1,y >1,n>1的所有正整数解 (x ,y ,m ,n)     

关于Diophantine方程(x2)-1=qn-1/q-1

设q=p＇，其中p是素数，r是正整数．本文证明了：当p〈100时，如果p≠2，13，17，19，43，47，53，59，67，83或89，则方程（x2）-1=（q^n-1）/（q-1）没有正整数解（x，n）．     

关于Diophantine方程x^2—1=y^2（z^2-1）

给出了方程x^2-1=y^2(z^2-1)的全部正整数解．     

2-(2-羟基苯亚胺基)-6-哌嗪基-1H-苯并异喹啉-1,3-二酮的合成

西弗碱结构是重要的功能性片段,含有这类结构片段的化合物显示出有价值的实际应用.以便宜易得的4-溴-1,8-萘酐为起始原料,与水合肼反应生成萘酰亚胺,再与水杨醛反应,得到目标化合物2-(2-羟基苯亚胺基)-6-哌嗪基-1H-苯并异喹啉-1,3-二酮.其结构经核磁氢谱证实.     

Electronic structure and magnetism ofRMn6Sn6 (R=Tb, Dy)

This article reports first-principles band structure calculations forRMn₆Sn₆ (R=Tb, Dy). The calculation uses the linear muffin-tin orbitals (LMTO) method in the atomic-sphere-approximation (ASA), and yields results showing that both TbMn₆Sn₆ and DyMn₆Sn₆ are ferrimagnetic compounds with antiparallel aligned moments ofR and Mn atoms. In this research the 4f states ofR atoms are treated as localized states, i.e., the hybridization of 4f states with other valence electrons is neglected. The moments of Mn in both compounds were determined to be 2.43 μ_B and 2.38 μ_B, respectively. The considerably small additional moments for Mn from the spin-orbit coupling indicates that the spin-orbital coupling is not dominated for Mn atoms. The total moments of Tb and Dy atoms are 10.28 μ_B and 11.20 μ_B. All the calculation findings accorded well with experimental results. Project supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry of China.     

配合物Ag_2L_4Br_2(L=1-甲基-2-巯基-3-H-咪唑)的合成及晶体结构

合成出一种新的配合物Ag2L4Br2(L=1-甲基-2-巯基-3-H-咪唑).通过X–射线单晶衍射分析表明,该化合物属于单斜晶系,P2(1)空间群,晶胞参数:a=7.9255(12),b=18.091(3),c=9.5431(14),α=γ=90o,β=99.772(2)o,V=1348.5(4)3,R=0.0421,wR=0.0969.配合物中心Ag(I)离子与来自4个1–甲基–2–巯基咪唑的4个巯基负离子以及2个溴负离子配位形成四配位银的双核结构.     

级数∞∑i=1(-1)n+1 1/n的重排

级数∞∑i=1（-1）^n＋1 1/n收敛于1n2，再由公式Hn=1nn＋C=εn，得出该级数按一定规律重排后的级数的收敛值。     

Synthesis of poly[methyl（3,3,3-trifluoropropyl）siloxane]-b-poly（ethylene oxide） block copolymers

A series of new amphiphilic poly[methyl（3,3,3-trifluoropropyl）siloxane]-b-poly（ethylene oxide） （PMTFPS-b-PEO） diblock copolymers with different ratios of hydrophobic segment to hydrophilic segment were prepared by coupling reactions of end-functlonal PMTFPS and PEO homopolymers. Copolymers were shown to be well defined and narrow molecular weight distribution （MWD） （1.07-1.3） by characterizations such as gel permeation chromatography （GPC） and ^1H-nudear magnetic resonance （^1H-NMR）.     

关于不定方程x3-1=38y2

利用递归数列、同余式证明了不定方程x3-1=38y2仅有整数解(x,y)=(1,0),从而得知关于不定方程x3-1=Dy2(0<D<100)的全部整数解的情况.     

头孢他啶侧链酸活性硫酯的合成研究

头孢他啶侧链酸在碱性条件下与DM缩合生成头孢他啶侧链酸活性硫酯时,用价格低廉的亚磷酸三乙酯代替价格昂贵的三苯基膦,通过设计正交实验优选出的较佳反应条件为：固定头孢他啶侧链酸19．8g,反应物料n（头孢他啶侧链酸）：n（DM）：n（亚磷酸三乙酯）：n（三乙胺）=1：1．2：1．2：1．2,反应溶剂乙腈150mL,于5℃反应5h,收率86．8％．     

|P(X)|=3、|SP(X)|=2和|P(X)|=2、|SP(X)|=3的四阶BCI-代数的计数问题

讨论了|P(X)|=3、|SP(X)|=2和|P(X)|=2、|SP(X)|=3两种情况下的四阶BCI-代数的计数问题，结论是：|P(X)|=3、|SP(X)|=2的四阶BCI-代数有三个；|P(X)|=2、|SP(X)|=3的四阶BCI-代数有一个。     

2-(2-氯乙基)-5-氯-6-苯基-3(2H)-哒嗪酮的合成

以易获得的苯和糠氯酸为原料,在温和的反应条件下,经三步反应合成出2-(2-氯乙基)-5-氯-6-苯基-3(2H)-哒嗪酮.化合物的结构经 1HNMR 和13CNMR谱得以证实.     

关于Pell方程x^2-5py^2=-1

运用初等数论的方法证明了Pell方程x^2-5py^2=-1有正整数解.这里p〉3且p是fermat素数.     

特殊级数∞(Σ)n=1(-1)n-1/(2n-1)2k-1与π2k-1的关系

根据傅立叶级数的性质,得到并运用数学归纳法证明了某一类特殊级数与π之间的关系.     

Ethene/norbornene copolymerization by [Me2Si(3-tertBuCp)(NtertBu)]TiCl2/MAO-catalyst

Ethene/norbornene copolymerization by the catalyst system [Me₂Si(3-^tertBuCp)(N^tertBu)]TiCl₂/MAO was investigated in detail at 30 °C, 60 °C, and 90 °C. A mass flow controller was used in this work to obtain kinetic data and investigate temperature's effects on activity, norbornene incorporation, copolymerization parameter, microstructure, glass transition temperature, and molar masses were described. High copolymerization valuesr _ξ and high alternation are determined. The number of isotactic alternating sequences is much higher than that of the syndiotactic alternating sequences.     

8-喹啉偶氮显色剂7-(8-喹啉偶氮)-1-氨基-8-羟基萘-3,6-二磺酸分光光度法测定微量钴

用作者合成的7-(8-喹啉偶氮)-1-氨基-8-羟基萘-3,6-二磺酸(7-QAH)作显色剂,系统研究了其 与Co(Ⅱ)的显色反应。在pH4.7的缓冲体系中,试剂与Co(Ⅱ)形成绿色配合物,其最大吸收波长位于648nm,表观 摩尔吸光系数为3.6×10~4 L·mol-1·cm-1,钴量在0～12μg/25mL范围内符合比尔定律。     

(E)-2-[2-(2-硝基苯基)乙烯基]-8-乙酰氧基喹啉的结构、光谱及热力学性质

使用密度泛函理论(DFT)和含时密度泛函理论TD-B3LYP方法,在B3LYP/6-311++G**水平上对(E)-2-[2-(2-硝基苯基)乙烯基]-8-乙酰氧基喹啉的分子结构、分子振动频率、电子吸收光谱及热力学性质进行理论研究.计算结果表明,标题化合物分子为E型反式非平面结构.分子在气相时的最低能量跃迁峰位于418nm处,对应S0→S1的电子跃迁,溶剂作用使其红移22—29nm,其红移程度随溶剂极性增强而增大.最强吸收峰位于289nm处,对应S0到S10的电子跃迁.在298.15K、标准大气压下,标题化合物分子的标准摩尔生成焓和标准摩尔生成自由能分别为-281.39和7.14kJ.mol-1.     

3-（6-溴吡啶-2）-2-（2-氟-6-氯苯）-噻唑酮-4的电子结构与抗HIV活性问关系的量子化学研究

采用AMI方法,对3-(6-溴吡啶-2)-2-(2-氟-6-氯苯)-噻唑酮-4(BPFCIZO)进行了量子化学计算,给出了分子的几何构型、原子的净电荷、键级、前沿分子轨道组成与能级、前沿轨道电子密度等参数．结果表明BPFCIZO分子的稳定构型呈蝴蝶状,噻唑酮环为主活性区,其上的2位C、4位N和6位O等原子很可能是其与RT酶作用的活性位点．