Details of the non-unitarity proof for highest weight representations of the Virasoro algebra

We give an exposition of the details of the proof that all highest weight representations of the Virasoro algebra forc<1 which are not in the discrete series are non-unitary.This work was supported in part by DOE grant DE-FG02-84ER-45144, NSF grant PHY-8451285 and the Sloan Foundation     

完全椭圆积分和Hersch-Pfluger偏差函数

该文建立了Hersch-Pfluger偏差函数ψK(r)和第二类完全椭圆积分ε(r)之间的关系. 通过对完全椭圆积分及某些初等函数的组合的单调性和凹凸性的研究获得了完全椭圆积分的一些不等式, 并且藉此得到Hersch-Pfluger偏差函数ψK(r)的几个渐进精确的上界估计.     

Synthesis and Characterization of Ti-ZSM-5 in a Non-alkaline Medium in the Presence of Fluoride Ions

Ti-ZSM-5 was synthesized by hydro thermal crystallization in the presence of fluoride via using a non-alkaline medium. pH values were 5~7. SEM showed perfect Ti-ZSM-5 crystals and a large single crystal growing from the favourable medium. Substitution of titanium for silicon in the ZSM-5 framework led to a decrease of crystal size and of the length/width ratio. Electron microprobe analysis indicated a homogeneous distribution of titanium in the ZSM-5 framework. The unit cell parameters of the Ti-ZSM-5 determined by XRD increased with an increase in titanium content in the framework. TiO4tetrahedron vibrations were found in the IR spectrum. Si(1Ti) peakwas seen in the 29Si MAS NMR spectrum at -1O1ppm(from TMS) and 13CMAS NMR analysis verified the effect of (C3H7)4N F- occluded in thechannels. XPS study on the precursors, calcined and H2O2 adsorbed Ti-ZSM-5 was performed and some interesting results were observed.     

Catalyst-free and solvent-free method for the synthesis of quinoxalines under microwave irradiation

A facile procedure for the synthesis.of quinoxalines is being reported starting from benzil and 1,2-diaminobenzene. Thereactions were carried out catalyst-free, solvent-free and under microwave irradiation conditions in high yield (84-98%) with short time (3-6 rain) and environmental benign, as well as convenient operation. The structures of all the compounds have been confirmed on the basis of their IR, 1H NMR, and/or 13C NMR, mass spectral data.     

对溴偶氮氯膦流动注射分光光度法测定岩矿中的钪

本文研究了对溴偶氮氯膦与钪在盐酸介质中的显色反应。在波长740nm,络合物的摩尔吸光系数为7.0×10~4,7～18μg Sc_2O_3/25ml符合比尔定律。采用流动注射分光光度法,联合使用微型计算机,测出工作曲线的线性范围为5～45μg Sc_2O_3/25ml,比普通分光光度法扩大1.5倍。应用于测定岩矿中的微量钪,方法快速、准确。     

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。     

Studies on nucleic acid chemistry: VII. Synthesis of four oligoribonucleotides of dihydrouridine (D) loop of yeast alanine transfer RNA

This article described the preparation and the protection of 3′-DMP and dihydrouridine (Dr) as well as the synthesis of four oligoribonucleotides composed of them. DMP and Dr were obtained by hydrogenation of 3′-UMP and Ur under acidic conditions in the presence of platinum dioxide. They were monomethoxytritylated and benzoylated to (MeOTr)-D_bzp and (MeOTr) D_bzs, respectively. The latter was converted to D_bzs, by demonomethoxytritylation. The oligoribonucleotides containing DMP or Dr—ApGpD, DpApG, ApGpDpC and ApGpDpCpGpG were synthesized via phosphodiester approach and DCC was used as condensing reagent. DpApG was also synthesized via phosphotriester approach and TPST, MSTe, MSNI and MSNT were used as condensing reagents for a preliminary comparison of the coupling yields. These synthetic oligoribonucleotides were checked for purity and nucleotide sequences as usual. ApGpDpCpGpG and DpApG had been used for enzymatic synthesis of ApGpDpCpGpGpDpApG, which had been in turn successfully used for the total syntheses of the 5′-half molecule and the whole molecule of yeast alanine t-RNA     

Effect of POSS on crystalline transitions and physical properties of polyamide 12

Polyamide 12/Trisilanolphenyl‐POSS (PA 12/POSS) composites were prepared via melt‐compounding. The effect of polyhedral oligomeric silsesquioxane (POSS) on crystalline structure and crystalline transition of PA 12 was investigated by wide‐angle X‐ray diffraction (WAXD) and real time fourier transform infrared spectroscopy (FTIR). WAXD results indicated that PA 12 crystallized into γ‐form as slowly cooling from melt and the presence of POSS did not influence the crystalline structure of PA 12. Both PA 12 and PA 12/POSS composites underwent Brill transitions when they were heated from room temperature to melt point. Real time FTIR patterns showed that an absorption band at 697 cm^?1 ascribed to Amide V (α) mode was emerged along with the disappearance of Amide VI (γ) band at 628 cm^?1 with the increase of the temperature for PA 12 and PA 12/POSS composites, which suggested that the γ‐form crystalline has transformed into α form. The Brill bands were identified and the transformed mechanism was discussed based on the real FTIR results. The addition of POSS enhanced the tensile strength and thermal stability of PA 12. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 121–129, 2009     

Blue electroluminescence from 3,6‐silafluorene‐based copolymers

Poly(3,6‐silafluorene) is a typical wide band‐gap conjugated polymer with ultraviolet light emission. The blue electroluminescence from the 3,6‐silafluorene‐based copolymers via intrachain energy transfer was reported in this study. The monomer containing vinylene, anthracene, and tri‐arylamine moieties incorporated into the poly(3,6‐silafluorene) backbone can form efficient deep‐blue emitting copolymers with EL efficiency of 1.1–1.9%. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3286–3295, 2009