A note on the crossed product R(A, α) associated with PSL_2(R)

Given the hyperbolic measure dxdy/y2 on the upper half plane H, the rational actions of PSL2(R) on H induces a continuous unitary representation α of this group on the Hilbert space L2(H, dxdy/y2). Supposing that A = {Mf : f ∈ L∞(H, dxdy/y2)}, we show that the crossed product R(A,α) is of type I. In fact, the crossed product R(A,α) is *-isomorphic to the von Neumann algebra B(L2(P,ν))■LK, where LK is the abelian group von Neumann algebra generated by the left regular representation of K.     

Synthesis,Structure,and Ring-opening Metathesis Polymerization of η~5-Pentamethylcyclopentadienyl-(η~5-exo-tricyclo [5.2.1.0~(2,6)]deca-2,5,8-trien-6-yl) Iron

η5-Pentamethylcyclopentadienyl-(η5-exo-tricyclo[5.2.1.02,6]deca-2,5,8-trien-6-yl) iron(3) was synthesized and characterized by 1H NMR, 13C NMR, MS, elemental analysis, IR, UV and X-ray diffraction analysis. Compound 3 was polymerized with ring-opening metathesis polymerization(ROMP) initiator (PCy3)2Cl2Ru=CHPh. 1H NMR and IR spectra revealed the presence of CH=CH units in the polymer and supported the ROMP mechanism. GPC analysis of the polymer showed that the weight-average molecular weights(Mw) was 5967, ...     

X射线能谱分析和金相分析确定仿银合金的成分、组织及工艺

两种仿银合金经x射线能谱分析其组分均为银锡合金,经半定量计算,两种合金的银,锡相对比均为28.6:71.4。用金相显微镜观察,合金(1)的组织为先凝固的固溶体∑相和(∑ Sn)共晶体的铸态组织。合金(2)的金相组织为加工态组织。     

研究金属切削中组织变化的网格高速摄影装置

研究金属切削过程中的变化,对改进切削工艺、实现高速、自动化和精密加工具有重要意义。高速显微摄影是实现从宏观到微观、从定性到定量、从静态到动态研究的有效方法。     

使用ZFK-500型高速摄影机对液中放电现象的摄影观察

液中放电是通过放电的方式将电能高速转化为热、光、力、声等其他形式的能量。它具有一系列独特的优点,使它广泛应用于许多领域。因此,关于液中放电的研究具有重要的理论与实践意义。我们使用ZFK-500型高速摄影机对液中放电的击穿与弧道过程、冲击波的形成与传播过程,进行了比较成功的观察。大量清晰的摄影,记录了击穿时微弱光线的光导及其在整个放电阶段的情况;记录了液中放电弧道膨胀的特点 此外,不发光现象-冲击波形成与传播过程的记录,都为液中放电的理论研究,提供了十分宝贵的科学依据。     

Study of the Electrical Double Layer of a Spherical Micelle: Functional Theoretical Approach

The electrical double layer theory is the base of the colloid stability theory (DLVO theory), and the PB eq. is a key to the study of the layer1,2. For a spherical particle, the PB eq. is (1) where and are the dielectric constant of the medium, the valence of ions, the elementary charge, the concentration of ions far away from the particle, the Boltzmann's constant and the temperature of the system, respectively. Since this eq. is a second order nonlinear differential one, only the anal…     

Spectral and Mechanistic Studies of the Reactions of Substituted 1,5-Benzothiazepine with Dichloroacetyl Chloride and Triethylamine

A lot of attentions have been paid to the synthesis of benzothiazepines and derivatives1,2 due to their significant physiological activities. It has been reported that b-lactam, a major part of the antibiotic skeleton, can be introduced to a molecule by reaction of an imine moiety with ketene3,4. We introduced a b-lactam skeleton to benzothiazepine and hoped the new compounds may possess certain biological activities. SHNH3ClCHCHCOC2H5OHSNClCla: ortho-Clb: para-Cl+PyridineScheme …     

Two New Compounds from Goniothalamus Cheliensis Hu

Goniothalamus cheliensis Hu (Annonaceace) is a small tree or shrub in Yunnan Province, southwest of China. Acetogenins, styryllactones and alkaloids1-3 from the genus were reported in the previous literature and many of them showed strong cytotoxic activities against a number of human cancer cell lines4. The titled plant has been the subject of our investigation due to the impressive cytotoxicity of its organic extract against mouse lymphocytic leukemia cells in preliminary pharmacological s…     

Two novel fluorescent calix[4]arene derivatives with benzoazole units in 1,3-alternate conformation for selective recognition to Fe~(3+) and Cr~(3+)

Two novel fluorescent calix[4]arene derivatives 1a and 1b with benzoxazole or benzothiazole units in 1,3-alternate conformation have been synthesized and characterized by IR,~1H NMR,~(13)C NMR and MS.Their complexation properties to different heavy and transition metal ions have been studied by UV-vis spectroscopy and fluorescence spectrometer.Compounds 1a and 1b show selective recognition to Fe~(3+) and Cr~(3+).     

Asymmetric synthesis of pedamide using I_2-induced heterocyclization to construct the skeleton

An alternative approach to synthesize pedamide,a key building block of pederin was described.Iodine-induced asymmetric heterocyclization was used as the key step to construct the skeleton,a tetrahydropyran ring with three chiral centers.Brown's asymmetric allylation and Lewis acid-mediated allylation were investigated to introduce chains and chiral alcohols.Sharpless dihydroxylation decorated the side chain.And high optically pure target was obtained by removing the epimers formed in these reactions on c...