SU(1,1) Lie Algebra Applied to the General Time-dependent Quadratic Hamiltonian System

Exact quantum states of the time-dependent quadratic Hamiltonian system are investigated using SU(1,1) Lie algebra. We realized SU(1,1) Lie algebra by defining appropriate SU(1,1) generators and derived exact wave functions using this algebra for the system. Raising and lowering operators of SU(1,1) Lie algebra expressed by multiplying a time-constant magnitude and a time-dependent phase factor. Two kinds of the SU(1,1) coherent states, i.e., even and odd coherent states and Perelomov coherent states are studied. We applied our result to the Caldirola–Kanai oscillator. The probability density of these coherent states for the Caldirola–Kanai oscillator converged to the center as time goes by, due to the damping constant γ. All the coherent state probability densities for the driven system are somewhat deformed. PACS Numbers: 02.20.Sv, 03.65.-w, 03.65.Fd     

New cyclic and macrocyclic silaolefins via ring-closing metathesis of 1,1-bis(silyl)ethene-tethered dienes

Dialkenyl-substituted 1,1-bis(silyl)ethenes of the general formulae (CH₂CH(CH₂)_nMe₂Si)₂CCH₂ and (CH₂CH(CH₂)_nOMe₂Si)₂CCH₂, (where n = 1-3) have been successfully converted into new silacyclic or silamacrocyclic compounds in the presence of ruthenium-benzylidene complex (first generation Grubbs catalyst). The structures of both macrocyclic silaolefins have been confirmed using X-ray diffraction.     

A one-pot, non-catalytic approach to 1,2,4-benzothiadiazine-1,1-dioxides

Condensations of o-halo-substituted benzenesulfonyl chlorides with 2-aminopyridines and amidines may give the corresponding 1,2,4-benzothiadiazine-1,1-dioxides under mild, non-catalytic conditions in nearly quantitative yields. The successful one-pot cyclization depends on three factors: (i) the nature of the o-halogen, (ii) the electronic character of the benzene ring substituent, and (iii) the steric load around the amidine unit. O-Fluorobenzenesulfonyl chlorides bearing methylcarboxyl- or nitro-group and o-chloro- and o-bromobenzenesulfonyl chlorides bearing nitro-group are reactive enough to give the desired 1,2,4-benzothiadiazine-1,1-dioxides in a one-pot base-promoted reaction. In all other cases, open-chain sulfonylated amidine intermediates are isolated. The latter are converted to the title compounds either in the presence of potassium carbonate or upon the addition of a copper(I) catalyst.     

多重氢键自组装联萘酚和含氮化合物

作为相互识别的结果,(±)-2,2′-二羟基-1,1′-联萘酚可与4,4′,6,6′-四甲基-2,2′-联嘧啶、1,2-双(4-吡啶)乙烷、反式-1,2-双(4-吡啶)乙烯、4,4′-联吡啶-N,N′-双氧化物及双-2-吡啶基甲酮等多种含氮化合物分别形成外形良好的共晶化合物1,2,3,4及5.本文对5个共晶化合物的晶体...     

Keggin型多金属氧酸盐催化醛与乙酸酐合成1,1-二乙酸酯

合成了一系列具有Keggin结构的M<,x>PW<,12>O<,40>·nH<,2>O和M<,x>PMo<,12>O·nH<,2>O多金属氧酸盐(其中,M=Fe、Mn、Ni、Cu、Zn;x=1、1.5),采用傅里叶变换红外光谱和X射线衍射等方法对其结构进行了表征;考察了醛与酸酐的摩尔比、催化剂用量、反应时间等反应条件对...     

亚甲基二膦酸为配位体的无氰碱性镀铜

提出一种以亚甲基二膦酸(MDPA, H₄L)为主配位剂的无氰镀铜体系. 采用pH 电位滴定法分别测定MDPA的四级解离常数和MDPA-Cu(II)的稳定常数, 并比较MDPA-Cu(II)和羟基乙叉二膦酸(HEDPA)-Cu(II)的循环伏安曲线和阴极极化曲线. 结果表明: MDPA各级解离常数为, pK₁=1.86, pK₂=2.65, pK₃=6.81, pK₄=9.04;MDPA与Cu²⁺形成分级配合物的稳定常数为, pK_ML=10.65, pK_ML2 = 5.59, pK_ML3 = 2.50; 随着pH升高, 形成的配合物依次为, Cu(H₃L)₂、[Cu(H₃L)(H₂L)]-和[Cu(H₂L)₂]^2-; 当pH在7-10 时, MDPA较HEDPA更易与Cu²⁺配位. 当pH=9 时, MDPA碱性镀铜体系阴极主要发生的是[Cu(H₃L)(H₂L)]^-和[Cu(H₂L)₂]^2-还原生成铜的过程; 在10 °C,MDPA体系的铜配位化合物还原生成铜的电位比HEDPA体系负移, 扩散速度更快.     

Nanofluorides

The present review article covers major aspects of inorganic chemistry of nanofluorides, including methods of their synthesis (thermolysis of the precursors, co-precipitation from solutions, reversed micelle technique, hydro- and solvo-thermal techniques, sol–gel method, etc.), nanochemical effects (enhanced chemical activity, self-organization and self-assembly, non-classical mechanism of the single crystal growth, synthesis of non-equilibrium phases), targeted preparation of 1D, 2D, and 3D nanostructures, surface modification of the nanoparticles, fluoride nanocomposites (glass- and nano-ceramics) as well as applications of nanofluorides.     

上海股票市场和国际主要股票市场之间波动溢出效应的实证研究

使用BEKK—二元GARCH(1,1)模型,对于我国股票市场和国际主要股票市场之间的波动溢出效应进行了实证研究.分析结果表明,上证综指和标准普尔500指数、日经225指数之间存在单向波动溢出效应,而上证综指和香港恒生指数之间存在双向波动溢出效应,上证综指和新加坡海峡时报指数之间不存在波动溢出效应.     

Chiral nematic liquid crystals with helix inversion from (R)-1,1′-binaphthyl and cholesteryl ester moieties

In this study, on the concept of intramolecular chiral conflict between the (R)-1,1′-binaphthyl and cholesteryl ester moieties, we have designed and synthesised a new liquid crystal (LC) (R)-dicholesteryl 6,6′-[1,1′-binaphthyl-2,2′-diylbis(oxy)]dihexanoate [(R)-DC]. A helix inversion could be observed for the chiral nematic liquid crystal (N*-LC) comprising the commercial nematic LC (N-LC) host SLC1717 and (R)-DC on heating. As a comparison, (S)-dicholesteryl 6,6′-[1,1′-binaphthyl-2,2′-diylbis(oxy)]dihexanoate [(S)-DC] was also prepared. Due to the intramolecular chiral superposition between the (S)-1,1′-binaphthyl and cholesteryl ester moieties, the N*-LC comprising SLC1717 and (S)-DC also exhibited excellent temperature sensitivity.     

Polystyrene-supported TiCl4 as a novel,efficient and reusable polymeric Lewis acid catalyst for the chemoselective synthesis and deprotection of 1,1-diacetates under eco-friendly conditions

Copolymer beads of styrene and divinylbenzene (5–7%) were synthesized and combined with titanium tetrachloride in CS₂ to form a stable complex. The PS/TiCl₄ complex was used as a mild and efficient polymer-supported Lewis acid catalyst for the preparation of 1,1-diacetates from various types of aldehydes under heterogeneous conditions at room temperature. Deprotection of the resulting 1,1-diacetates has also been achieved using the same catalyst in methanol. This new protocol has the advantages of easy availability, stability, reusability of the eco-friendly catalyst, high to excellent yields, chemoselectivity, simple experimental and work-up procedure. Moreover, this polymeric catalyst could be recovered easily and reused several times without significant loss in activity.