On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Photochemistry of β, γ-unsaturated ketones-V: The direct irradiation of some γ-phenyl β, γ-enones

The photochemistry of some members of the two series of γ-phenyl substituted acyclic β, γ-unsaturated ketones 1 and 2 upon direct irradiation with γ 310nm has been investigated, viz 1c–1h and 2b+2c.The alkyl substituted (E)-5-phenyl-4-penten-2-ones 1c–1h yield the corresponding 1,3-acyl shift products and (Z)-isomers, and 1g and 1h in addition two decarbonylated products. 2b only yields the (Z)-isomer and some benzaldehyde, but 2c yields the 1,3-acyl shift product, the ODPM product, three hydrocarbons formed by disproportionation of the allyl radical, and some benzaldehyde. The β-phenyl β, γ-UK 3a proved to be photostable. The 1,3-acyl shift products of 1c–1h result mainly from the singlet excited state in a cage radical process. The exclusive formation of the (E)-configuration of the 1,3-acyl shift product is explained in terms of conformational preference of the intermediate allyl radical. It is proposed that the formation of the (Z)-isomer proceeds from ¹T(π -π^*) which is populated according to

. Evidence is presented which supports the proposed mechanism.The β,γ-UK 2b containing a benzoyl moiety leads to a higher degree of (E)-(Z) isomerization than the corresponding 1d which has an acetyl moiety.The triplet energies of (E)- and (Z)-1h are 56 and ca 70 kcal/mol respectively.     

Molecular structure of carbonyl bromide as studied by gas electron diffraction

The molecular structure of COBr₂ has been determined as follows by an analysis of electron diffraction intensity: r_g(CO) = 1.178 ± 0.009 Å, r_g(C-Br) = 1.923 ± 0.005 Å and θ°_α(Br-C-Br) = 112.3 ± 0.4°. The uncertainties represent estimated limits of error. The observed systematic trends in the bond lengths and bond angles in carbonyl and thiocarbonyl halides are discussed.     

α-Tetralone glycosides from the green walnut husks of Juglans mandshurica Maxim. and their cytotoxic activities

Abstract

Five new α-tetralone glycosides, juglanbiosides A-E (1–5), together with an α-tetralone derivative (15) and nine known 1,4-naphthoquinones (6–14) were isolated from the 95% EtOH extract of green walnut husks of Juglans mandshurica Maxim. Their structures were elucidated by comprehensive spectroscopic methods (¹H, ¹³C NMR, DEPT, HSQC, HMBC, CD, HR-ESI-MS). In vitro cytotoxicities of all the isolated compounds were evaluated against BGC-823, HCT-15 and K562 cancer cell lines.

     

基于双尺度渐近分析的有限元算法

1．引言正如文山所说，由于复合材料和周期结构的材料系数ail（x）在局部区域内间断且跳跃性很大，加上区域内含有周期性洞穴或裂缝，且周期长度很小．一般而言，直接采用有限元方法进行数值模拟，其计算量大得惊人，甚至难以实现．文山针对这种特征，提出了一种可计算的双尺度渐近分析模式，本文在此基础上给出了相应的有限元算法，它包括：1．周期解在一个基本构造上的有限元计算；2．边界层的有限元计算．同时，给出了相应的误差分析．2．周期解的有限元计算首先考虑下列形式的边值问题；其中把，代E尸（on叫，iii（0关于E—（EI，ZZ…     

本征值有限元近似的一个抽象误差估计式

设T：LZ（fi）MLZ（fi）是自共轭全连续算子，SgCLZ（fi）是分片。次有限元空间，几：LZ、St是有限秩自共轭算子，IITh-Tllo、0（h、0）．考虑本征值问题：及其近似用（·，·）和DD·D【。·分别表示h（m中内积和范数·ID·卜F表示w认｝（m中范数，简记D卜队。为D卜卜·因为T自共轭全连续，所以它有可数无穷个本征值h，人，...人，...．其相应的本征函数（2丹构成完全标准直交系，所以VZELZ（m设几的本征值为A。l，汕。，...，汕n，相应的本征函数为如山，卜则。二1·不失一般性，可EitL。设tik一大干二＞，E是到Ah对应的本…     

TH型区间值模糊正规子群

本文在区间值模糊集空间上，引入了幂等区间范数ＴＨ，在此基础上，定义了ＴＨ型区间值模糊正规子群，并研究了它的一些性质和结构特征，从而拓广了区间值模糊集的理论。     

颈内静脉原位导丝法换置中心静脉长期血液透析导管的临床应用

目的探讨经颈内静脉原位导丝法换置中心静脉长期血液透析导管在维持性血液透析（MHD）患者中的应用价值。方法选取近3年在颈内静脉留置的中心静脉长期血液透析导管因功能障碍后，并经颈内静脉原位导丝法换置长期导管，术后及每次透析后均改用尿激酶封管患者16例（原位换置组）；选取同期首次经颈内静脉留置中心静脉长期血液透析导管,普通肝素封管患者20例作为对照组；分析两组患者围术期泵控血流量及随访期的反应及开存期率、次开存期率。结果围术期泵控血流量原位换置组高于对照组，有统计学差异（P＜0.05）；两组比较感染例次/1000导管日0.9%与1.0%，无统计学差异（P＞0.05）。原位换置组围术期未发生中重度并发症，12个月开存期率81.2%、次开存期率93.8%；对照组开存期率为65%、次开存期率85%；两组比较无统计学差异（P＞0.05）。结论颈内静脉原位导丝法换置中心静脉长期血液透析导管，在MHD患者中的使用是安全的、可行的。     

A Sharp Condition for the Ground State of Difference Equation

This note is concerned with a novel inequality condition for the existence of ground states of partial difference systems. Our result is potentially applicable to the estimation of eigenvalues of the loaded strings and nets.