The computation of the representation matrices of the generators of the unitary group

A method is presented for the efficient computation of the representation matrices of the unitary group, U(n) in the Gelfand—Tsetlin basis (corresponding to the usual spin-symmetry adapted basis for an N electron CI). The present scheme is conceptually and computationally attractive in that it is formulated directly in terms of Weyl tableaux and also that it permits simultaneous basis vector generation and matrix element evaluation. In addition the basis vectors are ordered so that subsequent restriction to the three dimensional rotation group is facilitated. An illustrative example is also presented.Taken in part from a thesis submitted to the University of London in partial fulfilment of the requirements for the degree of PhD.     

Statistics of transfer matrices for disordered quantum thin metallic slabs

In the quantum transport problem of a tight-binding Anderson model, the statistics of eigenvalues for the transfer matrices of thin disordered slabs is studied. Numerical simulations indicate that the probability distribution of nearest neighbor eigenvalue spacing and the ₃ statistics have already become close to that of the Gaussian orthogonal ensemble for sample lengths of the order of the mean free path, provided that transverse localization effects are not important. An intuitive argument is given why this should occur independently of the size of the matrix. Therefore, good mixing of the channels is not essential for obtaining Gaussian orthogonal ensemble type statistics and universal conductance fluctuations.     

Properties of balanced and perfect matrices

In this paper we define wheel matrices and characterize some properties of matrices that are perfect but not balanced. A consequence of our results is that if a matrixA is perfect then we can construct a polynomial number of submatricesA _I,,A _n ofA such thatA is balanced if and only if all the submatricesA ₁,,A _n ofA are perfect. This implies that if the problem of testing perfection is polynomially solvable, then so is the problem of testing balancedness.Partial support under NSF Grants DMS-8606188, ECS-8800281 and DDM-8800281.     

Homologies cyclique et de Hochschild de certains espaces homogènes quantiques

Nous quantifions certaines inclusions d'algèbres de Lie semi-simpleshg. Nous calculons les homologies associées aux quantifications, surC((h)), d'une part des algèbres de fonctions formelles surG/H, pourHG une inclusion de groupes de Lie semi-simples associée, et d'autre part des fonctions algébriques sur SL(2,C)/T.We quantize certain inclusions of semisimple Lie algebrashg. We compute the cyclic and Hochschild homologies for theC((h))-quantizations of

Viscosimetric Study of Some Cyclic Ethers with Benzene, Toluene, or Halobenzene

Experimental viscosities and the corresponding viscosity deviations for the binary mixtures of a cyclic ether (tetrahydrofuran, tetrahydropyran, 2-methyltetrahydrofuran, or 2,5-dimethyltetrahydrofuran) with benzene, toluene, fluorobenzene, or chlorobenzene are given at 25°C. The kinematic viscosities and the corresponding densities were measured with an uncertainty of ±10^{– 4} mm²-s^{– 1} and ±(5×10^{– 3}) kg-m^{– 3}, respectively. The viscosity data were correlated by the equations of Grunberg–Nissan, McAllister, and Heric. On the other hand, the results have been compared to the predictions, by the method proposed by Asfour.     

Catalysis in Organic Solvents with Lipase Immobilized by Sol-Gel Technique

A series of immobilized lipases were obtained by sol-gel process, using silica prepolymers prepared from tetramethoxysilane, methyltrimethoxysilane, propyltrimethoxysilane and (3-aminopropyl)triethoxysilane. The activities of these biocatalysts were compared with the lipase adsorbed on poly(methylhydroxysiloxane) and encapsulated into a silicone rubber, lipase entrapped in nanoporous silica matrix and commercial sol-gel lipase. Model reactions were the esterification of stearic acid and Corey lactone bisalcohol (an intermediate of prostaglandin synthesis). The positive effect of hydrophobic-hydrophilic interface, created by the addition of organosilanes, on the activity of biocatalysts was partially reduced by decreasing specific surface of mesopores. Hydrophobic solvents increased the activity of the lipase entrapped in tetramethoxysilane–methyltrimethoxysilane prepolymer in the sequence acetone < toluene < benzene < decane < hexane. The activity of silicone rubber-encapsulated biocatalysts was proportional to polymer swelling in organic solvents (hexane > toluene > acetone).     

Facile Synthesis of Tricyclic 1,2,4-Oxadiazolines-Fused Tetrahydro-Isoquinolines from Oxime Chlorides with 3,4-Dihydroisoquinoline Imines

A mild and efficient strategy for the synthesis of tricyclic 1,2,4-oxadiazolines-fused tetrahydro-isoquinolines derivatives via [3 + 2] cycloaddition reaction is reported. The reactions provided the functionalized tricyclic 1,2,4-oxadiazolines in high yields (up to 96%). This protocol is simple and easy to handle. Moreover, a gram-scale experiment further highlights the synthetic utility. The chemical structure of the product was determined by X-ray single-crystal structure analysis. A possible mechanism for this transformation is proposed to explain the reaction process.     

Three-Mode Cyclic Squeezed States Constructed via EPR Entangled State

We construct the three-mode cyclic squeezed states and analyze its squeezing property by using the technique of integration within an ordered product of operators and the natural representation of the two-mode squeezing operator in the Einstein-Podolsky-Rosen entangled state basis.     

适用于圆筒形增益区的同轴四镜腔的失调分析

采用矩阵光学方法,对适用于可见光的圆筒形增益区同轴四镜腔中的腔镜因倾斜而产生的失调特性进行了分析,给出了相关计算公式。该四镜腔由同轴的一个复曲面全反镜和两个光学玻璃加工的透镜和一个平面输出镜组成。以He-Ne激光器为例,给出了数值计算结果,关键元件复曲面镜的失调对输出的影响较大。这为腔元件的加工以及腔镜的安装调试提供了参考。     

Antiviral Activity of a Cyclic Pro-Pro-β3-HoPhe-Phe Tetrapeptide against HSV-1 and HAdV-5

The core of Cyclolinopeptide A (CLA, cyclo(LIILVPPFF)), responsible for its high immunosuppressive activity, contains a Pro-Pro-Phe-Phe sequence. A newly synthesized cyclic tetrapeptide, cyclo(Pro-Pro-β³-HoPhe-Phe) (denoted as 4B8M) bearing the active sequence of CLA, was recently shown to exhibit a wide array of anti-inflammatory properties in mouse models. In this investigation, we demonstrate that the peptide significantly inhibits the replication of human adenovirus C serotype 5 (HAdV-5) and Herpes simplex virus type-1 (HSV-1) in epithelial lung cell line A-549, applying Cidofovir and Acyclovir as reference drugs. Based on a previously established mechanism of its action, we propose that the peptide may inhibit virus replication by the induction of PGE2 acting via EP2/EP4 receptors in epithelial cells. In summary, we reveal a new, antiviral property of this anti-inflammatory peptide.