The Orevkov invariant of an affine plane curve

We show that although the fundamental group of the complement of an algebraic affine plane curve is not easy to compute, it possesses a more accessible quotient, which we call the Orevkov invariant.

     

Construction of Graded Covariant GL(m/n) Modules Using Tableaux

Irreducible covariant tensor modules for the Lie supergroups GL(m/n) and the Lie superalgebras gl(m/n) and sl(m/n) are obtained through the use of Young tableaux techniques. The starting point is the graded permutation action, first introduced by Dondi and Jarvis, on V ^l . The isomorphism between this group of actions and the symmetric group S _l enables the graded generalization of the Young symmetrizers, and hence of the column relations and Garnir relations, to be made. Consequently, corresponding to each partition of l an irreducible GL(m/n) module may be obtained as a submodule of V ^l . A basis for the module labeled by the partition is provided by GL(m/n)–standard tableaux of shape defined by Berele and Regev. The reduction of an arbitrary tableau to standard form is accomplished through the use of graded column relations and graded Garnir relations. The standardization procedure is algorithmic and allows matrix representations of the Lie superalgebras gl(m/n) and sl(m/n) to be constructed explicitly over the field of rational numbers. All the various steps of the standardization algorithm are exemplified, as well as the explicit construction of matrices representing particular elements of gl(m/n) and sl(m/n).     

Universal nature of particle displacements close to glass and jamming transitions

We examine the structure of the distribution of single particle displacements (van Hove function) in a broad class of materials close to glass and jamming transitions. In a wide time window comprising structural relaxation, van Hove functions reflect the coexistence of slow and fast particles (dynamic heterogeneity). The tails of the distributions exhibit exponential, rather than Gaussian, decay. We argue that this behavior is universal in glassy materials and should be considered the analog, in space, of the stretched exponential decay of time correlation functions. We introduce a dynamical model that describes quantitatively numerical and experimental data in supercooled liquids, colloidal hard spheres, and granular materials. The tails of the distributions directly explain the decoupling between translational diffusion and structural relaxation observed in glassy materials.     

流动系统中鲁米诺电生化学发光(ECL)系统研究初探

本文描述了一个新的鲁米诺电生化学发光流动系统.通过微铂电极流动池,H2O2被还原为OH-以维持鲁米诺化学发光所要求的pH条件.本文对鲁米诺化学发光机理进行了初步探讨,并详细研究了ECL的最佳条件,该系统明显降低了反应噪声,优于混合反应系统,可作为液相色谱间接测定检测器.     

Optimization in Solvent Selection for Chlorin e6 in Photodynamic Therapy

The photophysical properties of chlorin e6 (Ce6) in twelve different protic, aprotic and non-polar solvents were investigated using ultraviolet–visible and fluorescence spectroscopic methods. Solvatochromic effects were determined by the changes in quantum yield, Stokes shift, fluorescence half-life and excited state dipole moments of Ce6 in the different solvents. The absorption shifts observed in different solvents were further analyzed using the Kamlet-Abboud-Taft model and the nature of solute-solvent interactions between Ce6 and different protic and aprotic solvents was elucidated. The quantum yields were found highest in protic solvents (except water), followed by aprotic and non-polar solvents. Solvent polarity parameters showed a linear increasing trend with Stokes shift and fluorescence half-life, which indicated the presence of Ce6-solvent interaction. Using the Kamlet-Abboud-Taft model, a direct correlation between the solvent polarity parameters and absorption shift was observed, which substantiated the existence of Ce6-solvent interaction by hydrogen bond formation. The excited state dipole moments in specific protic and aprotic solvents were found to be higher than the ground state dipole moments, implying a more polar nature of Ce6 during excited state transition.