Calculation of Normal Vibrations of Chlorin by the Method of Density Functionals

Using the DFT/B3LYP method with a 6-31G(d) basis set, the structure, normal vibration frequencies, and the absolute band intensities in the IR spectra of the chlorin molecule and its four symmetric isotopomers have been calculated. Scaling of the force field by the Pulay method in independent and natural coordinates has been carried out. A method for obtaining effective force fields without using experimental data on the fundamental vibration frequencies is proposed. By comparing the vibration modes and constructing special matrices, complete assignment of the fundamental frequencies of porphin and chlorin has been carried out. It has been shown that the majority of porphin macroring vibrations upon pyrrolenine ring hydrogenation are frequency-characteristic and only 12 vibrations change considerably. A frequency correlation with regard for the mode transition between chlorin and all its isotopomers under consideration has been established. Comparative analysis of the force fields of porphin and chlorin in dependent natural coordinates has revealed the unique nonlocal character of the change in force constants of the macroring upon hydrogenation of one pyrrolenine ring. Modeling of the IR spectra of chlorin and its isotopomers has been performed. Assignment and interpretation of the normal vibrations of the molecules under consideration have been carried out.     

BIFURCATIONS OF ROUGH 3—POINT—LOOP WITH HIGHER DIMENSIONS

The authors study the bifurcation problems of rough heteroclinic loop connecting three saddle points for the case β1 > 1, β2 > 1, β3 < 1 and β1β2β3 < 1. The existence, number, coexistence and incoexistence of 2-point-loop, 1-homoclinic orbit and 1-periodic orbit are studied. Meanwhile, the bifurcation surfaces and existence regions are given.     

The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator

Abstract The existence of infinitely many solutions to Sturm-Liouville boundary value problem with aLaplacian-like operator is studied by applying generalized polar coordinates.     

Barycentric coordinates for convex sets

In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally, we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they can be used to perform freeform deformations.      

地质建模中的B样条曲面拟合

Pigel和Tiller提出了简明、灵活的B样条曲面拟合方法.本文在Pigel和Tiller的方法的基础上,提出了适用于地质建模的基于重采样的B样条曲面拟合方法.该方法首先用重心坐标对原始的数据点进行重采样,然后对重采样得到的数据点进行拟合.拟合的误差可以通过修改控制顶点的个数来控制.结果表明:拟合得到的B样条曲面是光顺的.     

一种新型有机电致微腔结构的双模发射

采用结构Glass／DBR／ITO／NPB／NPB：Alq／Alq／Al制作了有机微腔电致发光器件。将空穴传输材料与发光材料以一定比例混合作为发光层，为了便于对比，在不改变有机层的膜厚的情况下同时制作了传统的异质结微腔器件，发现两种器件的发光光谱有很大不同，器件的复合效率与传统的异质结器件相比也得到了很大提高，这是因为将两种有机材料混合能消除界面势垒，提高器件的复合效率，从而提高了器件的发光性能，实现了微腔双模发射，且两个模式的半峰全宽分别为8nm和12nm。通过进一步优化器件结构可以实现微腔白光发射。     

Three-pencil lattices on triangulations

In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S ₃ on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.      

Chromium and yttrium-doped magnesium aluminum oxides prepared from layered double hydroxides

Layered double hydroxides with the hydrotalcite-like structures, containing Mg²⁺ and Al³⁺, doped with Cr³⁺ and Y³⁺, have been prepared by precipitation at constant pH. The weight percentages of Cr³⁺ and Y³⁺ were 1, 2, or 3%, and 0.5 or 1%, respectively. Single phases were obtained in all cases, whose crystallinity decreased as the content in Cr and Y was increased. The solids have been characterised by element chemical analysis, powder X-ray diffraction, thermal analyses (differential, thermogravimetric and programmed reduction), FT-IR and UV–vis spectroscopies; the specific surface areas have been determined from nitrogen adsorption isotherms at −196 °C. Upon calcination at 1200 °C for 5 h in air all solids display a mixed structure (spinel and rock salt for MgO); these solids have also been characterised by these techniques and their chromatic coordinates (CIE – L^*a^*b^*) have been determined. Their pink colour makes these solids suitable for being used as ceramic pigments.     

超球坐标下原子、分子体系的变分计算：—氦原子和氢负离子基态

应用超球会标表示氦原子和氢负离子的薛定谔方程，将二电子原子在三维空间中的运动转化为单电子原子在六维空间中受广义库仑力作用的运动，我们给出了六维空间广义角动量算符的本征值与本征函数，并以此本征函数微基构造超球波函数，得到超球径微分方程，以广义Laguerre 多项式表示超球径波函数，运用密度矩阵和线性变分法得到非正交基下超球径波函数满足的久期方程，最后求得能量和波函数，计算结果与精确的计算符合良好。