Calculation of electronic spectra of porphin and its derivatives by a modified INDO/S method

Quantum-chemical calculations of excited electronic states of porphin (H₂P) and Mg-porphin (MgP) have been carried out in the framework of the INDO/S method with varying off-diagonal matrix elements of the one-electron Hamiltonian {ie027-01} and electron-electron interaction integrals {ie027-02} as functions of the internuclear distance. It has been found that a simultaneous increase in the π-type overlap factor for {ie027-03} and decrease in the {ie027-04} integrals, as compared with {ie027-05} calculated by the Nishimoto-Mataga formula, make it possible to reproduce the positions of the Q-and B-transitions in the experimental absorption spectrum with a precision of ∼300 cm⁻¹. In this case, the N_x-transition intensity of the H₂P molecule is halved, which means that only two B-transitions should be related to the Soret band as in the four-orbital model. Using the proposed parameterization (INDO/Sm), electronic spectra have been calculated for a number of porphyrin compounds including chlorine, bacteriochlorin, tetrabenzoporphin, and tetraazaporphin. The results obtained agree with the experimental data to an accuracy of 300–700 cm⁻¹ whereas the accuracy of the standard INDO/S calculation is no better than 3000 cm⁻¹. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 1, pp. 28–35, January–February, 2008.     

Convex combination maps over triangulations, tilings, and tetrahedral meshes

In a recent paper by the first author, a simple proof was given of a result by Tutte on the validity of barycentric mappings, recast in terms of the injectivity of piecewise linear mappings over triangulations. In this note, we make a short extension to the proof to deal with arbitrary tilings. We also give a simple counterexample to show that convex combination mappings over tetrahedral meshes are not necessarily one-to-one. Mathematics subject classifications (2000) 05C10, 05C85, 65D17, 58E20     

On the conditions for the coincidence of two cubic Bézier curves

In a recent article, Wang et al. [2] derive a necessary and sufficient condition for the coincidence of two cubic Bézier curves with non-collinear control points. The condition reads that their control points must be either coincident or in reverse order. We point out that this uniqueness of the control points for polynomial cubics is a straightforward consequence of a previous and more general result of Barry and Patterson, namely the uniqueness of the control points for rational Bézier curves. Moreover, this uniqueness applies to properly parameterized polynomial curves of arbitrary degree.     

基于新的整数型分子图论指数M系统探索烷烃核磁共振碳谱(13C NMR)化学位移和CSS规律

系统研究了核磁共振碳谱与化学位移和规律,以及拓扑图论方法在定量结构波谱关系(QSSR)中的应用.本文基于路径长度矢量p=p1,p2,p3,…,pm)组合研究提出了一种新的整数型拓扑图论指数M=(p1+p2)+(p1-p3),并发现它与烷烃¹³C NMR化学位移和有良好线性相关性:回归方程及其统计参数为CSS=+14.329^* M-21.089;n=65,R=0.991,SD=7.684,F=3648.021,U=215381.656,Q=3719.563;交互校验CV结果为:R=0.990,R²(01)=0.981,SD(01)=8.086,F(01)=3288.113,U(01)=214982.172,Q(01)=4119.042.     

保持C2连续的一类弧长参数化方法

讨论了C^2参数曲线的弧长参数化。在弧长区间选择性地取若干插值节点，利用原参数曲线的C^2连续性质，构造一类局部性Hermite插值三次样条，反插值参数曲线的弧长函数。所导致的近似弧长参数方程几何上完全描述原参数曲线，且自然地保持C^2连续。近似弧长参数化曲线对于精确弧长参数曲线具有实际应用所期望的逼近性质。     

Interweaving Markov Chain Monte Carlo Strategies for Efficient Estimation of Dynamic Linear Models

In dynamic linear models (DLMs) with unknown fixed parameters, a standard Markov chain Monte Carlo (MCMC) sampling strategy is to alternate sampling of latent states conditional on fixed parameters and sampling of fixed parameters conditional on latent states. In some regions of the parameter space, this standard data augmentation (DA) algorithm can be inefficient. To improve efficiency, we apply the interweaving strategies of Yu and Meng to DLMs. For this, we introduce three novel alternative DAs for DLMs: the scaled errors, wrongly scaled errors, and wrongly scaled disturbances. With the latent states and the less well known scaled disturbances, this yields five unique DAs to employ in MCMC algorithms. Each DA implies a unique MCMC sampling strategy and they can be combined into interweaving and alternating strategies that improve MCMC efficiency. We assess these strategies using the local level model and demonstrate that several strategies improve efficiency relative to the standard approach and the most efficient strategy interweaves the scaled errors and scaled disturbances. Supplementary materials are available online for this article.