Electron-pairing analysis from localization and delocalization indices in the framework of the atoms-in-molecules theory

This article presents an overview of recent advances in the study of electron pairing through the use of localization and delocalization indices obtained from double integration over atomic basins of the exchange–correlation density in the framework of the atoms-in-molecules theory. These localization and delocalization indices describe the intra- and interatomic distribution of the electron pairs in a molecule. The main results of the application of these second-order indices to the analysis of molecular structure and chemical reactivity are briefly reviewed. It is shown that localization and delocalization indices represent a powerful tool to describe the electron-pair structure of molecules, which, in turn, provides deeper insight into relevant chemical phenomena such as electron correlation effects and the formation of localized α, β electron pairs. Received: 8 April 2002 / Accepted: 26 June 2002 / Published online: 6 September 2002 Acknowledgements. Financial help was furnished by the Spanish DGES projects no. PB98-0457-C02-01 and BQU2002-04112-C02-02. J.P. thanks the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya for benefiting from a doctoral fellowship, no. 2000FI-00582. M.S. is indebted to the Departament d'Universitats, Recerca i Societat de la Informació of the Generalitat de Catalunya for financial support through the Distinguished University Research Promotion, 2001. We also thank the Centre de Supercomputació de Catalunya for providing us with computing facilities. Correspondence to: M. Solà e-mail: miquel.sola@udg.es     

形体老化与疾病的非线性主成分分析

本文把 5个形体老化指标及 13种慢性病指标分别做成两个综合指标 ,再去研究人体老化、疾病与性别及年龄的关系。文中使用非线性主成分法及指出一般线性主成分法的局限性     

Sets and indices in linear programming modelling and their integration with relational data models

LP models are usually constructed using index sets and data tables which are closely related to the attributes and relations of relational database (RDB) systems. We extend the syntax of MPL, an existing LP modelling language, in order to connect it to a given RDB system. This approach reuses existing modelling and database software, provides a rich modelling environment and achieves model and data independence. This integrated software enables Mathematical Programming to be widely used as a decision support tool by unlocking the data residing in corporate databases.     

Refractive indices of biaxial crystals evaluated from the refractive indices ellipsoid equation

The expressions of the refractive indices corresponding wave vector k(θ,) are given by using coordinate transformations for the refractive indices ellipsoid equation of biaxial crystals. The refractive index expression of the wave, whose velocity is slower, is given by

and that of the wave, whose velocity is faster, is given by

     

Mixing and decomposition behavior of {[4bmpy][Tf2N] + [emim][EtSO4]} and {[4bmpy][Tf2N] + [emim][TFES]} ionic liquid mixtures

Mixing ionic liquids (ILs) has been revealed as a useful way to finely tune the properties of IL-based solvents. The scarce available studies on IL mixtures have shown a quasi-ideal behavior of their physical properties. In this work, we have performed a thermophysical characterization of two binary IL mixtures, namely {4-methyl-N-butylpyridinium bis(trifluoromethylsulfonyl)imide ([4bmpy][Tf₂N]) + 1-ethyl-3-methylimidazolium ethylsulfate ([emim][EtSO₄])} and {[4bmpy][Tf₂N] + 1-ethyl-3-methylimidazolium 1,1,2,2-tetrafluoroethanesulfonate [emim][TFES]}. Both binary IL mixtures have been recently proposed as promising solvents in the (liquid + liquid) extraction of aromatic hydrocarbons from mixtures with alkanes. Densities, viscosities, refractive indices, thermal stability, and specific heats of the {[4bmpy][Tf₂N] + [emim][EtSO₄]} and {[4bmpy][Tf₂N] + [emim][TFES]} IL mixtures have been measured as a function of both temperature and composition. Dynamic viscosities, refractive indices, and thermal stability of the {[4bmpy][Tf₂N] + [emim][EtSO₄]} mixture have exhibited strong deviations from the ideality, in contrast with the quasi-ideal properties of the {[4bmpy][Tf₂N] + [emim][TFES]} mixture and the behavior of the imidazolium and pyridinium-based IL mixtures studied hitherto. The reliability of predictive methods of the thermophysical properties of the mixtures has also been evaluated.     

Generalized potentials in variable exponent Lebesgue spaces on homogeneous spaces

We consider generalized potential operators with the kernel on bounded quasimetric measure space (X, μ, d) with doubling measure μ satisfying the upper growth condition μB(x, r) ? Kr^N, N ∈ (0, ∞). Under some natural assumptions on a(r) in terms of almost monotonicity we prove that such potential operators are bounded from the variable exponent Lebesgue space L^p(?)(X, μ) into a certain Musielak‐Orlicz space L^p(X, μ) with the N‐function Φ(x, r) defined by the exponent p(x) and the function a(r). A reformulation of the obtained result in terms of the Matuszewska‐Orlicz indices of the function a(r) is also given. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Comparison of certain value-at-risk estimation methods for the two-parameter Weibull loss distribution

The Weibull distribution is one of the most important distributions that is utilized as a probability model for loss amounts in connection with actuarial and financial risk management problems. This paper considers the Weibull distribution and its quantiles in the context of estimation of a risk measure called Value-at-Risk (VaR). VaR is simply the maximum loss in a specified period with a pre-assigned probability level. We attempt to present certain estimation methods for VaR as a quantile of a distribution and compare these methods with respect to their deficiency (Def) values. Along this line, the results of some Monte Carlo simulations, that we have conducted for detailed investigations on the efficiency of the estimators as compared to MLE, are provided.     

Gas chromatographic identification of chlorination products of aliphatic ketones

Chlorinated derivatives of aliphatic ketones are a class of organic compounds poorly characterized by both mass spectra and chromatographic retention indices up to present. It is caused by objective difficulties of isolation of individual products from reaction mixtures formed in the result of non-selective chlorination of parent carbonyl compounds. Nevertheless the differences of GC retention indices for structurally analogous chlorination products of different ketones and initial substrates indicate the constancy depending on the number and position of chlorine atoms in the molecules. This feature permits us to use the simplest kind of additive schemes in identification of such chlorinated derivatives, including diastereomeric α,α'-dichloro-k-alkanones (k>2). Hence, the identification of chlorination products of aliphatic ketones becomes possible for any compounds of this class without using mass spectrometric data only in the result of accurate measurement of their GC retention indices.     

Classification of Positive Ground State Solutions with Different Morse Indices for Nonlinear N-Coupled Schr(o)dinger System

In this paper,we study the following N-coupled nonlinear Schr(o)dinger sys-tem{-△uj+ uj =μju3j + ∑i≠jβi,ju3iuj,in Rn,uj＞0 in Rn,uj(x)→0 as |x|→+∞,j=1,…,N,where n ≤ 3,N ≥ 3,μj ＞ 0,βi,j =βj,i ＞ 0 are constants and βj,j =μj,j =1,…,N.There have been intensive studies for the system on existence/non-existence and clas-sification of ground state solutions when N =2.However fewer results about the classification of ground state solution are available for N ≥ 3.In this paper,we first give a complete classification result on ground state solutions with Morse indices 1,2 or 3 for three-coupled Schr(o)dinger system.Then we generalize our results to N-coupled Schr(o)dinger system for ground state solutions with Morse indices 1 and N.We show that any positive ground state solutions with Morse index 1 or Morse index N must be the form of (d1w,d2w,…,dNw) under suitable conditions,where w is the unique positive ground state solution of certain equation.Finally,we generalize our results to fractional N-coupled Schr(o)dinger system.     

Bond orders and electron delocalization indices for S–N,S–C and S–S bonds in 1,2,3-dithiazole systems

A parametric QTAIM-based (topological) model of bond orders and a modification of the Pauling bond order model are proposed for N,S-containing heterocycles, in particular, for 1,2,3-dithiazoles and 1,2,3-dithiazolium systems, which are prone to the formation of stable radicals and therefore are promising compounds in photovoltaics. These models have been parameterized for covalent S–N, S–C and S–S bonds using the electron delocalization indices. A modified Pauling’s bond order model uses turning radii, that is, the distances within which the potential acting on an electron in a system still tends to return that electron to the atomic basin, and avoids the need to choose the hybridization state of bound atoms arbitrarily.