Evaluation of a retention model in comprehensive two-dimensional gas chromatography

Modeling the retention in comprehensive two-dimensional gas chromatography (GC x GC) was achieved using retention indices obtained in conventional GC. Predicted results were compared with experimental data obtained in the two-dimensional separation of a synthetic hydrocarbon mixture. This proved to be helpful in optimizing the operating conditions of GC x GC separation of a complex petroleum sample and in identifying chemical families.     

Helly-type theorems for homothets of planar convex curves

Helly's theorem implies that if is a finite collection of (positive) homothets of a planar convex body , any three having non-empty intersection, then has non-empty intersection. We show that for collections of homothets (including translates) of the boundary , if any four curves in have non-empty intersection, then has non-empty intersection. We prove the following dual version: If any four points of a finite set in the plane can be covered by a translate [homothet] of , then can be covered by a translate [homothet] of . These results are best possible in general.

     

Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. VI*

The present Part VI of this series of articles provides a mathematical and methodical link between (i) fundamental methodology in the repeat space theory (RST), which is referred to as the approach via the aspect of form and general topology and which has universal unifying power to handle additivity problems of molecules that have many identical moieties, and (ii) frontier electron theory of reactivity indices. Using theoretical tools required to link (i) and (ii), we establish a theorem from which the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in the previous Part V) directly follows. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 389–400, 2001     

Portfolio selection under strict uncertainty: A multi-criteria methodology and its application to the Frankfurt and Vienna Stock Exchanges

In modern portfolio theory, it is common practice to first compute the risk-reward efficient frontier and then to support an individual investor in selecting a portfolio that meets his/her preferences for profitability and risk. Potential flaws include (a) the assumption that past data provide sufficient evidence for predicting the future performances of the securities under consideration and (b) the necessity to mathematically determine or approximate the investor’s utility function. In this paper, we propose a methodology whose initial phase filters portfolios that are inefficient from a historical perspective. While this is consistent with traditional approaches, the second phase differs from the standard approach as it uses a decision table constructed by considering multiple scenarios assuming strict uncertainty. The table cells measure consequences by a multi-criteria linear performance index of simulated future returns, which avoids difficulties with performance ratios. The real world applicability is illustrated through two studies based on data from the stock exchanges in Frankfurt and Vienna.     

Characterizations of the Deegan–Packel and Johnston power indices

In this paper, we provide a new characterization of the Deegan–Packel power index, which uses a new monotonicity property, and two characterizations of the Johnston power index by employing some usual properties of the literature and two new transfer properties. Finally, a real-world numerical example taken from the political field illustrates the main differences between these two indices.     

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