Definition and detection of data-based uniqueness in evaluating bilinear (two-way) chemical measurements

Multivariate curve resolution methods, frequently used in analyzing bilinear data sets, result in ambiguous decomposition in general. Implementing the adequate constraints may lead to reduce the so-called rotational ambiguity drastically, and in the most favorable cases to the unique solution. However, in some special cases, non-negativity constraint as minimal information of the system is a sufficient condition to resolve profiles uniquely. Although, several studies on exploring the uniqueness of the bilinear non-negatively constrained multivariate curve resolution methods have been made in the literature, it has still remained a mysterious question. In 1995, Manne published his profile-based theorems giving the necessary and sufficient conditions of the unique resolution. In this study, a new term, i.e., data-based uniqueness is defined and investigated in details, and a general procedure is suggested for detection of uniquely recovered profile(s) on the basis of data set structure in the abstract space. Close inspection of Borgen plots of these data sets leads to realize the comprehensive information of local rank, and these argumentations furnish a basis for data-based uniqueness theorem. The reported phenomenon and its exploration is a new stage (it can be said fundament) in understanding and describing the bilinear (matrix-type) chemical data in general.     

Van't Hoff analysis in chiral chromatography

The present review discusses the theory and application of van't Hoff analysis in chiral chromatography, with main focus on liquid chromatography. The topics considered include the physical meaning of van't Hoff equation's parameters, interpretation of thermodynamic data in terms of retention and enantioseparation mechanisms, abnormal behavior of van't Hoff plots, and best practices to avoid biased results.     

首次穿过边界概率及其在金融中的应用

本文把数学和管理科学有机结合,为数学应用提出问题,得出新结果,推广了J.Michel Harrison(1985)[1]第43页的命题27,并给出了在金融中的应用.     

矩母函数:拟对称概率测度

本文用凸函数的方法研究了概率测度的矩母函数和由C.J.Stone提出的拟对称性,并刻画了Martin边界的法向量.拟对称性在随机游动的比例极限定理中是一个重要的概念.这些结果可应用于Levy过程的研究.     

几种新的回归诊断图示模型及其医学应用

本文在变量选择问题的基础上，提出了一种新的图示模型──减变残差图。并给出它的两种推广形式：均值平移异常值检验图和部分影响诊断图。通过它们不但可以容易地考察一个变量在模型中的作用和检验异常值，而且可以诊断样本点对模型和变量的影响大小。     

“String” formulation of the dynamics of the forward interest rate curve

We propose a formulation of the term structure of interest rates in which the forward curve is seen as the deformation of a string. We derive the general condition that the partial differential equations governing the motion of such string must obey in order to account for the condition of absence of arbitrage opportunities. This condition takes a form similar to a fluctuation-dissipation theorem, albeit on the same quantity (the forward rate), linking the bias to the covariance of variation fluctuations. We provide the general structure of the models that obey this constraint in the framework of stochastic partial (possibly non-linear) differential equations. We derive the general solution for the pricing and hedging of interest rate derivatives within this framework, albeit for the linear case (we also provide in the appendix a simple and intuitive derivation of the standard European option problem). We also show how the “string” formulation simplifies into a standard N-factor model under a Galerkin approximation. Received: 30 January 1998 / Revised: 12 February 1998 / Accepted: 16 February 1998     

Entropic criterion for model selection

Model or variable selection is usually achieved through ranking models according to the increasing order of preference. One of methods is applying Kullback–Leibler distance or relative entropy as a selection criterion. Yet that will raise two questions, why use this criterion and are there any other criteria. Besides, conventional approaches require a reference prior, which is usually difficult to get. Following the logic of inductive inference proposed by Caticha [Relative entropy and inductive inference, in: G. Erickson, Y. Zhai (Eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, vol. 707, 2004 (available from arXiv.org/abs/physics/0311093)], we show relative entropy to be a unique criterion, which requires no prior information and can be applied to different fields. We examine this criterion by considering a physical problem, simple fluids, and results are promising.     

How electrons guard the space: shape optimization with probability distribution criteria

Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume ³ for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue     

Optimization of the process variables for the synthesis of cardanol-based novolac-type phenolic resin using response surface methodology

Models capable of predicting the maximum extent of conversion (p) of cardanol-based novolac-type phenolic resin, have been developed using response surface methodology to determine the optimum reaction conditions. Three-dimensional response surface and their contour plot were drawn. The maximum extent of conversion (98.93%) was predicted when the cardanol was condensed with formaldehyde (molar ratio 1:0.652) at 119.84 °C for a time period of 3 h with the catalyst (e.g., citric acid) concentration of 1.988% of total volume of cardanol and formaldehyde. The pH of the reaction mixture was maintained at 3.0. These predicted values for optimum process conditions were in good agreement with experimental data.     

XPS and XAES analysis of copper,arsenic and sulfur chemical state in enargites

Enargite, a copper arsenic sulfide with the formula Cu₃AsS₄ is of environmental concern due to its potential to release toxic arsenic species. The oxidation and dissolution of enargite are governed by the composition and chemical state of the outermost surface layer. Qualitative and quantitative analysis of the enargite surface can be initially obtained on the basis of X‐ray photoelectron spectroscopy (XPS) binding energy and intensity data. However, a more precise determination of the chemical state of the principal elements of enargite (copper, arsenic and sulfur) in the altered surface layer and in the bulk of the mineral requires a combined analysis based on XPS photoelectron lines and the corresponding X‐ray excited Auger lines. On the basis of results obtained on natural and synthetic enargite samples and on standards of sulfides and oxides, the Auger parameter α′ of different compounds was calculated and the Wagner chemical state plots were drawn for arsenic, copper and sulfur. Arsenic in enargite is found to be in a chemical environment similar to that of arsenides or elemental arsenic, whereas copper in enargite is in a chemical state that corresponds to copper sulfide, Cu₂S, for all samples irrespective of surface treatment (natural or freshly cleaved). Only sulfur changed from a chemical state similar to that of copper or iron sulfide in freshly cleaved samples to another state in natural enargite in the as‐received state. Thus, it is the sulfur atom at the surface of enargite that is most susceptible to changes in the enargite surface state and composition. A more detailed interpretation of this behavior, based on differences in the initial and final state effects, is proposed here. The concept of Auger parameter and chemical state plot, used here for the first time for investigating enargite, has proved to be a method to unambiguously assign the chemical state of the principal elements copper, arsenic and sulfur in these minerals. Copyright © 2006 John Wiley & Sons, Ltd.