Development of a Sequential Injection Analysis Device for the Determination of Total Polyphenol Index in Wine

A sequential injection analysis method is developed for the determination of the total polyphenol index in wines. The determination is based on the Folin-Ciocalteu reaction, which is monitored spectrophotometrically. Interactions between experimental variables and their optimal levels were investigated using factorial designs. The proposed system is fully computerised and is able to monitor polyphenol index in real samples of white, sweet and red wines. The calibration graph is linear from 5 to 200mg·L^–1 using Tannic acid as standard, with a detection limit of 3.2mg·L^–1. Interferences are studied. For validation purposes the proposed methodology was applied to the determination of the total polyphenol index in different types of wines and compared with earlier alternatives in order to assess their performance.     

Nontrivial Solutions for a Semilinear Dirichlet Problem with Nonlinearity Crossing Multiple Eigenvalues

In this paper we prove that a semilinear elliptic boundary value problem has at least three nontrivial solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues of the Laplacian and all solutions are nondegenerate. A pair are of one sign (positive and negative, respectively). The one sign solutions are of Morse index less than or equal to 1 and the third solution has Morse index greater than or equal to 2. Extensive use is made of the mountain pass theorem, and Morse index arguments of the type Lazer–Solimini (see Lazer and Solimini, Nonlinear Anal. 12(8), 761–775, 1988). Our result extends and complements a theorem of Cossio and Veléz, Rev. Colombiana Mat. 37(1), 25–36, 2003.AMS Subject classification: 35J20; 35J25; 35J60.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

Deformational Properties of Irradiated Composite Materials Based on PET and PE

Considering the wide applicability of polymeric composite materials, heterogeneous blends of poly(ethylene terephtalate) (PET) and polyethylenes of high and low densities (HDPE and LDPE, respectively) were investigated. Rheological (the flow-behavior index), mechanical (the yield strength and the Charpy impact strength), and morphological (crystallinity and the melting temperature) properties were detected for individual blend components and different blend compositions. A radiation treatment (-rays) was applied to improve certain characteristics of the heterogeneous blends. The results of this investigation show that the radiation modification can be successfully used to improve some physical properties of the PET-based blends and to choose individual blend components, optimum irradiation conditions, and desirable blend compositions, which allows producing materials with a predictable set of mechanical properties.     

Estimation of heavy-tailed probability density function with application to Web data

Summary  Common non-parametric estimators of a probability density function (PDF) show bad performance for heavy-tailed PDFs. Using a parametric approximation of the true cumulative distribution function (CDF), the transformation-retransformation of the data is explored here as a useful tool for the reliable PDF prediction. The PDF estimators are compared by their capacity to solve a classification problem. Simulation results and an application to Web data analysis are presented, too.     

A characterization of the finite simple groups with set of indices of their maximal subgroups

We study the problem concerning the influence of indices of maximal subgroups of a simple group on the structure of a group. We obtain a characterization property of all finite simple groups.     

Multiple Solutions and Its Morse Index for One-Dimensional Nonlinear Problem

The multiple solutions for one-dimensional cubic nonlinear problem u" u~3=0,u(0)=u(π)=0are computed,on the basis of the eigenpairs of-φ"_k=λ_(kφk),k=1,2,3....There exist two nonzero solutions±u_k corresponding to each k,and their Morse index MI(k) for 1(?)k(?)20 is to be exactly determined.It isshown by the numerical results that MI(k)(?)k.     

NO dissociation pathways on Rh(1 0 0), (1 1 0), and (1 1 1) surfaces: A comparative density functional theory study

The chemisorption and dissociation pathways of NO on the Rh(1 0 0), (1 1 0), and (1 1 1) surfaces are studied by the plane-wave density functional theory (DFT) with CASTEP program. In addition, the electronic and geometrical effects that affect the NO dissociation reactions have been investigated in detail. The calculation results are presented as following: The effective activation energies of the best NO dissociation pathways on the Rh(1 0 0), the Rh(1 1 0), and the Rh(1 1 1) are 0.63, 0.66 and 1.77 eV, respectively. The activity of the Rh planes for NO dissociation is in the order of Rh(1 0 0) ≈ Rh(1 1 0) > Rh(1 1 1). The low dissociation barrier for Rh(1 0 0) and Rh(1 1 0) is associated with the existence of a lying-down NO structure which acts as a precursor for dissociation. By Mulliken population analysis and structure analysis, both electronic and geometrical effects are found to affect the NO dissociation reactions, but the geometrical effect exceed the electronic. The energy decomposition scheme has been used to provide further insight into the NO dissociation reactions. Based on the calculations, the interaction energy between N and O in the transition state on the Rh(1 1 1) is found much larger than that on the Rh(1 0 0) and the Rh(1 1 0). The major differences of should originate from the variation of the bonding competition effect.     

扭化的Atiyah-Singer算子(I)

本文证明黎曼流表上的ｄｅ Ｒｈａｍ以及Ｓｉｇｎａｔｕｒｅ算子都同构于扭化的Ａｔｉｙａｈ－Ｓｉｎｇｅｒ算子。这两类算子的局部指数定理和局部Ｌｅｆｓｃｈｅｔｚ不动点公式都可以从扭化的Ａｔｉｙａｈ－Ｓｉｎｇｅｒ算子得到。