Non-destructive method for determination of hydroxyl value of soybean polyol by LS-SVM using HATR/FT-IR

This paper presents the use of least-squares support vector machine (LS-SVM) for quantitative determination of hydroxyl value (OHV) of hydroxylated soybean oils by horizontal attenuated total reflection Fourier transform infrared (HATR/FT-IR) spectroscopy. A least-squares support vector machine (LS-SVM) calibration model for the prediction of hydroxyl value (OHV) was developed using the range 1805.1-649.9 cm(-1). Validation of the method was carried out by comparing the OHV of a series of hydroxylated soybean oil predicted by the LS-SVM model to the values obtained by the AOCS standard method. A correlation coefficient equal to 0.989 and RMSEP = 4.96 mg of KOH/g was obtained. This study demonstrates a better prediction ability of the LS-SVM technique to determine OHV in hydroxylated soybean oil samples by HATR/FT-IR spectra.     

Factoring ideals in Prüfer domains

We show that in certain Prüfer domains, each nonzero ideal I can be factored as , where I^v is the divisorial closure of I and is a product of maximal ideals. This is always possible when the Prüfer domain is h-local, and in this case such factorizations have certain uniqueness properties. This leads to new characterizations of the h-local property in Prüfer domains. We also explore consequences of these factorizations and give illustrative examples.     

A <Emphasis Type="Italic">V</Emphasis>-cycle Multigrid for multilevel matrix algebras: proof of optimality

We analyze the convergence rate of a multigrid method for multilevel linear systems whose coefficient matrices are generated by a real and nonnegative multivariate polynomial f and belong to multilevel matrix algebras like circulant, tau, Hartley, or are of Toeplitz type. In the case of matrix algebra linear systems, we prove that the convergence rate is independent of the system dimension even in presence of asymptotical ill-conditioning (this happens iff f takes the zero value). More precisely, if the d-level coefficient matrix has partial dimension n _r at level r, with , then the size of the system is , , and O(N(n)) operations are required by the considered V-cycle Multigrid in order to compute the solution within a fixed accuracy. Since the total arithmetic cost is asymptotically equivalent to the one of a matrix-vector product, the proposed method is optimal. Some numerical experiments concerning linear systems arising in 2D and 3D applications are considered and discussed.     

Laplacian Operators and Radon Transforms on Grassmann Graphs

Let Ω be a vector space over a finite field with q elements. Let G denote the general linear group of automorphisms of Ω and let us consider the left regular representation associated with the natural action of G on the set X of linear subspaces of Ω. In this paper we study a natural basis B of the algebra End_G(L ₂(X)) of intertwining maps on L ₂(X). By using a Laplacian operator on Grassmann graphs, we identify the kernels in B as solutions of a basic hypergeometric difference equation. This provides two expressions for these kernels. One in terms of the q-Hahn polynomials and the other by means of a Rodrigues type formula. Finally, we obtain a useful product formula for the mappings in B. We give two different proofs. One uses the theory of classical hypergeometric polynomials and the other is supported by a characterization of spherical functions in finite symmetric spaces. Both proofs require the use of certain associated Radon transforms.     

An investigation on the nature of the peptide at m/z 904, overexpressed in plasma of patients with colorectal cancer and familial adenomatous polyposis

In an investigation devoted to the search for plasma markers for colorectal cancer (CRC), carried out by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry, a series of overexpressed peptides were identified in the plasma of patients. Among them the peptide with molecular weight 903 Da was the most abundant one, with a mean +/- (SD) relative abundance of 37 +/- 17% and a frequency over 60%. Interestingly, also in plasma samples of ten subjects affected by familial adenomatous polyposis (FAP), the peptide with molecular weight 903 was overexpressed. In this investigation, MALDI/MS/MS experiments were carried out on the ion at m/z 904 detected in the MALDI mass spectra of CRC and FAP patients. The data analysis by SwissProt.2007.01.09 indicates that this peptide is due to the sequence RPPGFSPF, found in the kininogen-1 precursor, which is an alpha-2-thiol proteinase inhibitor. In the case of subjects affected by a particular FAP syndrome, the MALDI/MS/MS spectra were quite different from those obtained from CRC and FAP patients. In fact, two sequences have been evidenced: RPPGFSPF belonging to kininogen-1 precursor, and PRKSSSSR belonging to Forkhead box protein 01A.     

An esterase-activated magnetic resonance contrast agent

A Gd(III) complex bearing pendant acetoxymethyl esters is activated on exposure to porcine liver esterase; the 84% increase in relaxivity is a result of suppression of HCO(3)(-)/CO(3)(2-) binding by the resulting negative charge.