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.     

Homo- and hetero-dinuclear anion complexes

The tripodal system 4, in which urea fragments are appended to the three terminal amine nitrogen atoms of a tris(2-aminoethyl)amine (tren) subunit, includes a Cu(II) ion and two anions X-, according to a cascade mechanism through three well defined stepwise equilibria in a DMSO solution. The first anion X- (halide, N3-, NCS-, NO2-, H2PO4-) seeks the Cu(II) centre coordinated by the tren moiety; the second anion X- interacts with the trisurea cavity, but this occurs only if the stronger H-bond acceptors, such as N3- and H2PO4-, are used. Binding of the second X- ion is favoured by the preorganising effect exerted by the metal and disfavoured by the steric and electrostatic repulsions between the anions. Under the appropriate conditions, heterodinuclear complexes of formula [Cu(II)(4)(Cl)(H2PO4)] can be obtained in solution, in which Cl- is bound to the metal centre and H2PO4- interacts with the trisurea compartment.     

Multivariate calibration on NIR data: development of a model for the rapid evaluation of ethanol content in bakery products

A new NIR method based on multivariate calibration for determination of ethanol in industrially packed wholemeal bread was developed and validated. GC-FID was used as reference method for the determination of actual ethanol concentration of different samples of wholemeal bread with proper content of added ethanol, ranging from 0 to 3.5% (w/w). Stepwise discriminant analysis was carried out on the NIR dataset, in order to reduce the number of original variables by selecting those that were able to discriminate between the samples of different ethanol concentrations. With the so selected variables a multivariate calibration model was then obtained by multiple linear regression. The prediction power of the linear model was optimized by a new “leave one out” method, so that the number of original variables resulted further reduced.     

An investigation on calcium (II) oxalate as solubility and universal standard

The investigation on calcium (II) oxalate is carried out in order to study its solubility in different ionic media. In the same conditions the protonation constants of oxalate and the stability of complex species have been determined. As the stoichiometric composition of the solid calcium (II) oxalate prepared for the investigation was accurately checked, the salt CaC2O4 x H2O is proposed as universal (chelometry, redox, acidimetry) standard. Results of titrations support this possibility.