Vector-Orthogonality and Lanczos-Type Methods

A method for solving a linear system is defined. It is a Lanczos-type method, but it uses formal vector orthogonality instead of scalar orthogonality. Moreover, the dimension of vector orthogonality may vary which gives a large freedom in leading the algorithm, and controlling the numerical problems. The ideas of truncated and restarted methods are revisited. The obtained residuals are exactly orthogonal to a space of increasing dimension. Some experiments are done, the problem of finding automaticaly good directions of projection remains partly open.     

Infinite Random Geometric Graphs

We introduce a new class of countably infinite random geometric graphs, whose vertices V are points in a metric space, and vertices are adjacent independently with probability p ? (0, 1){p \in (0, 1)} if the metric distance between the vertices is below a given threshold. For certain choices of V as a countable dense set in \mathbbRⁿ{\mathbb{R}^n} equipped with the metric derived from the L _∞-norm, it is shown that with probability 1 such infinite random geometric graphs have a unique isomorphism type. The isomorphism type, which we call GR _n , is characterized by a geometric analogue of the existentially closed adjacency property, and we give a deterministic construction of GR _n . In contrast, we show that infinite random geometric graphs in \mathbbR²{\mathbb{R}^{2}} with the Euclidean metric are not necessarily isomorphic.     

Estimation of integrated volatility in stochastic volatility models

In the framework of stochastic volatility models we examine estimators for the integrated volatility based on the pth power variation (i.e. the sum of pth absolute powers of the log‐returns). We derive consistency and distributional results for the estimators given high‐frequency data, especially taking into account what kind of process we may add to our model without affecting the estimate of the integrated volatility. This may on the one hand be interpreted as a possible flexibility in modelling, for example adding jumps or even leaving the framework of semimartingales by adding a fractional Brownian motion, or on the other hand as robustness against model misspecification. We will discuss possible choices of p under different model assumptions and irregularly spaced data. Copyright © 2005 John Wiley & Sons, Ltd.     

Transferrin immunoextraction for determination of carbohydrate‐deficient transferrin in human serum by capillary zone electrophoresis

CZE‐based assays for carbohydrate‐deficient transferrin (CDT) in which serum is mixed with an Fe(III) ion‐containing solution prior to analysis are effective approaches for the determination of CDT in patient samples. Sera of patients with progressed diseases, however, are prone to interferences comigrating with transferrin (Tf) that prevent the proper determination of CDT by CZE in these samples. The need of a simple and economic approach to immunoextract Tf from human serum prompted us to investigate the use of a laboratory‐made anti‐Tf spin column containing polyclonal rabbit anti‐human Tf antibodies linked to Sepharose 4 Fast Flow beads. This article reports extraction column manufacturing and column characterization with sera having normal and elevated CDT levels. The developed procedure was applied to a number of relevant hepatology and dialysis patient samples and could thereby be shown to represent an effective method for extraction and concentration of all Tf isoforms. Furthermore, lipemic sera were delipidated using a mixture of diisopropyl ether and butanol prior to immunoextraction. CDT could unambiguously be determined in all pretreated samples.     

On the use of x-ray-excited optical luminescence (XEOL) for the analysis of multisite rare-earth systems

The realization of a XEOL (X-ray-excited optical luminescence) spectrometer is reported. The aim of the present paper is to show that a comparison between UV-excited emission spectra and XEOL spectra can be helpful in the assignment of some weak transitions for multiple site rare-earth compounds. The case of c-Y₂O₃ doped with Eu³⁺ cations is considered in some detail, as in the XEOL spectrum three lines to be assigned to transitions occurring at the centrosymmetrical Eu³⁺ (C_3i) site are strongly enhanced. Additional site-selective UV-excited emission spectra are also reported supporting the present discussion.     

On a site-selective exafs experiment using optical emission

X-ray-excited optical luminescence (XEOL) is known to offer an alternative detection scheme of EXAFS spectra. Although this secondary emission appears restricted to a rather limited number of systems, we show that it can afford, under appropriate circumstances, an interesting property of site selectivity. The case of a ZnO + ZnTPP mixture was chosen as an illustrative example. The relevant formulation of the phenomenon for powdered samples is developed and the requirements for site selectivity are discussed.     

Matrix Continued Fraction for the Resolvent Function of the Band Operator

The aim of this paper is the expansion of a matrix function in terms of a matrix-continued fraction as defined by Sorokin and Van Iseghem. The function under study is the Weyl function or resolvent function of an operator, given in the standard basis by a bi-infinite band matrix, with p subdiagonals and q superdiagonals, where the p + q – 1 intermediate diagonals are zero. The main goal of this paper is to find, for the moments, an explicit form in terms of the coefficients of the continued fraction, called genetic sums, which lead to a generalization of the notion of a Stieltjes continued fraction. These results are extension of some results already found for the vector case (p = 1) and are a step in the direction towards the solution of the direct and inverse spectral problem. The actual computation of the approximants of the given function as the convergents of the continued fraction is shown to be effective. Some possible extensions are considered.     

Preparation and spectroscopic properties of 2-benzothiazolyl araldehyde hydrazones

Notwithstanding its tendency toward air oxidation in solution, 2-hydrazinobenzothiazole I reacted with aromatic aldehydes in ethanol to give the corresponding hydrazones III-XV in high yields and analytical purity. In related examples, acylation took place under similar conditions to produce hydrazides XVI-XX . The near-infrared bands of the absorption spectra of the araldehyde hydrazones have been associated with charge transfer and appeared to correlate with structural elements of the compounds in a way suggesting that the charge transfer was intermolecular.     

Characterisation of archaeological waterlogged wood by pyrolytic and mass spectrometric techniques

Two techniques based on analytical pyrolysis and mass spectrometry, direct exposure-MS (DE-MS) and pyrolysis-gas chromatography/mass spectrometry (Py-GC/MS), were used to characterise waterlogged archaeological wood and to study degradation patterns of wood in aqueous environments. The two techniques were applied to samples from the excavation of the Site of the Ancient Ships of Pisa San Rossore in Pisa (Italy), and data were compared to those relative to native sound wood of the same species (pine, elm, beech). Both the methods result valuable in the analysis of ancient wood artefacts, avoiding the long wet-chemical procedures that are commonly used in wood analysis, and allowing us to use a minimal sample size. DE-MS achieves a global mass spectral fingerprint of lignin and polysaccharides pyrolysis compounds in few minutes, and the results have been interpreted with the support of principal component analysis (PCA) of mass spectra. Py-GC/MS permits detailed molecular analysis of pyrolysis compounds and highlights some chemical modifications of lignin in archaeological samples, as demethylation of both guaiacyl and syringyl lignin units. Both the techniques demonstrate consistent loss of polysaccharides in archaeological wood.