On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle

We consider the general problem of determining the maximum possible multiplicity of an eigenvalue in a Hermitian matrix whose graph contains exactly one cycle. For some cases we express that maximum multiplicity in terms of certain parameters associated with the graph.     

A novel approach based on recurrent neural networks applied to nonlinear systems optimization

This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid subspace technique. These parameters guarantee the convergence of the network to the equilibrium points that represent an optimal feasible solution. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network.     

Detection of hepatocarcinoma in rats by integration of the fluorescence spectrum: Experimental model

The incorporation of spectroscopic techniques into diagnostic procedures may greatly improve the chances for precise diagnostics. One promising technique is fluorescence spectroscopy, which has recently been used to detect many different types of diseases. In this work, we use laser-induced tissue fluorescence to detect hepatocarcinoma in rats using excitation light at wavelengths of 443 and 532 nm. Hepatocarcinoma was induced chemically in Wistar rats. The collected fluorescence spectrum ranges from the excitation wavelength up to 850 nm. A mathematical procedure carried out on the spectrum determines a figure of merit value, which allows the detection of hepatocarcinoma. The figure of merit involves a procedure which evaluates the ratio between the backscattered excitation wavelength and the broad emission fluorescence band. We demonstrate that a normalization allowed by integration of the fluorescence spectra is a simple operation that may allow the detection of hepatocarcinoma.     

Converged properties of clean metal surfaces by all-electron first-principles calculations

All-electron full-potential linearized augmented plane-wave calculations of the surface energy, work function, and interlayer spacings of close-packed metal surfaces are presented, in particular, for the free-electron-like metal surfaces, Mg(0 0 0 1) and Al(1 1 1), and for the transition metal surfaces, Ti(0 0 0 1), Cu(1 1 1), Pd(1 1 1), and Pt(1 1 1). We investigate the convergence of the surface energy as a function of the number of layers in the slab, using the Cu(1 1 1) surface as an example. The results show that the surface energy, as obtained using total energies of the slab and bulk from separate calculations, converges well with respect to the number of layers in the slab. Obviously, it is necessary that bulk and surface calculations are performed with the same high accuracy. Furthermore, we discuss the performance of the local-density and generalized gradient approximations for the exchange-correlation functional in describing the various surface properties.     

Immobilization of catalase on membranes of poly(ethylene)-g-co-acrylic acid and poly(tetrafluoroethylene)-g-co-acrylic acid and their application in hydrogen peroxide electrochemical sensors

The immobilization of catalase on grafted membranes of poly(ethylene)-g-co-acrylic acid and poly(tetrafluoroethylene)-g-co-acrylic acid and their application in hydrogen peroxide electrochemical sensors is described. The introduction of carboxylic acid groups onto a hydrophobic support provides a good environment for subsequent enzyme immobilization. This single membrane, hydrogen peroxide sensor showed significant improvement with respect to the double membrane versions. The response is very rapid, the linear range being from 10 μM up to 6 mM, with a detection limit of 4.7 μM, and a lifetime of more than 4 months.     

Mössbauer study of small amounts of iron in graphite,around the diamond-graphite pressure-temperature stability region

An exploratory Mössbauer spectroscopy study of the Fe-C system in the C rich region, prepared by high pressure-high temperature treatment near the graphite-diamond stability line, was made. The results obtained for the different processing conditions give no evidence of Fe intercalation in graphite. The presence of some water in the cell produced hydrated Fe complexes, which can explain the deleterious effect of water or hydrogen in the high pressure diamond synthesis.     

Anharmonic effects in large-amplitude vibrations of metal clusters

Two types of extreme collective motion, large-amplitude many-phonon vibration of the ionic core and rotation of the cluster with high angular momenta, are considered. The interplay between vibration and collective motion towards fission is discussed. A new mechanism of formation and rupture of the neck is proposed which is based on the Franck-Condon principle, and accounts for the interplay between vibration and fission. Under rotation, the change of the shape of the cluster and a phase transition from axially symmetric to triaxial ellipsoid are predicted. For studying the effects, vibrational motion can be induced by laser radiation. Rotational motion may arise in collisions of clusters. Received 26 April 2001 and Received in final form 15 October 2001     

Reaction of 1,3-dimethyl-5-acetyl-barbituric acid (DAB) with primary amines. Access to intermediates for selectively protected spermidines

The ability of 1,3-dimethyl-5-acetyl-barbituric acid (DAB) to react with primary amines in a chemoselective fashion was applied to the synthesis of a selectively protected spermidine.