Regularization of Discrete Ill-Posed Problems

The paper concerns conditioning aspects of finite-dimensional problems arising when the Tikhonov regularization is applied to discrete ill-posed problems. A relation between the regularization parameter and the sensitivity of the regularized solution is investigated. The main conclusion is that the condition number can be decreased only to the square root of that for the nonregularized problem. The convergence of solutions of regularized discrete problems to the exact generalized solution is analyzed just in the case when the regularization corresponds to the minimal condition number. The convergence theorem is proved under the assumption of the suitable relation between the discretization level and the data error. As an example the method of truncated singular value decomposition with regularization is considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

Structure and electrochemical behaviour of 4,7-diazaheptyl-trimethoxy-silane and vinyl-trialkoxy-silane adsorbed at silver surface

Novel self-assembled monolayers were obtained on silver using 4,7-diazaheptyl-trimethoxy-silane (SiN) and vinyl-trialkoxy-silane (SiVA, where the alkyl group is 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60-eicozaoxa- hexaheptaconan). It was shown that thus modified metal surface was protected against electrooxidation. A densely packed monolayer remained stable and did not desorb from the Ag electrode on the potential cycling. The structure of SiN and SiVA as well as their complexes with Li⁺ cations were calculated and visualised by the AM1d and PM5 semi-empirical methods.     

LocalH-theorem for a kinetic variational theory

A localH-theorem is derived for a recently proposed extension of Enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core.On leave from: Katedra Fizyki, Uniwersytetu Szczecinskiego, 70-451 Szczecin, Poland.     

Thermal analysis of glasses for proecological applications

Thermal behaviour and biochemical activity of potassium-silicate-phosphate glasses modified by addition of Ca, Mg, acting as ecological fertilisers of controlled release rate of the nutrients for plants were studied. It has been found that the biochemical activity of silicate-phosphate glasses depends on the nature and the number of components forming the glassy framework and is related to the thermal stability of glass demonstrated by the formation of new compounds during the process of crystallisation. It is proved that these seemingly different properties are determined by the same parameters which are the strengths bonds of glass network-formers and modifiers as well as their chemical affinity. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spectral decomposition of an elementary 3-fermion 2-body operator

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P²_g∧I¹A³∑_{1≤i≤j≤3}P²_g(i, j)A³ acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here P_g² denotes the projection operator onto a 2-particle antisymmetric function g², while A³ denotes the 3-particle antisymmetrizing operator.     

Development in Synthesis,Electrochemistry, LB Moieties of Phenothiazine Based Units

A convenient and higher yielding synthetic route to N‐alkyl‐bis(thiophene)phenothiazine derivatives is reported and their aggregation, electrochemical properties and polymerization are characterized. The key step in the synthesis of this group of compounds has been the Stille type coupling reaction between the N‐alkyldibromophenothiazine and tin derivatives of thiophene as the best way for preparation of conjugated N‐alkylphenothiazine derivatives. For this group of compounds we also present an electrochemical polymerization effect and widely adopted approach to prepare structurally ordered thin, electroconducting films by Langmuir–Blodgett technique.     

A fast method to measure the thickness of removed layer from etching of SSNTD based on EDXRF

Solid state nuclear track detectors are commonly used for measurements of concentrations of radon gas and/or radon progeny. All these measurements depend critically on the thickness of the removed layer during etching. However, the thickness of removed layer calculated using the etching period does not necessarily provide a sufficiently accurate measure of the thickness. For example, the bulk etch rate depends on the strength of stirring during etching for the LR 115 detector. We propose here to measure the thickness of the removed layer by using energy-dispersive X-ray fluorescence spectrometry. In the present work, a reference silver nitrate pellet is placed beneath the LR 115 detector, and the fluorescence X-ray intensity for silver is then measured. We have found a linear relationship between the X-ray intensity and the thickness of the removed layer for LR 115 detector. This provides a fast method to measure the thickness of removed layer from etching of LR 115 detector. However, this method was found to be inapplicable for the CR-39 detector. Therefore, alternative methods have yet to be explored for the CR-39 detector.