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.     

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.     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Time structure of iodine laser pulse in the free running mode of operation

Time structure of iodine laser pulse in the free running mode of operation was studied using the power amplifier of laser system PERUN as the laser oscillator. Two characteristic shapes of laser pulse correspond to different regimes of laser operation, the existence of which is ascribed to the critical concentration of I₂ molecules. Simultaneously an additional chemical pumping was proved at least in the initial phase of photodissociation and in a late-time lasing after the end of flashlamps pumping light.