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.     

A multi-technique nondestructive approach for characterizing the state of conservation of ancient bookbindings

Journal of Thermal Analysis and Calorimetry - The aim of this work is to evaluate the potentiality of a multi-technique nondestructive approach for characterizing the state of conservation of...     

Experimental confirmation by galvanomagnetic methods of a complex transport model in In0.53Ga0.47As layers deposited by MBE on SI-InP

At low temperatures In_0.53Ga_0.47As samples show an increase of carrier concentration, which can be explained in terms of a two carriers transport model. This type of problem exists since the beginning of the semiconductor era, dating back to monocrystalline germanium.We propose that in all the investigated layers, there are X atoms or charged dislocations in the region of the first monolayers, which are built in during epitaxial growth. The layers were intentionally undoped. They form an impurity band in which low mobility carriers dominate over the localised electron scattering due to the s-d exchange interaction. These carriers do not freeze out at liquid helium temperature and give rise to two transport media for electrons; a conduction band at higher temperatures and an impurity band at lower temperatures. The electron which fall down onto the previously ionised X atoms, then move by thermally activated hopping. We show that the two carriers model for In_0.53Ga_0.47As epitaxial layers are confirmed by the carrier concentration-temperature, carrier concentration-magnetic field, resistivity-magnetic field behaviour, and also by YKA theory also. The differences between the two transport models are so distinctive that observed phenomena may exist. This paper presents experimental results, which constitute comprehensive evidence for the complicated structure of the semiconductor epitaxial layers on the sample of n-type In_0.53Ga_0.47As/InP layer with n=2.2×10¹⁵/cm³.     

Wavelet moment method for the Cauchy problem for the Helmholtz equation

The paper is concerned with the problem of reconstruction of acoustic or electromagnetic field from inexact data given on an open part of the boundary of a given domain. A regularization concept is presented for the moment problem that is equivalent to a Cauchy problem for the Helmholtz equation. A method of regularization by projection with application of the Meyer wavelet subspaces is introduced and analyzed. The derived formula, describing the projection level in terms of the error bound of the inexact Cauchy data, allows us to prove the convergence and stability of the method.     

Investigations of molecular interactions in propionic acid–N,N-dimethyl formamide binary system—FTIR study

FTIR spectra of propionic acid (PA), N,N-dimethyl formamide (DMF) and its binary mixtures with varying molefractions of the PA were recorded in the region 500–3500 cm⁻¹, to investigate the formation of hydrogen bonded complexes in a mixed system. The observed features in ν(CO), δ(OC–N) and ν_as(CN) of DMF, ν(CO) and ν(CO) of PA have been explained in terms of the hydrogen bonding interactions between DMF and PA and dipole–dipole interaction. The intrinsic bandwidth for the vibrational modes ν_as(CN) and ν(CO) has been elucidated using Bondarev and Mardaeva model.     

Application of Wavelet Shrinkage to Solving the Sideways Heat Equation

The sideways heat equation is considered in terms of the ill-posed operator equation Au = g, g R(A) L ²(), with a given noisy right hand side. For a reconstruction of the solution from indirect data the dual least square method generated by the family of Meyer wavelet subspaces is applied. An explicit relation between the truncation level of the wavelet expansion and the data error bound is found under which convergence results including error estimation are obtained. Next, a certain simple nonlinear modification of the method based on local refinements of the wavelet expansion of the noisy data is investigated. Moreover, it is shown that an accuracy of the solution reconstruction can be improved by adding some sufficiently large coefficients on the level higher than that indicated by the convergence theorem.This revised version was published online in October 2005 with corrections to the Cover Date.     

A class of regularization methods for ill posed problems

The paper deals with regularization methods for solving ill posed problems with nonselfadjoint bounded linear operators acting on a Hilbert space. A class of methods generated by certain families of functions is considered. In the case of exact data the convergence of approximate solutions to the exact one (provided that it exists) is proved and error estimations are presented. An integral representation of functions of an auxiliary operator is obtained and subsequently used in error estimation.     

Analysis of electrical conduction in an <Emphasis Type="BoldItalic">n</Emphasis> -type GaAs epilayer

The magnetic field dependence of conductivity tensor components, magnetoresistance, and the Hall coefficient have been analyzed in an n-type Si-doped GaAs epilayer at temperatures from 11 to 295 K. Carriers from the conduction band and the impurity band take part in the electrical conduction. The conduction band is located in the epilayer and the impurity band is located in a narrow layer, less than 0.1 m thick, between the GaAs buffer and GaAs semi-insulating substrate. At temperatures below 20 K the localization and magnetic freeze-out of the conduction band electrons have been taken into account as quantum corrections to the electrical conduction. The dependence of the mobility on energy has been considered in the analysis of the experimental data. A wide peak of partial conductions versus mobility appears in the mobility spectrum. From the analysis of the mobility spectrum of conduction band electrons it follows that at low temperatures the mobility of non-degenerated conduction band electrons is limited by scattering on screened charge centers. The mobility spectrum technique has been used as a tool for interpolation and extrapolation of the experimental data beyond the experimentally investigated magnetic field range. PACS 72.20.-i; 72.60.+g