Positive symmetric quotients and their selfadjoint extensions

We define a quotient of bounded operators and on a Hilbert space with a kernel condition as the mapping , . A quotient is said to be positive symmetric if . In this paper, we give a simple construction of positive selfadjoint extensions of a given positive symmetric quotient .

     

Simultaneous confidence bands for the integrated hazard function

The construction of the simultaneous confidence bands for the integrated hazard function is considered. The Nelson–Aalen estimator is used. The simultaneous confidence bands based on bootstrap methods are presented. Four methods of construction of such confidence bands are proposed. The weird and conditional bootstrap methods are used for resampling. Simulations are made to compare the actual coverage probability of the bootstrap and the asymptotic simultaneous confidence bands. It is shown that the equal-tailed bootstrap confidence band has the coverage probability closest to the nominal one. We also present application of our confidence bands to the data regarding survival after heart transplant. This research was partly supported by AGH grant No. 10.420.03.     

Über den Begriff der „Pseudogruppe von Transformationen”

Ohne Zusammenfassung     

Applications of small iridium-based mercury electrodes to high concentrations of depolarizers

Voltammetric and microscopic data on the analytical properties of small iridium-based (127- μm diameter) mercury film electrodes are presented. A method of estimating and controlling the size of the deposit is described. The voltammetric behaviour of electrodes with mercury deposits varying from a film to a near-hemisphere is discussed for linear-scan, differential- and normal- pulse voltammetry. The systems Pb²⁺/Pb, Fe³⁺/Fe²⁺ and Co²⁺/Co, are used to show that, by changing the size of the deposit, either time-dependent or almost time-independent (steady-state) voltammograms can be obtained under the same instrumental conditions. Possible applications to the determination of high concentrations of depolarizers are outlined; voltammetric data for the determination of lead in the range 10–120 mM are presented. The evaluation of diffusion coefficients is discussed.     

Application of carbon nanotubes as solid-phase extraction sorbent for analysis of chlorophenols in water samples

The aim of this work was to investigate the efficiency of various MWCNTs as SPE materials for the preconcentration of chlorophenols. The COOH-functionalized MWCNTs and MWCNTs were used as SPE sorbents. To evaluate the capability of MWCNTs for the preconcentration of chlorophenols from water samples, 2,4-chlorophenol, 4-chlorophenol, 2,4,6-chlorophenol, 2,6-chlorophenol, 3,4-chlorophenol, and 2-chlorophenol were used as model compounds. Chlorophenols were extracted with acetone, methanol, ethanol, and dichloromethane, and determined by gas chromatography–mass spectrometry. COOH-functionalized MWCNTs <8 nm were found to be the best sorbent for the tested chlorophenols. For COOH-functionalized MWCNTs <8 nm, the recovery rates for all chlorophenols were higher than 50% when acetone or ethanol was used as eluents. In the case of dichloromethane elution, recovery rates for chlorophenols were from 62.0% for 2,6-DCP to 116.8% for 2,4-DCP; only for 2,4,6-TCP was the recovery rate 30.6%. Similar percentage recoveries were achieved with methanol as the eluent.     

Reductive carboxylation of alkyl halides with CO2 by use of photoinduced SmI2/Sm reduction system

Upon visible-light irradiation, reductive carboxylation of alkyl halides takes place by using a SmI₂/Sm mixed system under atmospheric CO₂ to afford the corresponding carboxylic acids in good to excellent yields.     

Fast image enlargement using predefined codebook and eigenspace backprojection for lost pixel

In this paper, a new image enlargement method applying the backprojection for lost pixel (BPLP) to the predefined codebook-based method is proposed. BPLP is a method for image restoration. In BPLP, the eigenspace reflecting the characteristics of an input image is generated from the remained pixels and is used to restore the missing pixels. In the proposed method, the eigenspace is replaced by one generated from the predefined codebook (PDC). PDC represents edge-blurring properties in a small image patch and consists of pairs of low- and high-frequency image patches on various edge patterns. By replacing the PDC-based estimation of lost high-frequency components with BPLP, a fast image enlargement method retaining its performance can be developed. Through some experiments, the effectiveness of the proposed method was demonstrated. Especially, it was confirmed that the processing time of the proposed method was shortened to about 1/50 that of the PDC-based method.     

Local structure and magnetism of Fe, Co and Ni doped Cr3Si

The lattice site occupation of 3d-type impurities in Cr₃Si doped with Fe, Co and Ni were studied using the Extended X-ray Absorption Fine Structure (EXAFS) technique, X-rays and magnetic susceptibility measurements. The EXAFS measurements were performed particularly carefully on the K-edge of chromium and cobalt. EXAFS data strengthened by simulations of the spectra show unambiguously that the impurities are occupying mostly Cr-sites. The magnetic state of the alloys has been studied theoretically using the Wien2k code. It is observed that if calculations are not carried out on an appropriately fine mesh of points in k-space, one can get the result indicating ferromagnetism although the overall magnetic moment per formula unit is weak.     

Corona discharges in sub-millimeter electrode gaps

Atmospheric pressure wire-to-plane positive corona discharges have been explored experimentally in electrode gaps from 0.3 mm to 5 mm. Reductions in the gap distance and wire diameter resulted in a significant increase in discharge currents and lowered onset potentials, and the current–voltage characteristics followed the typical Townsend’s relationship. The experimentally observed onset potentials were higher than Peek’s prediction although they still showed the same logarithmic behavior with gap distance. Additionally, a theoretical relationship for the current–voltage discharge in a wire-to-plane configuration was derived to obtain the dependence on the geometric parameters, and it compared well with the experimental results.