Complete second order linear differential operator equations in Hilbert space and applications in hydrodynamics

We study the Cauchy problem for a complete second order linear differential operator equation in a Hilbert space of the form

Problems of this kind arise, e.g., in hydrodynamics where the coefficients , , and are unbounded selfadjoint operators. It is assumed that is the dominating operator in the Cauchy problem above, i.e.,

We also suppose that and are bounded from below, but the operator coefficients are not assumed to commute. The main results concern the existence of strong solutions to the stated Cauchy problem and applications of these results to the Cauchy problem associated with small motions of some hydrodynamical systems.

     

Method for direct determination of mitomycin C in urinary bladder for surface cancer treatment

A technique was developed for the quantitative determination of mitomycin C in urinary-bladder tissues. We used the method of gradient high-performance liquid chromatography with mass-spectrometry detection in the electrospray ionization mode. The range of linearity of the calibration plot was 20?C440 ??g/L. The detection limit was 15 ng/L. We proposed a sampling procedure that consisted of water extraction. Importantly, this procedure allows one to determine the quantity of mitomycin C in tissues. In our study, this method was utilized to estimate the quantity of mitomycin C in the urinary bladder.     

Structure and Chemical Composition of Manganese-Doped GaSb Dislocations

Electron microscopic observations showed that the preparation of magnetic semiconductor GaSb〈Mn〉 by melt quenching is accompanied by discrete manganese precipitation on GaSb dislocations, this precipitation generating inclusions sized from a split micrometer to several micrometers. The chemical composition of microinclusions was determined by electron probe microanalysis. The superposition of the magnetic properties of compounds that are formed in the Mn–Sb system determines the magnetic properties of GaSb〈Mn〉.     

Combination of two chromatographic methods in the study of the chemical composition of officinal herbs

Two complementary chromatographic methods, ion exclusion chromatography and gas-liquid chromatography, are suggested for the analysis of the chemical composition and the standardization of raw herbs. The potentialities and limitations of these methods are illustrated by the example of common valerian (Valeriana officinalis) and yarrow (Achillea millefolium). The chromatographic conditions required for the determination of ascorbic acid by the ion exclusion chromatography are determined.     

Choice of optimal conditions for X‐ray fluorescence analysis of milk products with varying fat content

The design of experiments was used to study sources of errors in the sample preparation and to choose optimal conditions for X‐ray fluorescence (XRF) analysis of milk products of varying fat content. The measurements were performed using the conventional wavelength‐dispersive XRF (WDXRF) and the total reflection XRF (TXRF) techniques. For WDXRF, the dried milk samples were pelletized, and the mathematical models were constructed, which described the dependence of XRF intensity on the pelletizing pressure, the pellet weight and the milk fat content. The effect of radiation time on the stability of pressed milk powder samples was also estimated. When applying TXRF, the sample preparation involved diluting milk samples with the ultrapure water, adding the internal standard (Ga) and drying of a sample aliquot on a quartz glass sample carrier. The mathematical models were designed, which described the dependence of the sample preparation error on the dilution ratio and sample aliquot pipetted on the carrier. A physical interpretation of the obtained mathematical models was proposed. Copyright © 2013 John Wiley & Sons, Ltd.     

A miniaturized multichamber solution isoelectric focusing device for separation of protein digests

A miniaturized multichamber device was constructed for solution isoelectric focusing (IEF) separation of complex peptide mixtures. The system, based on immobilized pH gels, consisted of 96 minichambers ( approximately 75 nuL each) arranged in eight rows. Neighboring chambers in a given row were separated by short glass tubes (4 mm inner diameter, 3 mm long), within which Immobiline gels of specific pH values were polymerized. During focusing, the device was sandwiched between two supporting blocks incorporating the reservoirs for anolyte and catholyte. In principle, multiple samples could be simultaneously fractionated, each separated into 12 fractions of various pI ranges. A variety of standard peptide mixtures and tryptic digests of proteins were separated by IEF using this device, and the fractions were characterized by mass spectrometry. For a codigested nine-protein mixture, both the total number of peptides identified and the average sequence coverage were similar to the results of ion-exchange chromatography (IEC), according to matrix assisted laser/desorption/ionization--time of flight (MALDI-TOF) data. The IEF separation provided concentrated and desalted fractions, suitable for an additional separation liquid chromatography, capillary electrophoresis (LC, CE) or mass spectrometry (MS) detection without additional sample cleanup. High loading capacity was achieved for the miniaturized multichamber IEF device. Importantly, a linear correlation was found between the experimentally determined and calculated pI values of peptides.     

Location of Framework Al Atoms in the Channels of ZSM‐5: Effect of the (Hydrothermal) Synthesis

²⁷Al 3Q MAS NMR and UV/Vis spectroscopy with bare Co^II ions as probes of Al pairs in the zeolite framework were employed to analyze the location of framework Al atoms in the channel system of zeolite ZSM‐5. Furthermore, the effect of Na⁺ ions together with tetrapropylammonium cation (TPA⁺) in the ZSM‐5 synthesis gel on the location of Al in the channel system was investigated. Zeolites prepared using exclusively TPA⁺ as a structure‐directing agent (i.e., in the absence of Na⁺ ions) led to 55–90 % of Al atoms located at the channel intersection, regardless the presence or absence of Al pairs [Al?O?(Si?O)₂?Al sequences in one ring] in the zeolite framework. The presence of Na⁺ ions in the synthesis gel did not modify the Al location at the channel intersection (55–95 % of Al atoms) and led only to changes in i) the distribution of framework Al atoms between Al pairs (decrease) and single isolated Al atoms (increase), and ii) the siting of Al in distinguishable framework tetrahedral sites.     

Structure of Polymers With Phenyl Benzoate Side Groups By X-Ray Evidence

Structure of four polymers were studied: poly-p-methacryloyloxy phenyl esters of p-n-hexyloxy benzoic acid (PMB-6), p-n-heptyl benzoic acid (PMH-7) and p-n-heptyl - trans-cyclohexane carboxylyc acid (PMC-7) and poly-p-n-hexyloxy phenyl ester of pmethacryloyloxy benzoic acid (PM-06). Diffractions parameters and polymer organization were discussed in terms of both crystallinity and paracrystal. The structural organization of PMB-6, PMH-7 and PM-06 was interpreted on the basis of block model. Structure of PMC-7 assumed to be organized similar to cybotactic nematics.     

Solid solutions based on iron-substituted cobaltites MnFe x Co2-x O4 in CO oxidation

The influence of the chemical composition and conditions of heat treatment of MnFe _x Co_2?x O₄ system on its phase composition and catalytic properties in CO oxidation was studied. The formation of substitutional solid solutions of spinel structure was established. The optimum chemical composition of the catalyst, ensuring complete CO conversion at 190°C, was determined.     

Ferromagnetism of GaSb (2% Mn) alloy

A polycrystalline sample of composition GaSb + 2% Mn was prepared by melt quenching. Manganese substitutes for gallium positions to form limited solid solution Ga_{1 ? x} Mn _x Sb, as shown by X-ray powder diffraction and SEM, but most manganese is consumed in the formation of magnetically ordered Mn_1.1Sb inclusions having the Curie point T _C ≈ 560 K, as shown by magnetic studies.