Relative modular convergence of positive linear operators

In this paper we define a new type of modular convergence by using the notion of the relatively uniform convergence. We prove a Korovkin-type approximation theorem via this type of convergence in modular spaces. Then, we construct an example such that our new approximation result works but its classical cases do not work.     

Effect of composition changes on properties and defect structure of crystalline Sm-doped ZrO<Subscript>2</Subscript>

Polymorphous structure, electrical conductivity, absorption coefficient, refractive index, and mechanical characteristics of crystalline system ZrO₂ + x Sm₂O₃ (x = 4–43 mol %) is investigated. Vickers microhardness is investigated by the well-known quasi-static indentation method. Plastic microhardness and the effective elastic modulus are studied by the depth-sensing indentation technique. Special attention is devoted to the ordered defect fluorite structure, pyrochlore phase Sm₂Zr₂O₇, observed for x = 43 mol %. Potential applications of the investigated system are discussed. Published in Russian in Elektrokhimiya, 2007, Vol. 43, No. 4, pp. 402–411. The text was submitted by the authors in English.     

Low-dimensional Compounds Containing Cyano Groups. XI. Preparation,Crystal Structure and Properties of Two Copper(II) Dicyanamide Complexes with PF<Stack><Subscript>6</Subscript><Superscript>−</Superscript></Stack> Anions

From the reaction mixtures containing Cu(NO₃)₂, Na[N(CN)₂], KPF₆ and 2,2′-bipyridine (bpy) or 1,10- phenanthroline (phen) in 1:1:1:2 molar ratios, [Cu(bpy)₂N(CN)₂][Cu(bpy)₂(H₂O)](PF₆)₃ (1b) and [Cu (phen)₂N(CN)₂]PF₆ (1p) complexes were isolated. Measured i.r. spectra confirm the presence of all functional groups in both complexes and, moreover, they indicate monodentate coordination of dicyanamide through the cyano nitrogen atom in (1p). The structure of (1b) contains two crystallographically independent complex cations. In both, Cu is coordinated by two chelating bpy molecules, and either dicyanamide anion or water molecule fills the fifth position, completing the basal plane. The Cu^II atoms in (1p) are coordinated by two chelating phen ligands and by one dicyanamide anion in the equatorial plane. Hexafluorophosphate anions in (1b) and (1p) remain uncoordinated. Besides the ionic forces in both structures, the structure of (1b) is stabilized by strong O—H···F and O—H···N hydrogen bonds and, moreover, both structures are stabilized by weak C—H···F hydrogen bonds and possible π-π interactions between pyridine rings of bpy or phen molecules.     

Magneto-Optical Characteristics of Co, Ti-Substituted Barium Hexaferrite Films Deposited by the Dip-Coating Method

Pure and Co, Ti-substituted hexagonal barium ferrite (BaFe₁₂O₁₉, BaM) films were prepared by the dip-coating method from alkoxides. After repeated dipping, drying and calcining at 500°C for about 15 minutes in an oxygen atmosphere, polycrystalline films with a thickness of 1–1.8 μm on SiO₂ substrates were obtained. Spectral dependencies of the Faraday rotation and the optical transmission of BaCo _x Ti _x Fe_12−2x O₁₉(0≤x≤0.8) films were measured in the range from 500 to 2500 nm at room temperature. The absorption coefficient did not display much structure, but specific Faraday rotation spectra of Co, Ti-ferrite films showed local maxima at 720, 1475 and 1750 nm. At those wavelengths, the magneto-optical figure of merit attains its maximum values. For comparison of the crystallization and magnetic properties, Ba(CoTi) _x Fe_12−2x O₁₉ (x=0.9) powder has also been prepared by the sol-gel method.     

Asymmetric Synthesis of Diazepino-β-lactams by [2 + 2] Cycloaddition of an ‘Evans-Sjogven’ Ketene with 1H-1,2-Diazepines

The ketene derivative of the chiral oxazolidinone 1 underwent non-concerted stereo specific [2 + 2] cycloadditions with the (Z)-imine moiety of diazepines 2 , leading thereby with good diastereoselection to the trans-β-lactam adducts 3 (major) and 4 (minor). The absolute configuration of the major cycloadduct 3a was determined by an X-ray analysis. Its formation is discussed in terms of minimisation of steric interaction in the two transition states which give sequencially the zwitterionic intermediates and the final cycloadducts.     

Thermospray liquid chromatographic-mass spectrometric analysis of mutagenic substances present in tryptophan pyrolysates

During protein pyrolysis, as can occur when broiling meat or fish, mutagenic substances are formed, as shown by in vitro mutagenicity assays. Some of the most active compounds have been shown to originate from tryptophan (Trp). Hundreds of grams of Trp had to be used previously to study the formation of these compounds by classical separation and detection methods. Studies have been made of the formation of two active heterocyclic amines, 3-amino-1,4-dimethyl-5H-pyrido[4,3-b]indole (Trp-P-1) and 3-amino-1-methyl-5H-pyrido[4,3-b]indole (Trp-P-2), by heating Trp at different temperatures and for different periods at time. Advantage was taken of the high selectivity and sensitivity of thermospray liquid chromatography-mass spectrometry coupling, which permitted the use of much smaller amounts (10 g) of starting material. These conditions permit a more accurate control of the pyrolysis temperature and the method of extraction can be shortened and simplified. The results show that Trp-P-1 and Trp-P-2 were already formed at 250 degrees C. These substances were detectable in the low ppb range, i.e., less than the threshold levels necessary to elicit a positive response in the Ames test under standard conditions.     

Vinylogous Mannich reactions: some theoretical studies on the origins of diastereoselectivity

[reaction: see text] Ab initio calculations at the RHF/3-21G level were used to investigate the limiting transition states in the addition of 2-methoxyfuran to a pyrrolinium ion. Four stationary points were found on the potential energy surface with relative energies of threo Diels-Alder, 0.0 kcal/mol; erythro open, 0.9 kcal/mol; erythro Diels-Alder, 1.3 kcal/mol; and threo open, 1.8 kcal/mol.     

Determination of the content and identity of lidocaine solutions with UV-visible spectroscopy and multivariate calibration

A method is proposed for the determination of the content and identity of the active compound in pharmaceutical solutions by means of ultraviolet-visible (UV-Vis) spectroscopy, orthogonal signal correction (OSC) and multivariate calibration with soft independent modelling of class analogy (SIMCA) classification and partial least squares (PLS) regression. The content was determined with PLS regression and the identity with PLS regression and SIMCA classification. The method was tested on the local anaesthetic compound lidocaine. For the validation, external test sets of both manufactured sample solutions and samples from a stability study were used. For comparison with this new method, liquid chromatography was used as a reference method. The results show that in respect of accuracy, precision and repeatability, the new method is comparable to the reference method. The main advantage over liquid chromatography is the much shorter time of analysis and the simpler analytical procedure. An estimate of the analysis time saved with the proposed method compared with using liquid chromatography, together with practical considerations, is given.     

Synthesis of azapolycyclic systems via the intramolecular [4 + 2] cycloaddition chemistry of 2-(alkylthio)-5-amidofurans

A series of 2-(methylthio)-5-amidofurans containing tethered unsaturation were prepared via the reaction of dimethyl(methylthio)sulfonium tetrafluoroborate (DMTSF) with beta-alkoxy-gamma-dithiane amides 13-16 and 27-32 in 40-70% yield. Thermolysis of these furans resulted in an intramolecular Diels-Alder reaction (IMDAF). With the exception of 45 and 46, the oxa-bridged cycloadducts could not be isolated but immediately underwent a 1,2-methylthio shift to form bicyclic lactams in 60-100% yield. It was determined that incorporation of the amido carbonyl in the tether allowed the IMDAF reaction to proceed at a lower temperature. A dramatic example of this is seen in the IMDAF reaction of furan 35, in which the presence of an amido carbonyl as part of the dienophile tether, as opposed to the annealed ring (66) or the lack of a carbonyl (67), was necessary for the cycloaddition to occur. Furan 37, annealed to an azepine ring, underwent the IMDAF reaction at or below room temperature. To identify structural features that promote the IMDAF reaction, a computational study was undertaken. Ground-state and transition-state energies were calculated for furans 17, 33, 37, and 64 using the Becke 3LYP/6-31G model. The theoretical results were in good agreement with those observed. The results indicate that the incorporation of an amide carbonyl as part of the tether system works to place the dienophile in closer proximity to the furan ring, thereby lowering the activation energy needed to reach the transition state.     

Letter: collision-induced dissociation of peptide thioesters: influence of the peptide length on the fragmentation

Five peptide thioesters of increasing length were fragmented under two processes, in-source and in- collision cell fragmentation, using an electrospray source coupled to a triple quadrupole. Comparison of their fragmentations was made in regard to the length. The two fragmentation conditions show that the peptide length has no influence on structural information and that the fragmentation efficiency is higher for the smallest peptides than for the longest. The particularity of these peptide thioesters consists on the neutral loss of ethanethiol. The absence of the a3 fragment ion and the presence of the (a3-17) ion on the CID mass spectra are noted.