Crystal structure and magnetic properties of Ce7Ni5±xGe3±xIn6 and Pr7Ni5±xGe3±xIn6

The indides Ce₇Ni_5±xGe_3±xIn₆ and Pr₇Ni_5±xGe_3±xIn₆ were synthesized from the elements by arc-melting of the components. Single crystals were grown via special annealing sequences. Both structures were solved from X-ray single crystal diffraction data: new structure type, P6/m, Z=1, a=11.385(2), c=4.212(1) Å, wR₂=0.0640, 634F² values, 25 variables for Ce₇Ni_4.73Ge_3.27In₆ and a=11.355(6), c=4.183(2) Å, wR₂=0.0539, 563F² values, 25 variables for Pr₇Ni_4.96Ge_3.04In₆. Both indides show homogeneity ranges through Ni/Ge mixing (M sites). This new structure type can be derived from the AlB₂ structure type by a substitution of the Al and B atoms by CeM₁₂ and NiIn₆Ce₃ polyhedra (tricapped trigonal prism). Magnetic susceptibility measurements on a polycrystalline sample of Ce₇Ni₅Ge₃In₆ indicated Curie-Weiss like paramagnetic behavior down to 1.71 K with the effective magnetic moment slightly reduced in relation to the value expected for trivalent cerium ions. No magnetic ordering is evident.     

Bis(tetraethylammonium) tetrabromocobaltate(II) and bis(tetrabutylammonium) tetrabromomanganate(II): structure and magnetic properties

The crystal structures of tetrabromocobaltate(II) and tetrabromomanganate(II) salts of general formula [(C₂H₅)₄N]₂[CoBr₄] (1) and [(C₄H₉)₄N]₂[MnBr₄] (2) were determined. The manganese and cobalt cations are four-coordinated by bromide anions and they adopt a slightly distorted tetrahedral coordination. In the structure of both compounds there are neither hydrogen bonds nor any unusual short-range intermolecular interactions. Magnetic measurements of the powdered samples gave negative values of the Weiss constants equal to −4.9 and −1.1 K for (1) and (2), respectively, which suggest antiferromagnetic interactions to be transferred within the crystal lattice.     

On formal Laurent series

Several kinds of formal Laurent series have been introduced with some restrictions so far. This paper systematically sets up a natural definition and structure of formal Laurent series without those restrictions, including introducing a multiplication between formal Laurent series. This paper also provides some results on the algebraic structure of the space of formal Laurent series, denoted by \mathbbL\mathbb{L}. By means of the results of the generalized composition of formal power series, we define a composition of a Laurent series with a formal power series and provide a necessary and sufficient condition for the existence of such compositions. The calculus about formal Laurent series is also introduced.     

Ultrasonic system for accurate distance measurement in the air

This paper presents a system that accurately measures the distance travelled by ultrasound waves through the air. The simple design of the system and its obtained accuracy provide a tool for non-contact distance measurements required in the laser’s optical system that investigates the surface of the eyeball.     

Monte Carlo simulation code for confocal 3D micro‐beam X‐ray fluorescence analysis of stratified materials

Stratified materials are of great importance for many branches of modern industry, e.g. electronics or optics and for biomedical applications. Examination of chemical composition of individual layers and determination of their thickness helps to get information on their properties and function. A confocal 3D micro X‐ray fluorescence (3D µXRF) spectroscopy is an analytical method giving the possibility to investigate 3D distribution of chemical elements in a sample with spatial resolution in the micrometer regime in a non‐destructive way. Thin foils of Ti, Cu and Au, a bulk sample of Cu and a three‐layered sandwich sample, made of two thin Fe/Ni alloy foils, separated by polypropylene, were used as test samples. A Monte Carlo (MC) simulation code for the determination of elemental concentrations and thickness of individual layers in stratified materials with the use of confocal 3D µXRF spectroscopy was developed. The X‐ray intensity profiles versus the depth below surface, obtained from 3D µXRF experiments, MC simulation and an analytical approach were compared. Correlation coefficients between experimental versus simulated, and experimental versus analytical model X‐ray profiles were calculated. The correlation coefficients were comparable for both methods and exceeded 99%. The experimental X‐ray intensity profiles were deconvoluted with iterative MC simulation and by using analytical expression. The MC method produced slightly more accurate elemental concentrations and thickness of successive layers as compared to the results of the analytical approach. This MC code is a robust tool for simulation of scanning confocal 3D µXRF experiments on stratified materials and for quantitative interpretation of experimental results. Copyright © 2011 John Wiley & Sons, Ltd.     

1H NMR assignment corrections and 1H, 13C, 15N NMR coordination shifts structural correlations in Fe(II), Ru(II) and Os(II) cationic complexes with 2,2′‐bipyridine and 1,10‐phenanthroline

¹H, ¹³C and ¹⁵N NMR studies of iron(II), ruthenium(II) and osmium(II) tris‐chelated cationic complexes with 2,2′‐bipyridine and 1,10‐phenanthroline of the general formula [M(LL)₃]²⁺ (M = Fe, Ru, Os; LL = bpy, phen) were performed. Inconsistent literature ¹H signal assignments were corrected. Significant shielding of nitrogen‐adjacent protons [H(6) in bpy, H(2) in phen] and metal‐bonded nitrogens was observed, being enhanced in the series Ru(II) → Os(II) → Fe(II) for ¹H, Fe(II) → Ru(II) → Os(II) for ¹⁵N and bpy → phen for both nuclei. The carbons are deshielded, the effect increasing in the order Ru(II) → Os(II) → Fe(II). Copyright © 2010 John Wiley & Sons, Ltd.     

On a problem of Eidelheit from The Scottish Book concerning absolutely continuous functions

A negative solution of Problem 188 posed by Max Eidelheit in the Scottish Book concerning superpositions of separately absolutely continuous functions is presented. We discuss here this and some related problems which have also negative solutions. Finally, we give an explanation of such negative answers from the “embeddings of Banach spaces” point of view.     

Topotecan dynamics,tautomerism and reactivity—1H/13C NMR and ESI MS study

Topotecan (TPT) is in clinical use as an antitumor agent, hycamtin^?. Because of this, it requires both biologically and chemically useful information to be available. TPT acts by binding to the covalent complex formed by nicked DNA and topoisomerase I. This has a poisonous effect since inserted into the single‐strand nick and TPT inhibits its religation. We used NMR to trace TPT dynamics, tautomerism and solvolysis products in various solvents and conditions. Chemical stability was assessed in methanol and DMSO as compared to water, and the regioselectivity of the N‐ and O‐methylation was studied using various alkylating agents. The reaction products of quaternization of the nitrogen atom and methylation of the oxygen atom were characterized by means of ESI MS, ¹H/¹³C‐HMBC and ‐HSQCAD NMR. We have focused on the NMR characterization of TPT with an anticipation that its aggregation, tumbling properties and the intramolecular dipolar interactions will be a common feature for other compounds described in this article. These features can also be useful in tracing the interactions of this class of topoisomerase I (TopoI) poisons with DNA. Moreover, the results explained shed light on the recently disclosed problem of lack of stability of TPT in the heart tissue homogenate samples using the analytical assays developed for this class of compounds carried out in the presence of methanol. Copyright © 2010 John Wiley & Sons, Ltd.     

Martingale and stationary solutions for stochastic Navier-Stokes equations

Summary We prove the existence of martingale solutions and of stationary solutions of stochastic Navier-Stokes equations under very general hypotheses on the diffusion term. The stationary martingale solutions yield the existence of invariant measures, when the transition semigroup is well defined. The results are obtained by a new method of compactness.