The Campbell- Hausdorff Series of Local Analytic Bruck Loops

The class of local analyitic Bruck loops (or equivalently K-loops) is strongly related to locally symmetric spaces. In particular, both have Lie triple systems as their tangent algebra. In this paper, we consider the existence and some properties of the Campbell-Hausdorff series of local analytic Bruck loops (K-loops). This formula can be used to determine the local symmetries of the associated symmetric space.     

On the Number of k‐Dominating Independent Sets

We study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erd?s and Moser—is widely investigated, much less is known in general. In this paper we settle the question for trees and prove that the maximum number of k‐dominating independent sets in n‐vertex graphs is between and if , moreover the maximum number of 2‐dominating independent sets in n‐vertex graphs is between and . Graph constructions containing a large number of k‐dominating independent sets are coming from product graphs, complete bipartite graphs, and finite geometries. The product graph construction is associated with the number of certain Maximum Distance Separable (MDS) codes.     

Determination of EDTA by catalytic amperometric and catalytic potentiometric titration at a small constant current

Summary Amperometric and potentiometric methods at a small constant current were developed to follow the course of catalytic titrations. In ammoniacal medium EDTA was determined by titration with 0.1 M copper(II) chloride in the presence of hydrogen peroxide as the indicator. Amounts of 42.26–126.87 mg of EDTA were determined with a maximal average deviation of 0.55 %. The results obtained are in good agreement with those of comparable methods.

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Bestimmung von ÄDTA mit Hilfe der katalytischen amperometrischen und der katalytischen potentiometrischen Titration bei kleinem konstantem Strom

Zusammenfassung Die amperometrische und die potentiometrische Methode bei kleinem konstantem Strom wurden für die Verfolgung katalytischer Titrationen ausgearbeitet. ÄDTA wurde in Ammoniakmedium mit 0,1 M Kupfer(II)-chlorid in Anwesenheit von Wasserstoffperoxid als Indicator titriert. Mengen von 42,26–126,87 mg ÄDTA wurden mit einer mittleren Abweichung von 0,55% bestimmt. Die Ergebnisse stimmen gut mit denen vergleichbarer Methoden überein.

The authors thank the SIZ for researchs of SAP Vojvodina for the partial financial support of the present work.     

Saturated heterocycles. Part 209. Synthesis of 1-cyclohexyl-substituted isoquinoline derivatives

In contrast with earlier literature data [7], both acrylic esters and acrylonitrile underwent Michael addition to l-methyl-3,4-dihydroisoquinolines 1-4 to yield the diesters 5-9 or the dinitrile 10 , respectively. Compounds 5-10 were converted by Claisen condensation to 1-[(3′-methoxycarbonyl- or 1-[(3′-ethoxycarbonyl-4′-oxo)-l'-cyclohexyl]-3,4-dihydroisoquinoline derivatives 11-16 . Several derivatives of 12 were prepared. The new compounds possess various pharmacological actions.     

Line shape of <Superscript>57</Superscript>Co sources exhibiting self absorption

The effect of selfabsorption in Mössbauer sources is studied in detail. Spectra were measured using an old ⁵⁷ C o/R h source of 74M B q activity with an original activity of ca. 3.7G B q and a 0.15G B q ⁵⁷ C o/α ? F e source magnetized by an in-plane magnetic field of 0.2 T. The ⁵⁷ C o/α ? F e source of a thickness of 25 μ was used both from the active and the inactive side giving cause to very different selfabsorption effects. The absorber was a single crystal of ferrous ammonium sulphate hexahydrate (FAS). Its absorption properties were taken over from a detailed study (Bull et al., Hyperfine Interact. 94(1–3), 1; Spiering et al. 2). FAS (space group P21/c) crystallizes as flat plates containing the (\(\overline {2}\)01) plane. The γ-direction was orthogonal to the crystal plate. The ⁵⁷ C o atoms of the ⁵⁷ C o/R h source were assumed to be homogeneously distributed over a 6μ thick Rh foil and to follow a one dimensional diffusion profile in the 25 μ Fe-foil. The diffusion length was fitted to 10 μ. The theory follows the Blume-Kistner equations for forward scattering (Blume and Kistner, Phys. Rev. 171, 417, 3) by integrating over the source sampled up to 128 layers.     

Robust regression for mixed Poisson–Gaussian model

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson–Gaussian noise, and when there are additional outliers in the measured data. The Poisson–Gaussian noise leads to a weighted minimization problem, with solution-dependent weights. To address outliers, the standard least squares fit-to-data metric is replaced by the Talwar robust regression function. Convexity, regularization parameter selection schemes, and incorporation of non-negative constraints are investigated. A projected Newton algorithm is used to solve the resulting constrained optimization problem, and a preconditioner is proposed to accelerate conjugate gradient Hessian solves. Numerical experiments on problems from image deblurring illustrate the effectiveness of the methods.     

Thermally stable silarylene-1,3,4-oxadiazole polymers

The effects of incorporating a p-phenylene- (or m-phenylene)-1,3,4-oxadiazole fragment into the backbone of poly[1,4-phenylene(diphenylsilyl)-1,4-phenylene-2,5-(1,3,4-oxadiazole)], which was developed by the authors, was investigated. Bis[(p-carbohydrazidophenyl)]diphenylsilane was copolymerized with dipentachlorophenyl terephthalate or isophthalate to produce the prepolymers poly[N-(p-diphenylsilylbenzoyl)-N′N″-(terephthaloyl)-N″′-(p-benzoyl)dihydrazide] and poly[N-(p-diphenylsilylbenzoyl)-N′,-N″-(isophthaloyl)-N″′-p-(benzoyl) dihydrazide], respectively. The polyhydrazides were converted by thermal dehydration into poly[1,4-phenylene(diphenylsilyl)-1,4-phenylene-(1,3,4-oxadiazole-2,5-diyl)-1,4-phenylene-2,5-(1,3,4-oxadiazole)] and poly[1,4-phenyl-ene(diphenylsilyl)-1,4-phenylene-(1,3,4-oxadiazole-2,5-diyl)-1,3,4-(oxadiazole)]. The new polymers were soluble in organic solvents. Films cast from these solutions exhibited good adhesion to glass and metal surfaces. Thermal analysis showed that the heat stability of all these polymers was about the same and that they were resistant to decomposition when heated in air to about 400°C. The results also indicated that these polymers were somewhat less heat-resistant than samples of poly-[1,4-phenylene(diphenylsilyl)-1,4-phenylene-2,5-]1,3,4-(oxadiazole) synthesized from bis(p-carbohydrazidophenyl)diphenylsilane and bis-(p-carbopentachlorophenoxy-phenyl)diphenylsilane.     

Direct analysis in real time mass spectrometry (DART‐MS) of highly non‐polar low molecular weight polyisobutylenes

Low molecular weight polyisobutylenes (PIB) with chlorine, olefin and succinic acid end‐groups were studied using direct analysis in real time mass spectrometry (DART‐MS). To facilitate the adduct ion formation under DART conditions, NH₄Cl as an auxiliary reagent was deposited onto the PIB surface. It was found that chlorinated adduct ions of olefin and chlorine telechelic PIBs, i.e. [M + Cl]^? up to m/z 1100, and the deprotonated polyisobutylene succinic acid [M? H]^? were formed as observed in the negative ion mode. In the positive ion mode formation of [M + NH₄]⁺, adduct ions were detected. In the tandem mass (MS/MS) spectra of [M + Cl]^?, product ions were absent, suggesting a simple dissociation of the precursor [M + Cl]^? into a Cl^? ion and a neutral M without fragmentation of the PIB backbones. However, structurally important product ions were produced from the corresponding [M + NH₄]⁺ ions, allowing us to obtain valuable information on the arm‐length distributions of the PIBs containing aromatic initiator moiety. In addition, a model was developed to interpret the oligomer distributions and the number average molecular weights observed in DART‐MS for PIBs and other polymers of low molecular weight. Copyright © 2015 John Wiley & Sons, Ltd.     

A combined approach of differential scanning calorimetry and hot-stage microscopy with image analysis in the investigation of sulfathiazole polymorphism

A combination of differential scanning calorimetry and hot-stage microscopy with image analysis has been used to investigate the polymorphism of sulfathiazole. The use of light intensity profiles obtained from the HSM images, as an alternative way to present results of the HSM analysis, was found to be useful in describing and verifying thermal events. The approach provides a unique insight into the polymorphic transformations and thermal behaviour exhibited by this compound. The results of the experiments show that sulfathiazole tends to crystallise as mixtures of polymorphs, even though the literature methods for producing pure polymorph were followed.