A Kotz and Steutel type of characterization of the gamma family

Let X and Y be independent identically distributed (i.i.d.) nondegenerate and positive random variables with a common absolutely continuous distribution function F(x). We use the notation Z?=?max(X, Y) and W?=?min(X, Y). In the present paper, we prove that ${\frac{(Z - W)}{(Z + W)}}$ and (Z +?W) are independent if and only if X and Y have gamma distribution.     

A thermoanalytical assessment of an organoclay

High resolution thermogravimetric analysis (TG) has attracted much attention in the synthesis of organoclays and its applications. In this study, organoclays were synthesised through ion exchange of a single cationic surfactant for sodium ions, and characterised by methods including X-ray diffraction (XRD) and TG. The changes of surface properties in montmorillonite (MMT) and organoclays intercalated with surfactant were determined using XRD through the changes in the basal spacing. The TG was applied in this study to investigate more information of the configuration and structural changes in the organoclays with thermal decomposition. There are four different decompositions steps in differential thermogravimetric curves. The obtained TG steps are relevant to the arrangement of the surfactant molecules intercalated in MMT and the thermal analysis indicates the thermal stability of surfactant modified clays. This investigation provides new insights into the properties of organoclays and is important in the synthesis and processing of organoclays for environmental applications.     

How Carbon Nanotube Crushing can Improve Flame Retardant Behaviour in Polymer Nanocomposites?

Nanocomposites based on an ethylene–vinyl acetate copolymer (27 wt.‐% vinyl acetate) and multiwall carbon nanotubes (MWNTs) have been prepared by melt blending and their thermal degradation and flame retardant properties have been evaluated. Special attention has been paid to the influence of the nanotube nature on the flammability properties and more particularly on the time to ignition (TTI) as measured by cone calorimetry. It has been shown that there is a strong influence of the nature of carbon nanotubes on the fire behaviour of the composites, especially previous MWNTs crushing proved to substantially delay the TTI while maintaining much reduced heat release rate (HRR). Such a remarkable behaviour might be explained by the chemical reactivity of radical species present at the surface/extremities of crushed MWNTs during the combustion process.

     

Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators

A mesh independent bound is given for the superlinear convergence of the CGM for preconditioned self-adjoint linear elliptic problems using suitable equivalent operators. The results rely on K-condition numbers and related estimates for compact Hilbert-Schmidt operators in Hilbert space.This research was supported by the Hungarian National Research Fund OTKA under grant No. T043765.     

Minimizing the weighted number of late jobs in UET open shops

We consider a two-machine open shop problem where the jobs have release dates and due dates, and where all single operations have unit processing times. The goal is to minimize the weighted number of late jobs. We derive a polynomial time algorithm for this problem, thereby answering an open question posed in a recent paper by Brucker et al.This research was supported by the Christian Doppler Laboratorium für Diskrete Optimierung.     

Differential pulse polarographic determination of europium in the presence of humic substances

Humic substances (HS) and other substance of similar nature (“building blocks” of HS, such as salicylates or phthalates) influence strongly a polarographic behaviour of europium at a mercury drop electrode. An addition of these substances into the supporting electrolyte causes an enhancement of the differential pulse polarographic (DPP) peak of Eu and an anodic shift of the maximum peak potential. It was deduced from the dependence of the peak height on the pulse time and from other experimental dependencies that an adsorption of the Eu-HS (salicylate, phthalate) complexes on the working electrode is the main mechanism responsible for the peak enhancement. Because no peak distortion or splitting were observed, the DPP determination of Eu can be realised readily in the presence of HS, e.g. in environmental samples. The sensitivity of the measurements increased in the presence of HS, whereas the limit of detection (LOD) decreased (LODs were 255 and 140 nmol/l in the absence and in the presence of HS, respectively). However, the calibration dependencies were non-linear in the presence of HS. It was found that the non-linear calibration dependencies may be approximated by the Langmuir-type equation. Special procedures, such as a method of (at least) two standard additions and numerical iterative calculations, are necessary for an evaluation of measurements.     

Photocyclisierungen von 1, 1'-Polymethylen-di-2-pyridonen. 46. Mitteilung über Photoreaktionen

Photocyclization of 1, 1′-Polymethylene-di-2-pyridones . Benzophenone sensitized irradiation of the four dipyridones 1-4 gave the internal photocyclization products 6 (64%, Scheme 4), 7 (60%, Scheme 5), 8 (Scheme 6), and 11 (26%, Scheme 7), respectively. The decamethylene compound 5 yielded only polymeric material. The primary [2+2] photoproduct 8 from dipyridone 3 (Scheme 6) is relatively unstable. Further irradiation or heating to 65° induced a Cope rearrangement to give compound 9 which, on heating to 137°, was converted into the isomeric compound 10 . This product, as well as the other photoproducts mentioned, are rearranged back to their respective starting materials upon direct irradiation with 254 nm light or by heating to higher temperatures. The various possibilities for cycloadditions of pyridones are discussed as well as the possible factors which are responsible for the highly regioselective photoreactions of the dipyridones 1–4 .     

Eigenschaften und Verwendbarkeit des 10, 11-Dihydro-5H-dibenzo[a,d]cyclohepten-5-yl-Rests (= 5-Dibenzosuberyl-Rests) als neue Schutzgruppe für Amine,Aminosäuren,Alkohole, Thiole und Carbonsäuren

Properties and suitability of the 10,11-dihydro-5 H-dibenzo[a, d]cyclohepten-5-yl group (= 5-dibenzosuberyl group) as a new protecting group for amines, amino-acids, alcohols, thiols and carboxylic acids. The 10,11-dihydro-5H-dibenzo[a,d]cyclohepten-5-yl group (5-dibenzosuberyl group): has been found useful for protecting amines, alcohols, thiols, and carboxylic acids. Furthermore, the investigated 5-amino compounds are extremely stable in strongly acidic media (e. g. in hydrogen bromide) and still the amino group is easily cleaved under mild conditions, such as those used for N-trityl compounds (e.g. boiling in dilute acetic acid or catalytic hydrogenation). Hence this ring system could be a valuable and adaptable protecting group, especially in peptide chemistry.