A note on positive distributions in Gaussian analysis

We describe positive generalized functional in Gaussian analysis. We focus on the large distribution space (N)^–1. It is shown that a positive distribution is represented by a measure with specific growth of its moments. Equivalently, this statement can be replaced by the integrability condition.Dedicated to Yu. M. Berezanskii on the occasion of his 70th birthdayPublished in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 5, pp. 649–658, May, 1995.     

Clathrates of organic onium halides,V: preparation of new clathrates and structure of the 1-propanol inclusion of a bis-quinuclidinium salt

Organic onium salts (3–15) are prepared and their inclusion capacity towards solvent molecules is investigated. The crystal structure of the1·propanol·H₂O clathrate ofN,N-[5-tert-butyl-1,3-phenylenebis(methylene)]bis(quinuclidinium)dibromide (4) is reported and compared with the X-ray structures of related clathrates described earlier. Supplementary Data: Details of the crystal structure are available on request from the Fachinformationszentrum Energie-Physik-Mathematik, D-7517 Eggenstein, Leopoldshafen 2, by quoting the depository number CSD 50883, the names of the authors, and the journal citation.     

Peculiarities of polyacrylamide analysis by aqueous GPC

Various commercially available stationary phases of gel permeation chromatography (GPC) were tested to determine their effectiveness in aqueous exclusion chromatography. It was found that controlled pore glass (GPG) is the most suitable material for the separation of polyacrylamides and poly(acry1amide-co-sodium acrylate), dextrans, and poly(sodium styrene–sulfonates) in 0.1M aqueous Na₂S0₄ solutions of ionic strength 0.3. A calibration curve was established by using broad molecular weight distribution polyacrylamide standards in a trial and error procedure. To avoid artificial oscillations on the evaluated distribution curves a cubic B-spline representation of the calibration curve was used instead of the conventional polynomials. By applying this system the solution instability of polyacrylamides was observed by GPC and is discussed because of its general importance to the applicability of indirect molecular weight determination methods for polyacrylamides. The effectiveness of aqueous GPC was demonstrated in an evaluation of thermal degradation measurements of polyacrylamides. Finally, the feasibility of universal calibration of aqueous GPC by means of poly(sodium styrene–sulfonates) was investigated. It is apparent that in spite of some problems concerning adsorption of the polymer universal calibration is a successful tool for calibrating aqueous GPC.     

Ultrahigh Molecular mass Polyethylene/ Carbon Nanotube CompositesCrystallization and melting properties

Ultrahigh molecular mass polyethylene (UHMMPE) is filled with carbon nano-tubes (CNTs) by solution in the presence of maleic anhydride grafted styrene-(ethylene-co-butylene)-styrene copolymer (MA-SEBS) as a compatibilizer. The UHMMPE/CNT composites crystallized from melt were prepared at a cooling rate of 20°C min^-1. The melting and crystallization behaviors of UHMMPE/ CNT composites were investigated by differential scanning calorimetry. The results showed that onset melting temperature (T _m) and degree of crystallinity (X _c) of UHMMPE/CNT composites crystallized from solution are higher than those from melt due to the larger crystalline lamellar thickness. The onset crystallization temperature (T _c) of UHMMPE/CNT composites tends to shift to higher temperature region with increasing CNT content in the composites. Tm and Tc of UHMMPE phase in UHMMPE/CNT composites decrease with the addition of MA-SEBS. Moreover, the crystallization rate of UHMMPE phase in UHMMPE/CNT composite is increased due to the introduction of CNTs. MA-SEBS acts as compatilizer, enhances the dispersion of CNTs in the UHMMPE matrix. Thereby, the crystallization rate of UHMMPE phase in UHMMPE/CNT composite is further increased with the addition of MA-SEBS. This revised version was published online in August 2006 with corrections to the Cover Date.     

The singular modular forms on the 27-dimensional exceptional domain

Summary Due to a result of Resnikoff the non-constant singular modular forms on the 27-dimensional exceptional domain are exactly those of weight 4 and weight 8. They were constructed by Kim using analytic continuation of non-holomorphic Eisenstein series. In this paper a simpler construction is described. These modular forms arise from theta series on the Cayley half-plane of degree two, which is a 10-dimensional boundary component, by means of the Fourier-Jacobi expansion. This article was processed by the author using the IATEX style filecljour1 from Springer-Verlag.     

Vereinfachtes Verfahren zur Bestimmung des Kohlenstoffs und Wasserstoffs sowie des Schwefels organischer Substanzen

Zusammenfassung Es wird ein neues Verfahren zur Bestimmung des Kohlenstoffs und Wasserstoffs beschrieben. Die neuartige Arbeitsweise ist dadurch gekennzeichnet, daß zunächst die Destillations- bzw. thermischen Zersetzungsprodukte der zu untersuchenden Substanz mit Hilfe eines indifferenten Gases durch eine als Brenner wirkende erhitzte Capillare in den Verbrennungsraum des Reaktionsrohres geleitet werden, in dem sie im reinen Sauerstoffstrom verbrannt werden. Anschließend werden die festen Rückstände im Entgasungsraum mit reinem Sauerstoff vollständig verbrannt. Die sehr heiße Flamme am Capillarende sowie der Sauerstoffüberschuß gewährleisten eine vollständige Verbrennung der Entgasungsbzw. Destillationsprodukte, so daß weitere Oxydationsmittel nicht erforderlich sind. Die direkte Beobachtung der Verbrennungsflamme gestattet zudem, den Verbrennungsvorgang gut zu überwachen und zu steuern. Der apparative Aufwand für das Verfahren ist gering, da für die Beheizung des Entgasungsraumes sowie des Verbrennungs- und Absorptionsraumes nur zwei Bunsenbrenner erforderlich sind.Das gleiche Verbrennungsprinzip wird bei dem ebenfalls beschriebenen Verfahren zur Bestimmung des Schwefels angewandt.     

The Hecke-algebras related to the unimodular and modular group over the Hurwitz order of integral quaternions

In the present paper the elementary divisor theory over the Hurwitz order of integral quaternions is applied in order to determine the structure of the Hecke-algebras related to the attached unimodular and modular group of degreen. In the casen = 1 the Hecke-algebras fail to be commutative. Ifn > 1 the Hecke-algebras prove to be commutative and coincide with the tensor product of their primary components. Each primary component turns out to be a polynomial ring inn resp.n + 1 resp. 2n resp. 2n+1 algebraically independent elements. In the case of the modular group of degreen, the law of interchange with the Siegel ϕ-operator is described. The induced homomorphism of the Hecke-algebras is surjective except for the weightsr = 4n-4 andr = 4n-2.