Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks

We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation of the network behavior close to constant critical load in terms of the solution of a Skorokhod problem. Since we model the doubly infinite time interval, our results directly cover the stationary case.AMS subject classification: primary 90B15, secondary 60K25, 68M20     

Structural reliability and stochastic structural optimization

Mathematical Methods of Operations Research -     

Quantum confinement in layer-by-layer deposited colloidal HgTe nanocrystals determined by spectroscopic ellipsometry

We report spectroscopic ellipsometry studies in the energy range of 0.5-5 eV on samples of 1-10 bilayers of polymer and HgTe nanocrystals, which exhibit strong transitions at higher critical points in the dispersion relation. We show that the dispersion relation for nanocrystals can be modelled with the same concepts for critical points as used in semiconductor bulk optics. We find an energy shift of up to 0.4 eV of the critical points to higher energies compared to the HgTe bulk properties, caused by quantum confinement in the nanocrystals, which increases with decreasing nanocrystal size.     

Effect of impeller geometry on gas-liquid mass transfer coefficients in filamentous suspensions

Volumetric gas-liquid mass transfer coefficients were measured in suspensions of cellulose fibers with concentrations ranging from 0 to 20 g/L. The mass transfer coefficients were measured using the dynamic method. Results are presented for three different combinations of impellers at a variety of gassing rates and agitation speeds. Rheological properties of the cellulose fibers were also measured using the impeller viscometer method. Tests were conducted in a 20 L stirred-tank fermentor and in 65 L tank with a height to diameter ratio of 3:1. Power consumption was measured in both vessels. At low agitation rates, two Rushton turbines gave 20% better performance than the Rushton and hydrofoil combination and 40% better performance than the Rushton and propeller combination for oxygen transfer. At higher agitation rates, the Rushton and hydrofoil combination gave 14 and 25% better performance for oxygen transfer than two Rushton turbines and the Rushton and hydrofoil combination, respectively.

     

Eine ErweiterungT(V′) des Ordinalzahlensystems 58-0158-0158-01(Λ0) von G. Jäger

Summary This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger [3]. The generalized systemT(V) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V) is provable in a formal system of second order arithmetic with the axiom schema of ₂ ¹ -comprehension in a similar way, as it is proved in [6] for the weaker notation systemT(V).     

The synthesis of N-substituted ureas II: Nucleophilic substitution of ureas at the carbonyl group

Summary N-Arylsubstituted ureas undergo exchange of the N-residue upon reaction with amines. Using kinetic measurements, investigation of product distribution, regioselectivity, catalysis, and substrate influences, it was shown that this reaction proceeds via a second order nucleophilic substitution at the urea carbonyl center. By means of semiempirical calculations using the MNDO method the alternative mechanism of fragmentation was investigated.

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Zur Synthese N-substituierter Harnstoffe II: Nucleophile Substitution von Harnstoffen an der Carbonylgruppe

Zusammenfassung N-Arylsubstituierte Harnstoffe erleiden bei der Reaktion mit Aminen einen Austausch des N-Restes. Durch kinetische Messungen, Untersuchung der Produktverteilung, Regioselektivität, Katalyse und des Einflusses des Edukts konnte abgeleitet werden, daß es sich hiebei um eine nucleophile Substitution zweiter Ordnung am Carbonylzentrum des Harnstoffs handelt. Durch semiempirische Rechnungen mit Hilfe der MNDO Methode wurde der alternative Reaktionsmechanismus einer Fragmentierung untersucht.

     

Miscibility in systems containing aqueous solutions of various alkylbenzenesulfonates, toluene and, n-butanol

Miscibility relationships in four-component systems containing sodium alkylbenzenesulfonates, toluene, n-butanol, and water were studied at 25°C in the hope of clarifying the complex systems used in the “micellar flood” enhanced oil recovery process. Phase boundary curves for the pseudo three-component systems (constant sulfonate/water ratios, 2.5 moles sulfonate per kg water) were determined. The sulfonates included those of benzene, toluene, xylene, ethylbenzene, isopropylbenzene, mesitylene, cymene, methyl-t-butylbenzene, and diisopropylbenzene, in all of which the alkyl substituents are smaller than in the usual surfactants. The phase boundary curves have similar and fairly symmetrical shapes. The amount of n-butanol (cosolvent) required to produce miscibility decreases with increasing number of alkyl carbons on the benzene ring of the sulfonates and seems relatively independent of the isomeric structure. The sodium salt of diisopropylbenzenesulfonate gives the lowest phase boundary curve (least n-butanol required for miscibility) among the nine sulfonates studied.