Investigation of Multi Wall Carbon Nanotubes and Nanotube assemblies by a molecular mechanics approach

The present work describes the modeling techniques applied for the investigation of assemblies of Carbon Nanotubes (CNTs) and Multi Wall Carbon Nanotubes (MWNTs). Motivated from possible future applications, for instance in new composite materials, the investigations of the interaction behavior of individual Carbon Nanotubes within an assembly of Carbon Nanotubes is mandatory in order to understand the behavior of larger scale structures made from CNTs, e.g. Carbon Nanotube fibers. The present research applies the Lennard-Jones potential for modeling the van-der-Waals interaction occurring between the nanotubes realizing the interaction behavior. The individual Carbon Nanotubes within the assembly are assumed to be rigid. All van-der-Waals bonds are taken into account in order to calculate an overall potential surface describing the behavior of the investigated structure. An example consisting of a Multi Wall Carbon Nanotube made of three armchair Single Wall Carbon Nanotubes (SWNTs) is investigated (with and without additional outer force) with respect to equilibrium positions of the structure. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Product line selection and pricing under a share-of-surplus choice model

Product line selection and pricing decisions are critical to the profitability of many firms, particularly in today’s competitive business environment in which providers of goods and services are offering a broad array of products to satisfy customer needs.We address the problem of selecting a set of products to offer and their prices when customers select among the offered products according to a share-of-surplus choice model. A customer’s surplus is defined as the difference between his utility (willingness to pay) and the price of the product. Under the share-of-surplus model, the fraction of a customer segment that selects a product is defined as the ratio of the segment’s surplus from this particular product to the segment’s total surplus across all offered products with positive surplus for that segment.We develop a heuristic procedure for this non-concave, mixed-integer optimization problem. The procedure utilizes simulated annealing to handle the binary product selection variables, and a steepest-ascent-style procedure that relies on certain structural properties of the objective function to handle the non-concave, continuous portion of the problem involving the prices. We also develop a variant of our procedure to handle uncertainty in customer utilities. In computational studies, our basic procedures perform extremely well, producing solutions whose objective values are within about 5% of those obtained via enumerative methods. Our procedure to handle uncertain utilities also performs well, producing solutions with expected profit values that are roughly 10% higher than the corresponding expected profits from solutions obtained under the assumption of deterministic utilities.     

1,3‐Dipolar cycloaddition of unstabilized N‐methyl azomethine ylide to nitrobenzene annelated with azoles

The 1,3‐dipolar cycloaddition of unstabilized N‐methyl azomethine ylide to mononitro benzazoles was studied. Depending on the nature of substituents and annelated azoles, the reaction affords previously unknown isoindole fused heterocyclic systems. The reactivity of the cycloadducts was examined. J. Heterocyclic Chem., (2011).     

Ferrocene‐modified thiopyrimidines: synthesis,enantiomeric resolution,antitumor activity

Ferrocenylalkyl thiopyrimidines ( 6a–d to 9a–d ) were prepared via the reaction of the α‐(hydroxy)alkyl ferrocenes, FcCHR(OH) ( 1a–d ; Fc = ferrocenyl; R = H, Me, Et, Ph), with 2‐thiopyrimidines ( 2 – 5 ) in acetone at room temperature in the presence of TFA, yielding 50–95%. The resulting enantiomers were resolved using HPLC on modified cellulose as chiral selector. The antitumor activities of S‐ferrocenylethyl 2‐thiopyrimidine ( 6b ) against two murine solid tumor models, carcinoma 755 (Ca755) and Lewis lung carcinoma (LLC) were evaluated in vivo. The strong antitumor effect of compound 6b on Ca755 and LLC was demonstrated. The index of tumor growth inhibition on Ca755 equaled 95% in comparison with control. Copyright © 2010 John Wiley & Sons, Ltd.     

A boundary version of Ahlfors’ Lemma,locally complete conformal metrics and conformally invariant reflection principles for analytic maps

A boundary version of Ahlfors’ Lemma is established and used to show that the classical Schwarz-Carathéodory reflection principle for holomorphic functions has a purely conformal geometric formulation in terms of Riemannian metrics. This conformally invariant reflection principle generalizes naturally to analytic maps between Riemann surfaces and contains among other results a characterization of finite Blaschke products due to M. Heins. D. Kraus was supported by a HWP scholarship O. Roth and S. Ruscheweyh received partial support form the German-Israeli Foundation (grant G-809-234.6/2003)