Optical and microstructural properties of self-assembled InAs quantum structures in silicon

The InAs quantum structures were formed in silicon by sequential ion implantation and subsequent thermal annealing. Two kinds of crystalline InAs nanostructures were successfully synthesized: nanodots (NDs) and nanopyramids (NPs). The peaks at 215 and 235 cm^?1, corresponding to the transverse optical (TO) and longitudinal optical (LO) InAs single-phonon modes, respectively, are clearly visible in the Raman spectra. Moreover, the PL band at around 1.3 µm, due to light emission from InAs NDs with an average diameter 7±2 nm, was observed. The InAs NPs were found only in samples annealed for 20 ms at temperatures ranging from 1000 up to 1200°C. The crystallinity and pyramidal shape of InAs quantum structures were confirmed by HRTEM and XRD techniques. The average size of the NPs is 50 nm base and 50 nm height, and they are oriented parallel to the Si (001) planes. The lattice parameter of the NPs increases from 6.051 to 6.055 Å with the annealing temperature increasing from 1100 to 1200°C, due to lattice relaxation. Energy dispersive spectroscopy (EDS) shows almost stoichiometric composition of the InAs NPs.     

Omega theorems related to the general Euler totient function

We prove an omega estimate related to the general Euler totient function associated to a polynomial Euler product satisfying some natural analytic properties. For convenience, we work with a set of L-functions similar to the Selberg class, but in principle our results can be proved in a still more general setup. In a recent paper the authors treated a special case of Dirichlet L-functions with real characters. Greater generality of the present paper invites new technical difficulties. Effectiveness of the main theorem is illustrated by corollaries concerning Euler totient functions associated to the shifted Riemann zeta function, shifted Dirichlet L-functions and shifted L-functions of modular forms. Results are either of the same quality as the best known estimates or are entirely new.     

1H NMR assignment corrections and 1H, 13C, 15N NMR coordination shifts structural correlations in Fe(II), Ru(II) and Os(II) cationic complexes with 2,2′‐bipyridine and 1,10‐phenanthroline

¹H, ¹³C and ¹⁵N NMR studies of iron(II), ruthenium(II) and osmium(II) tris‐chelated cationic complexes with 2,2′‐bipyridine and 1,10‐phenanthroline of the general formula [M(LL)₃]²⁺ (M = Fe, Ru, Os; LL = bpy, phen) were performed. Inconsistent literature ¹H signal assignments were corrected. Significant shielding of nitrogen‐adjacent protons [H(6) in bpy, H(2) in phen] and metal‐bonded nitrogens was observed, being enhanced in the series Ru(II) → Os(II) → Fe(II) for ¹H, Fe(II) → Ru(II) → Os(II) for ¹⁵N and bpy → phen for both nuclei. The carbons are deshielded, the effect increasing in the order Ru(II) → Os(II) → Fe(II). Copyright © 2010 John Wiley & Sons, Ltd.     

Vesicle computers: Approximating a Voronoi diagram using Voronoi automata

Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata - finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one neighbour in an excited state. The cell precipitates if the ratio of excited cells in its neighbourhood versus the number of neighbours exceeds a certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto the automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate at the points of interaction. The configuration of the precipitate represents the edges of an approximated Voronoi diagram. We discover the relationship between the quality of the Voronoi diagram approximation and the precipitation threshold, and demonstrate the feasibility of our model in approximating Voronoi diagrams of arbitrary-shaped objects and in constructing a skeleton of a planar shape.     

Topotecan dynamics,tautomerism and reactivity—1H/13C NMR and ESI MS study

Topotecan (TPT) is in clinical use as an antitumor agent, hycamtin^?. Because of this, it requires both biologically and chemically useful information to be available. TPT acts by binding to the covalent complex formed by nicked DNA and topoisomerase I. This has a poisonous effect since inserted into the single‐strand nick and TPT inhibits its religation. We used NMR to trace TPT dynamics, tautomerism and solvolysis products in various solvents and conditions. Chemical stability was assessed in methanol and DMSO as compared to water, and the regioselectivity of the N‐ and O‐methylation was studied using various alkylating agents. The reaction products of quaternization of the nitrogen atom and methylation of the oxygen atom were characterized by means of ESI MS, ¹H/¹³C‐HMBC and ‐HSQCAD NMR. We have focused on the NMR characterization of TPT with an anticipation that its aggregation, tumbling properties and the intramolecular dipolar interactions will be a common feature for other compounds described in this article. These features can also be useful in tracing the interactions of this class of topoisomerase I (TopoI) poisons with DNA. Moreover, the results explained shed light on the recently disclosed problem of lack of stability of TPT in the heart tissue homogenate samples using the analytical assays developed for this class of compounds carried out in the presence of methanol. Copyright © 2010 John Wiley & Sons, Ltd.     

On fuzzy multi-valued functions, part 4: Fuzzy economic models

An application to fuzzy economic systems of the fuzzy multi-valued functions theory elaborated by both of us in our previous papers is presented. First, stationary and dynamic fuzzy economic models are defined. Next the optimality of fuzzy trajectories of these models is introduced and investigated.     

Optimal partitioning of a measurable space into countably many sets

Summary A notion of an optimal partition of a measurable space into countably many sets according to given nonatomic probability measures is defined. It is shown that the set of optimal partitions is nonempty. Bounds for the optimal value are given and the set of optimal partitions is characterized. Finally, an example related to statistical decision theory is presented.