Quaternionic operators with finite matrix trace

In this paper we consider bounded liner operators in quaternionic Hilbert space, having finite and invariant matrix trace. We prove that any such operator is selfadjoint. Besides, we prove that dual space of the real normed space of all such operators is isomorphic to the Banach space of all selfadjoint operators.This research was supported by Science Fund of Serbia, through the Mathematical Faculty of Belgrade.     

The influence of fluorine on the asymmetric reduction of fluoromethyl ketones

A comparative study of the asymmetric reduction of representative aryl and alkyl α-fluoro- and α-chloromethyl ketones using (−)-diisopinocampheylchloroborane [(−)-DIP-Chloride™] and (−)-B-isopinocampheyl-9-borabicyclo[3.3.1]nonane [R-Alpine-Borane^®] has been made. It was observed that DIP-Chloride™ is superior in terms of the rate and enantioselectivity for both classes of halo-ketones. While the reduction of monofluoroacetone and trifluoroacetone with DIP-Chloride™ provided the product alcohols in 61% ee and 96% ee, respectively, the reduction of difluoroacetone yielded only 5% ee. The influence of a lone halogen atom was not observed for monochloroacetone, all of which point towards a chelating effect of monofluoroacetone on the Lewis acidic chloroborane.     

Separation and determination of arsenic species in water by selective exchange and hybrid resins

A simple and efficient method for separation and determination of inorganic arsenic (iAs) and organic arsenic (oAs) in drinking, natural and wastewater was developed. If arsenic is present in water prevailing forms are inorganic acids of As(III) and As(V). oAs can be found in traces as monomethylarsenic acid, MMA(V), and dimethylarsenic acid, DMAs(V). Three types of resins: a strong base anion exchange (SBAE) and two hybrid (HY) resins: HY-Fe and HY-AgCl, based on the activity of hydrated iron oxides and a silver chloride were investigated. It was found that the sorption processes (ion exchange, adsorption and chemisorptions) of arsenic species on SBAE (ion exchange) and HY resins depend on pH values of water. The quantitative separation of molecular and ionic forms of iAs and oAs was achieved by SBAE and pH adjustment, the molecular form of As(III) that exists in the water at pH <8.0 was not bonded with SBAE, which was convenient for direct determination of As(III) concentration in the effluent. HY-Fe resin retained all arsenic species except DMAs(V), which makes possible direct measurements of this specie in the effluent. HY-AgCl resin retained all iAs which was convenient for direct determination of oAs species concentration in the effluent. The selective bonding of arsenic species on three types of resins makes possible the development of the procedure for measuring and calculation of all arsenic species in water. In order to determine capacity of resins the preliminary investigations were performed in batch system and fixed bed flow system. Resin capacities were calculated according to breakthrough points in a fixed bed flow system which is the first step in designing of solid phase extraction (SPE) module for arsenic speciation separation and determination. Arsenic adsorption behavior in the presence of impurities showed tolerance with the respect to potential interference of anionic compounds commonly found in natural water. Proposed method was established performing standard procedures: with external standard, certified reference material and standard addition method. Two analytical techniques: the inductively coupled plasma mass spectrometry (ICP-MS) and atomic absorption spectroscopy-hydride generation (AAS-GH) were comparatively applied for the determination of arsenic in all arsenic species in water. ICP-MS detection limit was 0.2 μg L⁻¹ and relative standard deviation (RSD) of all arsenic species investigated was between 3.5 and 5.1%.     

CdxHg(1−x)Te Alloy Colloidal Quantum Dots: Tuning Optical Properties from the Visible to Near‐Infrared by Ion Exchange

The energy gap between valence and conduction levels in colloidal semiconductor quantum dots can be tuned via the nanoparticle diameter when this is comparable to or less than the Bohr radius. In materials such as cadmium mercury telluride, which readily forms a single phase ternary alloy, this quantum confinement tuning can also be augmented by compositional tuning, which brings a further degree of freedom in the bandgap engineering. Here it is shown that compositional control of 2.3 nm diameter Cd_xHg_(1?x)Te nanocrystals by exchange of Hg²⁺ in place of Cd²⁺ ions can be used to tune their optical properties across a technologically useful range, from 500 nm to almost 1200 nm. Data on composition‐dependent changes in the optical properties are provided, including bandgap, extinction coefficient, emission energy and spectral shape, Stokes shift, quantum efficiency, and radiative lifetimes as the exchange process occurs, which are highly relevant for those seeking to use these technologically important QD materials.     

Some inequalities for symmetric functions and an application to orthogonal polynomials

We present some sharp inequalities for symmetric functions and give an application to orthogonal polynomials.     

Diffusion-controlled distribution of solute in Sn-1% Bi specimens solidified by the submerged heater method

Two 1.35 kg, 5.8 cm diameter Sn-1% Bi specimens were solidified using the submerged heater method (SHM). The distribution of solute was found to be uniform axially, indicating that diffusion-controlled steady-state segregation, though to be unattainable on earth because of the gravity induced interference, was achieved.