Structural and thermochemical studies of pyrrolidine borane and piperidine borane by gas electron diffraction and quantum chemical calculations

Structural Chemistry - The gaseous structures, thermochemical properties and dehydrogenation reaction energy profiles of the borane complexes of pyrrolidine and piperidine have been investigated...     

Non-hydrolytic sol–gel synthesis of tantalum sulfides

Non-hydrolytic sol–gel synthesis provides a low temperature solution based approach to solid-state materials. In this work, reactions of TaX₅ (X = F, Cl, Br, I) with the thio-ethers di-tert-butylsulfide and hexamethyldisilathiane were carried out in chloroform or acetonitrile. The influence of synthetic parameters such as temperature, reaction time, starting sulfur to tantalum ratio, and solvent volume were explored, and optimized conditions for the preparation of phase pure crystalline TaS₂ were established. Amorphous powders were recovered for most of the samples, but crystalline 1T- and 3R-TaS₂ modifications could be selectively prepared by heat treatments of the as-recovered precursors at 700 and 800 °C, respectively. The crystallite sizes could be adjusted by tuning the starting sulfur to tantalum ratios, and by choice of solvent. For specific conditions, nanocrystalline 1T-TaS₂ was directly recovered from solution. To our knowledge, this is the first time that crystalline TaS₂ was directly obtained from low temperature solution based routes.     

One‐Pot Approach to Organo‐Phosphorus–Chalcogen Macrocycles Incorporating Double OP(S)SCn or OP(Se)SeCn Scaffolds: A Synthetic and Structural Study

The development of new methodology for the preparation of functional macrocycles with practical applications is an important research area in macromolecular science. In this study, we report a new one‐pot route for the synthesis of a series of macro‐heterocycles by incorporating two phosphorus atoms and two chalcogen atoms and two oxygen atoms (double OP(S)SC_n or OP(Se)SeC_n scaffolds). The three‐component condensation reactions of 2,4‐diferrocenyl‐1,3,2,4‐diathiadiphosphetane 2,4‐disulfide ( FcLR , a ferrocene analogue of Lawesson's reagent) or 2,4‐bis(4‐methoxyphenyl)‐1,3,2,4‐dithiadiphosphetane 2,4‐disulfide ( LR , Lawesson's reagent), or 2,4‐diphenyl‐1,3,2,4‐diselenadiphosphetane 2,4‐diselenide ( WR , Woollins’ reagent), disodium alkenyl‐diols, and dihalogenated alkanes are performed, giving rise to soluble and air or moisture‐stable macrocycles in good‐to‐excellent yields (up to 92 %). This is the first systemically preparative and readily scalable example of one‐pot ring opening/ring extending reaction of three‐components to prepare phosphorus–chalcogen containing macrocycles. We also provide a systematic crystallographic study.     

A novel application of fluidization – Integrating three processes in reclaiming foundry sand

Immersion of automotive parts in a fluidized bed of foundry sand is used to both strip the castings free from moulding sand and to heat-treat the castings at 500℃. The fluid bed is heated by hot gases from a burner directed first into a serpentine heat exchanger located near one side-wall of the rectangular tank, and then into a distributor consisting of horizontal sparger pipes having maintenance standpipes fixed into their upper surfaces.     

The Taylor–Browder Spectrum on Prime C*-Algebras

We provide a formula for the Taylor–Browder spectrum of a pair (L _a , R _b ) of left and right multiplication operators acting on a prime C*-algebra with non-zero socle. We also compute ascent and descent for multiplication operators on a prime ring, characterise Browder elements in a prime C*-algebra and discuss upper semicontinuity for the Browder spectrum.     

A characterisation of virtually free groups

We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic. Received: 30 October 2006     

The Mixturegram: A Visualization Tool for Assessing the Number of Components in Finite Mixture Models

Certain practical and theoretical challenges surround the estimation of finite mixture models. One such challenge is how to determine the number of components when this is not assumed a priori. Available methods in the literature are primarily numerical and lack any substantial visualization component. Traditional numerical methods include the calculation of information criteria and bootstrapping approaches; however, such methods have known technical issues regarding the necessary regularity conditions for testing the number of components. The ability to visualize an appropriate number of components for a finite mixture model could serve to supplement the results from traditional methods or provide visual evidence when results from such methods are inconclusive. Our research fills this gap through development of a visualization tool, which we call a mixturegram. This tool is easy to implement and provides a quick way for researchers to assess the number of components for their hypothesized mixture model. Mixtures of univariate or multivariate data can be assessed. We validate our visualization assessments by comparing with results from information criteria and an ad hoc selection criterion based on calculations used for the mixturegram. We also construct the mixturegram for two datasets.     

Bounds on stochastic convex allocation problems

We consider a stochastic convex program arising in a certain resource allocation problem. The uncertainty is in the demand for a resource which is to be allocated among several competing activities under convex inventory holding and shortage costs. The problem is cast as a two–period stochastic convex program and we derive tight upper and lower bounds to the problem using marginal distributions of the demands, which may be stochastically dependent. It turns out that these bounds are tighter than the usual bounds in the literature which are based on limited moment information of the underlying random variables. Numerical examples illustrate the bounds.