Monitoring hydration state conversion by TG-DTA

Characterization of the solid-state form (hydrate or polymorph) of a pharmaceutical active is a key scientific and regulatory requirement during development of and prior to seeking approval for marketing of the drug product. A variety of analytical methods are available to perform this task. By nature of the fundamental information it provides, TG-DTA offers advantages over other methods in regards to monitoring and quantitation of hydration state changes. In a single experiment with only a few milligrams of sample, TG-DTA perceives minor changes in phase, quantitates total water content and percent conversion, and illustrates hydrate type. All of this is accomplished without the necessity of generating time-consuming standard curves representing the differing ratios of hydrated to anhydrous forms. This study describes the use of TG-DTA to monitor and quantitate humidity induced solid–solid phase conversion of nitrofurantoin and risedronate. Percent conversion was qualitatively observed by both TG and DTA signals and quantitated by the TG.     

Thickness dependence of the magnetic anisotropy of Fe layers separated by Al

Magnetic multilayers of ⁵⁷Fe with nominal thickness, T _nom, between 0.4 and 1.0 nm separated by 3.0 nm Al spacer layers were prepared by alternate deposition of the constituents in high vacuum. The samples were investigated at 4.2 K in external magnetic field. A fraction of Fe atoms corresponding to about 0.3 nm equivalent Fe-thickness was found to mix into the Al spacer. The extremely strong magnetic anisotropy observed for T _nom < 0.8 nm is attributed to Fe layers of approximately two atomic planes thick. The anisotropy decreases considerably after the building up of the third Fe atomic layer starts at T _nom = 0.8 nm, but full saturation was not achieved even for T _nom = 1 nm and 3 T magnetic field applied perpendicularly to the sample plane.     

Aluminum(III) complexes containing O,O chelating ligand

The stoichiometric reactions of trimethylaluminum with 2,6‐(MeOCH₂)₂C₆H₃OH (LH) revealed compounds L₃Al ( 1 ) and L₂AlMe ( 2 ). On the other hand reaction of 1 equiv. of LH with trimethylaluminum did not lead to the formation of complex LAlMe₂ ( 3 ), rather 2 together with Me₃Al were observed as a result of a disproportionation of 3 . Compounds 1 and 2 were characterized by elemental analysis, ¹H and ¹³C NMR spectroscopy and in the case of 1 by X‐ray diffraction. Derivative 2 underwent transmetalation with Ph₃SnOH, giving LSnPh₃ ( 4 ) as the result of a migration of ligand L from the aluminum to the tin atom. The identity of 4 was established by elemental analysis, ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy and ¹H, ¹¹⁹Sn HMBC experiments. The system 2 and B(C₆F₅)₃ in a 1:1 molar ratio was shown to be active in the polymerization of propylene oxide and ε‐caprolactone. Copyright © 2007 John Wiley & Sons, Ltd.     

Bull-free Berge graphs are perfect

Abull is the (self-complementary) graph with verticesa, b, c, d, e and edgesab, ac, bc, bd, ce; a graphG is calledBerge if neitherG not its complement contains a chordless cycle whose length is odd and at least five. We prove that bull-free Berge graphs are perfect; a part of our argument relies on a new property of minimal imperfect graphs.This work was done while both authors were at the School of Computer Science, McGill University; support by NSERC is gratefully acknowledged.     

On local optima in multiobjective combinatorial optimization problems

In this article, local optimality in multiobjective combinatorial optimization is used as a baseline for the design and analysis of two iterative improvement algorithms. Both algorithms search in a neighborhood that is defined on a collection of sets of feasible solutions and their acceptance criterion is based on outperformance relations. Proofs of the soundness and completeness of these algorithms are given.     

A note on the acyclicity of the Koszul complex of a module

We prove the vanishing of the Koszul homology group H _μ(Kos(M)_μ), where μ is the minimal number of generators of M. We give a counterexample that the Koszul complex of a module is not always acyclic and show its relationship with the homology of commutative rings.     

Corrigendum to the paper ``Adjoining an Order Unit to a Matrix Ordered Space'

An error has been detected (and also corrected) in Theorem 2.8 of the paper entitled “Adjoining an Order Unit to a Matrix Ordered Space” (Positivity, (2005)9: 207–223; DOI ). Accordingly, some of the results of the paper have been modified. Also, a notion of C*-matricially, Riesz normed spaces has been introduced.     

Modelling of composting of food waste in a column reactor

The composting of organic solid waste, the mixture of fruit and vegetable leftovers enriched with night soil, was investigated in a closed thermally insulated reactor. It was found that 80.9 % of the original substrate biodegraded after 14 days. A mathematical model of the column reactor was proposed where the biodegradation rate of the organic solid waste was described using simple n-thorder kinetics. A good prediction of process performance was obtained using the proposed kinetics and experimentally obtained reaction heat. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

Designing a majorization scheme for the recourse function in two-stage stochastic linear programming

We discuss issues pertaining to the domination from above of the second-stage recourse function of a stochastic linear program and we present a scheme to majorize this function using a simpler sublinear function. This majorization is constructed using special geometrical attributes of the recourse function. The result is a proper, simplicial function with a simple characterization which is well-suited for calculations of its expectation as required in the computation of stochastic programs. Experiments indicate that the majorizing function is well-behaved and stable.