Graphic matroids and the multicommodity transportation problem

A necessary and sufficient condition for unimodularity in the multicommodity transportation problem is established, and the constructive proof yields an equivalent, single commodity network flow problem for the class of problems satisfying the condition. The concept of a graphic matroid is used to establish the transformation.     

Decomposition algorithms for locating minimal cuts in a network

This paper provides decomposition algorithms for locating minimal cuts in a large directed network. The main theorem provides several cases for the algorithms. In the worst case, it is shown that the efficiency of one of the proposed algorithms is of the same order as a no-decomposition algorithm. As in linear programming, the obvious advantage of the proposed decomposition procedure is its ability to potentially handle larger problems than a no-decomposition algorithm.     

Determination of the crystal and molecular structure of 1,4-bis(p-chlorobenzoyl)-5-methylene-7-methyl-2,3,4,5-tetrahydro-1H-1,4-diazepine

The crystal and molecular structure of 1,4-bis(p-chlorobenzoyl)-5-methylene-7-methyl-2,3,4,5-tetrahydro-1H-1,4-diazepine has been determined by X-ray methods. The crystals are triclinic,P¯1,a = 10.605,b = 13.054,c = 7.351 Å, = 94.24, = 101.53, = 101.55 °,Z = 2. The structure was solved by direct methods, and refined by full-matrix least squares toR = 5.6% on 3495 observed reflections. The structure is of the enamide form with diacylation on nitrogen. There are no abnormal bond lengths or intermolecular contacts.     

Pyrrole β-amides: Synthesis and characterization of a dipyrrinone carboxylic acid and an N-Confused fluorescent dipyrrinone

Pyrrole β-amides are useful building blocks for the preparation of novel molecular architectures that can be used in supramolecular chemistry and sensor development. Under basic conditions, pyrrole β-amides with an α-aldehyde produce different condensation products when reacted with pyrrolinones depending on the amide substitution. Secondary amides form the expected dipyrrinones, but unexpectedly undergo a subsequent trans-amidation with the pyrrolinone nitrogen to produce an unsymmetrical imide (an N-confused fluorescent dipyrrinone). Under the same conditions, tertiary amides produce the expected dipyrrinone carboxylic acids, which have been shown to have strong self-association properties as determined by vapor pressure osmometry measurements, NMR studies, and X-ray crystal structure determination. Furthermore, an N-confused fluorescent dipyrrinone was produced from the same trans-amidation reaction during attempts to decarboxylate a dipyrrinone amide with a 9-carboxylic moiety.     

Coordination studies of Al-EDTA in aqueous solution

The degree of aluminum toxicity is based on its complexation with organic ligands. One of these complexes is AlEDTA- (Al = aluminum, EDTA = ethylenediaminetetraacetate), the structure of which in aqueous solution has been debated on the basis of X-ray absorption and NMR measurements with different interpretations proposing different coordination. In addition, there is a lack of consensus regarding the relationship of crystalline AlEDTA- and its geometry in solution. This debate must be resolved, not merely for scientific interest, but because the use of an incorrect coordination might lead to the wrong interpretation of bioactivity and kinetics data. In this work, we predict the coordination of Al in aqueous AlEDTA- by employing ab initio calculations and Car-Parrinello molecular dynamics simulations. Our results indicate that AlEDTA- favors Al in octahedral coordination in aqueous solution. Furthermore, the predicted crystalline and solution-phase structures of AlEDTA- are similar and agree well with recent X-ray measurements, supporting the strong chelating nature of this metal-organic complex in aqueous solution.     

Towards quantitatively reproducible substrates for SERS

There is a need for a method to facilitate the development of novel, reproducible colloidal surface-enhanced Raman scattering (SERS) substrates to encourage the use of SERS in applied studies. In this study we show for the first time that by using suitably designed SERS experiments in conjunction with multivariate analysis of variance (MANOVA), an objective assessment of colloidal SERS reproducibility can be made. This is demonstrated with the analyte cresyl violet, but could be extended to any analyte of interest for which reproducible SERS data are needed.