Metric and Involution Scores of Clifford Algebras

The notion of a metric score is introduced as a separate tally of the total number of standard (Grassmann) basis elements spanning a Clifford algebra \({C\ell_{p,q}}\) that square to + 1 and ?1. A closed-form expression is derived for any given vector space dimension n = p+q. This is then generalized to reversion and Clifford-conjugation. A central application is that two real Clifford algebras are isomorphic if and only if their metric scores are identical.     

Amino Acid derived enamides: synthesis and aminopeptidase activity

Recently developed copper-catalyzed coupling methodology has been applied to the synthesis of amino acid derived enamides. Bond formation proved to be strongly influenced by protection strategy and vinyl iodide substitution while tolerant of limited side chain functionality. Assessment of aminopeptidase activity revealed a preference for (E)-1,2-disubstituted constructs.     

Self-organization of water in lithium/nitrobenzene system

The effect of lithium ion on the ordering of water in water-saturated nitrobenzene has been probed by 2H NMR, diffusion ordered spectroscopy and neutron scattering. It was shown that increased water concentration in LiClO4/wet nitrobenzene results in the formation of a metastable solvatomer with mixed water and nitrobenzene character, Li+(W/NB). This species is shown to decay over hours to two solvatomers, one dominated by nitrobenzene Li+(NB) and the other dominated by water Li+(W). To confirm the assignment of these solvation states, diffusion ordered deuterium NMR spectroscopy has been used to elucidate the hydrodynamic radii of these solvatomers. Neutron scattering yields vibrational spectroscopy information that shows how addition of lithium to the nitrobenzene/water system results in relatively slow self-organization of the water environment (hours).     

A study of piperidinium structure-directing agents in the synthesis of silica molecular sieves under fluoride-based conditions

This study is a continuation of our efforts to understand the interplay in the self-assembly chemistry for formation of molecular sieves from guest organocations and inorganic silicon oxide. In this particular study we focus on the competitive interplay of the organocations and the synthesis cofactor fluoride anion. The anions play a key role in structure determination, as a function of net solution concentration. They compete with the role for the space-filling organocation in determining which molecular sieve host structure will be specified. In this study we look at this competition in the synthesis for a series of 33 different organocations derived from the piperidine ring system. Derivatives were prepared which both fixed substituents on the carbon and nitrogen centers on the ring. Results were discussed in terms of product selectivity from synthesis as a function of solution concentration for the reactants. A total of 17 different host topologies were found in this series, and a correlation was seen for (a) open-framework lattices (low framework densities) under the most concentrated reaction conditions and then (b) high framework density products once the conditions were more dilute. Some surprising synthesis differences are seen in comparing the performance of these structure directing agents (SDAs) in fluoride media vs hydroxide media (the more conventional environment for zeolite/molecular sieve syntheses involving silicate chemistry). Finally molecular modeling was used to understand some of the trends in product selectivity for closely related guest (SDA) candidates.     

Hydrogen generation from weak acids: electrochemical and computational studies of a diiron hydrogenase mimic

Extended investigation of electrocatalytic generation of dihydrogen using [(mu-1,2-benzenedithiolato)][Fe(CO)3]2 has revealed that weak acids, such as acetic acid, can be used. The catalytic reduction producing dihydrogen occurs at approximately -2 V for several carboxylic acids and phenols resulting in overpotentials of only -0.44 to -0.71 V depending on the weak acid used. This unusual catalytic reduction occurs at a potential at which the starting material, in the absence of a proton source, does not show a reduction peak. The mechanism for this process and structures for the intermediates have been discerned by electrochemical and computational analysis. These studies reveal that the catalyst is the monoanion of the starting material and an ECEC mechanism occurs.     

Synthesis and characterization of immobilized PAMAM dendrons

This communication describes the synthesis and characterization of immobilized PAMAM dendrons onto a surface modified silicon wafer substrate (functionalized using plasma polymerized PAA) using a "growing from" strategy.     

Wurster's crowns: a comparative study of ortho- and para-phenylenediamine-containing macrocyclic receptors

Two series of isomeric, redox-responsive azacrown ethers based on ortho- and para-phenylenediamine (Wurster's crowns) have been synthesized and their properties explored through 13C NMR spectroscopy, electrospray ionization mass spectrometry, cyclic voltammetry, and X-ray crystallography. These crowns display strong affinity for alkali metal cations while maintaining comparable selectivity profiles to the parent crown ethers from which they are derived. Like Wurster's reagent (N,N,N',N'-tetramethyl-p-phenylenediamine or para-TMPD), the para-Wurster's crowns undergo two reversible one-electron oxidations. The integrity of the alkali metal ion complexes is maintained in the neutral and singly oxidized ligand states but not after removal of two electrons. In contrast, the oxidation of ortho-Wurster's crowns is scan rate dependent, occurring at potentials substantially higher than their para counterparts, with their complexes oxidizing irreversibly. X-ray crystal structures of representative complexes show, in all cases, participation of the redox-active phenylenediamine subunits in complex formation via direct bonding to the guest cation.     

Purification of deoxynivalenol from Fusarium graminearum rice culture and mouldy corn by high-speed counter-current chromatography

Deoxynivalenol (DON) is a mycotoxin produced by several Fusarium species and is toxic to a wide range of organisms, including human beings and livestock. To produce large amounts of pure DON for research purposes, a novel method using high-speed counter-current chromatography (HSCCC) was developed. Rice cultured with Fusarium graminearum and field mouldy corn infected by F. graminearum were extracted with methanol and found to contain 1.16 and 1.30 mg DON/g, respectively. The extracts were concentrated and then separated using a biphasic solvent system consisting of ethyl acetate-water (1:1, v/v). Collected fractions were analyzed by high-performance liquid chromatography (HPLC) and identified by congruent retention time and UV/vis spectrum and mass spectrometric data. Fractions containing DON were combined and freeze-dried. This method produced 116 mg and 65 mg DON with a purity of greater than 94.9% from 200 g of the rice culture and the mouldy corn, respectively. The HSCCC method had a recovery rate of DON at 88% from the crude extracts of both samples. This one-step purification method provided a simple and effective tool for obtaining a large amount of DON, an essential material for studies related to toxicology and detoxification of this mycotoxin.     

Anomaly detection in a mobile communication network

Mobile communication networks produce massive amounts of data which may be useful in identifying the location of an emergency situation and the area it affects. We propose a one pass clustering algorithm for quickly identifying anomalous data points. We evaluate this algorithm’s ability to detect outliers in a data set and describe how such an algorithm may be used as a component of an emergency response management system.

Increasing the Weight of Minimum Spanning Trees

The problems of computing the maximum increase in the weight of the minimum spanning trees of a graph caused by the removal of a given number of edges, or by finite increases in the weights of the edges, are investigated. For the case of edge removals, the problem is shown to be NP-hard and an Ω(1/log k)-approximation algorithm is presented for it, where (input parameter) k > 1 is the number of edges to be removed. The second problem is studied, assuming that the increase in the weight of an edge has an associated cost proportional to the magnitude of the change. An O(n³m² log(n²/m)) time algorithm is presented to solve it.