Concerning multiplier automorphisms of cyclic Steiner triple systems

A cyclic Steiner triple system, presented additively over Z _v as a set B of starter blocks, has a non-trivial multiplier automorphism λ ≠ 1 when λB is a set of starter blocks for the same Steiner triple system. When does a cyclic Steiner triple system of order v having a nontrivial multiplier automorphism exist? Constructions are developed for such systems; of most interest, a novel extension of Netto's classical construction for prime orders congruent to 1 (mod 6) to prime powers is proved. Nonexistence results are then established, particularly in the cases when v = (2^β + 1)^α, when v = 9p with p ≡ 5 (mod 6), and in certain cases when all prime divisors are congruent to 5 (mod 6). Finally, a complete solution is given for all v < 1000, in which the remaining cases are produced by simple computations.     

On the Characterisation of AG(n,q) by its Parameters asa Nearly Triply Regular Design

We show that a non-symmetric nearly triply regular designD with and in which every line has at least q points is AG(n,q) for prime power q > 2 and positiveinteger n 3.     

A fully integrated high-throughput screening methodology for the discovery of new polyolefin catalysts: discovery of a new class of high temperature single-site group (IV) copolymerization catalysts

For the first time, new catalysts for olefin polymerization have been discovered through the application of fully integrated high-throughput primary and secondary screening techniques supported by rapid polymer characterization methods. Microscale 1-octene primary screening polymerization experiments combining arrays of ligands with reactive metal complexes M(CH(2)Ph)(4) (M = Zr, Hf) and multiple activation conditions represent a new high-throughput technique for discovering novel group (IV) polymerization catalysts. The primary screening methods described here have been validated using a commercially relevant polyolefin catalyst, and implemented rapidly to discover the new amide-ether based hafnium catalyst [eta(2)-(N,O)[bond](2-MeO[bond]C(6)H(4))(2,4,6-Me(3)C(6)H(2))N]Hf(CH(2)Ph)(3) (1), which is capable of polymerizing 1-octene to high conversion. The molecular structure of 1 has been determined by X-ray diffraction. Larger scale secondary screening experiments performed on a focused 96-member amine-ether library demonstrated the versatile high temperature ethylene-1-octene copolymerization capabilities of this catalyst class, and led to significant performance improvements over the initial primary screening discovery. Conventional one gallon batch reactor copolymerizations performed using selected amide-ether hafnium compounds confirmed the performance features of this new catalyst class, serving to fully validate the experimental results from the high-throughput approaches described herein.     

Kinetics and thermodynamics of copper(II) binding to apoazurin

The binding of copper(II) to apoazurin has been probed by isothermal titration calorimetry in cholamine buffer at pH 7.0. The standard enthalpy change was determined to be -10.0 +/- 1.4 kcal/mol. Each calorimetric trace reveals an initial exothermic phase followed by an endothermic phase. The calorimetric data could be fit to a kinetic model involving a bimolecular combination of copper(II) and apoazurin in an exothermic process (k = 2 +/-1 x 103 M-1 s-1, DeltaH degrees = -19 +/- 3 kcal/mol) to form an intermediate that spontaneously converts to Cu(II)-azurin in an endothermic process (k = 0.024 +/- 0.01 s-1, DeltaH degrees = +9 +/- 3 kcal/mol). These data suggest that copper(II) first combines with apoazurin in an irreversible process to form an intermediate that converts to copper(II)-azurin in a process driven by the release of water. The overall standard free energy of copper(II) binding to apoazurin is estimated to be -18.8 kcal/mol.     

Structure and dynamics of t-butyldimethylsilyl amides

A series of N-alkyl- and N-aryl-t-butyldimethylsilyl amides have been prepared by amination and their structures determined by IR and NMR spectroscopy. Like their trimethylsilyl counterparts, the N-alkyl derivatives exist as amides while the N-aryl derivates exist as amide/imidate mixtures. The percentage of imidate and the free energies of activation for the imidate/amide exchange in the aryl derivatives are greater than those in the trimethylsilyl derivatives. The barriers to rotation in the amide form of the aryl derivatives are similar to those of the trimethylsilyl derivatives. The barrier for rotation in t-butyldimethylsilyl-N-methyl formamide, however, is lower than that of the trimethylsilyl derivative. Isomer ratios and free energies of activation are rationalized in terms of the steric effect of the t-butyl group.     

Infinite highly arc transitive digraphs and universal covering digraphs

A digraph (that is a directed graph) is said to be highly arc transitive if its automorphism group is transitive on the set ofs-arcs for eachs0. Several new constructions are given of infinite highly arc transitive digraphs. In particular, for a connected, 1-arc transitive, bipartite digraph, a highly arc transitive digraphDL() is constructed and is shown to be a covering digraph for every digraph in a certain classD() of connected digraphs. Moreover, if is locally finite, thenDL() is a universal covering digraph forD(). Further constructions of infinite highly arc transitive digraphs are given.The second author wishes to acknowledge the hospitality of the Mathematical Institute of the University of Oxford, and the University of Auckland, during the period when the research for this paper was doneResearch supported by the Australian Research Council     

Analytical scale supercritical fluid fractionation of a low molecular weight,high density polyethylene wax with carbon dioxide

This paper reports on the use of supercritical carbon dioxide to fractionate a low molecular weight, high density polyethylene into very narrow molecular weight distributions (MWDs). A simple extraction system was developed that allowed relatively trouble free extractions of the polyethylene samples. Fractions were collected at successively higher densities of CO₂ at constant temperature and then analyzed by capillary supercritical fluid chromatography (SFC), or high temperature gel permeation chromatography (GPC) and/or differential scanning calorimetry (DSC). Fractionations were performed at three different temperatures (60,80, and 100°C). Higher temperatures were found to yield greater recoveries and higher MWDs at any given density. Reducing the increment between successive extraction steps resulted in polydispersities being reduced to nearly “monodisperse” levels. Total recoveries ranged from 12 to 33% depending on the temperature, and the highest molecular weight fraction extracted by the CO₂ was centered around 1500.     

Regiospecific synthesis of 6-alkyltropan-2-ones

A new synthetic approach for the regiospecific alkylation of the 6-position of the tropane ring system has been developed. Alkylation, desulfonylation and deprotection of tropanes 5 and 12 furnished a series of 6-endo-alkyltropan-2-one derivatives 8a-e, 15a-e and 16a-e (R = Me, Et, n-Pr, n-Bu, Bn) stereoselectively in good yields. The 6-endo isomers 15a-e and 6-exo isomers 16a-e were easily obtained as pure diastereoisomers.     

The Utility of Interaction Analysis for Generalizing Characteristics of Science Classrooms

Validating and generalizing from holistic observation protocols of classroom practice have proven difficult. These tools miss crucial classroom characteristics, like the type of instruction, the organization of learners, and the level of cognitive engagement that occur differentially in the time span of a lesson. As a result, this study examined the potential of interaction analysis for drawing detailed inferences about science classrooms. Holistic and interaction analysis techniques were applied to an existing set of observational data from a group of high school teachers (N = 21) who were participating in long‐term professional development. Results indicate that interaction analysis provides crucial details that are otherwise absent. Questions are raised about the overall benefit and use of holistic observation protocols without supplemental information.