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.     

A Synthesis of Furans from Epoxycarbonyl Precursors

Following our study of the preparation of 2-ethyl-4-methylfuran (2a) by rearrangement of 5-methyl-5,6-epoxy-3-hexanone (1a),¹ we undertook an investigation of the conversion of other epoxycarbonyl precursors to furans in order to determine the scope and utility of this transformation. The transformations examined in the present study are shown below. The epoxycarbonyl substrates were conveniently prepared from commercially available unsaturated alcohols by first expoxidation with m-chloroperoxybenzoic acid followed by oxidation with chromium trioxide-pyridine reagent in methylene chloride solution.²     

Homogeneous factorisations of complete graphs with edge-transitive factors

A factorisation of a complete graph K _n is a partition of its edges with each part corresponding to a spanning subgraph (not necessarily connected), called a factor. A factorisation is called homogeneous if there are subgroups M<G≤S _n such that M is vertex-transitive and fixes each factor setwise, and G permutes the factors transitively. We classify the homogeneous factorisations of K _n for which there are such subgroups G,M with M transitive on the edges of a factor as well as the vertices. We give infinitely many new examples. This paper forms part of an Australian Research Council Discovery Grant project, and was a major part of the PhD project of the second author.     

Laryngeal Hyperfunction During Whispering: Reality or Myth?

For years, otolaryngologists and voice therapists have warned voice patients that whispering causes more trauma to the larynx than normal speech. However, no large series of patients has ever been examined fiberoptically during whispering to test this hypothesis. As part of our routine examination, patients are asked to count from 1 to 10 in a normal voice and in a whispered voice. We reviewed recorded fiberoptic examinations of 100 patients who had voice complaints. We compared supraglottic hyperfunction and vocal fold closure during the normal and whispered phonation of each patient. Sixty-nine percent of the patients demonstrated increased supraglottic hyperfunction with whispered voice. Eighteen percent had no change, and 13% had less severe hyperfunction. The most common glottal configuration during whisper was an inverted Y, which resulted from compression of the anterior and middle thirds of the true vocal folds. However, 12 patients had no true vocal fold contact during whispered voice, despite having adequate glottic closure with normal voice. Although whispering involves more severe hyperfunction in most patients, it does not seem to do so in all patients. In some patients, it may be less traumatic than normal voice.     

Delandtsheer–Doyen parameters for block-transitive point-imprimitive 2-designs

Designs, Codes and Cryptography - Delandtsheer and Doyen bounded, in terms of the block size, the number of points of a point-imprimitive, block-transitive 2-design. To do this they introduced two...