Ordinary abelian varieties having small embedding degree

Miyaji, Nakabayashi and Takano (MNT) gave families of group orders of ordinary elliptic curves with embedding degree suitable for pairing applications. In this paper we generalise their results by giving families corresponding to non-prime group orders. We also consider the case of ordinary abelian varieties of dimension 2. We give families of group orders with embedding degrees 5, 10 and 12.     

Conceptual mis(understandings) of beginning undergraduates

In order to understand a set of mathematical skills of some importance to beginning undergraduates in engineering and mathematics, a taxonomy of three levels in increasing order of mathematical demand is proposed. The construction of a test instrument is discussed relating its purpose to the concerns of the preparation of students voiced by such as Anderson et al., to underlying theories of learning, Slavit, and to other taxonomies, Smith et al. The results of applying the questionnaire to 423 students in the period 1994–1996 is analysed and evaluated, focusing on the distributions of the distractors chosen by the students. Results suggest that the instrument is robust, that the taxonomy used is effective and raises questions that affect the teaching and learning paradigms used for mathematics pre-university and on entry to university.     

Distinguishing dose populations in sediment mixtures: a test of single-grain optical dating procedures using mixtures of laboratory-dosed quartz

Many natural deposits contain grains that have different burial histories, but reliable procedures to extract the component doses from mixed-dose samples have not been developed in optical dating. Here we present results for synthetic two- and three-component mixtures of data derived from laboratory-dosed sedimentary quartz using a single-aliquot regenerative-dose protocol and statistical models for finite mixtures. Composite sets of data were created from the doses measured for individual grains that had been bleached by sunlight and then given a beta dose of 5, 10 or 20 Gy. We found that the correct number of dose components, corresponding doses, and relative proportions of each component may be estimated if the within-component dispersion is small or is known. We also found, however, that recuperation of the OSL signal in sun-bleached quartz may produce artificially high dose estimates for some grains, an effect that should be taken into account when modelling natural mixtures.     

Energy level clusters for ν2 + ν3 type combination bands of tetrahedral molecules

Clustering of tetrahedral levels is shown to occur in ν₂ + ν₃ type combination bands of spherical top molecules due to Coriolis and vibrational anharmonic interactions. Cluster correlation diagrams are shown for cases where the vibrational splitting is both large and small compared to the Coriolis splitting, and cluster approximations are given for both cases.     

The Probability that the Number of Points on an Elliptic Curve over a Finite Field is Prime

The paper gives a formula for the probability that a randomlychosen elliptic curve over a finite field has a prime numberof points. Two heuristic arguments in support of the formulaare given as well as experimental evidence. The paper also givesa formula for the probability that a randomly chosen ellipticcurve over a finite field has kq points where k is a small numberand q is a prime.     

Extending the age range of optical dating using single ‘supergrains’ of quartz

Luminescence dating methods have been used to obtain reliable age estimates for quartz sediments deposited within the last 500 ka, but it has proven difficult to extend the age range much beyond this limit. Here we report the results of a study of individual quartz grains from Australian sedimentary deposits that range in age from 250 to 950 ka. A small number of the grains examined are strongly luminescent and saturate at unusually high doses. These ‘supergrains’ may permit reliable age determination to 1 Ma, and possibly beyond. Some other grains are in, or close to, dose-saturation, so that only minimum age estimates may be obtained. Most of the grains examined are very weakly luminescent and have palaeodoses much less than expected, while the palaeodoses of some grains cannot be estimated because of anomalous dose–response characteristics. We offer some possible explanations for the behaviour of aberrant grains.     

Discovery and characterization of a cell-permeable, small-molecule c-Abl kinase activator that binds to the myristoyl binding site

c-Abl kinase activity is regulated by a unique mechanism involving the formation of an autoinhibited conformation in which the N-terminal myristoyl group binds intramolecularly to the myristoyl binding site on the kinase domain and induces the bending of the αI helix that creates a docking surface for the SH2 domain. Here, we report a small-molecule c-Abl activator, DPH, that displays potent enzymatic and cellular activity in stimulating c-Abl activation. Structural analyses indicate that DPH binds to the myristoyl binding site and prevents the formation of the bent conformation of the αI helix through steric hindrance, a mode of action distinct from the previously identified allosteric c-Abl inhibitor, GNF-2, that also binds to the myristoyl binding site. DPH represents the first cell-permeable, small-molecule tool compound for c-Abl activation.