On the uniform domination number of a finite simple group

Let $G$ be a finite simple group. By a theorem of Guralnick and Kantor, $G$ contains a conjugacy class $C$ such that for each non-identity element $x \in G$, there exists $y \in C$ with $G = \langle x,y\rangle$. Building on this deep result, we introduce a new invariant $\gamma_u(G)$, which we call the uniform domination number of $G$. This is the minimal size of a subset $S$ of conjugate elements such that for each $1 \ne x \in G$, there exists $s \in S$ with $G = \langle x, s \rangle$. (This invariant is closely related to the total domination number of the generating graph of $G$, which explains our choice of terminology.) By the result of Guralnick and Kantor, we have $\gamma_u(G) \leqslant |C|$ for some conjugacy class $C$ of $G$, and the aim of this paper is to determine close to best possible bounds on $\gamma_u(G)$ for each family of simple groups. For example, we will prove that there are infinitely many non-abelian simple groups $G$ with $\gamma_u(G) = 2$. To do this, we develop a probabilistic approach, based on fixed point ratio estimates. We also establish a connection to the theory of bases for permutation groups, which allows us to apply recent results on base sizes for primitive actions of simple groups.Comment: 35 pages; to appear in Trans. Amer. Math. So

On the number of prime order subgroups of finite groups

Let G be a finite group and let ?(G) be the number of prime order subgroups of G. We determine the groups G with the property ?(G)??G?/2?1, extending earlier work of C. T. C. Wall, and we use our classification to obtain new results on the generation of near-rings by units of prime order

On the uniqueness of community banks

To the public, all banks seem alike. But banking insiders make important distinctions between community banks and all other banks. Policymakers worry that community banks’ unique characteristics threaten their survival in the face of industry consolidation. However, despite dramatic regulatory and technological changes in the industry in the past two decades, community banks have not only survived but often prospered. ; This article explores the differences between community banks and larger banks to discover what makes community banks unique. Large banks engage primarily in transactional banking—the provision of highly standardized intermediation services, such as gathering deposits and extending loans, that require little human input to manage. Community banks, in contrast, typically focus on relationship banking, which requires more human input, more detailed credit evaluation, and localized decision making. ; Examining profit and risk measures for the 1998–2002 period for both community banks and large banking organizations, the authors find evidence that small banks were generally profitable. In all but the smallest size category, community banks have performed as well as, and often better than, large banks in managing net interest margins, aggregate profits, and credit risk. Also, community banks are more likely to adopt Subchapter S tax status, which allows them to avoid direct federal income taxation and pass tax benefits on to shareholders. These institutions typically have relatively higher returns on both equity and assets than larger banks do. Whether community banks will be able to sustain this good performance will depend, the authors conclude, on how well managers find valuable relationship lending niches, invest bank capital, and balance asset quality with growth.Community banks

Economic Performance in Alberta Dairy: An Application of the Mimic Model

Dairy production at the farm-level is undergoing a rapid transformation in preparation for more open competition in the future. However, the means by which dairy farms can best improve their economic performance is of some question. Using measures of allocative, technical, and overall efficiency as indicators of a latent "performance" variable, this study specifies and estimates a multiple-indicator, multiple-cause (MIMIC) model of Alberta dairy production. Variables thought to "cause" performance include herd size, milk yield, breeding and veterinary expense, capital-to-labour ratio, concentrate-to-forage ratio, and operator experience. The results show that gains in performance may be made through increased capital intensity, greater spending on breeding and herd health, and, albeit marginally, through increased milk yields. Despite current trends toward larger dairy herds, this may not be a fruitful avenue for future improvements in dairy efficiency.Livestock Production/Industries,

Modification of Poly(5,6-epoxy-l-norleucine) Gives Functional Polypeptides with Alternative Side-Chain Linkages.

The preparation and characterization of a new epoxide containing polypeptide, poly(5,6-epoxy-l-norleucine), via postpolymerization modification of poly(l-homoallylglycine) is described. Addition of thiols to the epoxide groups in poly(5,6-epoxy-l-norleucine) was studied as a means to prepare side-chain functional polypeptides. The solution properties of the derivatized polypeptides were studied in water and compared to similar thioether containing functional polypeptides prepared via different routes. Subtle differences in side-chain linkage chemistry were found to influence polypeptide solubility, chain conformation in solution, and thermoresponsive behavior. Poly(5,6-epoxy-l-norleucine) was found to be useful as a readily prepared intermediate that can be reacted with thiols to give a variety of functional polypeptides

Cost and Efficiency in Alberta Dairy Production

This study investigates the relationships between farm size, milk yield, cost of production, and technical efficiency in the Alberta dairy industry. Estimates of a stochastic production frontier are obtained with two alternative methods; an iterative "average frontier: (AF) procedure and a maximum-likelihood composed error (CE) term method. An index of technical efficiency is calculated for every herd in the sample, with the AF method resulting in an average efficiency ratio of 85 percent, and the CE method producing an average efficiency ratio of 83 percent. Regressions of production cost on milk output, herd size, and efficiency are used to test for the effects of size economies, yield economies, and technical efficiency on production cost. These results suggest that herd expansion, on average, would lower the average cost of production throughout the province. Romain and Lambert use a similar method in a study of Quebec and Ontario dairy farmers which shows a limited potential to exploit economies of herd size. While not a formal test of the similarity of the two industries, the results of this study indicate a significant difference between the optimal structure of dairy production in Alberta and Quebec. Such regional differences will have important implications for the possible reapportionment of the national milk market, whether by regulatory or free-market mechanisms.Livestock Production/Industries,

Spectrograms of ship wakes: identifying linear and nonlinear wave signals

A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high speed ferry data have identified additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time-frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. We use a simple weakly nonlinear theory to identify higher order effects in a spectrogram and, while the high speed ferry data is very noisy, we propose that certain additional features in the experimental data are caused by nonlinearity. Finally, we provide a possible explanation for a further discrepancy between the high speed ferry spectrograms and linear theory by accounting for ship acceleration.Comment: 21 pages, 10 figures, submitte

Drug diffusion from polymeric delivery devices: a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective