The number of rational points of a class of Artin-Schreier curves

We determine the number of F-q-rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound. (C) 2002 Elsevier Science (USA).

A class of compact dwarf galaxies from disruptive processes in galaxy clusters

Dwarf galaxies have attracted increased attention in recent years, because of their susceptibility to galaxy transformation processes within rich galaxy clusters. Direct evidence for these processes, however, has been difficult to obtain, with a small number of diffuse light trails and intra-cluster stars, being the only signs of galaxy disruption. Furthermore, our current knowledge of dwarf galaxy populations may be very incomplete, because traditional galaxy surveys are insensitive to extremely diffuse or compact galaxies. Aware of these concerns, we recently undertook an all-object survey of the Fornax galaxy cluster. This revealed a new population of compact members, overlooked in previous conventional surveys. Here we demonstrate that these 'ultra-compact' dwarf galaxies are structurally and dynamically distinct from both globular star clusters and known types of dwarf galaxy, and thus represent a new class of dwarf galaxy. Our data are consistent with the interpretation that these are the remnant nuclei of disrupted dwarf galaxies, making them an easily observed tracer of galaxy disruption.

The compositional inverse of a class of permutation polynomials over a finite field

A new class of bilinear permutation polynomials was recently identified. In this note we determine the class of permutation polynomials which represents the functional inverse of the bilinear class.

A new class of critical sets in Latin squares

Previously the process of finding critical sets in Latin squares has been inside cumbersome by the complexity and number of Latin trades that, must be constructed. In this paper we develop a theory of Latin trades that yields more transparent constructions. We use these Latin trades to find a new class of critical sets for Latin squares which are a product of the Latin square of order 2 with a. back circulant Latin square of odd order.

Receptor binding studies disclose a novel class of high-affinity inhibitors of the Escherichia coli FimH adhesin

Mannose-binding type 1 pili are important virulence factors for the establishment of Escherichia coli urinary tract infections (UTIs). These infections are initiated by adhesion of uropathogenic E. coli to uroplakin receptors in the uroepithelium via the FimH adhesin located at the tips of type 1 pili. Blocking of bacterial adhesion is able to prevent infection. Here, we provide for the first time binding data of the molecular events underlying type 1 fimbrial adherence, by crystallographic analyses of the FimH receptor binding domains from a uropathogenic and a K-12 strain, and affinity measurements with mannose, common mono- and disaccharides, and a series of alkyl and aryl mannosides. Our results illustrate that the lectin domain of the FimH adhesin is a stable and functional entity and that an exogenous butyl alpha- D-mannoside, bound in the crystal structures, exhibits a significantly better affinity for FimH (K-d = 0.15 muM) than mannose (K-d = 2.3 muM). Exploration of the binding affinities of alpha-D-mannosides with longer alkyl tails revealed affinities up to 5 nM. Aryl mannosides and fructose can also bind with high affinities to the FimH lectin domain, with a 100-fold improvement and 15-fold reduction in affinity, respectively, compared with mannose. Taken together, these relative FimH affinities correlate exceptionally well with the relative concentrations of the same glycans needed for the inhibition of adherence of type 1 piliated E. coli. We foresee that our findings will spark new ideas and initiatives for the development of UTI vaccines and anti-adhesive drugs to prevent anticipated and recurrent UTIs.

A class of self-stabilizing MCA learning algorithms

In this letter, we propose a class of self-stabilizing learning algorithms for minor component analysis (MCA), which includes a few well-known MCA learning algorithms. Self-stabilizing means that the sign of the weight vector length change is independent of the presented input vector. For these algorithms, rigorous global convergence proof is given and the convergence rate is also discussed. By combining the positive properties of these algorithms, a new learning algorithm is proposed which can improve the performance. Simulations are employed to confirm our theoretical results.

Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

Ultra-compact dwarf galaxies: a new class of compact stellar system discovered in the Fornax Cluster

We have used the 2dF spectrograph on the Anglo-Australian Telescope to obtain a complete spectroscopic sample of all objects in the magnitude range, 16.5 < bj < 19.8, regardless of morphology, in an area centred on the Fornax Cluster of galaxies. Among the unresolved targets are five objects which are members of the Fornax Cluster. They are extremely compact stellar systems with scale lengths less than 40 parsecs. These ultra-compact dwarfs are unlike any known type of stellar system, being more compact and significantly less luminous than other compact dwarf galaxies, yet much brighter than any globular cluster.

Constructing a class of designs with proportional balance

Text serves as a sequel to 'Computational and Constructive Design Theory,' c1996; containing research papers and surveys of recent research work on design construction and computer-aided study of designs. For researchers in theory of computational designs.

Balancing the number and size of sites: An economic approach to the optimal design of cluster samples

The design of randomized controlled trials entails decisions that have economic as well as statistical implications. In particular, the choice of an individual or cluster randomization design may affect the cost of achieving the desired level of power, other things being equal. Furthermore, if cluster randomization is chosen, the researcher must decide how to balance the number of clusters, or sites, and the size of each site. This article investigates these interrelated statistical and economic issues. Its principal purpose is to elucidate the statistical and economic trade-offs to assist researchers to employ randomized controlled trials that have desired economic, as well as statistical, properties. (C) 2003 Elsevier Inc. All rights reserved.