Coherence of the real symmetric Hardy algebra

Let D denote the open unit disk in C centered at 0. Let H-R(infinity) denote the set of all bounded and holomorphic functions defined in D that also satisfy f(z) = <(f <(z)over bar>)over bar> for all z is an element of D. It is shown that H-R(infinity) is a coherent ring.

COMPLEX GEODESICS, THEIR BOUNDARY REGULARITY, AND A HARDY-LITTLEWOOD-TYPE LEMMA

We begin by giving an example of a smoothly bounded convex domain that has complex geodesics that do not extend continuously up to partial derivative D. This example suggests that continuity at the boundary of the complex geodesics of a convex domain Omega (sic) C-n, n >= 2, is affected by the extent to which partial derivative Omega curves or bends at each boundary point. We provide a sufficient condition to this effect (on C-1-smoothly bounded convex domains), which admits domains having boundary points at which the boundary is infinitely flat. Along the way, we establish a Hardy-Littlewood-type lemma that might be of independent interest.

How well does the Continuous Plankton Recorder (CPR) sample zooplankton? A comparison with the Longhurst Hardy Plankton Recorder (LHPR) in the northeast Atlantic

The Continuous Plankton Recorder (CPR) survey has collected data on basin- scale zooplankton abundance in the North Atlantic since the 1930s. These data have been used in many studies to elucidate seasonal patterns and long-term change in plankton populations, as well as more recently to validate ecosystem models. There has, however, been relatively little comparison of the data from the CPR with that from other samplers. In this study we compare zooplankton abundance estimated from the CPR in the northeast Atlantic with near-surface samples collected by a Longhurst-Hardy Plankton Recorder (LHPR) at Ocean Weather Station India (59 degree N, 19 degree W) between 1971 and 1975. Comparisons were made for six common copepods in the region: Acartia clausi, Calanus finmarchicus, Euchaeta norvegica, Metridia lucens, Oithona sp. and Pleuromamma robusta. Seasonal cycles based on CPR data were similar to those recorded by the LHPR. Differences in absolute abundances were apparent, however, with the CPR underestimating abundances by a factor of between 5 and 40, with the exception of A. clausi. Active avoidance by zooplankton is thought to be responsible. This avoidance is species specific, so that care must be taken describing communities, as the CPR emphasises those species that are preferentially caught, a problem common to many plankton samplers.

Comparison of Zooplankton Sampling Performance of Longhurst-Hardy Plankton Recorder and Bongo Nets

Data on the abundance and biomass of zooplankton off the northwestern Portuguese coast, separately estimated with a Longhurst-Hardy Plankton Recorder (LHPR) and a Bongo net, were analysed to assess the comparative performance of the samplers. Zooplankton was collected along four transects perpendicular to the coast, deployments alternating between samplers. Total zooplankton biomass measured using the LHPR was significantly higher than that using the Bongo net. Apart from Appendicularia and Cladocera, abundances of other taxa (Copepoda, Mysidacea, Euphausiacea, Decapoda larvae, Amphipoda, Siphonophora, Hydromedusae, Chaetognatha and Fish eggs) were also consistently higher in the LHPR. Some of these differences were probably due to avoidance by the zooplankton of the Bongo net. This was supported by a comparative analysis of prosome length of the copepod Calanus helgolandicus sampled by the two nets that showed that Calanus in the LHPR samples were on average significantly larger, particularly in day samples. A ratio estimator was used to produce a factor to convert Bongo net biomass and abundance estimates to equate them with those taken with the LHPR. This method demonstrates how results from complementary zooplankton sampling strategies can be made more equivalent.

Hardy-Weinberg Equilibrium and the Ternary Plot

The Hardy-Weinberg law, formulated about 100 years ago, states that under certain assumptions, the three genotypes AA, AB and BB at a bi-allelic locus are expected to occur in the proportions p2, 2pq, and q2 respectively, where p is the allele frequency of A, and q = 1-p. There are many statistical tests being used to check whether empirical marker data obeys the Hardy-Weinberg principle. Among these are the classical xi-square test (with or without continuity correction), the likelihood ratio test, Fisher's Exact test, and exact tests in combination with Monte Carlo and Markov Chain algorithms. Tests for Hardy-Weinberg equilibrium (HWE) are numerical in nature, requiring the computation of a test statistic and a p-value. There is however, ample space for the use of graphics in HWE tests, in particular for the ternary plot. Nowadays, many genetical studies are using genetical markers known as Single Nucleotide Polymorphisms (SNPs). SNP data comes in the form of counts, but from the counts one typically computes genotype frequencies and allele frequencies. These frequencies satisfy the unit-sum constraint, and their analysis therefore falls within the realm of compositional data analysis (Aitchison, 1986). SNPs are usually bi-allelic, which implies that the genotype frequencies can be adequately represented in a ternary plot. Compositions that are in exact HWE describe a parabola in the ternary plot. Compositions for which HWE cannot be rejected in a statistical test are typically “close" to the parabola, whereas compositions that differ significantly from HWE are “far". By rewriting the statistics used to test for HWE in terms of heterozygote frequencies, acceptance regions for HWE can be obtained that can be depicted in the ternary plot. This way, compositions can be tested for HWE purely on the basis of their position in the ternary plot (Graffelman & Morales, 2008). This leads to nice graphical representations where large numbers of SNPs can be tested for HWE in a single graph. Several examples of graphical tests for HWE (implemented in R software), will be shown, using SNP data from different human populations

Tess of the d'Urbervilles. Thomas Hardy : AS-A level English literature resource pack.

Guía del profesor para el estudio de la obra 'Tess of the d'Urbervilles' (publicada a finales del siglo XIX) del autor británico Thomas Hardy, en el nivel AS-A (bachillerato) de la asignatura de Literatura Inglesa. Los materiales están divididos en cuatro secciones: contextos, actividades, evaluación y recursos. El objetivo es ayudar a los estudiantes a familiarizarse con el texto, a apreciar su importancia como obra literaria, y a responder de forma detallada y analítica en el desarrollo de un trabajo de curso o un examen. Para ello se trata ampliamente la caracterización de los personajes, los temas y el lenguaje, y se incluyen prácticas de examen de redacción y ensayo.