Diagonal conditions in ordered spaces

Abstract. For a space X and a regular uncountable cardinal κ ≤ |X| we say that then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization theorems for such spaces, proving, for example, that a Lindelöf linearly ordered space with a small diagonal is metrizable. We give examples showing that our results are the sharpest possible, e.g., that there is a first countable, perfect, paracompacť Cech-complete linearly ordered space with an H-diagonal that is not metrizable. Our example shows that a recent CH-result of Juhász and Szentmiklóssy on metrizability of compact Hausdorff spaces with small diagonals cannot be generalized beyond the class of locally compact spaces. We present examples showing the interplay of the above diagonal conditions with set theory in a natural extension of the Michael line construction

1968: Abilene Christian College Bible Lectures - Full Text

CROWNING FIFTY YEARS” Being the Fiftieth Annual ABILENE CHRISTIAN COLLEGE BIBLE LECTURES - 1968 J. D. THOMAS, LECTURESHIP DIRECTOR, EDITOR Published by ABILENE CHRISTIAN COLLEGE ACC Station, Abilene, Texas 7960

Review of Coronal Oscillations - An Observer's View

Recent observations show a variety of oscillation modes in the corona. Early non-imaging observations in radio wavelengths showed a number of fast-period oscillations in the order of seconds, which have been interpreted as fast sausage mode oscillations. TRACE observations from 1998 have for the first time revealed the lateral displacements of fast kink mode oscillations, with periods of ~3-5 minutes, apparently triggered by nearby flares and destabilizing filaments. Recently, SUMER discovered with Doppler shift measurements loop oscillations with longer periods (10-30 minutes) and relatively short damping times in hot (7 MK) loops, which seem to correspond to longitudinal slow magnetoacoustic waves. In addition, propagating longitudinal waves have also been detected with EIT and TRACE in the lowest density scale height of loops near sunspots. All these new observations seem to confirm the theoretically predicted oscillation modes and can now be used as a powerful tool for ``coronal seismology'' diagnostic.Comment: 5 Figure

Mitochondrial Genome Sequences Effectively Reveal the Phylogeny of Hylobates Gibbons

BACKGROUND: Uniquely among hominoids, gibbons exist as multiple geographically contiguous taxa exhibiting distinctive behavioral, morphological, and karyotypic characteristics. However, our understanding of the evolutionary relationships of the various gibbons, especially among Hylobates species, is still limited because previous studies used limited taxon sampling or short mitochondrial DNA (mtDNA) sequences. Here we use mtDNA genome sequences to reconstruct gibbon phylogenetic relationships and reveal the pattern and timing of divergence events in gibbon evolutionary history. METHODOLOGY/PRINCIPAL FINDINGS: We sequenced the mitochondrial genomes of 51 individuals representing 11 species belonging to three genera (Hylobates, Nomascus and Symphalangus) using the high-throughput 454 sequencing system with the parallel tagged sequencing approach. Three phylogenetic analyses (maximum likelihood, Bayesian analysis and neighbor-joining) depicted the gibbon phylogenetic relationships congruently and with strong support values. Most notably, we recover a well-supported phylogeny of the Hylobates gibbons. The estimation of divergence times using Bayesian analysis with relaxed clock model suggests a much more rapid speciation process in Hylobates than in Nomascus. CONCLUSIONS/SIGNIFICANCE: Use of more than 15 kb sequences of the mitochondrial genome provided more informative and robust data than previous studies of short mitochondrial segments (e.g., control region or cytochrome b) as shown by the reliable reconstruction of divergence patterns among Hylobates gibbons. Moreover, molecular dating of the mitogenomic divergence times implied that biogeographic change during the last five million years may be a factor promoting the speciation of Sundaland animals, including Hylobates species