The Las Campanas/Anglo-Australian Telescope Rich Cluster Survey - III. Spectroscopic studies of X-ray bright galaxy clusters at z similar to 0.1

We present the analysis of the spectroscopic and photometric catalogues of 11 X-ray luminous clusters at 0.07 < z < 0.16 from the Las Campanas/Anglo-Australian Telescope Rich Cluster Survey. Our spectroscopic data set consists of over 1600 galaxy cluster members, of which two-thirds are outside r(200). These spectra allow us to assign cluster membership using a detailed mass model and expand on our previous work on the cluster colour-magnitude relation ( CMR) where membership was inferred statistically. We confirm that the modal colours of galaxies on the CMR become progressively bluer with increasing radius d( B - R)/dr(p) = - 0.011 +/- 0.003 and with decreasing local galaxy density d( B - R)/dlog ( Sigma)= - 0.062 +/- 0.009. Interpreted as an age effect, we hypothesize that these trends in galaxy colour should be reflected in mean H delta equivalent width. We confirm that passive galaxies in the cluster increase in Hd line strength as dH delta/dr(p) = 0.35 +/- 0.06. Therefore, those galaxies in the cluster outskirts may have younger luminosity-weighted stellar populations; up to 3 Gyr younger than those in the cluster centre assuming d( B - R)/dt = 0.03 mag per Gyr. A variation of star formation rate, as measured by [ O II]lambda 3727 angstrom, with increasing local density of the environment is discernible and is shown to be in broad agreement with previous studies from the 2dF Galaxy Redshift Survey and the Sloan Digital Sky Survey. We divide our spectra into a variety of types based upon the MORPHs classification scheme. We find that clusters at z similar to 0.1 are less active than their higher-redshift analogues: about 60 per cent of the cluster galaxy population is non-star forming, with a further 20 per cent in the post-starburst class and 20 per cent in the currently active class, demonstrating that evolution is visible within the past 2 - 3 Gyr. We also investigate unusual populations of blue and very red non-star forming galaxies and we suggest that the former are likely to be the progenitors of galaxies which will lie on the CMR, while the colours of the latter possibly reflect dust reddening. We show that the cluster galaxies at large radii consist of both backsplash ones and those that are infalling to the cluster for the first time. We make a comparison to the field population at z similar to 0.1 and examine the broad differences between the two populations. Individually, the clusters show significant variation in their galaxy populations which we suggest reflects their recent infall histories.

Infraslow (<0.1 Hz) oscillations in thalamic relay nuclei basic mechanisms and significance to health and disease states

In the absence of external stimuli, the mammalian brain continues to display a rich variety of spontaneous activity. Such activity is often highly stereotypical, is invariably rhythmic, and can occur with periodicities ranging from a few milliseconds to several minutes. Recently, there has been a particular resurgence of interest in fluctuations in brain activity occurring at <0.1 Hz, commonly referred to as very slow or infraslow oscillations (ISOs). Whilst this is primarily due to the emergence of functional magnetic resonance imaging (fMRI) as a technique which has revolutionized the study of human brain dynamics, it is also a consequence of the application of full band electroencephalography (fbEEG). Despite these technical advances, the precise mechanisms which lead to ISOs in the brain remain unclear. In a host of animal studies, one brain region that consistently shows oscillations at <0.1 Hz is the thalamus. Importantly, similar oscillations can also be observed in slices of isolated thalamic relay nuclei maintained in vitro. Here, we discuss the nature and mechanisms of these oscillations, paying particular attention to a potential role for astrocytes in their genesis. We also highlight the relationship between this activity and ongoing local network oscillations in the alpha (a; ~8-13 Hz) band, drawing clear parallels with observations made in vivo. Last, we consider the relevance of these thalamic ISOs to the pathological activity that occurs in certain types of epilepsy.

Novel sol–gel preparation of (P2O5)0.4–(CaO)0.25–(Na2O)X–(TiO2)(0.35−X) bioresorbable glasses (X = 0.05, 0.1, and 0.15)

Quaternary phosphate-based glasses in the P2O5–CaO–Na2O–TiO2 system with a fixed P2O5 and CaO content of 40 and 25 mol% respectively have been successfully synthesised via sol–gel method and bulk, transparent samples were obtained. The structure, elemental proportion, and thermal properties of stabilised sol–gel glasses have been characterised using X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDX), 31P nuclear magnetic resonance (31P NMR), titanium K-edge X-ray absorption near-edge structure (XANES), fourier transform infrared (FTIR) spectroscopy, and differential thermal analysis (DTA). The XRD results confirmed the amorphous nature for all stabilized sol–gel derived glasses. The EDX result shows the relatively low loss of phosphorus during the sol–gel process and Ti K-edge XANES confirmed titanium in the glass structure is in mainly six-fold coordination environment. The 31P NMR and FTIR results revealed that the glass structure consist of mainly Q1 and Q2 phosphate units and the Ti4+ cation was acting as a cross-linking between phosphate units. In addition DTA results confirmed a decrease in the glass transition and crystallisation temperature with increasing Na2O content. Ion release studies also demonstrated a decrease in degradation rates with increasing TiO2 content therefore supporting the use of these glasses for biomedical applications that require a degree of control over glass degradation. These sol–gel glasses also offer the potential to incorporate proactive molecules for drug delivery application due to the low synthesis temperature employed.

The Interval [0,1] Admits no Functorial Embedding into a Finite-Dimensional or Metrizable Topological Group

An embedding X ⊂ G of a topological space X into a topological group G is called functorial if every homeomorphism of X extends to a continuous group homomorphism of G. It is shown that the interval [0, 1] admits no functorial embedding into a finite-dimensional or metrizable topological group.

The Space of Differences of Convex Functions on [0, 1]

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).

Description Reduction for Restricted Sets of (0,1) Matrices

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

Algorithmic Minimization of Non-zero Entries in 0,1-Matrices

In this paper we present algorithms which work on pairs of 0,1- matrices which multiply again a matrix of zero and one entries. When applied over a pair, the algorithms change the number of non-zero entries present in the matrices, meanwhile their product remains unchanged. We establish the conditions under which the number of 1s decreases. We recursively define as well pairs of matrices which product is a specific matrix and such that by applying on them these algorithms, we minimize the total number of non-zero entries present in both matrices. These matrices may be interpreted as solutions for a well known information retrieval problem, and in this case the number of 1 entries represent the complexity of the retrieve and information update operations.

Automata–based Method for Solving Systems of Linear Constraints in {0,1}

We consider a finite state automata based method of solving a system of linear Diophantine equations with coefficients from the set {-1,0,1} and solutions in {0,1}.

Differential Balanced Trees and (0,1) Matrices

* The research was supported by INTAS 00-397 and 00-626 Projects.

On the Convergence of (0,1,2) Interpolation

2000 Mathematics Subject Classification: 41A05.