Compact groups of galaxies selected by stellar mass: the 2MASS compact group catalogue

We present a photometric catalogue of compact groups of galaxies (p2MCGs) automatically extracted from the Two-Micron All Sky Survey (2MASS) extended source catalogue. A total of 262 p2MCGs are identified, following the criteria defined by Hickson, of which 230 survive visual inspection (given occasional galaxy fragmentation and blends in the 2MASS parent catalogue). Only one quarter of these 230 groups were previously known compact groups (CGs). Among the 144 p2MCGs that have all their galaxies with known redshifts, 85 (59?per cent) have four or more accordant galaxies. This v2MCG sample of velocity-filtered p2MCGs constitutes the largest sample of CGs (with N = 4) catalogued to date, with both well-defined selection criteria and velocity filtering, and is the first CG sample selected by stellar mass. It is fairly complete up to Kgroup similar to 9 and radial velocity of similar to 6000?km?s-1. We compared the properties of the 78 v2MCGs with median velocities greater than 3000?km?s-1 with the properties of other CG samples, as well as those (mvCGs) extracted from the semi-analytical model (SAM) of Guo et al. run on the high-resolution Millennium-II simulation. This mvCG sample is similar (i.e. with 2/3 of physically dense CGs) to those we had previously extracted on three other SAMs run on the Millennium simulation with 125 times worse spatial and mass resolutions. The space density of v2MCGs within 6000?km?s-1 is 8.0 X 10-5?h3?Mpc-3, i.e. four times that of the Hickson sample [Hickson Compact Group (HCG)] up to the same distance and with the same criteria used in this work, but still 40?per cent less than that of mvCGs. The v2MCG constitutes the first group catalogue to show a statistically large firstsecond ranked galaxy magnitude gap according to TremaineRichstone statistics, as expected if the first ranked group members tend to be the products of galaxy mergers, and as confirmed in the mvCGs. The v2MCG is also the first observed sample to show that first-ranked galaxies tend to be centrally located, again consistent with the predictions obtained from mvCGs. We found no significant correlation of group apparent elongation and velocity dispersion in the quartets among the v2MCGs, and the velocity dispersions of apparently round quartets are not significantly larger than those of chain-like ones, in contrast to what has been previously reported in HCGs. By virtue of its automatic selection with the popular Hickson criteria, its size, its selection on stellar mass, and its statistical signs of mergers and centrally located brightest galaxies, the v2MCG catalogue appears to be the laboratory of choice to study physically dense groups of four or more galaxies of comparable luminosity.

A countably compact free Abelian group of size continuum that admits a non-trivial convergent sequence

We show that it is consistent with ZFC that the free Abelian group of cardinality c admits a topological group topology that makes it countably compact with a non-trivial convergent sequence. (C) 2011 Elsevier B.V. All rights reserved.

Galaxy triplets in Sloan Digital Sky Survey Data Release 7: II. A connection with compact groups?

We analyse a sample of 71 triplets of luminous galaxies derived from the work of O’Mill et al. We compare the properties of triplets and their members with those of control samples of compact groups, the 10 brightest members of rich clusters and galaxies in pairs. The triplets are restricted to have members with spectroscopic redshifts in the range 0.01 ≤ z ≤ 0.14 and absolute r-band luminosities brighter than Mr = −20.5. For these member galaxies, we analyse the stellar mass content, the star formation rates, the Dn(4000) parameter and (Mg − Mr) colour index. Since galaxies in triplets may finally merge in a single system, we analyse different global properties of these systems. We calculate the probability that the properties of galaxies in triplets are strongly correlated. We also study total star formation activity and global colours, and define the triplet compactness as a measure of the percentage of the system total area that is filled by the light of member galaxies. We concentrate in the comparison of our results with those of compact groups to assess how the triplets are a natural extension of these compact systems. Our analysis suggests that triplet galaxy members behave similarly to compact group members and galaxies in rich clusters. We also find that systems comprising three blue, star-forming, young stellar population galaxies (blue triplets) are most probably real systems and not a chance configuration of interloping galaxies. The same holds for triplets composed of three red, non-star-forming galaxies, showing the correlation of galaxy properties in these systems. From the analysis of the triplet as a whole, we conclude that, at a given total stellar mass content, triplets show a total star formation activity and global colours similar to compact groups. However, blue triplets show a high total star formation activity with a lower stellar mass content. From an analysis of the compactness parameter of the systems we find that light is even more concentrated in triplets than in compact groups. We propose that triplets composed of three luminous galaxies, should not be considered as an analogous of galaxy pairs with a third extra member, but rather they are a natural extension of compact groups.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

Sorafenib in Combination With Capecitabine: An Oral Regimen for Patients With HER2-Negative Locally Advanced or Metastatic Breast Cancer

Purpose Sorafenib is a multikinase inhibitor with antiangiogenic/antiproliferative activity. A randomized, double-blind, placebo-controlled phase IIB trial assessed sorafenib with capecitabine for locally advanced or metastatic human epidermal growth factor receptor 2 (HER2) -negative breast cancer. Patients and Methods Patients were randomly assigned to first-or second-line capecitabine 1,000 mg/m(2) orally twice a day for days 1 to 14 of every 21-day cycle with sorafenib 400 mg orally twice a day or placebo. The primary end point was progression-free survival (PFS). Results In total, 229 patients were enrolled. The addition of sorafenib to capecitabine resulted in a significant improvement in PFS versus placebo (median, 6.4 v 4.1 months; hazard ratio [HR], 0.58; 95% CI, 0.41 to 0.81; P = .001) with sorafenib favored across subgroups, including first-line (HR, 0.50; 95% CI, 0.30 to 0.82) and second-line (HR, 0.65; 95% CI, 0.41 to 1.04) treatment. There was no significant improvement for overall survival (median, 22.2 v 20.9 months; HR, 0.86; 95% CI, 0.61 to 1.23; P = .42) and overall response (38% v 31%; P = .25). Toxicities (sorafenib v placebo) of any grade included rash (22% v 8%), diarrhea (58% v 30%), mucosal inflammation (33% v 21%), neutropenia (13% v 4%), hypertension (18% v 12%), and hand-foot skin reaction/hand-foot syndrome (HFSR/HFS; 90% v 66%); grade 3 to 4 toxicities were comparable between treatment arms except HFSR/HFS (44% v 14%). Reasons for discontinuation in the sorafenib and placebo arms included disease progression (63% v 82%, respectively), adverse events (20% v 9%, respectively), and death (0% v 1%, respectively). Conclusion Addition of sorafenib to capecitabine improved PFS in patients with HER2-negative advanced breast cancer. The dose of sorafenib used in this trial resulted in unacceptable toxicity for many patients. A phase III confirmatory trial has been initiated with a reduced sorafenib dose.

Almost p-compact groups

We show that if p is a selective ultrafilter, then for each cardinal alpha <= omega(1), there exists a topological group G such that G(beta) is almost p-compact (in particular, countably compact), for beta < alpha, but G(alpha) is not countably compact. If in addition, we assume Martin's Axiom, then the result above holds for every alpha < c. (C) 2012 Elsevier By. All rights reserved.

Surrogate endpoints for prostate cancer-specific mortality after radiotherapy and androgen suppression therapy in men with localised or locally advanced prostate cancer: an analysis of two randomised trials

Background Androgen suppression therapy and radiotherapy are used to treat locally advanced prostate cancer. 3 years of androgen suppression confers a small survival benefit compared with 6 months of therapy in this setting, but is associated with more toxic effects. Early identification of men in whom radiotherapy and 6 months of androgen suppression is insufficient for cure is important. Thus, we assessed whether prostate-specific antigen (PSA) values can act as an early surrogate for prostate cancer-specific mortality (PCSM). Methods We systematically reviewed randomised controlled trials that showed improved overall and prostate cancer-specific survival with radiotherapy and 6 months of androgen suppression compared with radio therapy alone and measured lowest PSA concentrations (PSA nadir) and those immediately after treatment (PSA end). We assessed a cohort of 734 men with localised or locally advanced prostate cancer from two eligible trials in the USA and Australasia that randomly allocated participants between Feb 2, 1996, and Dec 27, 2001. We used Prentice criteria to assess whether reported PSA nadir or PSA end concentrations of more than 0.5 ng/mL were surrogates for PCSM. Findings Men treated with radiotherapy and 6 months of androgen suppression in both trials were significantly less likely to have PSA end and PSA nadir values of more than 0.5 ng/mL than were those treated with radiotherapy alone (p<0.0001). Presence of candidate surrogates (ie, PSA end and PSA nadir values >0.5 ng/mL) alone and when assessed in conjunction with the randomised treatment group increased risk of PCSM in the US trial (PSA nadir p=0.0016; PSA end p=0.017) and Australasian trial (PSA nadir p<0.0001; PSA end p=0.0012). In both trials, the randomised treatment group was no longer associated with PCSM (p >= 0.20) when the candidate surrogates were included in the model. Therefore, both PSA metrics satisfied Prentice criteria for surrogacy. Interpretation After radiotherapy and 6 months of androgen suppression, men with PSA end values exceeding 0.5 ng/mL should be considered for long-term androgen suppression and those with localised or locally advanced prostate cancer with PSA nadir values exceeding 0.5 ng/mL should be considered for inclusion in randomised trials investigating the use of drugs that have extended survival in castration-resistant metastatic prostate cancer.

Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.