Income stratification and the measurement of interdistributional inequality between multiple groups

This paper proposes a new class of stratification indices that measure interdistributional inequality between multiple groups. The class is based on a conceptualisation of stratification as a process that results in a hierarchical ordering of groups and therefore seeks to capture not only the extent to which groups form well-defined strata in the income distribution but also the scale of the resultant differences in income standards between them, where these two factors play the same role as identification and alienation respectively in the measurement of polarisation. The properties of the class as a whole are investigated as well as those of selected members of it: zeroth and first power indices may be interpreted as measuring the overall incidence and depth of stratification respectively, while higher power indices members are directly sensitive to the severity of stratification between groups. An illustrative application provides an empirical analysis of global income stratification by regions in 1993.

Statistical properties of subgroups of free groups

The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations are determined) by randomly chosen k-tuples of reduced words, whose maximal length is allowed to tend to infinity. In this paper we adopt a different, though equally natural point of view: we investigate the statistical properties of the same objects, but with respect to the so-called graph-based distribution, recently introduced by Bassino, Nicaud and Weil. Here, subgroups (and finite presentations) are determined by randomly chosen Stallings graphs whose number of vertices tends to infinity. Our results show that these two distributions behave quite differently from each other, shedding a new light on which properties of finitely generated subgroups can be considered frequent or rare. For example, we show that malnormal subgroups of a free group are negligible in the raph-based distribution, while they are exponentially generic in the word-based distribution. Quite surprisingly, a random finite presentation generically presents the trivial group in this new distribution, while in the classical one it is known to generically present an infinite hyperbolic group.

Impact of relative size and language on the attitudes between nations and linguistic groups : The case of Switzerland

This study explores the impact of relative size on the intra- and intergroup attitudes of groups who either share a language or have a different language. For that purpose, we examined international attitudes, comparing a small nation, Switzerland, and two larger nations, Germany and France. We found support for the assumption that large neighbouring nations pose a threat to the smaller nation's identity, especially when they are linguistically similar. Consequently, in line with Tajfel's Social Identity Theory (1978), the smaller nation's inhabitants evaluate those of the larger nation less positively, liking them less and perceiving them to be more arrogant than vice versa. By investigating the special case of the French-speaking and the German-speaking Swiss as linguistic groups within their own nation we were able to demonstrate that these groups seek support with the larger-linguistically-similar nation to defend themselves against the more direct in-country threat to their identity. They acknowledge the similarity with the larger nation, yet keep defending their social identity by expressing a dislike for this perceived similarity.

The influence of halo assembly on galaxies and galaxy groups

In this paper, we study the variations of groups (galaxy properties according to the assembly history in Sloan Digital Sky Survey Data Release 6 (SDSS-DR6) selected groups. Using mock SDSS group catalogues, we find two suitable indicators of group formation time: (i) the isolation of the group, defined as the distance to the nearest neighbour ill terms of its virial radius and 00 the concentration. measured as the groups inner density calculated using the fifth nearest bright galaxy to the groups centre. Groups Within narrow ranges of Mass ill the mock catalO-Lie show increasing Ifl-OLIP alle With isolation and concentration. However, in the observational data the stellar age, as indicated by the spectral type, only shows a correlation with concentration. We study groups of similar mass and different assembly history. finding important differences ill their galaxy population. Particularly, ill high-mass SDSS groups. the number of members. mass-to-light ratios, red galaxy fractions and the magnitude difference between the brightest and second-brightest group galaxies, show different trends as a function of isolation and concentration, even when it is expected that the latter two quantities correlate with group age. Conversely. low-mass SDSS groups appear to be less sensitive to their assembly history. The correlations detected in the SDSS are not consistent with the trends measured in the mock catalogues. However, discrepancies can he explained in terms of the disagreement found in the a-e-isolation trends, suggesting that the model might be overestimating the effects of, environment, We discuss how the modelling of the cold gas ill satellite galaxies could be responsible for this problem. These results call be Used to improve our Understanding of the evolution of galaxies ill high-density environments.

Segregation effects according to the evolutionary stage of galaxy groups

We study segregation phenomena in 57 groups selected from the 2dF Percolation-Inferred Galaxy Groups (2PIGG) catalogue of galaxy groups. The sample corresponds to those systems located in areas of at least 80 per cent redshift coverage out to 10 times the radius of the groups. The dynamical state of the galaxy systems was determined after studying their velocity distributions. We have used the Anderson-Darling test to distinguish relaxed and non-relaxed systems. This analysis indicates that 84 per cent of groups have galaxy velocities consistent with the normal distribution, while 16 per cent of them have more complex underlying distributions. Properties of the member galaxies are investigated taking into account this classification. Our results indicate that galaxies in Gaussian groups are significantly more evolved than galaxies in non-relaxed systems out to distances of similar to 4R(200), presenting significantly redder (B - R) colours. We also find evidence that galaxies with M(R) <= -21.5 in Gaussian groups are closer to the condition of energy equipartition.

Effect of facilitation of local maternal-and-newborn stakeholder groups on neonatal mortality : cluster-randomized controlled trial

BACKGROUND: Facilitation of local women's groups may reportedly reduce neonatal mortality. It is not known whether facilitation of groups composed of local health care staff and politicians can improve perinatal outcomes. We hypothesised that facilitation of local stakeholder groups would reduce neonatal mortality (primary outcome) and improve maternal, delivery, and newborn care indicators (secondary outcomes) in Quang Ninh province, Vietnam. METHODS AND FINDINGS: In a cluster-randomized design 44 communes were allocated to intervention and 46 to control. Laywomen facilitated monthly meetings during 3 years in groups composed of health care staff and key persons in the communes. A problem-solving approach was employed. Births and neonatal deaths were monitored, and interviews were performed in households of neonatal deaths and of randomly selected surviving infants. A latent period before effect is expected in this type of intervention, but this timeframe was not pre-specified. Neonatal mortality rate (NMR) from July 2008 to June 2011 was 16.5/1,000 (195 deaths per 11,818 live births) in the intervention communes and 18.4/1,000 (194 per 10,559 live births) in control communes (adjusted odds ratio [OR] 0.96 [95% CI 0.73-1.25]). There was a significant downward time trend of NMR in intervention communes (p = 0.003) but not in control communes (p = 0.184). No significant difference in NMR was observed during the first two years (July 2008 to June 2010) while the third year (July 2010 to June 2011) had significantly lower NMR in intervention arm: adjusted OR 0.51 (95% CI 0.30-0.89). Women in intervention communes more frequently attended antenatal care (adjusted OR 2.27 [95% CI 1.07-4.8]). CONCLUSIONS: A randomized facilitation intervention with local stakeholder groups composed of primary care staff and local politicians working for three years with a perinatal problem-solving approach resulted in increased attendance to antenatal care and reduced neonatal mortality after a latent period. TRIAL REGISTRATION: Current Controlled Trials ISRCTN44599712. Please see later in the article for the Editors' Summary.

Some considerations about cohomology of finite groups

In this work we present some considerations about cohomology of finite groups. In the first part we use the restriction map in cohomology to obtain some results about subgroups of finite index in a group. In the second part, we use Tate cohomology to present an application of the theory of groups with periodic cohomology in topology.

EXTENSION OF AUTOMORPHISMS OF SUBGROUPS

Let G be a group such that, for any subgroup H of G, every automorphism of H can be extended to an automorphism of G. Such a group G is said to be of injective type. The finite abelian groups of injective type are precisely the quasi-injective groups. We prove that a finite non-abelian group G of injective type has even order. If, furthermore, G is also quasi-injective, then we prove that G = K x B, with B a quasi-injective abelian group of odd order and either K = Q(8) (the quaternion group of order 8) or K = Dih(A), a dihedral group on a quasi-injective abelian group A of odd order coprime with the order of B. We give a description of the supersoluble finite groups of injective type whose Sylow 2-subgroup are abelian showing that these groups are, in general, not quasi-injective. In particular, the characterisation of such groups is reduced to that of finite 2-groups that are of injective type. We give several restrictions on the latter. We also show that the alternating group A(5) is of injective type but that the binary icosahedral group SL(2, 5) is not.

The dynamical state of galaxy groups and their luminosity content

We analyse the dependence of the luminosity function (LF) of galaxies in groups on group dynamical state. We use the Gaussianity of the velocity distribution of galaxy members as a measurement of the dynamical equilibrium of groups identified in the Sloan Digital Sky Survey Data Release 7 by Zandivarez & Martinez. We apply the Anderson-Darling goodness-of-fit test to distinguish between groups according to whether they have Gaussian or non-Gaussian velocity distributions, i.e. whether they are relaxed or not. For these two subsamples, we compute the (0.1)r-band LF as a function of group virial mass and group total luminosity. For massive groups, , we find statistically significant differences between the LF of the two subsamples: the LFs of groups that have Gaussian velocity distributions have a brighter characteristic absolute magnitude (similar to 0.3 mag) and a steeper faint-end slope (similar to 0.25). We detect a similar effect when comparing the LF of bright [M-0.1r(group) - 5log(h) < -23.5] Gaussian and non-Gaussian groups. Our results indicate that, for massive/luminous groups, the dynamical state of the system is directly related to the luminosity of its galaxy members.

Generalized soluble groups of finite co-central rank

Eine Gruppe G hat endlichen Prüferrang (bzw. Ko-zentralrang) kleiner gleich r, wenn für jede endlich erzeugte Gruppe H gilt: H (bzw. H modulo seinem Zentrum) ist r-erzeugbar. In der vorliegenden Arbeit werden, soweit möglich, die bekannten Sätze über Gruppen von endlichem Prüferrang (kurz X-Gruppen), auf die wesentlich größere Klasse der Gruppen mit endlichem Ko-zentralrang (kurz R-Gruppen) verallgemeinert.Für lokal nilpotente R-Gruppen, welche torsionsfrei oder p-Gruppen sind, wird gezeigt, dass die Zentrumsfaktorgruppe eine X-Gruppe sein muss. Es folgt, dass Hyperzentralität und lokale Nilpotenz für R-Gruppen identische Bediungungen sind. Analog hierzu sind R-Gruppen genau dann lokal auflösbar, wenn sie hyperabelsch sind. Zentral für die Strukturtheorie hyperabelscher R-Gruppen ist die Tatsache, dass solche Gruppen eine aufsteigende Normalreihe abelscher X-Gruppen besitzen. Es wird eine Sylowtheorie für periodische hyperabelsche R-Gruppen entwickelt. Für torsionsfreie hyperabelsche R-Gruppen wird deren Auflösbarkeit bewiesen. Des weiteren sind lokal endliche R-Gruppen fast hyperabelsch. Für R-Gruppen fallen sehr große Gruppenklassen mit den fast hyperabelschen Gruppen zusammen. Hierzu wird der Begriff der Sektionsüberdeckung eingeführt und gezeigt, dass R-Gruppen mit fast hyperabelscher Sektionsüberdeckung fast hyperabelsch sind.

On Groups with Two Isomorphism Classes of Derived Subgroups

The structure of groups which have at most two isomorphism classes of derived subgroups (D-2-groups) is investigated. A complete description of D-2-groups is obtained in the case where the derived subgroup is finite: the solution leads an interesting number theoretic problem. In addition, detailed information is obtained about soluble D-2-groups, especially those with finite rank, where algebraic number fields play an important role. Also, detailed structural information about insoluble D-2-groups is found, and the locally free D-2-groups are characterized.

X-ray emission from clusters and groups of galaxies

Recent major advances in x-ray imaging and spectroscopy of clusters have allowed the determination of their mass and mass profile out to ≈1/2 the virial radius. In rich clusters, most of the baryonic mass is in the gas phase, and the ratio of mass in gas/stars varies by a factor of 2–4. The baryonic fractions vary by a factor of ≈3 from cluster to cluster and almost always exceed 0.09 h50−[3/2] and thus are in fundamental conflict with the assumption of Ω = 1 and the results of big bang nucleosynthesis. The derived Fe abundances are 0.2–0.45 solar, and the abundances of O and Si for low redshift systems are 0.6–1.0 solar. This distribution is consistent with an origin in pure type II supernova. The amount of light and energy produced by these supernovae is very large, indicating their importance in influencing the formation of clusters and galaxies. The lack of evolution of Fe to a redshift of z ≈ 0.4 argues for very early enrichment of the cluster gas. Groups show a wide range of abundances, 0.1–0.5 solar. The results of an x-ray survey indicate that the contribution of groups to the mass density of the universe is likely to be larger than 0.1 h50−2. Many of the very poor groups have large x-ray halos and are filled with small galaxies whose velocity dispersion is a good match to the x-ray temperatures.

Patterns of kinship in groups of free-living sperm whales (Physeter macrocephalus) revealed by multiple molecular genetic analyses.

Mature female sperm whales (Physeter macrocephalus) live in socially cohesive groups of 10-30, which include immature animals of both sexes, and within which there is communal care of the young. We examined kinship in such groups using analyses of microsatellite DNA, mitochondrial DNA sequence, and sex-linked markers on samples of sloughed skin collected noninvasively from animals in three groups off the coast of Ecuador. Social groups were defined through photographic identification of individuals. Each group contained about 26 members, mostly female (79%). Relatedness was greater within groups, as compared to between groups. Particular mitochondrial haplotypes were characteristic of groups, but all groups contained more than one haplotype. The data are generally consistent with each group being comprised of several matrillines from which males disperse at about the age of 6 years. There are indications of paternal relatedness among grouped individuals with different mitochondrial haplotypes, suggesting long-term associations between different matrilines.

Factorizations of some Groups of Lie Type of Lie Rank 4

Еленка Генчева, Цанко Генчев В настоящата работа се разглеждат крайни прости групи G , които могат да се представят като произведение на две свои собствени неабелеви прости подгрупи A и B. Всяко такова представяне G = AB е прието да се нарича факторизация на G, а тъй като множителите A и B са избрани да бъдат прости подгрупи на G, то разглежданите факторизации са известни още като прости факторизации на G. Тук се предполага, че G е проста група от лиев тип и лиев ранг 4 над крайно поле GF (q). Ключови думи: крайни прости групи, групи от лиев тип, факторизации на групи.

Groups of Order 32 as Galois Groups

2000 Mathematics Subject Classification: 12F12.