Fundamental Investigations on the Unit Groups of Commutative Group Algebras in Bulgaria

In this paper we give the first investigations and also some basic results on the unit groups of commutative group algebras in Bulgaria. These investigations continue some classical results. Namely, it is supposed that the cardinality of the starting group is arbitrary.

On the Compressibility of non-Abelian-Group Sources in a Distributed Source Coding Setting

We consider the problem of compression of a non-Abelian source.This is motivated by the problem of distributed function computation,where it is known that if one is only interested in computing a function of several sources, then one can often improve upon the compression rate required by the Slepian-Wolf bound. Let G be a non-Abelian group having center Z(G). We show here that it is impossible to compress a source with symbols drawn from G when Z(G) is trivial if one employs a homomorphic encoder and a typical-set decoder.We provide achievable upper bounds on the minimum rate required to compress a non-Abelian group with non-trivial center. Also, in a two source setting, we provide achievable upper bounds for compression of any non-Abelian group, using a non-homomorphic encoder.

The Riesz space structure of an Abelian W*-algebra

Let M be an Abelian W*-algebra of operators on a Hilbert space H. Let M₀ be the set of all linear, closed, densely defined transformations in H which commute with every unitary operator in the commutant M’ of M. A well known result of R. Pallu de Barriere states that if ɸ is a normal positive linear functional on M, then ɸ is of the form T → (Tx, x) for some x in H, where T is in M. An elementary proof of this result is given, using only those properties which are consequences of the fact that ReM is a Dedekind complete Riesz space with plenty of normal integrals. The techniques used lead to a natural construction of the class M₀, and an elementary proof is given of the fact that a positive self-adjoint transformation in M₀ has a unique positive square root in M₀. It is then shown that when the algebraic operations are suitably defined, then M₀ becomes a commutative algebra. If ReM₀ denotes the set of all self-adjoint elements of M₀, then it is proved that ReM₀ is Dedekind complete, universally complete Riesz spaces which contains ReM as an order dense ideal. A generalization of the result of R. Pallu de la Barriere is obtained for the Riesz space ReM₀ which characterizes the normal integrals on the order dense ideals of ReM₀. It is then shown that ReM₀ may be identified with the extended order dual of ReM, and that ReM₀ is perfect in the extended sense.

Some secondary questions related to the Riesz space ReM are also studied. In particular it is shown that ReM is a perfect Riesz space, and that every integral is normal under the assumption that every decomposition of the identity operator has non-measurable cardinal. The presence of atoms in ReM is examined briefly, and it is shown that ReM is finite dimensional if and only if every order bounded linear functional on ReM is a normal integral.

Young caregivers in the end-of-life setting: a population-based profile of an emerging group.

PURPOSE: Little is known about young caregivers of people with advanced life-limiting illness. Better understanding of the needs and characteristics of these young caregivers can inform development of palliative care and other support services. METHODS: A population-based analysis of caregivers was performed from piloted questions included in the 2001-2007 face-to-face annual health surveys of 23,706 South Australians on the death of a loved one, caregiving provided, and characteristics of the deceased individual and caregiver. The survey was representative of the population by age, gender, and region of residence. FINDINGS: Most active care was provided by older, close family members, but large numbers of young people (ages 15-29) also provided assistance to individuals with advanced life-limiting illness. They comprised 14.4% of those undertaking "hands-on" care on a daily or intermittent basis, whom we grouped together as active caregivers. Almost as many young males as females participate in active caregiving (men represent 46%); most provide care while being employed, including 38% who work full-time. Over half of those engaged in hands-on care indicated the experience to be worse or much worse than expected, with young people more frequently reporting dissatisfaction thereof. Young caregivers also exhibited an increased perception of the need for assistance with grief. CONCLUSION: Young people can be integral to end-of-life care, and represent a significant cohort of active caregivers with unique needs and experiences. They may have a more negative experience as caregivers, and increased needs for grief counseling services compared to other age cohorts of caregivers.

Time for review: supporting the work of an advisory group

This paper raises methodological issues about the challenges and dilemmas of inclusive research practices reflecting on the work of an advisory group carrying out research on using Information and Communication Technology (ICT) to enhance community participation. The interests of three parties can be identified – the commissioning agent, the researchers and the researched – and these interplayed throughout the course of the research determining the outcomes. Given the relationship between inclusive research and advocacy, there were particular gains in enabling the voice of the advisory group to shape the way in which the research was conducted and to disseminate the findings both within the organisation and beyond. However, the fragility of these new structures required organisational changes for the research to be truly empowering. The experience of the group suggests the need for their involvement at all stages of the research process

The Polish peasant in Europe and America; monograph of an immigrant group,

Mode of access: Internet.

The effectiveness of an inpatient group cognitive behavioral therapy program for alcohol dependence

The present study evaluated the effectiveness of attendance at a clinically based, short-term, in-patient group CBT program largely based on Monti, Abrams, Kadden, and Cooney(1) to treat problem drinking. Participants were 37 males and 34 females diagnosed with alcohol dependence. Patients attended 42 CBT sessions over three weeks, with each session being one hour in duration. Measures included the Khavari Alcohol Test (KAT), the Short Alcohol Dependence Data Questionnaire (SADD), the Beck Anxiety Index (BAI), the Symptom Checklist-90-Revised (SCL-90), a General Self-Efficacy scale (GSE), and the Drinking Expectancy Profile (DEP). Group attendance rates were monitored daily. Two structured phone calls were conducted at one month and three months post-discharge. Results showed that attendance rates at CBT group sessions were not associated with improvements found at the end of therapy or in drinking behaviors at three-month follow-up. Full support could not be found for the effectiveness of group CBT and cognitive models of problem drinking.

Philosophy of Computer Science and its Effect on Education: Towards the Construction of an Interdisciplinary Group

This article presents an interdisciplinary experience that brings together two areas of computer science; didactics and philosophy. As such, the article introduces a relatively unexplored area of research, not only in Uruguay but in the whole Latin American region. The reflection on the ontological status of computer science, its epistemic and educational problems, as well as their relationship with technology, allows us to elaborate a critical analysis of the discipline and a social perception of it as a basic science.

Sylow P-Subgroups of Abelian Group Rings

2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join-semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology.