Rings faithfully represented on their left socle

In 1964 A. W. Goldie [1] posed the problem of determining all rings with identity and minimal condition on left ideals which are faithfully represented on the right side of their left socle. Goldie showed that such a ring which is indecomposable and in which the left and right principal indecomposable ideals have, respectively, unique left and unique right composition series is a complete blocked triangular matrix ring over a skewfield. The general problem suggested above is very difficult. We obtain results under certain natural restrictions which are much weaker than the restrictive assumptions made by Goldie.

We characterize those rings in which the principal indecomposable left ideals each contain a unique minimal left ideal (Theorem (4.2)). It is sufficient to handle indecomposable rings (Lemma (1.4)). Such a ring is also a blocked triangular matrix ring. There exist r positive integers K₁,..., K_r such that the i,j^th block of a typical matrix is a K_i x K_j matrix with arbitrary entries in a subgroup D_ij of the additive group of a fixed skewfield D. Each D_ii is a sub-skewfield of D and D_ri = D for all i. Conversely, every matrix ring which has this form is indecomposable, faithfully represented on the right side of its left socle, and possesses the property that every principal indecomposable left ideal contains a unique minimal left ideal.

The principal indecomposable left ideals may have unique composition series even though the ring does not have minimal condition on right ideals. We characterize this situation by defining a partial ordering ρ on {i, 2,...,r} where we set iρj if D_ij ≠ 0. Every principal indecomposable left ideal has a unique composition series if and only if the diagram of ρ is an inverted tree and every D_ij is a one-dimensional left vector space over D_ii (Theorem (5.4)).

We show (Theorem (2.2)) that every ring A of the type we are studying is a unique subdirect sum of less complex rings A₁,...,A_s of the same type. Namely, each A_i has only one isomorphism class of minimal left ideals and the minimal left ideals of different A_i are non-isomorphic as left A-modules. We give (Theorem (2.1)) necessary and sufficient conditions for a ring which is a subdirect sum of rings A_i having these properties to be faithfully represented on the right side of its left socle. We show ((4.F), p. 42) that up to technical trivia the rings A_i are matrix rings of the form

[...]. Each Q_j comes from the faithful irreducible matrix representation of a certain skewfield over a fixed skewfield D. The bottom row is filled in by arbitrary elements of D.

In Part V we construct an interesting class of rings faithfully represented on their left socle from a given partial ordering on a finite set, given skewfields, and given additive groups. This class of rings contains the ones in which every principal indecomposable left ideal has a unique minimal left ideal. We identify the uniquely determined subdirect summands mentioned above in terms of the given partial ordering (Proposition (5.2)). We conjecture that this technique serves to construct all the rings which are a unique subdirect sum of rings each having the property that every principal-indecomposable left ideal contains a unique minimal left ideal.

Otto Kelland’s Model Dories and the Digital Archives Initiative

Otto Kelland was a truly unique individual in Newfoundland. During his long life he had several careers from being a prison superintendant to being an instructor at Marine Institute. During his life Kelland made hundreds of wooden boat models. They are beautifuly hand-crafted and represented the type of watercraft used by fishermen in Newfoundland. The collection of boat models made by Otto Kelland and owned by Marine Institute made an ideal object to be digitalized. In particular the collection of dories was an ideal group to be digitized. They were housed in one cabinet and accompanied by hand-written documents describing each model. The Digital Archives Initiative (DAI) is a “gateway to the learning and research-based cultural resources held by Memorial University of Newfoundland and partnering organizations.” The DAI hosts a variety of collections which together reinforce the importance, past and present, of Newfoundland and Labrador's history and culture. I will give an oral presentation of the project followed by a demonstration of the Otto Kelland Dories exhibit on the Digital Archives Initiative (DAI) at Memorial University of Newfoundland. I will be happy to answer questions following my presentation.

Part I. Coenzyme B12 as a hydroformylation-type catalyst. Part II. Mechanisms of hydrogen transfer in the methylmalonyl coenzyme a mutase reaction

Part I

The mechanism of the hydroformylation reaction was studied. Using cobalt deuterotetracarbonyl and 1-pentene as substrates, the first step in the reaction, addition of cobalt tetracarbonyl to an olefin, was shown to be reversible.

Part II

The role of coenzyme B₁₂ in the isomerization of methylmalonyl coenzyme A to succinyl coenzyme A by methylmalonyl coenzyme A mutase was studied. The reaction was allowed to proceed to partial completion using a mixture of methylmalonyl coenzyme A and 4, 4, 4-tri-²H-methylmalonyl coenzyme A as substrate. The deuterium distribution in the product, succinyl coenzyme A, was shown to best fit a model in which hydrogen is transferred from C-4 of methylmalonyl coenzyme A to C-5’ of the adenosyl moiety of coenzyme B₁₂ in the rate determining step. The three hydrogens at the 5’-adenosyl position of the coenzyme B₁₂ intermediate are then able to become enzymatically equivalent before hydrogen is transferred from the coenzyme B₁₂ intermediate to form succinyl coenzyme A.

Theoretical research on noncollinear match conditions of the type I optical parametric process

Broad bandwidth group match conditions are reported for a noncollinear type I optical parametric process. The theoretical calculations corresponding to two special situations in practice were made, respectively, which are in accordance with the published experimental results. Furthermore, we provide a method to not only achieve maximal parametric bandwidth output but also match the group velocities between three waves. (c) 2006 Optical Society of America.

Quando a magreza torna-se um ideal masculino: um estudo socioantropologico sobre a anorexia e a bulimia em homens

Esta dissertação pretende discutir o surgimento de casos de anorexia nervosa e bulimia nervosa em homens e sua relação com: a - as questões socioculturais ligadas ao culto à magreza e seus desdobramentos (como a noção de estilo de vida); e b - as discussões sobre masculinidades, experiências corporais e subjetivas desses sujeitos. Seu principal objetivo é compreender como estes transtornos alimentares, tidos como distúrbios de ordem psiquiátrica pela literatura biomédica, não estão restritos somente ao feminino, sugerindo também implicações ligadas ao processo de elaboração do saber médico, seus campos de pesquisa e atuação. A metodologia empregada foi a realização de entrevistas via MSN Messenger, com 20 homens entre 13 e 30 anos, que declaram passar ou ter passado por algum tipo de experiência envolvendo a anorexia e/ou bulimia.

Prevenção da úlcera de pressão: resultados da ação educativa junto à equipe de enfermagem

Os pacientes hospitalizados, acamados ou restritos ao leito, apresentam uma gama de fatores de risco para o desenvolvimento das úlceras por pressão, diante disso, necessitam de uma assistência de enfermagem qualificada e eficaz na prevenção dessas lesões, a fim de evitar o desenvolvimento das mesmas. Desta forma, a pesquisa teve como objetivo investigar a influência da ação educativa junto à equipe de enfermagem das enfermarias de Clínica Médica na prevenção das úlceras por pressão. Tratou-se de um estudo quantitativo com delineamento descritivo com dispositivo de intervenção do tipo antes e depois, tendo como cenário as enfermarias de Clínica Médica de um hospital universitário na cidade do Rio de Janeiro. Os sujeitos foram os enfermeiros (n=15) e técnicos de enfermagem (n=18) da Clínica Médica e a unidade de medida do estudo foi o número de vezes que as ações de enfermagem, referentes à prevenção das úlceras por pressão e desempenhadas pelos sujeitos, foram observadas pela pesquisadora. Obtivemos 396 observações antes da ação educativa e 204 depois da ação educativa. A pesquisa apresentou três etapas: observação sistematizada antes da ação educativa, realização da ação educativa e observação sistematizada depois da ação educativa. Os resultados foram obtidos através da análise dos Check list antes e depois da ação educativa e constatamos, por meio de valores percentuais, melhoras significativas. A categoria sempre, considerada o valor ideal para todas as variáveis, apresentou aumento de 20 pontos percentuais entre as observações; a categoria frequentemente apresentou aumento de 07 pontos e a categoria raramente apresentou decréscimo de 27 pontos. Isso demonstra que a ação educativa atingiu o objetivo de sensibilizar a equipe de enfermagem quanto a prevenir as úlceras por pressão de forma qualificada. Concluímos que as úlceras por pressão continuam sendo um grande problema de saúde pública, merecendo atenção especial por parte da equipe de enfermagem. Acreditamos que a ação educativa é capaz de sensibilizar a equipe de enfermagem e motivar a transformação das ações e condutas, porém, ela é pontual e é apenas uma parte do processo educacional. Para alcançarmos a mudança comportamental e proporcionar uma assistência qualificada e eficiente aos pacientes em risco de desenvolver as úlceras por pressão, sugerimos o desenvolvimento de uma prática educativa contínua e permanente, capaz de manter a equipe de enfermagem em constante aperfeiçoamento.

Optical setup and analysis of disk-type photopolymer high-density holographic storage

A relatively simple scheme for disk-type photopolymer high-density holographic storage based on angular and spatial multiplexing is described. The effects of the optical setup on the recording capacity and density are studied. Calculations and analysis show that this scheme is more effective than a scheme based on the spatioangular multiplexing for disk-type photopolymer high-density holographic storage, which has a limited medium thickness. Also an optimal beam recording angle exists to achieve maximum recording capacity and density. (C) 2002 Society of Photo-Optical Instrumentation Engineers.

Analysis on a new type magneto-optical disk for blue lasers

The conventional TbFeCo magneto-optical (MO) medium has a relatively smaller Kerr rotation angle in the blue region than in the red. With the recording wavelength gradually moving to the short wavelength, if TbFeCo is still used as recording medium, the conventional MO disk structure must be optimized to get a larger carrier to noise ratio (CNR). Sabi et al. have found that adding a metal layer attached to the TbFeCo film as thermal control layer is a useful way to get a high CNR. In this paper, we proved this through calculation, and carried out optimization of the new type of disk. Calculation results showed that the new structure is useful in preventing an excessive temperature increase, and has a better thermal response. (c) 2005 Elsevier B.V. All rights reserved.

Numerical analysis and comparison of three metal-oxide-type super-resolution near field structures

Based on the Fresnel-Kirchkoff diffraction theory, we build up a Gaussian diffraction model of metal-oxide-type super-resolution near field structure (super-RENS), which can describe far field optical properties. The spectral contrast induced by refractive index and the structural changes in AgOx, PtOx and PdOx thin films, which are the key functional layers in super-RENS, are studied by using this model. Comparison results indicate that the spectral contrast intensively on laser-induced distribution and change of the refractive index in the metal-oxide films. The readout mechanism of the metal-oxide-type super-RENS optical disc is further clarified. This Gaussian diffraction model can be used as a simple and effective method for choosing proper active materials in super-RENS.

The prevalence of diabetes-related complications and multimorbidity in the population with type 2 diabetes mellitus in the Basque Country

Background: Type 2 diabetes mellitus is associated with a diverse range of pathologies. The aim of the study was to determine the incidence of diabetes-related complications, the prevalence of coexistent chronic conditions and to report multimorbidity in people with type 2 diabetes living in the Basque Country. Methods: Administrative databases, in four cross sections (annually from 2007 to 2011) were consulted to analyse 149,015 individual records from patients aged >= 35 years with type 2 diabetes mellitus. The data observed were: age, sex, diabetes-related complications (annual rates of acute myocardial infarction, major amputations and avoidable hospitalisations), diabetes-related pathologies (prevalence of ischaemic heart disease, renal failure, stroke, heart failure, peripheral neuropathy, foot ulcers and diabetic retinopathy) and other unrelated pathologies (44 diseases). Results: The annual incidence for each condition progressively decreased during the four-year period: acute myocardial infarction (0.47 to 0.40%), major amputations (0.10 to 0.08%), and avoidable hospitalisations (5.85 to 5.5%). The prevalence for diabetes-related chronic pathologies was: ischaemic heart disease (11.5%), renal failure (8.4%), stroke (7.0%), heart failure (4.3%), peripheral neuropathy (1.3%), foot ulcers (2.0%) and diabetic retinopathy (7.2%). The prevalence of multimorbidity was 90.4%. The highest prevalence for other chronic conditions was 73.7% for hypertension, 13.8% for dyspepsia and 12.7% for anxiety. Conclusions: In the type 2 diabetes mellitus population living in the Basque Country, incidence rates of diabetes complications are not as high as in other places. However, they present a high prevalence of diabetes related and unrelated diseases. Multimorbidity is very common in this group, and is a factor to be taken into account to ensure correct clinical management.

Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

Study of crystal structure and phase transition studies in perovskite-type oxides using powder-diffraction techniques and symmetry-mode analysis.

251 p.

Coincidence and common fixed point theorems for Suzuki type hybrid contractions and applications

Coincidence and common fixed point theorems for a class of Suzuki hybrid contractions involving two pairs of single-valued and multivalued maps in a metric space are obtained. In addition, the existence of a common solution for a certain class of functional equations arising in a dynamic programming is also discussed.