Some properties of purely simple Kronecker modules, I

AbstractLet K be an algebraically closed field. A K2-system is a pair of K-vector spaces (V, W) together with a K-bilinear map from K2×V to W. The category of systems is equivalent to the category of right modules over some K-algebra, R. Most of the concepts in the theory of modules over the polynomial ring K[ξ] have analogues in Mod-R. Unlike the purely simple K[ξ]-modules, which are easily described, purely simple R-modules are quite complex. If M is a purely simple R-module of finite rank n then any submodule of M of rank less than n is finite-dimensional. The following corollaries are derived from this fact: 1.1.|Every non-zero endomorphism of M is monic.2.2.|Every torsion-free quotient of M is purely simple.3.3.|An ascending union of purely simple R-modules of increasing rank is not purely simple.It is also shown that a large class of torsion-free rank one modules can occur as the quotient of a purely simple system of rank n, n any positive integer. Moreover, starting from a purely simple system another purely simple module M' of the same rank is constructed and M' is shown to be both a submodule of M and a submodule of a rank 1 torsion-free system. Since the category of right R-modules is a full subcategory of right S-modules, where S is any finite-dimensional hereditary algebra of tame type, the paper provides a way of constructing infinite-dimensional indecomposable S-modules

Radiation Protection Knowledge and Awareness of Naturally Occurring Radioactive Materials among Underground Goldmine Workers in Ghana

The level of knowledge and awareness of naturally occurring radioactive materials and indoor radon among underground goldmine workers were measured using a well-structured closed ended five-point likert scale questionnaire using a one sample T test for the analysis. There was a significant relationship between the awareness and knowledge of NORM and radon gas among the underground workers apart from the awareness and knowledge of the increased risk of cancer due to exposure of radon for workers who smoke. The level of awareness and knowledge is positively correlated with the level of education of respondents and negatively correlated to the years of service and age of respondents, but the ANOVA table indicates a statistical significance between the demographic data and the awareness and knowledge of radon gas and NORM in their working environment with an adjusted R2 of 46.1%. Keywords: NORM, Indoor radon, correlation, awareness, knowledge. DOI: 10.7176/IKM/13-3-04 Publication date:April 30th 202

TIME SERIES ANALYSIS OF RADON CONCENTRATION AT DIFFERENT DEPTHS IN AN UNDERGROUND GOLDMINE

Indoor radon concentrations were collected monthly over a period of one year in 10 different levels in an underground goldmine and the data was analysed using a four moving average time series to determine the relationship between depths of the underground mine and the indoor radon concentration. The detectors were installed in batches within four quarters. The measurements were carried out using LR115 solid state nuclear track detectors. Statistical models are applied in the prediction and analysis of the radon concentration at various depths. The time series model predicted a positive relationship between the depth of the underground mine and the indoor radon concentration. Thus, elevated radon concentrations are expected at deeper levels of the underground mine, but the relationship was insignificant at the 5% level of significance with a negative adjusted R2 (R2 = – 0.021) due to an appropriate engineering and adequate ventilation rate in the underground mine. Keywords: LR115, Radon Concentration, Time Series, Underground goldmine, DOI: 10.7176/APTA/87-03 Publication date: April 30th 202

An Analysis of Institutional Maternal Death Audit Reports in the Western Region of Ghana

Institutional maternal deaths in the Western Region of Ghana increased from 133 in 2011 to 150 deaths per 100,000 live births in 2014. We reviewed available audit reports on deaths that occurred in 2014 in order to identify priorities for improvement. We undertook a manual search for audit reports and used a structured questionnaire to extract information on the sociodemographic characteristics of patients and the circumstances of care and death. We entered and analyzed the data using EPI-INFO (v.7). Analysis was largely descriptive. Audit reports were available for 75% of the 93 deaths recorded in the region in 2014. The mean (SD) age of death was 28 (±8) yrs. The majority (80%) involved women who made at least three Antenatal Clinic (ANC) visits. Hypertensive diseases (35.8%), hemorrhage (31.3%) and sepsis (7.5%) were the leading causes of death. Most (82%) deaths occurred in hospitals, with almost 75% after 24 hours of arrival. Data completeness and consistency were the major limitations in the analysis. There is a need to improve institutional maternal health care in the region, with interventions designed to address the causes of maternal deaths and to improve the survival of mothers and babies ultimately

Partnership for International Development:Finland-Nigeria Conference on Climate, Food, Health and Entrepreneurship

A joint collaboration between the Arctic Centre of the University of Lapland, Finland and the Federal Institute of Industrial Research, Oshodi, Lagos, Nigeria was organised as a hybrid conference on several topics that are related to climate, food, health and entrepreneurship. The utilisation of natural resources in both regions is an important theme in meeting the sustainable development goals agenda. The topics discussed were multidisciplinary, they include Nigerian indigenous foods, bioeconomy, circular economy, nutrition, health, innovation and entrepreneurship under four themes (Climate, Food, Health and Entrepreneurship). There were dignitaries from Finland and Nigeria. The presenters are researchers from Nigerian universities (University of Ibadan, University of Abuja and Eko university, Lagos), Nigerian Federal Institute of Industrial research centre and from the Finnish side we have the university of Lapland, Rovaniemi, University of Oulu, Oulu and the Centria University of Applied Sciences, Kokkola. The topics discussed will serve as training materials for students and learners, the discussion focussed on research opportunities for institutions in both countries. The experts from both countries will continue to dialogue on the possibility of promoting common topics as research agenda in these important areas with the possibilities of creating more jobs

Direct sums and direct products of finite-dimensional modules over path algebras

AbstractThe algebras in this paper are over the associative algebras R obtained from extended Coxeter-Dynkin quivers with no oriented cycles. The finite-dimensional indecomposable R-modules can, in principle, be described. Taking direct products and direct sums, respectively, of finite-dimensional R-modules over an infinite indexing set are two natural ways of getting infinite-dimensional R-modules. The latter are the infinite-dimensional pure-projective modules and direct summands of the former are the pure-injective modules. The focus in this paper is on these two classes of infinite-dimensional modules. Every module is a submodule of a pure-injective module and a quotient of a pure-projective module. When is an extension of a pure-injective module by a pure-injective module pure-injective? This question is answered in this paper. The answer is analogous to the answer of the corresponding question for pure-projective modules. The structures of some quotients of direct products of finite-dimensional modules are also obtained