Diagonal And Triangular Matrices

HAMDAN ALSULAIMANI, for the Master of Science in Mathematics, presented on NOV 6 2012, at Southern Illinois University Carbondale. TITLE: Diagonal (Triangular) Matrices PROFESSOR: Dr. R. Fitzgerald I present the Triangularization Lemma which says that let P be a set of properties, each of which is inherited by quotients. If every collection of transformations on a space of dimension greater than 1 that satisfies P is reducible, then every collection of transforma- tions satisfying P is triangularizable. I also present Burnside’s Theorem which says that the only irreducible algebra of linear transformations on the finite-dimensional vector space V of dimension greater than 1 is the algebra of all linear transformations mapping V into V. Moreover, I introduce McCoy’s Theorem which says that the pair {A,B} is triangularizable if and only if p(A,B)(AB-BA) is nilpotent for every noncommutative polynomial p. And then I show the relation between McCoy’s Theorem and Lie algebras

Do routinely measured risk factors for obesity explain the sex gap in its prevalence? Observations from Saudi Arabia.

BACKGROUND: The prevalence of adult obesity is higher in women than men in most countries. However, the pathways that link female sex with excess obesity are still not fully understood. We examine whether socioeconomic and behavioural factors may mediate the association between sex and obesity in the Saudi Arabian setting where there is female excess in obesity. METHODS: We performed a mediation analysis using a cross-sectional, national household survey from Saudi Arabia with 4758 participants (51% female). A series of multivariable regression models were fitted to test if socioeconomic position, physical activity, sedentary behaviour, diet, and smoking mediate the association between sex and obesity (BMI >=30). The findings were confirmed using causal mediation analysis. RESULTS: Women in this sample were roughly twice as likely as men to be obese (crude OR 1.9; 95% CI 1.6-2.3). The odds ratio remained significantly higher for women compared to men in models testing for mediation (OR range 1.95-2.06). Our data suggest that indicators of socio-economic position, physical activity, sedentary behaviour, diet, and smoking do not mediate the sex differences in obesity. CONCLUSIONS: Our analysis shows that most commonly measured risk factors for obesity do not explain the sex differences in its prevalence in the Saudi context. Further research is needed to understand what might explain the female excess in obesity prevalence. We discuss how data related to the lived experience of Saudi men and women may tap into underlying mechanisms by which the sex difference in obesity prevalence are produced

Survival and disinfection of SARS-Cov-2 in environment and contaminated surface

The detection of SARS-Cov-2 in the sewage and water resources has increased the awareness among the people about the possibility survival of SARS-Cov-2 in the environment and the potential to transmit into the human through food chain or water resources. Moreover, the surface contaminated by the virus need to be disinfected frequently by using an effective disinfectant, the current chapter discussed the efficiency of the most traditional treatment process of the sewage and wastewater, and their role in the elimination of the virus as well as the sterility assurance level concept. Moreover, the chemical disinfectant used currently and their temporary efficiency has been reviewed

Using Remote Sensing Data to Evaluate Habitat Loss in the Mobile, Galveston, and Tampa Bay Watersheds

The Gulf of Mexico has experienced dramatic wetland habitat area losses over the last two centuries. These losses not only damage species diversity, but contribute to water quality, flood control, and aspects of the Gulf coast economy. Overall wetland losses since the 1950s were examined using land cover/land use (LCLU) change analysis in three Gulf coast watershed regions: Mobile Bay, Galveston Bay, and Tampa Bay. Two primary causes of this loss, LCLU change and climate change, were then assessed using LCLU maps, U.S. census population data, and available current and historical climate data from NOAA. Sea level rise, precipitation, and temperature effects were addressed, with emphasis on analysis of the effects of sea level rise on salt marsh degradation. Ecological impacts of wetland loss, including fishery depletion, eutrophication, and hypoxia were addressed using existing literature and data available from NOAA. These ecological consequences in turn have had an affect on the Gulf coast economy, which was analyzed using fishery data and addressing public health impacts of changes in the environment caused by wetland habitat loss. While recent federal and state efforts to reduce wetland habitat loss have been relatively successful, this study implies a need for more aggressive action in the Gulf coast area, as the effects of wetland loss reach far beyond individual wetland systems themselves to the Gulf of Mexico as a whole

Technical and scale efficiency of automobile firms in Pakistan

The current study aimed at exploring the efficiency level of automobile firms in Pakistan.For this purpose, the current study has collected the data of 18 automobile and automobile parts firms from the year 2011 to the year 2015.To analyse the date, the current study has used the data envelopment analysis. Three models were used to calculate the firm efficiency such as constant return to scale, variable return to scale and scale efficiency.The results of the study have revealed that most of the automobile firms are not efficient during these years. In addition, the results were consistent based on the three efficiency models

Risks and foreign direct investment inflows: evidence from Yemen

This study aims to find the relationship between the political, exchange rate and inflation risk factors with the yearly foreign direct investment (YFDI) in Yemen, over the period between 1990 to 2010. Secondary data results showed that political risk and exchange rate risk have an inverse relationship with YFDI, while inflation risk has a significant positive relationship. Further analysis on a survey collected from 62 multinational enterprises (MNEs) operating in Yemen showed an insignificant relationship between the perceived political, exchange rate and inflation risk factors and corporate foreign direct investment (CFDI). The conflicting results possibly imply that the MNEs’ subsequent capital investments may not be affected by the perceived political, exchange rate and inflation risks that would nonetheless have been considered during the initial business plan. It is likely that MNEs that were already operating in Yemen may have developed capabilities in terms of knowledge, bargaining and lobbying skills. Therefore, perceived risks are no longer seem to influence their investment decisions