A research report submitted to the Faculty of Commerce, Law and Management, University of the Witwatersrand, Johannesburg, in partial fulfilment of the requirements for the degree of Master of Commerce (specialising in Marketing) / The twentieth-century dietary evolution has resulted in livestock being used as the primary source of protein in many countries. This has various implications on the wellbeing of humans, animals, and planet earth itself. The choices consumers make regarding food not only affect our personal health, but it also directly affects the wellbeing of our current ecosystems where modern meat production systems place a worrying burden on the environment. Sustainable consumption practice is often a result of two main driving forces, the first being individual or health (egoistic) motives and the second being animal welfare and environmental concern (altruistic) motives. The growing demand for meat products worldwide is unsustainable and there is a clear gap between our responsible intentions as citizens of the world and our hedonic needs as consumers referred to as the ‘Citizen-Consumer’ gap. Experts argue that technological innovations and more efficient production methods would serve as a future solution for the environmental and social implications of the livestock industry however current scholars emphasise that a technological fix will not be sufficient and that it is imperative for society to undertake a behavioural fix, such as lowering meat intake and discovering more sustainable means of protein consumption Consequently, the purpose of this study is to assess health consciousness, environmental concern and animal welfare as key predictors of consumers’ locus of control and attitudes towards meat consumption among university students, in Johannesburg, South Africa. The study used a design that was quantitative in nature, which resulted in the researcher employing a deductive approach, using a positivistic method. Data was collected by means of a survey questionnaire and was used to test the hypotheses. By means of Partial Least Squares – Structural Equation Modeling (PLS-SEM), the significance of the hypotheses statements was determined from a sample of 172 students enrolled at the University of the Witwatersrand, Johannesburg, South Africa. The findings generated by SmartPLS 3 statistical software revealed that health consciousness was the key predictor of external locus of control and that external locus of control had the most significant relationship with consumers’ attitude toward meat consumption, as compared to the second mediator variable – internal locus of control. It is anticipated that the findings of this study will contribute to both theory and practice in modern society, and it is trusted that the findings of this study will greatly inform future research endeavours. / NG (2020)

The set PLS(a, b; n) is the set of all partial latin squares of order n with a completed rows, b completed columns and all other cells empty. We identify reductions of partial latin squares in PLS(2, 3; n) by using permutations described by filled rows and intersections of filled rows and columns. We find that all partial latin squares in PLS(2, 3;n), where n is sufficiently large, can be completed if such a reduction can be completed. We also show that all partial latin squares in PLS(2, 3; n) where the intersection of filled rows and columns form a latin rectangle have completions for n ≥ 8.

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Shuffled linear regression concerns itself with linear models with an unknown correspondence between the input and the output. This correspondence is usually represented by a permutation matrix II*. The model we are interested in has one more complication which is that the design matrix is itself latent and is observed with noise. This is considered as a type of errors-in-variables (EIV) model. Our interest lies in the recovery of the permutation matrix. We propose an estimator for II* based on the total least squares (TLS) technique, a common method of estimation used in EIV model. The estimation problem can be viewed as approximating one matrix by another of lower rank and the quantity it seeks to minimize is the sum of the smallest singular values squared. Due to identifiability issue, we evaluate the proposed estimator by the normalized Procrustes quadratic loss which allows for an orthogonal rotation of the estimated design matrix. Our main result provides an upper bound on this quantity which states that it is required that the signal-to-noise ratio to go to infinity in order for the loss to go to zero. On the computational front, since the problem of permutation recovery is NP-hard to solve, we propose a simple and efficient algorithm named alternating LAP/TLS algorithm (ALTA) to approximate the estimator, and we use it to empirically examine the main result. The main idea of the algorithm is to alternate between estimating the unknown coefficient matrix using the TLS method and estimating the latent permutation matrix by solving a linear assignment problem (LAP) which runs in polynomial time. Lastly, we propose a hypothesis testing procedure based on graph matching which we apply in the field of digital humanities, on character social networks constructed from novel series.

Mississippi has a surprising amount and variety of town squares. The square provides a central, pedestrian civic space in the towns in which they are located. The purpose of this thesis is to explore the evolution of town squares in Mississippi. The method employed was historical research of primary sources that included historic photographs and Sanborn Fire Insurance maps. The photographs were examined using the The Secretary of the Interior’s Standards for the Treatment of Historic Properties investigating such elements as vegetation, site furnishings, and circulation patterns. Canton, Holly Springs, and Lexington were chosen to be studied in more detail to give a clearer picture of how squares have changed over time. It was determined that there are approximately 69 towns with squares in Mississippi. The most numerous types of squares used are Shelbyville squares. The vitality of the square varies greatly from town to town.

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Optimization based domain decomposition methods for the solution of partial differential equations are considered. The crux of the method is a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the common boundaries between subdomains; the constraints are the partial differential equations. First, we consider a linear constraint. The existence of optimal solutions for the optimization problem is shown as is its convergence to the exact solution of the given problem. We then derive an optimality system of partial differential equations from which solutions of the domain decomposition problem may be determined. Finite element approximations to solutions of the optimality system are defined and analyzed as is an eminently parallelizable gradient method for solving the optimality system. The linear constraint minimization problem is also recast as a linear least squares problem and is solved by a conjugate gradient method. The domain decomposition method can be extended to nonlinear problems such as the Navier-Stokes equations. This results from the fact that the objective functional for the minimization problem involves the jump in dependent variables across the interfaces between subdomains. Thus, the method does not require that the partial differential equations themselves be derivable through an extremal problem. An optimality system is derived by applying a Lagrange multiplier rule to a constrained optimization problem. Error estimates for finite element approximations are presented as is a gradient method to solve the optimality system. We also use a Gauss-Newton method to solve the minimization problem with the nonlinear constraint. / Ph. D.

This paper will examine analogues of Cantor sets, called fractal squares, and some of the geometric ways in which fractal squares raise issues not raised by Cantor sets. Also discussed will be a technique using directed graphs to prove bilipschitz equivalence of two fractal squares. / Ph. D.