Review: New Initiatives in Agricultural Economics Education at the University of Stellenbosch

Teaching/Communication/Extension/Profession,

NEW INITIATIVES IN AGRICULTURAL ECONOMICS EDUCATION AT THE UNIVERSITY OF THE NORTH

Teaching/Communication/Extension/Profession,

Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables

Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter

Warping geometric structures and abelianizing SL(2,R) local systems

The abelianization process of Gaiotto, Hollands, Moore, and Neitzke parameterizes SL(K,C) local systems on a punctured surface by turning them into C^\times local systems, which have a much simpler moduli space. When applied to an SL(2,R) local system describing a hyperbolic structure, abelianization produces an R^\times local system whose holonomies encode the shear parameters of the hyperbolic structure. This dissertation extends abelianization to SL(2,R) local systems on a compact surface, using tools from dynamics to overcome the technical challenges that arise in the compact setting. Thurston's shear parameterization of hyperbolic structures, which has its own technical subtleties on a compact surface, once again emerges as a special case.Mathematic

Regular singular Volterra equations on complex domains

The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular singularities can become a Volterra equation with regular singularities. It can also reveal hidden structure, especially when the Volterra equation extends to a complex domain. Our main result is to show that for a certain kind of regular singular Volterra equation on a complex domain, there is always a unique solution of a certain form. As a motivating example, this kind of Volterra equation arises when using Laplace transform methods to solve a level 1 differential equation.Comment: 28 pages, 1 figur

The Economic Rationale for Agricultural Regeneration and Rural Infrastructure Investment in South Africa

This paper informs government policy insofar as it relates to the agricultural and rural development sectors and infrastructure investment within these sectors. The paper first quantifies the role of agriculture in the South African economy. This is done within the context of, inter alia, food security, agriculture’s contribution to gross domestic product (GDP), economic linkages and multipliers with respect to the agricultural sector, as well as agriculture’s employment creation and external stabilisation capacity. Investment in the agricultural and rural sectors are then analysed with a view of supporting the argument that agriculture’s role in the economy is sufficiently important to warrant regenerative strategies, including renewed emphasis on agricultural and rural infrastructure investment by South African policy makers. The quantification of the agricultural sector in relation to the total economy and that of agricultural and rural infrastructure investment are investigated against the backdrop of declining government support, increasing production risks due to a variety of exogenous events like climate change, and increasing dynamic trade impacts. In this paper, the authors offer both supporting arguments in terms of current economic policy and recommendations for more decisive policy measures aimed at agricultural regeneration and rural infrastructure investment.

Quantum Cybernetics: A New Perspective for Nelson's Stochastic Theory, Nonlocality, and the Klein-Gordon Equation

The Klein-Gordon equation is shown to be equivalent to coupled partial differential equations for a sub-quantum Brownian movement of a ''particle'', which is both passively affected by, and actively affecting, a diffusion process of its generally nonlocal environment. This indicates circularly causal, or ''cybernetic'', relationships between ''particles'' and their surroundings. Moreover, in the relativistic domain, the original stochastic theory of Nelson is shown to hold as a limiting case only, i.e., for a vanishing quantum potential.Comment: 21 pages; published in Phys. Lett. A 296 (2002) 1 -