7 p. / There are a number of disease-causing viruses transmitted to people primarily through the bite of infected mosquitoes. Female mosquitoes take blood meals to produce eggs. A mosquito that bites an infected animal may pick up a virus within the blood meal. If the mosquito is the appropriate species, and conditions inside the insect and the surrounding environment are supportive, the virus reproduces within the mosquito. Later, the mosquito may pass the virus on to other animals (including humans) as they feed again.

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12 pp. / Mosquitoes are the most important insect pests that affect the health and well-being of humans and domestic animals worldwide. They can cause a variety of health problems due to their ability to transfer (vector) viruses and other disease-causing pathogens, including in the arid Southwest U.S. This publication describes the mosquito life-cycle, introduces common pest mosquito species and the diseases associated with them. Mosquito management for residents is covered.

D.Ing. / Aerial Vehicle (UAV)-based observation system, by using the principles of strapdown inertial measurement and navigation systems. Effort is concentrated around the mathematical implementation thereof and analysis and proof of the concept in a computer simulation environment. Although the principles of the strapdown system approach to camera-to-target vector estimation are universal to any type of airborne platform that can carry the observation payload, the application thereof is specifically tailored for a UAV system. More specifically, the operational scenario and UAV parameters of a typical close-range UAV system that is used for artillery observation, is used in the derivation of the models and equations. The secondary objective of this research is to derive a realizable mathematical implementation for this strapdown system based camera-to-target vector estimation methodology, by performing a systematic tradeoff between the use of Euler angles and quaternions for describing the camera-to-target vector, and by incorporating the principles of Kalman filtering. This dissertation fully describes the approach that was followed in the derivation of the strapdown system equations for the camera-to-target vector estimation. The mathematical models and principles used are universal for any airborne targeting application with a real-time video down-link. The results as presented in this dissertation, prove that the methodology provides satisfactory results in both a pure digital computer simulation environment, as well as in a digital computer simulation that is hybridized with experimentally determined sensor outputs. It has led to a realizable and workable implementation that could form the basis of practical implementation thereof in operational targeting systems. It further proves that the slant range between a camera and a stationary target on the ground, can be estimated effectively without the use of a laser rangefinder.

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In this thesis we study some questions related to vector bundles over hypersurfaces. More precisely, for hypersurfaces of dimension ≥ 2, we study the extension problem of vector bundles. We find some cohomological conditions under which a vector bundle over an ample divisor of non-singular projective variety, extends as a vector bundle to an open set containing that ample divisor. Our method is to follow the general Groethendieck-Lefschetz theory by showing that a vector bundle extension exists over various thickenings of the ample divisor. For vector bundles of rank > 1, we find two separate cohomological conditions on vector bundles which shows the extension to an open set containing the ample divisor. For the case of line bundles, our method unifies and recovers the generalized Noether-Lefschetz theorems by Joshi and Ravindra-Srinivas. In the last part of the thesis, we make a specific study of vector bundles over elliptic curve.

If r > 1 is an integer then U(r) denotes the vector space of r-fold symmetric tensors and Pr[U] is the set of rank 1 tensors in U(r). Let U be a finite-dimensional vector space over an algebraically closed field of characteristic not a prime p if r = p[formula omitted] for some positive integer k. We first determine the maximal subspaces of rank 1 symmetric tensors. Suppose h is a linear mapping of U(r) such that h(Pr[U]) ⊆ Pr[U] and ker h ⋂ Pr[U] = 0. We have shown that every such h is induced by a non-singular linear mapping of U, provided dim U > r+1 . This work partially answers a question raised by Marcus and Newman (Ann. of Math., 75, (1962) p.62.). / Science, Faculty of / Mathematics, Department of / Graduate

We begin by constructing a vector space over a field F , which we call a (G,σ) space of the set W = V₁xV₂... xVn , a cartesian product, where Vi is a finite-dimensional vector space over an arbitrary field F , G is a subgroup of the full symmetric group Sn and σ is a linear character of G . This space generalizes the spaces called the symmetry class of tensors defined by Marcus and Newman [1]. We can obtain the classical spaces, namely the Tensor space, the Grassman space and the symmetric space, by particularizing the group G and the linear character σ in our (G,σ) space. If (v₁,v₂,..., vn ) ∈ W , we shall denote the "decomposable" element in our space by v₁Δv₂…Δvn and call it the (G,σ) product or the Pure product if there is no confusion regarding G and σ, of the vectors v₁,v₂,..., vn . This corresponds to the tensor product, the skew symmetric product and the symmetric product in the classical spaces. The purpose of this thesis is to determine a necessary and sufficient condition for the vanishing of the (G,σ) product of the vectors v₁,v₂,..., vn in the general case. The results for the classical spaces are well-known and are deduced from our main theorem. We use the "universal mapping property" of the (G,σ) space to prove the necessity of our condition. These conditions are stated in terms of determinant-like functions of the matrices associated with the set of vectors v₁,v₂,...,vn. / Science, Faculty of / Mathematics, Department of / Graduate

The study of bifurcations of vectorfields is concerned with changes in qualitative behaviour that can occur when a non-structurally stable vectorfield is perturbed. In a sense, this is the study of how such a vectorfield fails to be structurally stable. Finding a systematic approach to the study of such questions is a difficult problem. One approach to bifurcations of vectorfields, known as "generic bifurcation theory," is the subject of much of the work of Sotomayor (Sotomayor [1973a], Sotomayor [1973b],Sotomayor [1974]). This approach attempts to construct generic families of k-parameter vectorfields (usually for k=1), for which all the bifurcations can be described. In Sotomayor [1973a] it is stated that the vectorfields associated with the "generic" bifurcations of individual critical elements for k-parameter vectorfields form submanifolds of codimension ≤ k of the Banach space ϰʳ (M) of vectorfields on a compact manifold M. The bifurcations associated with one of these submanifolds of codimension-k are called generic codimension-k bifurcations. In Sotomayor [1974] the construction of these submanifolds and the description of the associated bifurcations of codimension-1 for vectorfields on two dimensional manifolds is presented in detail. The bifurcations that occur are due to the parameterised vectorfield crossing one of these manifolds transversely as the parameter changes. Abraham and Robbin used transversality results for evaluation maps to prove the Kupka-Smale theorem in Abraham and Robbin [1967]. In this thesis, we shall show how an extension of these evaluation transversality techniques will allow us to construct the submanifolds of ϰʳ (M) associated with one type of generic bifurcation of critical elements, and we shall consider how this approach might be extended to include the other well known generic bifurcations. For saddle-node type bifurcations of critical points, we will show that the changes in qualitative behaviour are related to geometric properties of the submanifold Σ₀ of ϰʳ (M) x M, where Σ₀ is the pull-back of the set of zero vectors-or zero section-by the evaluation map for vectorfields. We will look at the relationship between the Taylor series of a vector-field X at a critical point ⍴ and the geometry of Σ₀ at the corresponding point (X,⍴) of ϰʳ (M) x M. This will motivate the non-degeneracy conditions for the saddle-node bifurcations, and will provide a more general geometric picture of this approach to studying bifurcations of critical points. Finally, we shall consider how this approach might be generalised to include other bifurcations of critical elements. / Science, Faculty of / Mathematics, Department of / Graduate

We study the order convergence of sequences on a vector lattice. It is shown that this mode of convergence is induced by a convergence structure. One such a convergence structure is defined and its properties are studied. We apply the results obtained to find the completion of C(X). We also obtain a Banach-Steinhauss theorem for ó-order continuous operators. / Dissertation (Magister Scientiae)--University of Pretoria, 2007. / Mathematics and Applied Mathematics / unrestricted