Thesis (M.S.)--University of Wisconsin--Madison, 1966. / eContent provider-neutral record in process. Description based on print version record. Bibliography: l. 68.

Proefschrift--Utrecht. / "Conspectus" (in Latin) : p. [75]-76. "Stellingen" (2 leaves) inserted. "References" at end of each chapter.

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

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In this thesis we utilise a form for the Hubble constant first proposed by Berman (1983) to study a variety of cosmological models. In particular we investigate the Robertson-Walker spacetimes, the Bianchi I spacetime, and the scalar-tensor theory of gravitation of Lau and Prokhovnik (1986). The Einstein field equations with variable cosmological constant and gravitational constant are discussed and the Friedmann models are reviewed. The relationship between observation and the Friedmann models is reviewed. We present a number of new solutions to the Einstein field equations with variable cosmological constant and gravitational constant in the Robertson-Walker spacetimes for the assumed form of the Hubble parameter. We explicitly find forms for the scale factor, cosmological constant, gravitational constant, energy density and pressure in each case. Some of the models have an equation of state for an ideal gas. The gravitational constant may be increasing in certain regions of spacetime. The Bianchi I spacetime, which is homogeneous and anisotropic, is shown to be consistent with the Berman (1983) law by defining a function which reduces to the scale factor of Robertson-Walker. We illustrate that the scalar-tensor theory of Lau and Prokhovnik (1986) also admits solutions consistent with the Hubble variation proposed by Berman. This demonstrates that this approach is useful in seeking solutions to the Einstein field equations in general relativity and alternate theories of gravity. / Thesis (M.Sc.)-University of Natal, 1992.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 61-63).

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2004. / Includes bibliographical references (leaves 158-162). Also available in electronic version. Access restricted to campus users.