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University of Arizona

1. Griesan, Raymond William. Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles.

Degree: 1988, University of Arizona

URL: http://hdl.handle.net/10150/184510

Metric topologies can be viewed as one-dimensional measures. This dissertation is a topological study of two-dimensional measures. Attention is focused on locally convex vector topologies on infinite dimensional real spaces. A nabla (referred to in the literature as a 2-norm) is the analogue of a norm which assigns areas to the parallelograms. Nablas are defined for the classical normed spaces and techniques are developed for defining nablas on arbitrary spaces. The work here brings out a strong connection with tensor and wedge products. Aside from the normable theory, it is shown that nabla topologies need not be metrizable or Mackey. A class of concretely given non-Mackey nablas on the ℓp and Lp spaces is introduced and extensively analyzed. Among other results it is found that the topological dual of ℓ₁ with respect to these nabla topologies is C₀, one of the spaces infamous for having no normed predual. Also, a connection is made with the theory of two-norm convergence (not to be confused with 2-norms). In addition to the hard analysis on the classical spaces, a duality framework from which to study the softer aspects is introduced. This theory is developed in analogy with polar duality. The ideas corresponding to barrelledness, quasi-barrelledness, equicontinuity and so on are developed. This dissertation concludes with a discussion of angles in arbitrary normed spaces and a list of open questions.
*Advisors/Committee Members: Lomont, John (advisor), Suchanek, Amy (committeemember), Wright, A. Larry (committeemember), Benson, Clark (committeemember), Laetsch, Theodore (committeemember).*

Subjects/Keywords: Locally convex spaces.; Topological spaces.; Vector spaces.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Griesan, R. W. (1988). Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/184510

Chicago Manual of Style (16^{th} Edition):

Griesan, Raymond William. “Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. ” 1988. Doctoral Dissertation, University of Arizona. Accessed April 19, 2021. http://hdl.handle.net/10150/184510.

MLA Handbook (7^{th} Edition):

Griesan, Raymond William. “Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. ” 1988. Web. 19 Apr 2021.

Vancouver:

Griesan RW. Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. [Internet] [Doctoral dissertation]. University of Arizona; 1988. [cited 2021 Apr 19]. Available from: http://hdl.handle.net/10150/184510.

Council of Science Editors:

Griesan RW. Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles. [Doctoral Dissertation]. University of Arizona; 1988. Available from: http://hdl.handle.net/10150/184510

University of Arizona

2. McShane, Janet Marie. Computation of polynomial invariants of finite groups.

Degree: 1992, University of Arizona

URL: http://hdl.handle.net/10150/186000

If G is a finite subgroup of GL(n,K), K a field of characteristic 0, it is well known that the algebra I of polynomial invariants of G is Cohen-Macaulay. Consequently I has a subalgebra J of Krull dimension n so that I is a free J-module of finite rank. A sequence (f₁,...,f(n);g₁,...,g(m)) of homogeneous invariants is a Cohen-Macaulay (or CM) basis if J = K[f₁,...,f(n)] and {g₁,...,g(m)} is a basis for I as a J-module. We discuss an algorithm, and an implementation using the systems GAP and Maple, for the calculation of CM-bases.
*Advisors/Committee Members: Fan, Paul (committeemember), Gay, David (committeemember), Flaschka, Hermann (committeemember), Laetsch, Theodore (committeemember).*

Subjects/Keywords: Dissertations, Academic.; Mathematics.

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

McShane, J. M. (1992). Computation of polynomial invariants of finite groups. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/186000

Chicago Manual of Style (16^{th} Edition):

McShane, Janet Marie. “Computation of polynomial invariants of finite groups. ” 1992. Doctoral Dissertation, University of Arizona. Accessed April 19, 2021. http://hdl.handle.net/10150/186000.

MLA Handbook (7^{th} Edition):

McShane, Janet Marie. “Computation of polynomial invariants of finite groups. ” 1992. Web. 19 Apr 2021.

Vancouver:

McShane JM. Computation of polynomial invariants of finite groups. [Internet] [Doctoral dissertation]. University of Arizona; 1992. [cited 2021 Apr 19]. Available from: http://hdl.handle.net/10150/186000.

Council of Science Editors:

McShane JM. Computation of polynomial invariants of finite groups. [Doctoral Dissertation]. University of Arizona; 1992. Available from: http://hdl.handle.net/10150/186000