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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 āp and Lp spaces is introduced and extensively analyzed. Among other results it is found that the topological dual of āā with respect to these nabla topologies is Cā, 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 January 16, 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. 16 Jan 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 Jan 16]. 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. Roko, Raoul Olatounbossoun. Roughness influence on strength and deformation behavior of rock discontinuities.

Degree: 1990, University of Arizona

URL: http://hdl.handle.net/10150/185322

The influence of discontinuity roughness on the shear strength and deformation behavior of rock joint is analyzed. The study is divided into three parts: laboratory direct shear test on rock samples having different roughness characteristics, characterization of roughness profiles using variogram and probability density distribution and the application of dynamical systems theory to analyze the stability condition of the sliding motion. The relative motion along the rough joint is erratic particularly at a low normal load. A steady motion develops as the normal load increases. The kinematics of translational motion has two distinct characteristics: the translation occurs as a result of a gross and uniform motion (sliding) and/or through localized inhomogeneous motion (slipping). Three modes of volumetric changes are observed during the tangential motion: a dilatant-contractant behavior with the overall volumetric change being strictly dilatant, a dilatant-contractant behavior with the overall volumetric change varying from dilatant to contractant and the strictly contractant behavior. The size of the sheared zones is a function of the distribution of the asperities and of the interface strength. The coefficient of friction decreases as the normal load increases. It may or may not increase when the normal load is decreased. The probability density distribution of the height of the interface asperities is not always Gaussian. The variation of the experimental distribution (histogram) indicates that the asperities are not necessarily sheared off in order of decreasing height but rather on the basis of the condition underlying the existence of contact. The slope of the initial portion of the variogram and the sill, when it exists, are used to characterize the surface morphology of the discontinuity. The lower the slope, the smoother the surface. Two types of anisotropy are observed: geometic anisotropy (elliptic shape) and zonal anisotropy. The rate of collapse of the boundary of the loop describing the roughness of the interface describes the deformation of the discontinuity. The location of the orbit with respect to the stagnation line depends on the normalized stiffness. As the normalized shear stiffness increases, the orbit tends to collapse towards the stagnation axis.
*Advisors/Committee Members: Daemen, Jaak (advisor), Glass, Charles (committeemember), Farmer, Ian (committeemember), Benson, Clark (committeemember), Myers, Donald (committeemember).*

Subjects/Keywords: Engineering.

Record Details Similar Records

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

APA (6^{th} Edition):

Roko, R. O. (1990). Roughness influence on strength and deformation behavior of rock discontinuities. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/185322

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

Roko, Raoul Olatounbossoun. “Roughness influence on strength and deformation behavior of rock discontinuities. ” 1990. Doctoral Dissertation, University of Arizona. Accessed January 16, 2021. http://hdl.handle.net/10150/185322.

MLA Handbook (7^{th} Edition):

Roko, Raoul Olatounbossoun. “Roughness influence on strength and deformation behavior of rock discontinuities. ” 1990. Web. 16 Jan 2021.

Vancouver:

Roko RO. Roughness influence on strength and deformation behavior of rock discontinuities. [Internet] [Doctoral dissertation]. University of Arizona; 1990. [cited 2021 Jan 16]. Available from: http://hdl.handle.net/10150/185322.

Council of Science Editors:

Roko RO. Roughness influence on strength and deformation behavior of rock discontinuities. [Doctoral Dissertation]. University of Arizona; 1990. Available from: http://hdl.handle.net/10150/185322

University of Arizona

3. Modisett, Matthew Clayton. A characterization of the circularity of certain balanced incomplete block designs.

Degree: 1988, University of Arizona

URL: http://hdl.handle.net/10150/184393

When defining a structure to fulfill a set of axioms that are similar to those prescribed by Euclid, one must select a set of points and then define what is meant by a line and what is meant by a circle. When properly defined these labels will have properties which are similar to their counterparts in the (complex) plane, the lines and circles which Euclid undoubtedly had in mind. In this manner, the geometer may employ his intuition from the complex plane to prove theorems about other systems. Most "finite geometries" have clearly defined notions of points and lines but fail to define circles. The two notable exceptions are the circles in a finite affine plane and the circles in a Mobius plane. Using the geometry of Euclid as motivation, we strive to develop structures with both lines and circles. The only successful example other than the complex plane is the affine plane over a finite field, where all of Euclid's geometry holds except for any assertions involving order or continuity. To complement the prolific work concerning finite geometries and their lines, we provide a general definition of a circle, or more correctly, of a collection of circles and present some preliminary results concerning the construction of such structures. Our definition includes the circles of an affine plane over a finite field and the circles in a Mobius plane as special cases. We develop a necessary and sufficient condition for circularity, present computational techniques for determining circularity and give varying constructions. We devote a chapter to the use of circular designs in coding theory. It is proven that these structures are not useful in the theory of error-correcting codes, since more efficient codes are known, for example the Reed-Muller codes. However, the theory developed in the earlier chapters does have applications to Cryptology. We present five encryption methods utilizing circular structures.
*Advisors/Committee Members: Clay, James R (advisor), Benson, Clark (committeemember), Brillhart, John (committeemember), Gay, David (committeemember), Greenlee, W. M. (committeemember).*

Subjects/Keywords: Incomplete block designs.; Combinatorial designs and configurations.; Circle.

Record Details Similar Records

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

APA (6^{th} Edition):

Modisett, M. C. (1988). A characterization of the circularity of certain balanced incomplete block designs. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/184393

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

Modisett, Matthew Clayton. “A characterization of the circularity of certain balanced incomplete block designs. ” 1988. Doctoral Dissertation, University of Arizona. Accessed January 16, 2021. http://hdl.handle.net/10150/184393.

MLA Handbook (7^{th} Edition):

Modisett, Matthew Clayton. “A characterization of the circularity of certain balanced incomplete block designs. ” 1988. Web. 16 Jan 2021.

Vancouver:

Modisett MC. A characterization of the circularity of certain balanced incomplete block designs. [Internet] [Doctoral dissertation]. University of Arizona; 1988. [cited 2021 Jan 16]. Available from: http://hdl.handle.net/10150/184393.

Council of Science Editors:

Modisett MC. A characterization of the circularity of certain balanced incomplete block designs. [Doctoral Dissertation]. University of Arizona; 1988. Available from: http://hdl.handle.net/10150/184393