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University of Arizona
1.
Gillis, Gregory Nelson, 1965-.
Design considerations in manufacturing composite conductors: An exposition of Percolation Theory
.
Degree: 1998, University of Arizona
URL: http://hdl.handle.net/10150/282664 
► This dissertation is an exposition of Percolation Theory, directed to the audience of beginning undergraduate mathematics students, though this can include gifted high school students.…
(more)
▼ This dissertation is an exposition of Percolation Theory, directed to the audience of beginning undergraduate mathematics students, though this can include gifted high school students. The vehicle by which the theory is taught is that of problem solving. The reader of the dissertation is invited into a web of mathematical exploration and inquiry by attempting to solve the real real-world problem of designing composite conductors. By making real composite conductors, carrying out various experiments, using computers to do data collecting, and using calculators for subsequent data analysis the reader can participate in the creation of mathematics, the development of mathematical techniques, and in the discovery of new and unexpected connections. The mathematics of Percolation Theory are in this way constructed with the reader. The necessity and importance of this work are many-fold. It is the first such treatise on Percolation Theory that makes the theory accessible to a larger audience than mathematics graduate or senior college students. It will be of interest to high school and beginning college students who desire to know in what real-world contexts some of the mathematics they know can be put. This work will be of interest to educators for the hands-on way in which it reinforces the student's current mathematical ability, while enriching the student's understanding of problem solving, mathematical modeling, use of technology, and probability.
Advisors/Committee Members: Gay, David A (advisor).
Subjects/Keywords: Education, Mathematics.;
Mathematics.;
Education, Curriculum and Instruction.
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APA (6th Edition):
Gillis, Gregory Nelson, 1. (1998). Design considerations in manufacturing composite conductors: An exposition of Percolation Theory
. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/282664
Chicago Manual of Style (16th Edition):
Gillis, Gregory Nelson, 1965-. “Design considerations in manufacturing composite conductors: An exposition of Percolation Theory
.” 1998. Doctoral Dissertation, University of Arizona. Accessed January 16, 2021.
http://hdl.handle.net/10150/282664.
MLA Handbook (7th Edition):
Gillis, Gregory Nelson, 1965-. “Design considerations in manufacturing composite conductors: An exposition of Percolation Theory
.” 1998. Web. 16 Jan 2021.
Vancouver:
Gillis, Gregory Nelson 1. Design considerations in manufacturing composite conductors: An exposition of Percolation Theory
. [Internet] [Doctoral dissertation]. University of Arizona; 1998. [cited 2021 Jan 16].
Available from: http://hdl.handle.net/10150/282664.
Council of Science Editors:
Gillis, Gregory Nelson 1. Design considerations in manufacturing composite conductors: An exposition of Percolation Theory
. [Doctoral Dissertation]. University of Arizona; 1998. Available from: http://hdl.handle.net/10150/282664
University of Arizona
2.
Barrera Mora, Jose Felix Fernando.
On radical extensions and radical towers.
Degree: 1989, University of Arizona
URL: http://hdl.handle.net/10150/184833
► Let K/F be a separable extension. (i) If K = F(α) with αⁿ ∈ F for some n, K/F is said to be a radical…
(more)
▼ Let K/F be a separable extension. (i) If K = F(α) with αⁿ ∈ F for some n, K/F is said to be a radical extension. (ii) If there exists a sequence of fields F = F₀ ⊆ F₁ ⊆ ... ⊆ F(s) = K so that Fᵢ₊₁ = Fᵢ(αᵢ) with αᵢⁿ⁽ⁱ⁾ ∈ Fᵢ for some nᵢ ∈ N, charF ∧nᵢ for every i, and [Fᵢ₊₁ : Fᵢ] = nᵢ, K/F is said to be a radical tower. In the first part of this work, we present two theorems which give sufficient conditions for a field extension K/F to be radical. In the second part, we present results which provide conditions under which every subfield of a radical tower is also a radical tower.
Advisors/Committee Members: Velez, William (advisor), Grove, Larry (committeemember), Gay, David (committeemember).
Subjects/Keywords: Field extensions (Mathematics);
Abelian groups.
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APA (6th Edition):
Barrera Mora, J. F. F. (1989). On radical extensions and radical towers.
(Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/184833
Chicago Manual of Style (16th Edition):
Barrera Mora, Jose Felix Fernando. “On radical extensions and radical towers.
” 1989. Doctoral Dissertation, University of Arizona. Accessed January 16, 2021.
http://hdl.handle.net/10150/184833.
MLA Handbook (7th Edition):
Barrera Mora, Jose Felix Fernando. “On radical extensions and radical towers.
” 1989. Web. 16 Jan 2021.
Vancouver:
Barrera Mora JFF. On radical extensions and radical towers.
[Internet] [Doctoral dissertation]. University of Arizona; 1989. [cited 2021 Jan 16].
Available from: http://hdl.handle.net/10150/184833.
Council of Science Editors:
Barrera Mora JFF. On radical extensions and radical towers.
[Doctoral Dissertation]. University of Arizona; 1989. Available from: http://hdl.handle.net/10150/184833
University of Arizona
3.
Ke, Wen-Fong.
Structures of circular planar nearrings
.
Degree: 1992, University of Arizona
URL: http://hdl.handle.net/10150/185884
► The family of planar nearrings enjoys quite a few geometric and combinatoric properties. Circular planar nearrings are members of this family which have the character…
(more)
▼ The family of planar nearrings enjoys quite a few geometric and combinatoric properties. Circular planar nearrings are members of this family which have the character of circles of the complex plane. On the other hand, they also have some properties which one may not find among the circles of the complex plane. In this dissertation, we first review the definition and characterization of a planar nearring, and some various ways of constructing planar nearrings, as well as various ways of constructing BIBD's from a planar nearring. Circularity of a planar nearring is then introduced, and examples of circularity planar nearrings are given. Then, some nonisomorphic BIBD's arising from the same additive group of a planar nearring are examined. To provide examples of nonabelian planar nearrings, the structures of Frobenius groups with kernel of order 64 are completely determined and described. On the other hand, examples of Ferrero pairs (N, Φ)'s with nonabelian Φ, which produce circular planar nearrings, are provided. Finally, we study the structures of circular planar nearrings generated from the finite prime fields from geometric and combinatoric points of view. This study is then carried back to the complex plane. In turn, it gives a good reason for calling a block from a circular planar nearring a "circle."
Advisors/Committee Members: Clay, James R (advisor), Gay, David A. (committeemember), Stevenson, Frederick W. (committeemember).
Subjects/Keywords: Rings (Algebra);
Near-rings.
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APA ·
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APA (6th Edition):
Ke, W. (1992). Structures of circular planar nearrings
. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/185884
Chicago Manual of Style (16th Edition):
Ke, Wen-Fong. “Structures of circular planar nearrings
.” 1992. Doctoral Dissertation, University of Arizona. Accessed January 16, 2021.
http://hdl.handle.net/10150/185884.
MLA Handbook (7th Edition):
Ke, Wen-Fong. “Structures of circular planar nearrings
.” 1992. Web. 16 Jan 2021.
Vancouver:
Ke W. Structures of circular planar nearrings
. [Internet] [Doctoral dissertation]. University of Arizona; 1992. [cited 2021 Jan 16].
Available from: http://hdl.handle.net/10150/185884.
Council of Science Editors:
Ke W. Structures of circular planar nearrings
. [Doctoral Dissertation]. University of Arizona; 1992. Available from: http://hdl.handle.net/10150/185884
University of Arizona
4.
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…
(more)
▼ 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.
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APA ·
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APA (6th 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 (16th Edition):
McShane, Janet Marie. “Computation of polynomial invariants of finite groups.
” 1992. Doctoral Dissertation, University of Arizona. Accessed January 16, 2021.
http://hdl.handle.net/10150/186000.
MLA Handbook (7th Edition):
McShane, Janet Marie. “Computation of polynomial invariants of finite groups.
” 1992. Web. 16 Jan 2021.
Vancouver:
McShane JM. Computation of polynomial invariants of finite groups.
[Internet] [Doctoral dissertation]. University of Arizona; 1992. [cited 2021 Jan 16].
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
University of Arizona
5.
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…
(more)
▼ 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.
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Record Details
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APA ·
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MLA ·
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CSE |
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APA (6th 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 (16th 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 (7th 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
University of Arizona
6.
Mishra, Shivakant.
Consul: A communication substrate for fault-tolerant distributed programs.
Degree: 1992, University of Arizona
URL: http://hdl.handle.net/10150/185824
► As human dependence on computing technology increases, so does the need for computer system dependability. This dissertation introduces Consul, a communication substrate designed to help…
(more)
▼ As human dependence on computing technology increases, so does the need for computer system dependability. This dissertation introduces Consul, a communication substrate designed to help improve system dependability by providing a platform for building fault-tolerant, distributed systems based on the replicated state machine approach. The key issues in this approach – ensuring replica consistency and reintegrating recovering replicas – are addressed in Consul by providing abstractions called fault-tolerant services. These include a broadcast service to deliver messages to a collection of processes reliably and in some consistent order, a membership service to maintain a consistent system-wide view of which processes are functioning and which have failed, and a recovery service to recover a failed process. Fault-tolerant services are implemented in Consul by a unified collection of protocols that provide support for managing communication, redundancy, failures, and recovery in a distributed system. At the heart of Consul is Psync, a protocol that provides for multicast communication based on a context graph that explicitly records the partial (or causal) order of messages. This graph also serves as the basis for novel algorithms used in the ordering, membership, and recovery protocols. The ordering protocol combines the semantics of the operations encoded in messages with the partial order provided by Psync to increase the concurrency of the application. Similarly, the membership protocol exploits the partial ordering to allow different processes to conclude that a failure has occurred at different times relative to the sequence of messages received, thereby reducing the amount of synchronization required. The recovery protocol combines checkpointing with the replay of messages stored in the context graph to recover the state of a failed process. Moreover, this collection of protocols is implemented in a highly-configurable manner, thus allowing a system builder to easily tailor an instance of Consul from this collection of building-block protocols. Consul is built in the x-Kernel and executes standalone on a collection of Sun 3 work-stations. Initial testing and performance studies have been done using two applications: a replicated directory and a distributed wordgame. These studies show that the semantic based order is more efficient than a total order in many situations, and that the overhead imposed by the checkpointing, membership, and recovery protocols is insignificant.
Advisors/Committee Members: Schlichting, Richard D (advisor), Peterson, Larry L. (committeemember), Snodgrass, Richard T. (committeemember), Gay, David (committeemember), Leonard, John (committeemember).
Subjects/Keywords: Fault-tolerant computing.;
Computer network protocols.;
Software engineering.
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Mishra, S. (1992). Consul: A communication substrate for fault-tolerant distributed programs.
(Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/185824
Chicago Manual of Style (16th Edition):
Mishra, Shivakant. “Consul: A communication substrate for fault-tolerant distributed programs.
” 1992. Doctoral Dissertation, University of Arizona. Accessed January 16, 2021.
http://hdl.handle.net/10150/185824.
MLA Handbook (7th Edition):
Mishra, Shivakant. “Consul: A communication substrate for fault-tolerant distributed programs.
” 1992. Web. 16 Jan 2021.
Vancouver:
Mishra S. Consul: A communication substrate for fault-tolerant distributed programs.
[Internet] [Doctoral dissertation]. University of Arizona; 1992. [cited 2021 Jan 16].
Available from: http://hdl.handle.net/10150/185824.
Council of Science Editors:
Mishra S. Consul: A communication substrate for fault-tolerant distributed programs.
[Doctoral Dissertation]. University of Arizona; 1992. Available from: http://hdl.handle.net/10150/185824
. 
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