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Title
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A GROUP-THEORETIC PROOF OF BURNSIDE'S P('A)Q('B) THEOREM.
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Creator
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HOCH, ALLEN ANTON., Florida Atlantic University, Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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In this thesis we give a self-contained exposition of the group-theoretic proofs of the Burnside p^a g^b theorem. The Burnside p^a g^b theorem states that all groups of order p^a g^b are solvable, where p and q are primes. The proof was suggested by Thompson, and published by Goldschmidt, Bender, and Matsuyama.
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Date Issued
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1979
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PURL
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http://purl.flvc.org/fcla/dt/13983
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Subject Headings
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Mathematics--Research
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Format
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Document (PDF)
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Title
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THE MINIMUM K-CENTER PROBLEM FOR GRID GRAPH.
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Creator
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HSUEH, CHI-FU, Florida Atlantic University, Hadlock, Frank O., Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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A study was made of the problem of locating M facilities on a connected grid graph, so that M is the minimum and so that every demand node on the graph is within given distance K of one of these M facilities. We call this problem briefly the G(N,K,M) problem, with N denoting the total number of demand nodes. An algorithm for solving this problem by using backtrack technique is presented in this thesis. A heuristic algorithm is also present; although the resulting M is not always minimum, it...
Show moreA study was made of the problem of locating M facilities on a connected grid graph, so that M is the minimum and so that every demand node on the graph is within given distance K of one of these M facilities. We call this problem briefly the G(N,K,M) problem, with N denoting the total number of demand nodes. An algorithm for solving this problem by using backtrack technique is presented in this thesis. A heuristic algorithm is also present; although the resulting M is not always minimum, it tends to be near minimum. The advantage over the backtrack algorithm is that the heuristic algorithm operates very quickly. Algorithms represented in this thesis are programmed in the Pascal language for the Univac 1100 computer at Florida Atlantic University, Boca Raton, Florida.
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Date Issued
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1981
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PURL
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http://purl.flvc.org/fcla/dt/14077
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Subject Headings
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Graph theory, Algorithms
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Format
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Document (PDF)
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Title
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A proposal for a binary stream cipher based on chaos theory.
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Creator
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Kanser, Heather Lianna, Florida Atlantic University, Mullin, Ronald C., Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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Today new secure cryptosystems are in great demand. Computers are becoming more powerful and old cryptosystems, such as the Data Encryption Standard (DES), are becoming outdated. This thesis describes a new binary additive strewn cipher (HK cryptosystem) that is based on the logistic map. The logistic map is not random, but works under simple rules to become complex, thus making it ideal for implementation in cryptography. Instead of basing the algorithm on one logistic map, the HK...
Show moreToday new secure cryptosystems are in great demand. Computers are becoming more powerful and old cryptosystems, such as the Data Encryption Standard (DES), are becoming outdated. This thesis describes a new binary additive strewn cipher (HK cryptosystem) that is based on the logistic map. The logistic map is not random, but works under simple rules to become complex, thus making it ideal for implementation in cryptography. Instead of basing the algorithm on one logistic map, the HK cryptosystem. averages several uncoupled logistic maps. Averaging the maps increases the dimension of such a system, thus providing greater security. This thesis will explore the strengths and weaknesses of the HK cryptosystem and will end by introducing a modified version, called the HK8 cryptosystem that does not have the apparent weakness of the HK system.
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Date Issued
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2000
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PURL
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http://purl.flvc.org/fcla/dt/12685
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Subject Headings
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Chaotic behavior in systems, Computers--Access control, Cryptography
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Format
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Document (PDF)
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Title
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SYMMETRIES IN GOPPA CODES.
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Creator
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SAYRS, BRIAN GEORGE., Florida Atlantic University, Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
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Abstract/Description
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Properties of Goppa codes are studied. These are "good" codes in the sense that they asymptotically approach the Varshamov-Gilbert bound. E. N. Gilbert and R. R. Varshamov have shown (independently) that it is possible to construct an (n, k) linear code over GF(q) with minimum distance d if [equation] and there are long Goppa codes which achieve this bound [10]. Subclasses of Goppa codes which remain invariant under symmetries are given special attention.
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Date Issued
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1979
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PURL
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http://purl.flvc.org/fcla/dt/13989
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Subject Headings
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Mathematics--Research
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Format
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Document (PDF)
