Spelling suggestions: "subject:"tet theory"" "subject:"beet theory""
71 
Erasurecorrecting codes derived from Sudoku & related combinatorial structuresPhillips, Linzy January 2013 (has links)
This thesis presents the results of an investigation into the use of puzzlebased combinatorial structures for erasure correction purposes. The research encompasses two main combinatorial structures: the wellknown number placement puzzle Sudoku and a novel three component construction designed specifically with puzzlebased erasure correction in mind. The thesis describes the construction of outline erasure correction schemes incorporating each of the two structures. The research identifies that both of the structures contain a number of smaller substructures, the removal of which results in a grid with more than one potential solution  a detrimental property for erasure correction purposes. Extensive investigation into the properties of these substructures is carried out for each of the two outline erasure correction schemes, and results are determined that indicate that, although the schemes are theoretically feasible, the prevalence of substructures results in practically infeasible schemes. The thesis presents detailed classifications for the different cases of substructures observed in each of the outline erasure correction schemes. The anticipated similarities in the substructures of Sudoku and substructures of Latin Squares, an established area of combinatorial research, are observed and investigated, the proportion of Sudoku puzzles free of small substructures is calculated and a simulation comparing the recovery rates of small substructure free Sudoku and standard Sudoku is carried out. The analysis of substructures for the second erasure correction scheme involves detailed classification of a variety of small substructures; the thesis also derives probabilistic lower bounds for the expected numbers of casespecific substructures within the puzzle structure, indicating that specific types of substructure hinder recovery to such an extent that the scheme is infeasible for practical erasure correction. The consequences of complex cell interrelationships and wider issues with puzzlebased erasure correction, beyond the structures investigated in the thesis are also discussed, concluding that while there are suggestions in the literature that Sudoku and other puzzlebased combinatorial structures may be useful for erasure correction, the work of this thesis suggests that this is not the case.

72 
On the foundations of the theory of ordinal numbersDunik, Peter Anthony January 1966 (has links)
Three concepts of ordinal numbers are examined with a view to their intuitiveriess and existence in two principle systems of axiomatic set theory. The first is based on equivalence classes of the similarity relation between wellordered sets. Two alternatives are suggested in later chapters for overcoming the problems arizing from this definition. Next, ordinal numbers are defined as certain representatives of these equivalence classes,, and one of several such possible definitions is taken for proving the fundamental properties of these ordinals. Finally, a generalization of Peano's axioms provides us with a method of defining ordinal numbers which are the ultimate result of abstractions. / Science, Faculty of / Mathematics, Department of / Graduate

73 
Fundamental Properties of the ContingentHaggard, Paul W. 08 1900 (has links)
This thesis explores the fundamental properties of the contingent.

74 
Results on NonClub Isomorphic Aronszajn TreesChavez, Jose 08 1900 (has links)
In this dissertation we prove some results about the existence of families of Aronszajn trees on successors of regular cardinals which are pairwise not club isomorphic. The history of this topic begins with a theorem of Gaifman and Specker in the 1960s which asserts the existence from ZFC of many pairwise not isomorphic Aronszajn trees. Since that result was proven, the focus has turned to comparing Aronszajn trees with respect to isomorphisms on a club of levels, instead of on the entire tree. In the 1980s Abraham and Shelah proved that the Proper Forcing Axiom implies that any two Aronszajn trees on the first uncountable cardinal are club isomorphic. This theorem was generalized to higher cardinals in recent work of Krueger. Abraham and Shelah also proved that the opposite holds under diamond principles. In this dissertation we address the existence of pairwise not club isomorphic Aronszajn trees on higher cardinals from a variety of cardinal arithmetic and diamond principle assumptions. For example, on the successor of a regular cardinal, assuming GCH and the diamond principle on the critical cofinality, there exists a large collection of special Aronszajn trees such that any two of them do not contain club isomorphic subtrees.

75 
A Relation for Point Sets in a Topological SpaceWarndof, Joseph C. 08 1900 (has links)
The purpose of this thesis is to investigate the relation Z for point sets in a topological space. There were two original goals which caused the study.

76 
Distance spacesUnknown Date (has links)
"The purpose of this paper is to record the results of a study of an abstract set upon which a distance function, having certain properties, has been defined. It is assumed that the reader is familiar with the fundamental concepts of set theory"Introduction. / "June, 1959." / Typescript. / "Submitted to the Graduate School of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: H. C. Griffith, Professor Directing Paper. / Includes bibliographical references (leaf 26).

77 
Topics in combinatorial analysisUnknown Date (has links)
"This paper is concerned with systems of distinct representatives (abbreviated by S.D.R.) and related combinatorial topics"Introduction. / Typescript. / "August, 1959." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Marion F. Tinsley, Professor Directing Paper. / Includes bibliographical references (leaf 25).

78 
Definable Structures on the Space of Functions from Tuples of Integers into 2Olsen, Cody James 05 1900 (has links)
We give some background on the free part of the action of tuples of integers into 2. We will construct specific structures on this space, and then show that certain other structures cannot exist.

79 
On convergence and regularity of vectorvalued processes indexed by directed sets /Frangos, Nicholas E. January 1984 (has links)
No description available.

80 
On multipliers of abelian difference sets /McFarland, Robert Lee,1936 January 1970 (has links)
No description available.

Page generated in 0.056 seconds