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Title: ON SOLUTIONS OF A PERTURBED SCHROEDINGER EQUATION.
Creator: ARTERO, AGUSTIN., Florida Atlantic University, Schonbek, Tomas P., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: We study L^2 (R^k) solutions of the equation [..] where [..] and V is a non-negative L^2 function. Our main results are Theorems 1 and 2 of Chapter IV, in which we prove that these solutions depend continuously on V.
Date Issued: 1975
PURL: http://purl.flvc.org/fcla/dt/13716
Subject Headings: Schrödinger equation
Format: Document (PDF)

Title: SYMMETRIES IN GOPPA CODES.
Creator: SAYRS, BRIAN GEORGE., Florida Atlantic University, Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: 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.
Date Issued: 1979
PURL: http://purl.flvc.org/fcla/dt/13989
Subject Headings: Mathematics--Research
Format: Document (PDF)

Title: A GROUP-THEORETIC PROOF OF BURNSIDE'S P('A)Q('B) THEOREM.
Creator: HOCH, ALLEN ANTON., Florida Atlantic University, Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: 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.
Date Issued: 1979
PURL: http://purl.flvc.org/fcla/dt/13983
Subject Headings: Mathematics--Research
Format: Document (PDF)

Title: A FORTRAN 77 PREPROCESSOR.
Creator: LEACH, JOHN TIMOTHY, Florida Atlantic University, Levow, Roy B., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This thesis is concerned with the design, construction, and implementation of a FORTRAN 77 preprocessor. It demonstrates how the standard compiler-writing techniques for syntactic and lexical analysis can be greatly simplified in preprocessor construction. The input language is FORTRAN 77. The output language is UNIVAC ASCII FORTRAN Level 8R1.
Date Issued: 1980
PURL: http://purl.flvc.org/fcla/dt/14022
Subject Headings: FORTRAN (Computer program language)
Format: Document (PDF)

Title: THE MINIMUM K-CENTER PROBLEM FOR GRID GRAPH.
Creator: HSUEH, CHI-FU, Florida Atlantic University, Hadlock, Frank O., Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: 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: 1981
PURL: http://purl.flvc.org/fcla/dt/14077
Subject Headings: Graph theory, Algorithms
Format: Document (PDF)

Title: A SYNTACTIC APPROACH TO HAND PRINTED CHARACTER RECOGNITION.
Creator: KING, ALLAN KAI-CHUNG, Florida Atlantic University, Hadlock, Frank O., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: A study was made on the feasibility of the syntactic approach to the problem of hand printed character recognition. The characters are represented as postfix expressions in Picture Description Language. By comparing them with the prototype expressions, each character is classified as the prototype that is closest to it. Programs written in the Pascal language, which generate the postfix expressions for the characters, and recognize the characters, are presented.
Date Issued: 1983
PURL: http://purl.flvc.org/fcla/dt/14168
Subject Headings: Pattern recognition systems, Character sets (Data processing)
Format: Document (PDF)

Title: TPL, A TUTORIAL PROGRAMMING LANGUAGE.
Creator: Huang, Chien-Jen, Florida Atlantic University, Hadlock, Frank O., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The object of this reaearch is to define and implement an experimental language, Tutorial Programming Language (TPL). Basic language concepts and definitions are introduced initially to provide the background for defining TPL, which is intended as a means to illustrate language concepts, and has Type-3 grammar as a data type. A formal definition of TPL is given in the form of an SLR(1) grammar. TPL is implemented by a syntax directed compiler and a hypothetical machine for which the compiler...
Show moreThe object of this reaearch is to define and implement an experimental language, Tutorial Programming Language (TPL). Basic language concepts and definitions are introduced initially to provide the background for defining TPL, which is intended as a means to illustrate language concepts, and has Type-3 grammar as a data type. A formal definition of TPL is given in the form of an SLR(1) grammar. TPL is implemented by a syntax directed compiler and a hypothetical machine for which the compiler provides code. The machine is emulated by a Pascal program, making TPL highly portable. It is also possible for the interested user to enhance the power of TPL by writing more functions for practical purposes.
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Date Issued: 1986
PURL: http://purl.flvc.org/fcla/dt/14337
Subject Headings: Programming languages (Electronic computers)
Format: Document (PDF)

Title: Bijections for partition identities.
Creator: Lai, Jin-Mei Jeng, Florida Atlantic University, Meyerowitz, Aaron, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieve--equivalent families. Suppose A1' ... ,An are subsets of a finite set A and B1' ... ,Bn are subsets of a finite set B. Define AS=∩(i∈S) Ai and BS = ∩ (i∈S) Bi for all S⊆N={1,...,n}. Given explicit bijections fS: AS->BS for each S⊆N, A-∪Ai has the same size as B-∪Bi. Several authors have given algorithms for producing an explicit bijection between these...
Show moreThis paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieve--equivalent families. Suppose A1' ... ,An are subsets of a finite set A and B1' ... ,Bn are subsets of a finite set B. Define AS=∩(i∈S) Ai and BS = ∩ (i∈S) Bi for all S⊆N={1,...,n}. Given explicit bijections fS: AS->BS for each S⊆N, A-∪Ai has the same size as B-∪Bi. Several authors have given algorithms for producing an explicit bijection between these two sets. In certain important cases they give the same result. We discuss and compare algorithms, use Graph Theory to illustrate them, and provide PAS CAL programs for them.
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Date Issued: 1992
PURL: http://purl.flvc.org/fau/fd/FADT14826
Subject Headings: Algorithms, Partitions (Mathematics), Sieves (Mathematics)
Format: Document (PDF)

Title: The Cayley-Dickson algebras.
Creator: Khalil, Saidah Hasan, Florida Atlantic University, Yiu, Paul Y., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This thesis studies the various effects of the nonassociativity of the Cayley-Dickson algebras At, t>3, especially on the structure of their automorphism groups. Beginning with the problem of composition algebra structures on euclidean spaces, we shall explain the origin of the Cayley-Dickson algebras, and give a self-contained exposition on some important results on such algebras. These algebras being nonassociative, we focus on the study of the associators of the form (u,w,v) = (uw)v - u(wv...
Show moreThis thesis studies the various effects of the nonassociativity of the Cayley-Dickson algebras At, t>3, especially on the structure of their automorphism groups. Beginning with the problem of composition algebra structures on euclidean spaces, we shall explain the origin of the Cayley-Dickson algebras, and give a self-contained exposition on some important results on such algebras. These algebras being nonassociative, we focus on the study of the associators of the form (u,w,v) = (uw)v - u(wv). The first main result, that if u and v are elements in a Cayley-Dickson algebra for which (u, w, v) = 0 for all w, then u and v generate a 2-dimensional subalgebra isomorphic to C, was conjectured by P. Yiu, and proved by P. Eakin and A. Sathaye. We shall simplify the proof given by these latter authors. This is then used to give a simple proof of R. D. Schafer's theorem on derivations of Cayley-Dickson algebras, and following also Eakin and Sathaye, a proof of the conjecture by R. B. Brown on the structure of the automorphism groups of these algebras. Two simple proofs are presented for the beautiful characterization by H. Brandt that in the Cayley algebra A3 = K, conjugation by a unit element a is an automorphism if and only if a is a 6th root of unity. We shall present a geometric proof by M. A. Zorn and a purely algebraic one. The zero divisors of the Cayley-Dickson algebra A4 are also analyzed in detail.
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Date Issued: 1993
PURL: http://purl.flvc.org/fcla/dt/14993
Subject Headings: Cayley algebras
Format: Document (PDF)

Title: Time series analysis and correlation dimension estimation: Mathematical foundation and applications.
Creator: Jiang, Wangye, Florida Atlantic University, Ding, Mingzhou, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: A time series is a data set of a single quantity sampled at intervals T time units apart. It is widely used to represent a chaotic dynamical system. The correlation dimension measures the complexity of a dynamical system. Using the delay-coordinate map and the extended GP algorithm one can estimate the correlation dimension of an experimental dynamical system from measured time series. This thesis discusses the mathematical foundation of the methods and the corresponding applications. The...
Show moreA time series is a data set of a single quantity sampled at intervals T time units apart. It is widely used to represent a chaotic dynamical system. The correlation dimension measures the complexity of a dynamical system. Using the delay-coordinate map and the extended GP algorithm one can estimate the correlation dimension of an experimental dynamical system from measured time series. This thesis discusses the mathematical foundation of the methods and the corresponding applications. The embedding theorems and their relationship with dimension preservation are reviewed in detail, but more attention is focussed on the concept development.
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Date Issued: 1995
PURL: http://purl.flvc.org/fcla/dt/15213
Subject Headings: Time-series analysis--Mathematical models, Chaotic behavior in systems
Format: Document (PDF)

Title: Decay for time-dependent Schroedinger equations.
Creator: Zhou, Zhen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: We study the decay in time of solutions of Schrodinger equations of the type du/du=idelta u+iV(t)u, establishing that for small potentials and initial data in L1 the solution u satisfies sup[u(x,t)](x element of R)
Show moreWe study the decay in time of solutions of Schrodinger equations of the type du/du=idelta u+iV(t)u, establishing that for small potentials and initial data in L1 the solution u satisfies sup[u(x,t)](x element of R)Show less
Date Issued: 1996
PURL: http://purl.flvc.org/fcla/dt/12463
Subject Headings: Mathematics
Format: Document (PDF)

Title: On Boolean algebras and their role in analysis.
Creator: Winkowska-Nowak, Katarzyna, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The relations between complete and $\sigma$-complete covers of a Boolean algebra are examined. The Dedekind completion of a Boolean algebra is shown to be a quotient of any complete cover. Atoms of a Boolean algebra correspond to atoms of the Dedekind completion hence the Dedekind completion of an atomic Boolean algebra is isomorphic to the power set of the set of all atoms. There exists a correspondence between complete (sigma-complete) homomorphisms and full (sigma-complete) ideals. The...
Show moreThe relations between complete and $\sigma$-complete covers of a Boolean algebra are examined. The Dedekind completion of a Boolean algebra is shown to be a quotient of any complete cover. Atoms of a Boolean algebra correspond to atoms of the Dedekind completion hence the Dedekind completion of an atomic Boolean algebra is isomorphic to the power set of the set of all atoms. There exists a correspondence between complete (sigma-complete) homomorphisms and full (sigma-complete) ideals. The explicit form of the Dedekind completion is given for the Boolean algebra generated by all semiopen subintervals of [0,1) as the atomless, complete Boolean algebra of all regularly closed subsets of [0,1). A compatible topology for a Boolean algebra is a topology for which addition and multiplication are continuous. The properties concerning products, quotients, subspaces and uniform completions of topological Boolean algebras are examined. Compact algebras are isomorphic and homeomorphic with power sets, endowed with the product topology. Measure algebras endowed with the weak* topology are compatible if and only if the underlying measure is purely atomic. A new proof of Stone Representation Theorem for a field of sets is given, providing a tool for establishing relations between Stone representation spaces of algebras, covers, subalgebras and quotients.
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Date Issued: 1996
PURL: http://purl.flvc.org/fcla/dt/12454
Subject Headings: Mathematics
Format: Document (PDF)

Title: Galois groups of prime degree and the O'Nan-Scott theorem.
Creator: Kaufman, J., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Discussion begins with a modular method for determining cycle types of permutations in the Galois group of a given separable irreducible polynomial over Q. As the Galois group is a transitive permutation group on the n roots of its irreducible polynomial, a list of all transitive groups of degree n, together with the cycle type distributions of each group, allows a probablistic determination of the group in a process of elimination. In the case of prime degree, transitive groups are primitive...
Show moreDiscussion begins with a modular method for determining cycle types of permutations in the Galois group of a given separable irreducible polynomial over Q. As the Galois group is a transitive permutation group on the n roots of its irreducible polynomial, a list of all transitive groups of degree n, together with the cycle type distributions of each group, allows a probablistic determination of the group in a process of elimination. In the case of prime degree, transitive groups are primitive and by the O'Nan-Scott theorem are of restricted form. Theory is presented in order to arrive at these results and others, so that in conjunction with the classification theorem on finite simple groups, it is possible (in principle) to list all primitive permutation groups of particular prime degree. The case of degree 17 is examined to obtain a list of the transitive permutation groups of degree seventeen, as well as the cycle type of distributions of the groups identified.
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Date Issued: 1996
PURL: http://purl.flvc.org/fcla/dt/15289
Subject Headings: Mathematics
Format: Document (PDF)

$New methods for estimating fractal dimensions of coastlines$

Title: New methods for estimating fractal dimensions of coastlines.
Creator: Klotzbach, Jonathan David, Florida Atlantic University, Voss, Richard, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: A coastline is an example of a statistically self-similar fractal. A standard characterization walks a ruler of fixed size along the coast and estimates fractal dimension from the power-law relationship between length and ruler size. Multiple intersection can lead to ambiguity in choosing the next step. The standard method always chooses the first intersection along the curve. Variations were developed to choose intersections which highlight geographic properties. The land method measures...
Show moreA coastline is an example of a statistically self-similar fractal. A standard characterization walks a ruler of fixed size along the coast and estimates fractal dimension from the power-law relationship between length and ruler size. Multiple intersection can lead to ambiguity in choosing the next step. The standard method always chooses the first intersection along the curve. Variations were developed to choose intersections which highlight geographic properties. The land method measures accessibility to the coast from land at each size while the water method probes water access. Measurements on sections of the East and West Coasts of the United States typically showed the land length exceeding water. Jumps in water length as step size decreased were often caused by narrow rivers or bays which have few corresponding land features. Simple recursive constructions were inadequate to model this asymmetry.
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Date Issued: 1998
PURL: http://purl.flvc.org/fcla/dt/15545
Subject Headings: Fractals, Boundaries, Coasts
Format: Document (PDF)

Title: Input-to-state stability properties for discrete-time nonlinear systems.
Creator: Gao, Kehan, Florida Atlantic University, Wang, Yuan, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this thesis, we study the input-to-state stability (scISS) property and related characterizations for discrete-time nonlinear systems. Variations of scISS property were employed in solving particular control problems. The main contribution of this work is to provide a detailed analysis on the relations among various types of notations related to system stability and show that most scISS results for continuous-time nonlinear system can be extended to discrete-time case.
Date Issued: 1999
PURL: http://purl.flvc.org/fcla/dt/15688
Subject Headings: Discrete-time systems, Nonlinear systems, Stability, Control theory
Format: Document (PDF)

Title: Representation of groups in quantum mechanics.
Creator: Paskaleva, Elitza Dimitrova, Florida Atlantic University, Schroeck, Franklin E., Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: In this work, we discuss the conceptual framework of quantum mechanics in the Hilbert space formalism from a group representation point of view. After a brief review of the main results of the theory of groups and their representations, we describe mathematical models of the subject, and show the applications of this theory for getting numerical answers to problems in elementary particle physics.
Date Issued: 2000
PURL: http://purl.flvc.org/fcla/dt/15758
Subject Headings: Quantum theory, Particles (Nuclear physics), Representations of groups, Hilbert space
Format: Document (PDF)

Title: A proposal for a binary stream cipher based on chaos theory.
Creator: Kanser, Heather Lianna, Florida Atlantic University, Mullin, Ronald C., Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: 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: 2000
PURL: http://purl.flvc.org/fcla/dt/12685
Subject Headings: Chaotic behavior in systems, Computers--Access control, Cryptography
Format: Document (PDF)

Title: Wind speed analysis for Lake Okeechobee.
Creator: Hu, Mingyan, Florida Atlantic University, Qian, Lianfen, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this thesis, we analyze wind speeds collected by South Florida Water Management District at stations L001, L005, L006 and LZ40 in Lake Okeechobee from January 1995 to December 2000. There are many missing values and out-liers in this data. To impute the missing values, three different methods are used: Nearby window average imputation, Jones imputation using Kalman filter, and EM algorithm imputation. To detect outliers and remove impacts, we use ARIMA models of time series. Innovational...
Show moreIn this thesis, we analyze wind speeds collected by South Florida Water Management District at stations L001, L005, L006 and LZ40 in Lake Okeechobee from January 1995 to December 2000. There are many missing values and out-liers in this data. To impute the missing values, three different methods are used: Nearby window average imputation, Jones imputation using Kalman filter, and EM algorithm imputation. To detect outliers and remove impacts, we use ARIMA models of time series. Innovational and additive outliers are considered. It turns out that EM algorithm imputation is the best method for our wind speed data set. After imputing missing values, detecting outliers and removing the impacts, we obtain the best models for all four stations. They are all in the form of seasonal ARIMA(2, 0, 0) x (1, 0, 0)24 for the hourly wind speed data.
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Date Issued: 2002
PURL: http://purl.flvc.org/fcla/dt/12883
Subject Headings: Winds--Speed--Florida--Okeechobee, Lake, Okeechobee, Lake (Fla )--Environmental conditions
Format: Document (PDF)

Title: Detailed study of "polynomial structures in order statistics distributions".
Creator: Liu, Chih-Fan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This thesis is based on the paper "Polynomial Structures in Order Statistics Distributions" by M. Denuit, Cl. Lefevre and Ph. Picard. We study the exact order distributions for i.i.d. random variables with arbitrary common law. The left tail distributions can be written as Abel-Gontcharoff polynomials and the right tail distributions can be expressed by Appell polynomials. The polynomial structure makes it easier to obtain closed forms and recursive methods for evaluating the distribution of...
Show moreThis thesis is based on the paper "Polynomial Structures in Order Statistics Distributions" by M. Denuit, Cl. Lefevre and Ph. Picard. We study the exact order distributions for i.i.d. random variables with arbitrary common law. The left tail distributions can be written as Abel-Gontcharoff polynomials and the right tail distributions can be expressed by Appell polynomials. The polynomial structure makes it easier to obtain closed forms and recursive methods for evaluating the distribution of frequently occurring statistics related to empirical distribution functions.
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Date Issued: 2004
PURL: http://purl.flvc.org/fcla/dt/13116
Subject Headings: Mathematics
Format: Document (PDF)

Title: Diffie-Hellman key exchange protocol, its generalization and nilpotent groups.
Creator: Mahalanobis, Ayan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This dissertation has two chapters. In the first chapter we talk about the discrete logarithm problem, more specifically we concentrate on the Diffie-Hellman key exchange protocol. We survey the current state of security for the Diffie-Hellman key exchange protocol. We also motivate the reader to think about the Diffie-Hellman key exchange in terms of group automorphisms. In the second chapter we study two key exchange protocols similar to the Diffie-Hellman key exchange protocol using an...
Show moreThis dissertation has two chapters. In the first chapter we talk about the discrete logarithm problem, more specifically we concentrate on the Diffie-Hellman key exchange protocol. We survey the current state of security for the Diffie-Hellman key exchange protocol. We also motivate the reader to think about the Diffie-Hellman key exchange in terms of group automorphisms. In the second chapter we study two key exchange protocols similar to the Diffie-Hellman key exchange protocol using an abelian subgroup of the automorphism group of a non-abelian group. We also generalize group no. 92 of the Hall-Senior table, for arbitrary prime p and study the automorphism group of these generalized group. We show that for those groups, the group of central automorphisms is an abelian group. We use these central automorphisms for the key exchange we are studying. We also develop a signature scheme.
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Date Issued: 2005
PURL: http://purl.flvc.org/fcla/dt/12154
Subject Headings: Mathematics, Computer Science
Format: Document (PDF)

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