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Title: INFECTION AGE STRUCTURED VECTOR BORNE DISEASE MODEL WITH DIRECT TRANSMISSION.
Creator: Giri, Sunil, Tuncer, Necibe, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Mathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived....
Show moreMathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived. Dynamical analysis reveals the forward bifurcation in the first model. That is when the threshold value R0 < 1, disease free-equilibrium is stable locally implying that if there is small perturbation of the system, then after some time, the system will return to the disease free equilibrium. When R0 > 1 the unique endemic equilibrium is locally asymptotically stable. For the second model, analysis of the existence and stability of equilibria reveals the existence of backward bifurcation i.e. where the disease free equilibrium coexists with the endemic equilibrium when the reproduction number R02 is less than unity. This aspect shows that in order to control vector borne disease, it is not sufficient to have reproduction number less than unity although necessary. Thus, the infection can persist in the population even if the reproduction number is less than unity. Numerical simulation is presented to see the bifurcation behaviour in the model. By taking the reproduction number as the bifurcation parameter, we find the system undergoes backward bifurcation at R02 = 1. Thus, the model has backward bifurcation and have two positive endemic equilibrium when R02 < 1 and unique positive endemic equilibrium whenever R02 > 1. Stability analysis shows that disease free equilibrium is locally asymptotically stable when R02 < 1 and unstable when R02 > 1. When R02 < 1, lower endemic equilibrium in backward bifurcation is locally unstable.
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Date Issued: 2020
PURL: http://purl.flvc.org/fau/fd/FA00013552
Subject Headings: Vector Borne Diseases, Mathematical models, Simulations, Dynamics--Mathematical models
Format: Document (PDF)

Title: Maximally Prüfer rings.
Creator: Sharma, Madhav, Klingler, Lee, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this dissertation, we consider six Prufer-like conditions on acommutative ring R. These conditions form a hierarchy. Being a Prufer ring is not a local property: a Prufer ring may not remain a Prufer ring when localized at a prime or maximal ideal. We introduce a seventh condition based on this fact and extend the hierarchy. All the conditions of the hierarchy become equivalent in the case of a domain, namely a Prufer domain. We also seek the relationship of the hierarchy with strong...
Show moreIn this dissertation, we consider six Prufer-like conditions on acommutative ring R. These conditions form a hierarchy. Being a Prufer ring is not a local property: a Prufer ring may not remain a Prufer ring when localized at a prime or maximal ideal. We introduce a seventh condition based on this fact and extend the hierarchy. All the conditions of the hierarchy become equivalent in the case of a domain, namely a Prufer domain. We also seek the relationship of the hierarchy with strong Prufer rings.
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Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00004465, http://purl.flvc.org/fau/fd/FA00004465
Subject Headings: Approximation theory, Commutative algebra, Commutative rings, Geometry, Algebraic, Ideals (Algebra), Mathematical analysis, Prüfer rings, Rings (Algebra), Rings of integers
Format: Document (PDF)

Title: Techniques in Lattice Basis Reduction.
Creator: Khadka, Bal K., Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The mathematical theory of nding a basis of shortest possible vectors in a given lattice L is known as reduction theory and goes back to the work of Lagrange, Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who created the well known LLL algorithm, and many other researchers such as L. Babai and C. P. Schnorr who created signi cant new variants of basis reduction algorithms. The shortest...
Show moreThe mathematical theory of nding a basis of shortest possible vectors in a given lattice L is known as reduction theory and goes back to the work of Lagrange, Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who created the well known LLL algorithm, and many other researchers such as L. Babai and C. P. Schnorr who created signi cant new variants of basis reduction algorithms. The shortest vector (SVP) and closest vector (CVP) problems, presently considered intractable, are algorithmic tasks that lie at the core of many number theoretic problems, integer programming, nding irreducible factors of polynomials, minimal polynomials of algebraic numbers, and simultaneous diophantine approximation. Lattice basis reduction also has deep and extensive connections with modern cryptography, and cryptanalysis particularly in the post-quantum era. In this dissertation we study and compare current systems LLL and BKZ, and point out their strengths and drawbacks. In addition, we propose and investigate the e cacy of new optimization techniques, to be used along with LLL, such as hill climbing, random walks in groups, our lattice di usion-sub lattice fusion, and multistage hybrid LDSF-HC technique. The rst two methods rely on the sensitivity of LLL to permutations of the input basis B, and optimization ideas over the symmetric group Sm viewed as a metric space. The third technique relies on partitioning the lattice into sublattices, performing basis reduction in the partition sublattice blocks, fusing the sublattices, and repeating. We also point out places where parallel computation can reduce runtimes achieving almost linear speedup. The multistage hybrid technique relies on the lattice di usion and sublattice fusion and hill climbing algorithms. Unlike traditional methods, our approach brings in better results in terms of basis reduction towards nding shortest vectors and minimal weight bases. Using these techniques we have published the competitive lattice vectors of ideal lattice challenge on the lattice hall of fame. Toward the end of the dissertation we also discuss applications to the multidimensional knapsack problem that resulted in the discovery of new large sets of geometric designs still considered very rare. The research introduces innovative techniques in lattice basis reduction theory and provides some space for future researchers to contemplate lattices from a new viewpoint.
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Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004678
Subject Headings: Cryptography., Combinatorial analysis., Group theory.
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: New Results in Group Theoretic Cryptology.
Creator: Sramka, Michal, Florida Atlantic University, Magliveras, Spyros S., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: With the publication of Shor's quantum algorithm for solving discrete logarithms in finite cyclic groups, a need for new cryptographic primitives arose; namely, for more secure primitives that would prevail in the post-quantum era. The aim of this dissertation is to exploit some hard problems arising from group theory for use in cryptography. Over the years, there have been many such proposals. We first look at two recently proposed schemes based on some form of a generalization of the...
Show moreWith the publication of Shor's quantum algorithm for solving discrete logarithms in finite cyclic groups, a need for new cryptographic primitives arose; namely, for more secure primitives that would prevail in the post-quantum era. The aim of this dissertation is to exploit some hard problems arising from group theory for use in cryptography. Over the years, there have been many such proposals. We first look at two recently proposed schemes based on some form of a generalization of the discrete logari thm problem (DLP), identify their weaknesses, and cryptanalyze them. By applying the exper tise gained from the above cryptanalyses, we define our own generalization of the DLP to arbitrary finite groups. We show that such a definition leads to the design of signature schemes and pseudo-random number generators with provable security under a security assumption based on a group theoretic problem. In particular, our security assumption is based on the hardness of factorizing elements of the projective special linear group over a finite field in some representations. We construct a one-way function based on this group theoretic assumption and provide a security proof.
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Date Issued: 2006
PURL: http://purl.flvc.org/fau/fd/FA00000878
Subject Headings: Group theory, Mathematical statistics, Cryptography, Combinatorial designs and configurations, Data encryption (Computer science), Coding theory
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: 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: 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: 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 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: 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: 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: 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: 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: New Geometric Large Sets.
Creator: Hurley, Michael Robert, Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Let V be an n-dimensional vector space over the field of q elements. By a geometric t-[q^n, k, λ] design we mean a collection D of k-dimensional subspaces of V, called blocks, such that every t-dimensional subspace T of V appears in exactly λ blocks in D. A large set, LS [N] [t, k, q^n], of geometric designs is a collection on N disjoint t-[q^n, k, λ] designs that partitions [V K], the collection of k-dimensional subspaces of V. In this work we construct non-isomorphic large sets using...
Show moreLet V be an n-dimensional vector space over the field of q elements. By a geometric t-[q^n, k, λ] design we mean a collection D of k-dimensional subspaces of V, called blocks, such that every t-dimensional subspace T of V appears in exactly λ blocks in D. A large set, LS [N] [t, k, q^n], of geometric designs is a collection on N disjoint t-[q^n, k, λ] designs that partitions [V K], the collection of k-dimensional subspaces of V. In this work we construct non-isomorphic large sets using methods based on incidence structures known as the Kramer-Mesner matrices. These structures are induced by particular group actions on the collection of subspaces of the vector space V. Subsequently, we discuss and use computational techniques for solving certain linear problems of the form AX = B, where A is a large integral matrix and X is a {0,1} solution. These techniques involve (i) lattice basis-reduction, including variants of the LLL algorithm, and (ii) linear programming. Inspiration came from the 2013 work of Braun, Kohnert, Ostergard, and Wassermann, [17], who produced the first nontrivial large set of geometric designs with t ≥ 2. Bal Khadka and Michael Epstein provided the know-how for using the LLL and linear programming algorithms that we implemented to construct the large sets.
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Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004732, http://purl.flvc.org/fau/fd/FA00004732
Subject Headings: Group theory., Finite groups., Factorial experiment designs., Irregularities of distribution (Number theory), Combinatorial analysis.
Format: Document (PDF)

Title: Negligible Variation, Change of Variables, and a Smooth Analog of the Hobby-Rice Theorem.
Creator: Rutherfoord, Vermont Charles, Sagher, Yoram, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This dissertation concerns two topics in analysis. The rst section is an exposition of the Henstock-Kurzweil integral leading to a necessary and su cient condition for the change of variables formula to hold, with implications for the change of variables formula for the Lebesgue integral. As a corollary, a necessary and suf- cient condition for the Fundamental Theorem of Calculus to hold for the HK integral is obtained. The second section concerns a challenge raised in a paper by O. Lazarev...
Show moreThis dissertation concerns two topics in analysis. The rst section is an exposition of the Henstock-Kurzweil integral leading to a necessary and su cient condition for the change of variables formula to hold, with implications for the change of variables formula for the Lebesgue integral. As a corollary, a necessary and suf- cient condition for the Fundamental Theorem of Calculus to hold for the HK integral is obtained. The second section concerns a challenge raised in a paper by O. Lazarev and E. H. Lieb, where they proved that, given f1….,fn ∈ L1 ([0,1] ; C), there exists a smooth function φ that takes values on the unit circle and annihilates span {f1...., fn}. We give an alternative proof of that fact that also shows the W1,1 norm of φ can be bounded by 5πn + 1. Answering a question raised by Lazarev and Lieb, we show that if p > 1 then there is no bound for the W1,p norm of any such multiplier in terms of the norms of f1...., fn.
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Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004627
Subject Headings: Mathematical analysis., Measure theory., Henstock-Kurzweil integral.
Format: Document (PDF)

Title: Norm Inequalities for the Fourier Coefficients of Some Almost Periodic Functions.
Creator: Boryshchak, Yarema, Sagher, Yoram, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Using C. Fefferman's embedding of a charge space in a measure space allows us to apply standard interpolation theorems to the establishment of norm inequalities for Besicovitch almost periodic functions. This yields a significant improvement to the results of A. Avantaggiati, G. Bruno and R. Iannacci.
Date Issued: 2019
PURL: http://purl.flvc.org/fau/fd/FA00013191
Subject Headings: Fourier series, Almost periodic functions, Norm
Format: Document (PDF)

Title: THE CHANGE POINT PROBLEM FOR TWO CLASSES OF STOCHASTIC PROCESSES.
Creator: Ball, Cory, Long, Hongwei, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: The change point problem is a problem where a process changes regimes because a parameter changes at a point in time called the change point. The objective of this problem is to estimate the change point and each of the parameters of the stochastic process. In this thesis, we examine the change point problem for two classes of stochastic processes. First, we consider the volatility change point problem for stochastic diffusion processes driven by Brownian motions. Then, we consider the drift...
Show moreThe change point problem is a problem where a process changes regimes because a parameter changes at a point in time called the change point. The objective of this problem is to estimate the change point and each of the parameters of the stochastic process. In this thesis, we examine the change point problem for two classes of stochastic processes. First, we consider the volatility change point problem for stochastic diffusion processes driven by Brownian motions. Then, we consider the drift change point problem for Ornstein-Uhlenbeck processes driven by _-stable Levy motions. In each problem, we establish the consistency of the estimators, determine asymptotic behavior for the changing parameters, and finally, we perform simulation studies to computationally assess the convergence of parameters.
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Date Issued: 2020
PURL: http://purl.flvc.org/fau/fd/FA00013462
Subject Headings: Stochastic processes, Change-point problems, Brownian motion processes, Ornstein-Uhlenbeck process, Computer simulation
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)

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