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Title: DETERMINANTS OF WOMEN'S ATTITUDE TOWARDS INTIMATE PARTNER VIOLENCE: EVIDENCE FROM BANGLADESH.
Creator: Khan, Md Tareq Ferdous, Qian, Lianfen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This thesis uses Bangladesh Demographic and Health Survey 2014 data to identify the important determinants due to which women justification towards intimate partner violence (IPV) varies. Statistical analyses reveal that among the individual-level independent variables age at first marriage, respondent's education, decision score, religion, NGO membership, access to information, husband's education, normalized wealth score, and division indicator have significant effects on the women's...
Show moreThis thesis uses Bangladesh Demographic and Health Survey 2014 data to identify the important determinants due to which women justification towards intimate partner violence (IPV) varies. Statistical analyses reveal that among the individual-level independent variables age at first marriage, respondent's education, decision score, religion, NGO membership, access to information, husband's education, normalized wealth score, and division indicator have significant effects on the women's attitude towards IPV. It shows that other than religion, NGO membership, and division indicator, the higher the value of the variable, the lower the likelihood of justifying IPV. However, being a Muslim, NGO member, and resident of other divisions, women are found more tolerant of IPV from their respective counterparts. Among the three community-level variables, only the mean decision score is found significant in lowering the likelihood. The thesis concludes with some policy recommendations and a proposal for future research.
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Date Issued: 2019
PURL: http://purl.flvc.org/fau/fd/FA00013325
Subject Headings: Intimate partner violence, Bangladesh, Women
Format: Document (PDF)

Title: DEVELOPING A DEEP LEARNING PIPELINE TO AUTOMATICALLY ANNOTATE GOLD PARTICLES IN IMMUNOELECTRON MICROSCOPY IMAGES.
Creator: Jerez, Diego Alejandro, Hahn, William, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Machine learning has been utilized in bio-imaging in recent years, however as it is relatively new and evolving, some researchers who wish to utilize machine learning tools have limited access because of a lack of programming knowledge. In electron microscopy (EM), immunogold labeling is commonly used to identify the target proteins, however the manual annotation of the gold particles in the images is a time-consuming and laborious process. Conventional image processing tools could provide...
Show moreMachine learning has been utilized in bio-imaging in recent years, however as it is relatively new and evolving, some researchers who wish to utilize machine learning tools have limited access because of a lack of programming knowledge. In electron microscopy (EM), immunogold labeling is commonly used to identify the target proteins, however the manual annotation of the gold particles in the images is a time-consuming and laborious process. Conventional image processing tools could provide semi-automated annotation, but those require that users make manual adjustments for every step of the analysis. To create a new high-throughput image analysis tool for immuno-EM, I developed a deep learning pipeline that was designed to deliver a completely automated annotation of immunogold particles in EM images. The program was made accessible for users without prior programming experience and was also expanded to be used on different types of immuno-EM images.
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Date Issued: 2020
PURL: http://purl.flvc.org/fau/fd/FA00013628
Subject Headings: Electron microscopy, Immunogold labeling, Image analysis, Deep learning
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)

Title: The discrete logarithm problem in non-abelian groups.
Creator: Iliâc, Ivana., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in non-abelian groups. The projective special linear groups PSL(2; p), where p is a prime, represented by matrices over the eld of order p, are investigated as potential candidates for implementation of the GDLP. Our results show that the GDLP with respect to specic pairs of PSL(2; p) generators is weak. In such cases the groups PSL(2; p) are...
Show moreThis dissertation contains results of the candidate's research on the generalized discrete logarithm problem (GDLP) and its applications to cryptology, in non-abelian groups. The projective special linear groups PSL(2; p), where p is a prime, represented by matrices over the eld of order p, are investigated as potential candidates for implementation of the GDLP. Our results show that the GDLP with respect to specic pairs of PSL(2; p) generators is weak. In such cases the groups PSL(2; p) are not good candidates for cryptographic applications which rely on the hardness of the GDLP. Results are presented on generalizing existing cryptographic primitives and protocols based on the hardness of the GDLP in non-abelian groups. A special instance of a cryptographic primitive dened over the groups SL(2; 2n), the Tillich-Zemor hash function, has been cryptanalyzed. In particular, an algorithm for constructing collisions of short length for any input parameter is presented. A series of mathematical results are developed to support the algorithm and to prove existence of short collisions.
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Date Issued: 2010
PURL: http://purl.flvc.org/FAU/3356783
Subject Headings: Data encryption (Computer science), Computer security, Cryptography, Combinatorial group theory, Data processing, Mapping (Mathematics)
Format: Document (PDF)

Title: Distinguishability of Public Keys and Experimental Validation: The McEliece Public-Keyed Cryptosystem.
Creator: Pham, Hai, Steinwandt, Rainer, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: As quantum computers continue to develop, they pose a threat to cryptography since many popular cryptosystems will be rendered vulnerable. This is because the security of most currently used asymmetric systems requires the computational hardness of the integer factorization problem, the discrete logarithm or the elliptic curve discrete logarithm problem. However, there are still some cryptosystems that resist quantum computing. We will look at code-based cryptography in general and the...
Show moreAs quantum computers continue to develop, they pose a threat to cryptography since many popular cryptosystems will be rendered vulnerable. This is because the security of most currently used asymmetric systems requires the computational hardness of the integer factorization problem, the discrete logarithm or the elliptic curve discrete logarithm problem. However, there are still some cryptosystems that resist quantum computing. We will look at code-based cryptography in general and the McEliece cryptosystem specifically. Our goal is to understand the structure behind the McEliece scheme, including the encryption and decryption processes, and what some advantages and disadvantages are that the system has to offer. In addition, using the results from Courtois, Finiasz, and Sendrier's paper in 2001, we will discuss a digital signature scheme based on the McEliece cryptosystem. We analyze one classical algebraic attack against the security analysis of the system based on the distinguishing problem whether the public key of the McEliece scheme is generated from a generating matrix of a binary Goppa code or a random binary matrix. The idea of the attack involves solving an algebraic system of equations and we examine the dimension of the solution space of the linearized system of equations. With the assistance from a paper in 2010 by Faugere, Gauthier-Umana, Otmani, Perret, Tillich, we will see the parameters needed for the intractability of the distinguishing problem.
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Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00004535, http://purl.flvc.org/fau/fd/FA00004535
Subject Headings: Coding theory, Combinatorial analysis, Data encryption (Computer science), Data transmission systems -- Security measures, Information theory, McEliece, Robert J. -- Influence, Public key cryptography
Format: Document (PDF)

Title: Elliptic curves: identity-based signing and quantum arithmetic.
Creator: Budhathoki, Parshuram, Steinwandt, Rainer, Eisenbarth, Thomas, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Pairing-friendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identity-based signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identity-based signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In...
Show morePairing-friendly curves and elliptic curves with a trapdoor for the discrete logarithm problem are versatile tools in the design of cryptographic protocols. We show that curves having both properties enable a deterministic identity-based signing with “short” signatures in the random oracle model. At PKC 2003, Choon and Cheon proposed an identity-based signature scheme along with a provable security reduction. We propose a modification of their scheme with several performance benefits. In addition to faster signing, for batch signing the signature size can be reduced, and if multiple signatures for the same identity need to be verified, the verification can be accelerated. Neither the signing nor the verification algorithm rely on the availability of a (pseudo)random generator, and we give a provable security reduction in the random oracle model to the (`-)Strong Diffie-Hellman problem. Implementing the group arithmetic is a cost-critical task when designing quantum circuits for Shor’s algorithm to solve the discrete logarithm problem. We introduce a tool for the automatic generation of addition circuits for ordinary binary elliptic curves, a prominent platform group for digital signatures. Our Python software generates circuit descriptions that, without increasing the number of qubits or T-depth, involve less than 39% of the number of T-gates in the best previous construction. The software also optimizes the (CNOT) depth for F2-linear operations by means of suitable graph colorings.
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Date Issued: 2014
PURL: http://purl.flvc.org/fau/fd/FA00004182, http://purl.flvc.org/fau/fd/FA00004182
Subject Headings: Coding theory, Computer network protocols, Computer networks -- Security measures, Data encryption (Computer science), Mathematical physics, Number theory -- Data processing
Format: Document (PDF)

Title: Empirical likelihood method for segmented linear regression.
Creator: Liu, Zhihua., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: For a segmented regression system with an unknown change-point over two domains of a predictor, a new empirical likelihood ratio test statistic is proposed to test the null hypothesis of no change. The proposed method is a non-parametric method which releases the assumption of the error distribution. Under the null hypothesis of no change, the proposed test statistic is shown empirically Gumbel distributed with robust location and scale parameters under various parameter settings and error...
Show moreFor a segmented regression system with an unknown change-point over two domains of a predictor, a new empirical likelihood ratio test statistic is proposed to test the null hypothesis of no change. The proposed method is a non-parametric method which releases the assumption of the error distribution. Under the null hypothesis of no change, the proposed test statistic is shown empirically Gumbel distributed with robust location and scale parameters under various parameter settings and error distributions. Under the alternative hypothesis with a change-point, the comparisons with two other methods (Chen's SIC method and Muggeo's SEG method) show that the proposed method performs better when the slope change is small. A power analysis is conducted to illustrate the performance of the test. The proposed method is also applied to analyze two real datasets: the plasma osmolality dataset and the gasoline price dataset.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3332719
Subject Headings: Change-point problems, Regression analysis, Econometrics, Limit theory (Probability theory)
Format: Document (PDF)

Title: The enumeration of lattice paths and walks.
Creator: Gao, Shanzhen., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: A well-known long standing problem in combinatorics and statistical mechanics is to find the generating function for self-avoiding walks (SAW) on a two-dimensional lattice, enumerated by perimeter. A SAW is a sequence of moves on a square lattice which does not visit the same point more than once. It has been considered by more than one hundred researchers in the pass one hundred years, including George Polya, Tony Guttmann, Laszlo Lovasz, Donald Knuth, Richard Stanley, Doron Zeilberger,...
Show moreA well-known long standing problem in combinatorics and statistical mechanics is to find the generating function for self-avoiding walks (SAW) on a two-dimensional lattice, enumerated by perimeter. A SAW is a sequence of moves on a square lattice which does not visit the same point more than once. It has been considered by more than one hundred researchers in the pass one hundred years, including George Polya, Tony Guttmann, Laszlo Lovasz, Donald Knuth, Richard Stanley, Doron Zeilberger, Mireille Bousquet-Mlou, Thomas Prellberg, Neal Madras, Gordon Slade, Agnes Dit- tel, E.J. Janse van Rensburg, Harry Kesten, Stuart G. Whittington, Lincoln Chayes, Iwan Jensen, Arthur T. Benjamin, and many others. More than three hundred papers and a few volumes of books were published in this area. A SAW is interesting for simulations because its properties cannot be calculated analytically. Calculating the number of self-avoiding walks is a common computational problem. A recently proposed model called prudent self-avoiding walks (PSAW) was first introduced to the mathematics community in an unpublished manuscript of Pra, who called them exterior walks. A prudent walk is a connected path on square lattice such that, at each step, the extension of that step along its current trajectory will never intersect any previously occupied vertex. A lattice path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. We will discuss some enumerative problems in self-avoiding walks, lattice paths and walks with several step vectors. Many open problems are posted.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3183129
Subject Headings: Combinatorial analysis, Approximation theory, Mathematical statistics, Limit theorems (Probabilty theory)
Format: Document (PDF)

Title: Enumeration of lattice paths using finite operator calculus.
Creator: Humphreys, Katherine L. B., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This dissertation discusses umbral calculus and lattice path enumeration and then continues by explicitly enumerating weighted directed lattice paths staying above a boundary using finite operator calculus. In Part I we discuss the history and representative results of the two topics. We separate umbral calculus into two fields, classical umbral calculus and finite operator calculus, and attempt to correct their intertwined histories. We discuss the beginnings of lattice path enumeration and...
Show moreThis dissertation discusses umbral calculus and lattice path enumeration and then continues by explicitly enumerating weighted directed lattice paths staying above a boundary using finite operator calculus. In Part I we discuss the history and representative results of the two topics. We separate umbral calculus into two fields, classical umbral calculus and finite operator calculus, and attempt to correct their intertwined histories. We discuss the beginnings of lattice path enumeration and survey the types of lattice path enumeration problems and solution methods found in the literature. In Part II, we give necessary conditions of a step set or of its equivalent operator equation such that the path count functions coincide with Sheffer polynomials where the path counts are nonzero. We derive the polynomials from an expansion theorem that includes a polynomial basis and initial conditions. The polynomial basis is derived from a known basic sequence with a transfer formula and a linear operator equation based on the step set. The initial conditions are functionals on the polynomials designed to vanish when evaluated along the boundary line for all but finitely many values. We solve lattice path enumeration problems with four types of boundary conditions and various step sets. We work out general solutions for paths that stay in the first quadrant, paths that stay in the first quadrant and above a line with an integer slope, and paths that can reach the boundary with an additional privileged access step set. We count the number of paths, and in one example we count the paths refined by the number of times they contact the boundary. We explore step sets including a general three-element step set, weighted finite step sets, weighted infinite step sets, and step sets that include paths as steps called pathlets. We research if our methods still give explicit solutions as we complicate and expand the step sets. The example sections include fourteen explicitly worked out problems. Part II of the dissertation includes and extends the three papers on the subject by Humphreys and Niederhausen written between 2000 and 2004.
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Date Issued: 2005
PURL: http://purl.flvc.org/fcla/dt/12165
Subject Headings: Mathematics
Format: Document (PDF)

Title: The existence of minimal logarithmic signatures for classical groups.
Creator: Singhi, Nikhil., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: A logarithmic signature (LS) for a nite group G is an ordered tuple = [A1;A2; : : : ;An] of subsets Ai of G, such that every element g 2 G can be expressed uniquely as a product g = a1a2 : : : ; an, where ai 2 Ai. Logarithmic signatures were dened by Magliveras in the late 1970's for arbitrary nite groups in the context of cryptography. They were also studied for abelian groups by Hajos in the 1930's. The length of an LS is defined to be `() = Pn i=1 jAij. It can be easily seen that for a...
Show moreA logarithmic signature (LS) for a nite group G is an ordered tuple = [A1;A2; : : : ;An] of subsets Ai of G, such that every element g 2 G can be expressed uniquely as a product g = a1a2 : : : ; an, where ai 2 Ai. Logarithmic signatures were dened by Magliveras in the late 1970's for arbitrary nite groups in the context of cryptography. They were also studied for abelian groups by Hajos in the 1930's. The length of an LS is defined to be `() = Pn i=1 jAij. It can be easily seen that for a group G of order Qk j=1 pj mj , the length of any LS for G satises `() Pk j=1mjpj . An LS for which this lower bound is achieved is called a minimal logarithmic signature (MLS). The MLS conjecture states that every finite simple group has an MLS. If the conjecture is true then every finite group will have an MLS. The conjecture was shown to be true by a number of researchers for a few classes of finite simple groups. However, the problem is still wide open. This dissertation addresses the MLS conjecture for the classical simple groups. In particular, it is shown that MLS's exist for the symplectic groups Sp2n(q), the orthogonal groups O 2n(q0) and the corresponding simple groups PSp2n(q) and 2n(q0) for all n 2 N, prime power q and even prime power q0. The existence of an MLS is also shown for all unitary groups GUn(q) for all odd n and q = 2s under the assumption that an MLS exists for GUn 1(q). The methods used are very general and algorithmic in nature and may be useful for studying all nite simple groups of Lie type and possibly also the sporadic groups. The blocks of logarithmic signatures constructed in this dissertation have cyclic structure and provide a sort of cyclic decomposition for these classical groups.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3172943
Subject Headings: Finite groups, Abelian groups, Number theory, Combinatorial group theory, Mathematical recreations, Linear algebraic groups, Lie groups
Format: Document (PDF)

Title: FINANCIAL TIME-SERIES ANALYSIS WITH DEEP NEURAL NETWORKS.
Creator: Rimal, Binod, Hahn, William Edward, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Financial time-series data are noisy, volatile, and nonlinear. The classic statistical linear models may not capture those underlying structures of the data. The rapid advancement in artificial intelligence and machine learning techniques, availability of large-scale data, and increased computational capabilities of a machine opens the door to developing sophisticated deep learning models to capture the nonlinearity and hidden information in the data. Creating a robust model by unlocking the...
Show moreFinancial time-series data are noisy, volatile, and nonlinear. The classic statistical linear models may not capture those underlying structures of the data. The rapid advancement in artificial intelligence and machine learning techniques, availability of large-scale data, and increased computational capabilities of a machine opens the door to developing sophisticated deep learning models to capture the nonlinearity and hidden information in the data. Creating a robust model by unlocking the power of a deep neural network and using real-time data is essential in this tech era. This study constructs a new computational framework to uncover the information in the financial time-series data and better inform the related parties. It carries out the comparative analysis of the performance of the deep learning models on stock price prediction with a well-balanced set of factors from fundamental data, macroeconomic data, and technical indicators responsible for stock price movement. We further build a novel computational framework through a merger of recurrent neural networks and random compression for the time-series analysis. The performance of the model is tested on a benchmark anomaly time-series dataset. This new computational framework in a compressed paradigm leads to improved computational efficiency and data privacy. Finally, this study develops a custom trading simulator and an agent-based hybrid model by combining gradient and gradient-free optimization methods. In particular, we explore the use of simulated annealing with stochastic gradient descent. The model trains a population of agents to predict appropriate trading behaviors such as buy, hold, or sell by optimizing the portfolio returns. Experimental results on S&P 500 index show that the proposed model outperforms the baseline models.
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Date Issued: 2022
PURL: http://purl.flvc.org/fau/fd/FA00014009
Subject Headings: Neural networks (Computer science), Deep learning (Machine learning), Time-series analysis, Stocks, Simulated annealing (Mathematics)
Format: Document (PDF)

Title: FORMATION, EVOLUTION, AND BREAKDOWN OF INVARIANT TORI IN DISSIPATIVE SYSTEMS: FROM VISUALIZATION TO COMPUTER ASSISTED PROOFS.
Creator: Fleurantin, Emmanuel, Mireles-James, Jason, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: The goal of this work is to study smooth invariant sets using high order approximation schemes. Whenever possible, existence of invariant sets are established using computer-assisted proofs. This provides a new set of tools for mathematically rigorous analysis of the invariant objects. The dissertation focuses on application of these tools to a family of three dimensional dissipative vector fields, derived from the normal form of a cusp-Hopf bifurcation. The vector field displays a Neimark...
Show moreThe goal of this work is to study smooth invariant sets using high order approximation schemes. Whenever possible, existence of invariant sets are established using computer-assisted proofs. This provides a new set of tools for mathematically rigorous analysis of the invariant objects. The dissertation focuses on application of these tools to a family of three dimensional dissipative vector fields, derived from the normal form of a cusp-Hopf bifurcation. The vector field displays a Neimark-Sacker bifurcation giving rise to an attracting invariant torus. We examine the torus via parameter continuation from its appearance to its breakdown, scrutinizing its dynamics between these events. We also study the embeddings of the stable/unstable manifolds of the hyperbolic equilibrium solutions over this parameter range. We focus on the role of the invariant manifolds as transport barriers and their participation in global bifurcations. We then study the existence and regularity properties for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations and lay out a constructive method of computer assisted proof which pertains to explicit problems in non-perturbative regimes. We get verifiable lower bounds on the regularity of the attractor in terms of the ratio of the expansion rate on the torus with the contraction rate near the torus. We look at two important cases of rotational and resonant tori. Finally, we study the related problem of approximating two dimensional subcenter manifolds of conservative systems. As an application, we compare two methods for computing the Taylor series expansion of the graph of the subcenter manifold near a saddle-center equilibrium solution of a Hamiltonian system.
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Date Issued: 2021
PURL: http://purl.flvc.org/fau/fd/FA00013812
Subject Headings: Invariants, Manifolds (Mathematics), Dynamical systems
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: 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)

Title: General monotonicity, interpolation of operators, and applications.
Creator: Grigoriev, Stepan M., Sagher, Yoram, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Assume that {φn} is an orthonormal uniformly bounded (ONB) sequence of complex-valued functions de ned on a measure space (Ω,Σ,µ), and f ∈ L1(Ω,Σ,µ). Let be the Fourier coefficients of f with respect to {φn} . R.E.A.C. Paley proved a theorem connecting the Lp-norm of f with a related norm of the sequence {cn}. Hardy and Littlewood subsequently proved that Paley’s result is best possible within its context. Their results were generalized by Dikarev, Macaev, Askey, Wainger, Sagher, and later by...
Show moreAssume that {φn} is an orthonormal uniformly bounded (ONB) sequence of complex-valued functions de ned on a measure space (Ω,Σ,µ), and f ∈ L1(Ω,Σ,µ). Let be the Fourier coefficients of f with respect to {φn} . R.E.A.C. Paley proved a theorem connecting the Lp-norm of f with a related norm of the sequence {cn}. Hardy and Littlewood subsequently proved that Paley’s result is best possible within its context. Their results were generalized by Dikarev, Macaev, Askey, Wainger, Sagher, and later by Tikhonov, Li yand, Booton and others.The present work continues the generalization of these results.
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Date Issued: 2014
PURL: http://purl.flvc.org/fau/fd/FA00004290, http://purl.flvc.org/fau/fd/FA00004290
Subject Headings: Combinatorial optimization, Differential dynamical systems, Functions of complex variables, Inequalities (Mathematics), Nonsmooth optimization
Format: Document (PDF)

Title: Graph labeling and non-separating trees.
Creator: Gottipati, Chenchu B., Locke, Stephen C., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This dissertation studies two independent problems, one is about graph labeling and the other problem is related to connectivity condition in a simple graph. Graph labeling is a rapidly developing area of research in graph theory, having connections with a variety of application-oriented areas such as VLSI optimization, data structures and data representation. Furthermore, the connectivity conditions in a simple graphs may help us to study the new aspects of ad hoc networks, social networks...
Show moreThis dissertation studies two independent problems, one is about graph labeling and the other problem is related to connectivity condition in a simple graph. Graph labeling is a rapidly developing area of research in graph theory, having connections with a variety of application-oriented areas such as VLSI optimization, data structures and data representation. Furthermore, the connectivity conditions in a simple graphs may help us to study the new aspects of ad hoc networks, social networks and web graphs. In chapter 2, we study path systems, reduced path systems and how to construct a super edge-graceful tree with any number of edges using path systems. First, we give an algorithm to reduce a labeled path system to a smaller labeled path system of a different type. First, we investigate the cases (m, k) = (3; 5) and (m, k) = (4; 7), where m is the number of paths and 2k is the length of each path, and then we give a generalization for any k, m = 3 and m = 4. We also describe a procedure to construct a super-edge-graceful tree with any number of edges.
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Date Issued: 2014
PURL: http://purl.flvc.org/fau/fd/FA00004289, http://purl.flvc.org/fau/fd/FA00004289
Subject Headings: Computational complexity, Computer graphics, Graph theory, Integrated circuits -- Very large scale integration, Mathematical optimization
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: H-LOCAL RINGS.
Creator: Omairi, Akeel, Klingler, Lee, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: We say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a _nite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains and in a 2011 paper Ay and Klingler obtain similar results for Noetherian reduced rings. We characterize the UDI property for Noetherian...
Show moreWe say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a _nite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains and in a 2011 paper Ay and Klingler obtain similar results for Noetherian reduced rings. We characterize the UDI property for Noetherian rings in general.
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Date Issued: 2019
PURL: http://purl.flvc.org/fau/fd/FA00013336
Subject Headings: Noetherian rings, Prüfer rings, Local rings
Format: Document (PDF)

Title: Higher order commutators in the method of orbits.
Creator: Kasprikova, Eva., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Benson spaces of higher order are introduced extending the idea of N. Krugljak and M. Milman, A distance between orbits that controls commutator estimates and invertibilty of operators, Advances in Mathematics 182 (2004), 78-123. The concept of Benson shift operators is introduced and a class of spaces equipped with these operators is considered. Commutator theorems of higher order on orbit spaces generated by a single element are proved for this class. It is shown that these results apply to...
Show moreBenson spaces of higher order are introduced extending the idea of N. Krugljak and M. Milman, A distance between orbits that controls commutator estimates and invertibilty of operators, Advances in Mathematics 182 (2004), 78-123. The concept of Benson shift operators is introduced and a class of spaces equipped with these operators is considered. Commutator theorems of higher order on orbit spaces generated by a single element are proved for this class. It is shown that these results apply to the complex method of interpolation and to the real method of interpolation for the case q=1. Two new characterizations are presented of the domain space of the "derivation" operator in the context of orbital methods. Comparisons to the work of others are made, especially the unifying paper of M. Cwikel, N. Kalton, M. Milman and R. Rochberg, A United Theory of Commutator Estimates for a Class of Interpolation Methods, Advances in Mathematics 169 2002, 241-312.
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/2684304
Subject Headings: Operator theory, Interpolation spaces, Finite groups, Sporadic groups (Mathematics)
Format: Document (PDF)

Title: HOMOCLINIC DYNAMICS IN A SPATIAL RESTRICTED FOUR BODY PROBLEM.
Creator: Murray, Maxime, James, Jason Mireles, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: The set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four body problem admits certain simple homoclinic orbits which form the skeleton of the complete homoclinic intersection, or homoclinic web. In this thesis, the planar restricted four body problem is viewed as an invariant subsystem of the spatial problem, and the influence of this planar homoclinic skeleton on the spatial dynamics is studied from a numerical point of view....
Show moreThe set of transverse homoclinic intersections for a saddle-focus equilibrium in the planar equilateral restricted four body problem admits certain simple homoclinic orbits which form the skeleton of the complete homoclinic intersection, or homoclinic web. In this thesis, the planar restricted four body problem is viewed as an invariant subsystem of the spatial problem, and the influence of this planar homoclinic skeleton on the spatial dynamics is studied from a numerical point of view. Starting from the vertical Lyapunov families emanating from saddle focus equilibria, we compute the stable/unstable manifolds of these spatial periodic orbits and look for intersections between these manifolds near the fundamental planar homoclinics. In this way, we are able to continue all of the basic planar homoclinic motions into the spatial problem as homoclinics for appropriate vertical Lyapunov orbits which, by the Smale Tangle theorem, suggest the existence of chaotic motions in the spatial problem. While the saddle-focus equilibrium solutions in the planar problems occur only at a discrete set of energy levels, the cycle-to-cycle homoclinics in the spatial problem are robust with respect to small changes in energy. The method uses high order Fourier-Taylor and Chebyshev series approximations in conjunction with the parameterization method, a general functional analytic framework for invariant manifolds. Tools that admit a natural notion of a-posteriori error analysis. Finally, we develop and implement a validation algorithm which we later use to obtain Theorems confirming the existence of homoclinic dynamics. This approach, known as the Radii polynomial, is a contraction mapping argument which can be applied to both the parameterized manifold and the Chebyshev arcs. When the Theorem applies, it guarantees the existence of a true solution near the approximation and it provides an upper bound on the C0 norm of the truncation error.
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Date Issued: 2021
PURL: http://purl.flvc.org/fau/fd/FA00013758
Subject Headings: Boundary value problems, Invariant manifolds, Applied mathematics
Format: Document (PDF)

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