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Pages
 Title
 Detailed study of "polynomial structures in order statistics distributions".
 Creator
 Liu, ChihFan, 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 AbelGontcharoff 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 AbelGontcharoff 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.
Show less  Date Issued
 2004
 PURL
 http://purl.flvc.org/fcla/dt/13116
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 Decay for timedependent 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 moreShow less  Date Issued
 1996
 PURL
 http://purl.flvc.org/fcla/dt/12463
 Subject Headings
 Mathematics
 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 threeelement 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.
Show less  Date Issued
 2005
 PURL
 http://purl.flvc.org/fcla/dt/12165
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 On Boolean algebras and their role in analysis.
 Creator
 WinkowskaNowak, 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 (sigmacomplete) homomorphisms and full (sigmacomplete) 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 (sigmacomplete) homomorphisms and full (sigmacomplete) 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.
Show less  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'NanScott 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'NanScott 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.
Show less  Date Issued
 1996
 PURL
 http://purl.flvc.org/fcla/dt/15289
 Subject Headings
 Mathematics
 Format
 Document (PDF)
 Title
 SPACES OF MINIMAL PRIME ELEMENTS OF ALGEBRAIC FRAMES WITHOUT FIP.
 Creator
 Madinya, Albert Anthony, Bhattacharjee, Papiya, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
 Abstract/Description

The following dissertation investigates algebraic frames and their spaces of minimal prime elements with respect to the HullKernel topology and Inverse topology. Much work by other authors has been done in obtaining internal characterizations in frametheoretic terms for when these spaces satisfy certain topological properties, but most of what is done is under the auspices of the finite intersection property. In the first half of this dissertation, we shall add to the literature more...
Show moreThe following dissertation investigates algebraic frames and their spaces of minimal prime elements with respect to the HullKernel topology and Inverse topology. Much work by other authors has been done in obtaining internal characterizations in frametheoretic terms for when these spaces satisfy certain topological properties, but most of what is done is under the auspices of the finite intersection property. In the first half of this dissertation, we shall add to the literature more characterizations in this context, and in the second half we will study general algebraic frames and investigate which, if any, of the known theorems generalize to algebraic frames not necessarily with the FIP. Throughout this investigative journey, we have found that certain ideals and filters of algebraic frames play a pivotal role in determining internal characterizations of the algebraic frames for when interesting topological properties occur in its space of minimal prime elements. In this dissertation, we investigate completely prime filters and compactly generated filters on algebraic frames. We introduce a new concept of subcompact elements and subcompactly generated filters. One of our main results is that the inverse topology on the space of minimal prime elements is compact if and only if every maximal subcompactly generated filter is completely prime. Furthermore, when the space of minimal prime elements is compact, then each minimal prime has what we are calling the compact absoluteness property.
Show less  Date Issued
 2024
 PURL
 http://purl.flvc.org/fau/fd/FA00014410
 Subject Headings
 Mathematics, Applied mathematics
 Format
 Document (PDF)
 Title
 SYSTEMS OF DIFFERENCE EQUATIONS IN ECONOMIC THEORY.
 Creator
 WONNACOTT, LARRY RUSSELL., Florida Atlantic University, Stronge, William B., College of Business, Department of Economics
 Abstract/Description

This study demonstrates the importance of dynamic economic analysis, the role played by difference equations in such analysis and the properties of systems of difference equations. This is accomplished by proving the significance of dynamics in general and difference equations in particular using the Cobweb model and the "correspondence principle". The properties of systems of linear, first order difference equations are discussed in detail and it is shown that a system of any order can be...
Show moreThis study demonstrates the importance of dynamic economic analysis, the role played by difference equations in such analysis and the properties of systems of difference equations. This is accomplished by proving the significance of dynamics in general and difference equations in particular using the Cobweb model and the "correspondence principle". The properties of systems of linear, first order difference equations are discussed in detail and it is shown that a system of any order can be reduced to first order so that the discussion is completely general. The properties included in this analysis ore the traverse, impact, delayed, cumulative and long run multipliers, and stability of a linear system. A simple Keynesian model of income determination is estimated and simulated by the computer to facilitate observation of these properties.
Show less  Date Issued
 1972
 PURL
 http://purl.flvc.org/fcla/dt/13521
 Subject Headings
 Economics, Mathematical
 Format
 Document (PDF)
 Title
 Bijections for partition identities.
 Creator
 Lai, JinMei 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 sieveequivalent 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 sieveequivalent 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.
Show less  Date Issued
 1992
 PURL
 http://purl.flvc.org/fau/fd/FADT14826
 Subject Headings
 Algorithms, Partitions (Mathematics), Sieves (Mathematics)
 Format
 Document (PDF)
 Title
 ON SPECTRAL SYSTEMS.
 Creator
 DEMSKY, SCOTT HARVEY., Florida Atlantic University
 Abstract/Description

In this thesis, we present a detailed study of the theory of spectral sequences, based on the notion of a spectral system. We present the general theory of spectral systems and the associated spectral sequences. We also present a complete discussion of the two particular situations most frequently encountered in applications, namely regular spectral systems and the spectral systems associated with double complexes.
 Date Issued
 1976
 PURL
 http://purl.flvc.org/fcla/dt/13751
 Subject Headings
 Spectral sequences (Mathematics), Sequences (Mathematics)
 Format
 Document (PDF)
 Title
 Modeling simple epidemics.
 Creator
 Segovia, Linda., Harriet L. Wilkes Honors College
 Abstract/Description

Epidemic models help us predict the outcome of an epidemic. I will discuss and compare two simple epidemic models: a deterministic model implemented by a simple differential equation, and a stochastic model, which is more realistic, but harder to analyze. In both models we assume, for simplicity, that each individual goes through only two stages: healthy (susceptible) and sick (infective). Such models, called SI epidemic models, describe infections with no immunity. We will show that, when...
Show moreEpidemic models help us predict the outcome of an epidemic. I will discuss and compare two simple epidemic models: a deterministic model implemented by a simple differential equation, and a stochastic model, which is more realistic, but harder to analyze. In both models we assume, for simplicity, that each individual goes through only two stages: healthy (susceptible) and sick (infective). Such models, called SI epidemic models, describe infections with no immunity. We will show that, when the population gets large, the more realistic stochastic model approaches the simple deterministic model on the average, which will allow us to see that the deterministic model is used for a good reason.
Show less  Date Issued
 2007
 PURL
 http://purl.flvc.org/FAU/40972
 Subject Headings
 Biomathematics, Medicine, Mathematics, Population biology, Mathematics, Epidemiology, Mathematical models
 Format
 Document (PDF)
 Title
 Cladistic analysis of juvenile and adult hominoid cranial shape variables.
 Creator
 DiVito, Thomas A. II, Dorothy F. Schmidt College of Arts and Letters, Department of Anthropology
 Abstract/Description

Phylogenies constructed from skeletal data often contradict those built from genetic data. This study evaluates the phylogenetic utility of adult male, female, and juvenile hominoid cranial bones. First, I used geometric morphometric methods to compare the cranial bone shapes of seven primate genera (Gorilla, Homo, Hylobates, Macaca, Nomascus, Pan, and Pongo). I then coded these shapes as continuous characters and constructed cladograms via parsimony analysis for the adult male, female, and...
Show morePhylogenies constructed from skeletal data often contradict those built from genetic data. This study evaluates the phylogenetic utility of adult male, female, and juvenile hominoid cranial bones. First, I used geometric morphometric methods to compare the cranial bone shapes of seven primate genera (Gorilla, Homo, Hylobates, Macaca, Nomascus, Pan, and Pongo). I then coded these shapes as continuous characters and constructed cladograms via parsimony analysis for the adult male, female, and juvenile character matrices. Finally, I evaluated the similarity of these cladograms to one another and to the genetic phylogeny using topological distance software. Cladograms did not differ from one another or the genetic phylogeny less than comparisons of randomly generated trees. These results suggest that cranial shapes are unlikely to provide accurate phylogenetic information, and agree with other analyses of skeletal data that fail to recover the molecular phylogeny (Collard & Wood, 2000, 2001; Springer et al., 2007).
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3175013
 Subject Headings
 Cladistic analysis, Mathematics, Morphology, Mathematics, Hominids, Evolution, Evolutionary genetics, Mathematics
 Format
 Document (PDF)
 Title
 Gravitational signature of corecollapse supernova results of CHIMERA simulations.
 Creator
 Yakunin, Konstantin., Charles E. Schmidt College of Science, Department of Physics
 Abstract/Description

Corecollapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of...
Show moreCorecollapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of the prime sources of gravitational waves for interferometric detectors. Gravitational waves can give us access to the electromagnetically hidden compact inner core of supernovae. They will provide valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. Detection of GW signals and analysis of the observations will require realistic signal predi ctions from the nonparameterized relativistic numerical simulations of CCSN. This dissertation presents the gravitational wave signature of corecollapse v supernovae. Previous studies have considered either parametric models or nonexploding models of CCSN. This work presents complete waveforms, through the explosion phase, based on firstprinciples models for the first time. We performed 2D simulations of CCSN using the CHIMERA code for 12, 15, and 25M nonrotating progenitors. CHIMERA incorporates most of the criteria for realistic corecollapse modeling, such as multifrequency neutrino transport coupled with relativistic hydrodynamics, eective GR potential, nuclear reaction network, and an industrystandard equation of state., Based on the results of our simulations, I produced the most realistic gravitational waveforms including all postbounce phases of corecollapse supernovae: the prompt convection, the stationary accretion shock instability, and the corresponding explosion. Additionally, the tracer particles applied in the analysis of the GW signal reveal the origin of lowfrequency component in the prompt part of gravitational waveform. Analysis of detectability of the GW signature from a Galactic event shows that the signal is within the bandpass of current and future GW observatories such as AdvLIGO, advanced Virgo, and LCGT.
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3322512
 Subject Headings
 Mathematical physics, Continuum mechanics, Supernovae, Mathematical models
 Format
 Document (PDF)
 Title
 Structured flows on manifolds: distributed functional architectures.
 Creator
 Pillai, Ajay S., Florida Atlantic University, Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
 Abstract/Description

Despite the highdimensional nature of the nervous system, humans produce lowdimensional cognitive and behavioral dynamics. How highdimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a...
Show moreDespite the highdimensional nature of the nervous system, humans produce lowdimensional cognitive and behavioral dynamics. How highdimensional networks with complex connectivity give rise to functionally meaningful dynamics is not well understood. How does a neural network encode function? How can functional dynamics be systematically obtained from networks? There exist few frameworks in the current literature that answer these questions satisfactorily. In this dissertation I propose a general theoretical framework entitled 'Structured Flows on Manifolds' and its underlying mathematical basis. The framework is based on the principles of nonlinear dynamical systems and Synergetics and can be used to understand how highdimensional systems that exhibit multiple timescale behavior can produce lowdimensional dynamics. Lowdimensional functional dynamics arises as a result of the timescale separation of the systems component's dynamics. The lowdimensional space in which the functi onal dynamics occurs is regarded as a manifold onto which the entire systems dynamics collapses. For the duration of the function the system will stay on the manifold and evolve along the manifold. From a network perspective the manifold is viewed as the product of the interactions of the network nodes. The subsequent flows on the manifold are a result of the asymmetries of network's interactions. A distributed functional architecture based on this perspective is presented. Within this distributed functional architecture, issues related to networks such as flexibility, redundancy and robustness of the network's dynamics are addressed. Flexibility in networks is demonstrated by showing how the same network can produce different types of dynamics as a function of the asymmetrical coupling between nodes. Redundancy can be achieved by systematically creating different networks that exhibit the same dynamics. The framework is also used to systematically probe the effects of lesion, (removal of nodes) on network dynamics. It is also shown how lowdimensional functional dynamics can be obtained from firingrate neuron models by placing biologically realistic constraints on the coupling. Finally the theoretical framework is applied to real data. Using the structured flows on manifolds approach we quantify team performance and team coordination and develop objective measures of team performance based on skill level.
Show less  Date Issued
 2008
 PURL
 http://purl.flvc.org/FAU/77649
 Subject Headings
 Manifolds (Mathematics), Differentiable dynamical systems, Mathematical physics
 Format
 Document (PDF)
 Title
 THE EFFECT OF THE INDIVIDUALIZED MANPOWER TRAINING SYSTEM INSTRUCTION PROGRAM IN BASIC MATH SKILLS ON THE ACHIEVEMENT LEVEL AND DROPOUT AND FAILURE RATE OF MATHEMATICS OF BUSINESS STUDENTS AT DAYTONA BEACH COMMUNITY COLLEGE (FLORIDA).
 Creator
 MILLER, KATHLEEN NOBLE., Florida Atlantic University
 Abstract/Description

The purpose of this study was to determine if requiring business mathematics students at Daytona Beach Community College (DBCC) to participate in a remedial mathematics program would increase their achievement level and decrease the failure and dropout rate. The 80 students enrolled in business mathematics who scored at the 9.9 grade level or below on the Test of Adult Basic Education (TABE), math fundamentals section, adapted from the California Achievement Test, 1967 edition, participated...
Show moreThe purpose of this study was to determine if requiring business mathematics students at Daytona Beach Community College (DBCC) to participate in a remedial mathematics program would increase their achievement level and decrease the failure and dropout rate. The 80 students enrolled in business mathematics who scored at the 9.9 grade level or below on the Test of Adult Basic Education (TABE), math fundamentals section, adapted from the California Achievement Test, 1967 edition, participated in the experiment. A posttest only control group design with randomization was developed. The 80 students were randomly divided into two groups. The treatment group participated in the Individualized Manpower Training System (IMTS) remedial program; the control group did not. Three achievement tests were developed, validated and administered to the students in both groups. The Finn Multivariate statistical program for multivariate analysis of variance (manova) and the SPSS statistical program for oneway analysis of variance (anova) were used to determine if no significant difference existed at the 0.05 level between the achievement levels of students who receive remedial instruction and those who did not. The scores from the three achievement tests were analyzed. The results of the manova and anova procedures indicated that the achievement level of the treatment group was significantly higher than the achievement level of the control group, and that the effects of the three achievement tests within each group were interacting. The SPSS program for chi square was used to determine if there were no significant differences between the number of students in the treatment group and control group who passed, failed or dropped the course. The computed chi square was not significant at the 0.05 level. Thus, no significant differences existed between the number of students in the treatment and control group who passed, failed or dropped the course. The conclusions drawn from the findings include: (1) Requiring business mathematics students at DBCC to participate in the IMTS diagnostic/prescriptive remedial program in business mathematics skills will raise their achievement level. (2) The IMTS remedial program in basic mathematics skills is not likely to significantly reduce the failure or dropout rate of business mathematics students at DBCC.
Show less  Date Issued
 1983
 PURL
 http://purl.flvc.org/fcla/dt/11843
 Subject Headings
 MathematicsRemedial teaching, Business mathematics
 Format
 Document (PDF)
 Title
 ON THE EXACT SEQUENCE OF TERMS OF LOW DEGREE IN A SPECTRAL SYSTEM.
 Creator
 MILLER, KATHLEEN SHOVAN, Florida Atlantic University
 Abstract/Description

On this thesis, we present a detailed study of the exact sequence of terms of low degree, which obtains when the spectral systems being considered are suitably restricted. Its validity is established under more general conditions than could be found in the literature on spectral sequences.
 Date Issued
 1977
 PURL
 http://purl.flvc.org/fcla/dt/13889
 Subject Headings
 Spectral sequences (Mathematics), Spectral theory (Mathematics)
 Format
 Document (PDF)
 Title
 Tiling Z with Triples Using Signed Permutation Matrices.
 Creator
 Cattell, Liam J., Meyerowitz, Aaron, Florida Atlantic University
 Abstract/Description

The topic of this paper is tiling the integers with triples, or more precisely to write Z as a disjoint union of translates of a given set of 3subsets composed of basic shapes called prototiles. We fix the set of proto tiles P = { { 0, a, a+ v} , { U. b, a+ b}} and define an algorithm which returns a sequence of translates of P when given an initial subset of Z representing integers that are already tiled. This algorithm is then adapted to describe all possible tilings with triples from P...
Show moreThe topic of this paper is tiling the integers with triples, or more precisely to write Z as a disjoint union of translates of a given set of 3subsets composed of basic shapes called prototiles. We fix the set of proto tiles P = { { 0, a, a+ v} , { U. b, a+ b}} and define an algorithm which returns a sequence of translates of P when given an initial subset of Z representing integers that are already tiled. This algorithm is then adapted to describe all possible tilings with triples from P using the action of certain signed permutation matrices on a subset of za+b , uamdy the 2" Yectors with all entries ±1. Given b > 2a, we research properties of the digraph of all possible tiling states and some related digraphs.
Show less  Date Issued
 2007
 PURL
 http://purl.flvc.org/fau/fd/FA00000732
 Subject Headings
 Tiling (Mathematics), Sequences (Mathematics), Permutation groups
 Format
 Document (PDF)
 Title
 SELECTED TOPICS IN QUANTUM AND POSTQUANTUM CRYPTOGRAPHY.
 Creator
 Johnson, Floyd, Bai, Shi, Steinwandt, Rainer, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
 Abstract/Description

In 1994 when Peter Shor released his namesake algorithm for factoring and solving the discrete logarithm problem he changed cryptography forever. Many of the stateoftheart cryptosystems for internet and other computerized communications will become obsolete with the advent of quantum computers. Two distinct approaches have grown to avoid the downfall of secure communication: quantum cryptography which is based in physics and information theory, and postquantum cryptography which uses...
Show moreIn 1994 when Peter Shor released his namesake algorithm for factoring and solving the discrete logarithm problem he changed cryptography forever. Many of the stateoftheart cryptosystems for internet and other computerized communications will become obsolete with the advent of quantum computers. Two distinct approaches have grown to avoid the downfall of secure communication: quantum cryptography which is based in physics and information theory, and postquantum cryptography which uses mathematical foundations believed not to be weak against even quantum assisted adversaries. This thesis is the culmination of several studies involving cryptanalysis of schemes in both the quantum and postquantum paradigms as well as mathematically founded constructions in the postquantum regime. The first two chapters of this thesis on background information are intended for the reader to more fully grasp the later chapters. The third chapter shows an attack and ultimate futility of a variety of related quantum authentication schemes. The fourth chapter shows a parametric improvement over other stateoftheart schemes in lattice based cryptography by utilizing a different cryptographic primitive. The fifth chapter proposes an attack on specific parameters of a specific latticebased cryptographic primitive. Finally, chapter six presents a construction for a fully homomorphic encryption scheme adapted to allow for privacy enhanced machine learning.
Show less  Date Issued
 2022
 PURL
 http://purl.flvc.org/fau/fd/FA00014088
 Subject Headings
 Quantum cryptography, Cryptography, Homomorphisms (Mathematics), Lattices (Mathematics)
 Format
 Document (PDF)
 Title
 Reduced path systems and superedgegraceful trees.
 Creator
 Gottipati, Chenchu B., Locke, Stephen C., Graduate College
 Date Issued
 20130412
 PURL
 http://purl.flvc.org/fcla/dt/3361301
 Subject Headings
 Mathematics, Path analysis
 Format
 Document (PDF)
 Title
 ALTERNATIVE INCOME SPECIFICATION IN MACROECONOMIC MODELS.
 Creator
 MELEAR, ERIK LAMONT., Florida Atlantic University, Hemley, David D., College of Business, Department of Economics
 Abstract/Description

This thesis emphasizes and evaluates the effect of different income specifications, absolute, relative and permanent, in the various stochastic equations comprising a macroeconomic model. Multiple least squares regression is employed to estimate the stochastic equations; and a dynamic multiplier simulation program evaluates the stability and calculates the impact and interim dynamic multipliers of each resultant model. The results point to an absolute income specification with the quickest...
Show moreThis thesis emphasizes and evaluates the effect of different income specifications, absolute, relative and permanent, in the various stochastic equations comprising a macroeconomic model. Multiple least squares regression is employed to estimate the stochastic equations; and a dynamic multiplier simulation program evaluates the stability and calculates the impact and interim dynamic multipliers of each resultant model. The results point to an absolute income specification with the quickest response to fiscal and monetary policy. In addition, there are inherent specification problems as enlightened by review of the size of the total impact multipliers.
Show less  Date Issued
 1975
 PURL
 http://purl.flvc.org/fcla/dt/13736
 Subject Headings
 IncomeMathematical models
 Format
 Document (PDF)
 Title
 A COMPARATIVE STUDY OF AN AUDIOTUTORIAL AND A TRADITIONAL METHOD OF TEACHING INTERMEDIATE COLLEGE ALGEBRA TO THE COMMUNITY COLLEGE STUDENTS.
 Creator
 CHINN, JAMES ALBERT, Florida Atlantic University, College of Education, Department of Curriculum, Culture, and Educational Inquiry
 Abstract/Description

The problem of this experiment was to test and compare the effects of an audiotutorial method and a traditional lecture method of instruction of Intermediate College Algebra at Broward Community College, and to determine how the commerciallyprepared and teachermade audiotutorial materials should be revised or altered for the improvement of the instruction of Intermediate College Algebra. The null hypotheses were based on the assumption that if significant initial differences in...
Show moreThe problem of this experiment was to test and compare the effects of an audiotutorial method and a traditional lecture method of instruction of Intermediate College Algebra at Broward Community College, and to determine how the commerciallyprepared and teachermade audiotutorial materials should be revised or altered for the improvement of the instruction of Intermediate College Algebra. The null hypotheses were based on the assumption that if significant initial differences in intellectual aptitude as measured by the Otis Mental Abilities Test, Form Am, existed between the groups, these differences would be adjusted with an Otis covariate. The Otis analysis revealed no significant differences, at the .05 level, between groups in mental ability. The seven null hypotheses were tested, as a part of the overall analysis of the study. The interpretation of analysis results lead to the rejection at the .05 level of the first hypothesis. (There is no significant difference in the mathematics achievement of the audiotutorial and traditionally taught students.) The other hypotheses, two through seven, were accepted. As a result of the rejection of only the first hypothesis and an investigation of the linear trends of the pre and posttest results it was concluded that the audiotutorial instructional method was superior, under the defined parameters, to the traditional method. It was concluded from the results of the attitude questionnaire that the audiotutorial instructional approach had a positive effect on the students' attitude toward the course.
Show less  Date Issued
 1973
 PURL
 http://purl.flvc.org/fcla/dt/11625
 Subject Headings
 Mathematics, Education, General
 Format
 Document (PDF)