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SPACES OF MINIMAL PRIME ELEMENTS OF ALGEBRAIC FRAMES WITHOUT FIP
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 Hull-Kernel topology and Inverse topology. Much work by other authors has been done in obtaining internal characterizations in frame-theoretic 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 Hull-Kernel topology and Inverse topology. Much work by other authors has been done in obtaining internal characterizations in frame-theoretic 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.
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Date Issued
2024
PURL
http://purl.flvc.org/fau/fd/FA00014410
Subject Headings
Mathematics, Applied mathematics
Format
Document (PDF)
HOMOCLINIC DYNAMICS IN A SPATIAL RESTRICTED FOUR BODY PROBLEM
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)
LATTICE SIGNATURES BASED ON MODULE-NTRU
Title
LATTICE SIGNATURES BASED ON MODULE-NTRU.
Creator
Kottal, Sulani Thakshila Baddhe Vidhanalage, Bai, Shi, Karabina, Koray, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description
Euclidean lattices have attracted considerable research interest as they can be used to construct efficient cryptographic schemes that are believed to be quantum-resistant. The NTRU problem, introduced by J. Hoffstein, J. Pipher, and J. H. Silverman in 1996 [16], serves as an important average-case computational problem in lattice-based cryptography. Following their pioneer work, the NTRU assumption and its variants have been used widely in modern cryptographic constructions such as...
Show moreEuclidean lattices have attracted considerable research interest as they can be used to construct efficient cryptographic schemes that are believed to be quantum-resistant. The NTRU problem, introduced by J. Hoffstein, J. Pipher, and J. H. Silverman in 1996 [16], serves as an important average-case computational problem in lattice-based cryptography. Following their pioneer work, the NTRU assumption and its variants have been used widely in modern cryptographic constructions such as encryption, signature, etc. Let Rq = Zq[x]/ (xn + 1) be a quotient polynomial ring. The standard NTRU problem asks to recover short polynomials f, g E Rq such that h - g/ f (mod q), given a public key h and the promise that such elements exist. In practice, the degree n is often a power of two. As a generalization of NTRU, the Module-NTRU problems were introduced by Cheon, Kim, Kim, and Son (IACR ePrint 2019/1468), and Chuengsatiansup, Prest, Stehle, Wallet, and Xagawa (ASIACCS '20). In this thesis, we presented two post-quantum Digital Signature Schemes based on the Module-NTRU problem and its variants.
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Date Issued
2024
PURL
http://purl.flvc.org/fau/fd/FA00014407
Subject Headings
Lattice theory, Cryptography, Public key cryptography, Applied mathematics
Format
Document (PDF)
Science fiction girlfriends transgender politics and US science fiction television, 1990–present
Title
Science fiction girlfriends transgender politics and US science fiction television, 1990–present.
Creator
Cava, Peter, Scodari, Christine, Florida Atlantic University, Dorothy F. Schmidt College of Arts and Letters, School of Communication and Multimedia Studies
Abstract/Description
The 1990s ushered in what historian Susan Stryker describes as “a tremendous burst of new transgender activism” in the United States. Concomitantly, the success of Star Trek: The Next Generation led to a renaissance of US science fiction television. This dissertation asks, what is the relation between transgender (trans) politics and US science fiction (sf) television from 1990 to the present? The theoretical framework is Trans/Elemental feminism, a new paradigm developed in the dissertation....
Show moreThe 1990s ushered in what historian Susan Stryker describes as “a tremendous burst of new transgender activism” in the United States. Concomitantly, the success of Star Trek: The Next Generation led to a renaissance of US science fiction television. This dissertation asks, what is the relation between transgender (trans) politics and US science fiction (sf) television from 1990 to the present? The theoretical framework is Trans/Elemental feminism, a new paradigm developed in the dissertation. The method is multiperspectival cultural studies, which considers how the production, content, and reception of media texts and their metatexts collectively determine the texts’ meaning. The data include trade articles about the television industry; published interviews with producers; 3,175 hours of televisual content; commercial advertisements for television programs; films, novels, and webisodes (Web episodes) in selected media franchises; professional reviews; online discussion boards; fan fiction; and fan videos.
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Date Issued
2015
PURL
http://purl.flvc.org/fau/fd/FA00004435, http://purl.flvc.org/fau/fd/FA00004435
Subject Headings
Computer science., Computers., Artificial intelligence., Applied mathematics., Engineering mathematics., Statistical physics., Dynamical systems., Vibration., Dynamics., Computer Science.
Format
Document (PDF)
Low Cost Robotic Car as a Way to Teach Mathematics
Title
Low Cost Robotic Car as a Way to Teach Mathematics.
Creator
Aguerrevere, Santiago Andres, Shankar, Ravi, Florida Atlantic University, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description
This report describes the development of a low cost open source semiautonomous robotic car and a way to communicate with it. It is a continuation of prior research done by other students at FAU and published in recent ASEE conferences. The objective of this project was the development of a new robotic platform with improved precision over the original, while still keeping the cost down. It was developed with the aim to allow a hands-on approach to the teaching of mathematics topics that are...
Show moreThis report describes the development of a low cost open source semiautonomous robotic car and a way to communicate with it. It is a continuation of prior research done by other students at FAU and published in recent ASEE conferences. The objective of this project was the development of a new robotic platform with improved precision over the original, while still keeping the cost down. It was developed with the aim to allow a hands-on approach to the teaching of mathematics topics that are taught in the K-12 syllabus. Improved robustness and reliability of the robotic platform for visually solving math problems was achieved using a combination of PID loops to keep track of distance and rotation. The precision was increased by changing the position of the encoders to the shafts of each motor. A mobile application was developed to allow the student to draw the geometric shapes on the screen before the car draws them. The mobile application consists of two parts, the canvas that the user uses to draw the figure and the configure section that lets the user change the parameters of the controller. Results show that the robot can draw standard geometric and complex geometric shapes. It has high precision and sufficient accuracy, the accuracy can be improved with some mechanical adjustments. During testing a Pythagorean triangle was drawn to show visually the key mathematics concept. The eventual goal of this project will be a K-12 class room study to obtain the feedback of the teachers and students on the feasibility of using a robotic car to teach math. Subsequent to that necessary changes will be made to manufacture a unit that is easy to assemble by the teacher.
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Date Issued
2016
PURL
http://purl.flvc.org/fau/fd/FA00004712, http://purl.flvc.org/fau/fd/FA00004712
Subject Headings
Adaptive control systems, Applied mathematics, Artificial intelligence, Computers, Special purpose, Mathematics -- Study and teaching, User interfaces (Computer systems)
Format
Document (PDF)
How interpersonal coordination changes the self: Theory, experiment, and adaptive HKB model of social memory
Title
How interpersonal coordination changes the self: Theory, experiment, and adaptive HKB model of social memory.
Creator
Nordham, Craig A, Kelso, J. A. Scott, Tognoli, Emmanuelle, Florida Atlantic University, Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
Abstract/Description
How one behaves after interacting with a friend may not be the same as before the interaction began What factors a ect the formation of social interactions between people and, once formed, how do social interactions leave lasting changes on individual behavior? In this dissertation, a thorough review and conceptual synthesis is provided Major features of coordination dynamics are demonstrated with examples from both the intrapersonal and interpersonal coordination literature that are...
Show moreHow one behaves after interacting with a friend may not be the same as before the interaction began What factors a ect the formation of social interactions between people and, once formed, how do social interactions leave lasting changes on individual behavior? In this dissertation, a thorough review and conceptual synthesis is provided Major features of coordination dynamics are demonstrated with examples from both the intrapersonal and interpersonal coordination literature that are interpreted via a conceptual scheme, the causal loops of coordination dynamics An empirical, behavioral study of interpersonal coordination was conducted to determine which spontaneous patterns of coordination formed and whether a remnant of the interaction ensued ("social memory") To assess social memory in dyads, the behavior preceding and following episodes of interaction was compared In the experiment, pairs of people sat facing one another and made continuous flexion-extension finger movements while a window acted as a shutter to control whether partners saw each other's movements Thus, vision ("social contact") allowed spontaneous information exchange between partners through observation Each trial consisted of three successive intervals lasting twenty seconds: without social contact ("me and you"), with social contact ("us"), and again without ("me and you") During social contact, a variety of patterns was observed ranging from phase coupling to transient or absent collective behavior Individuals also entered and exited social coordination differently In support of social memory, compared to before social contact, after contact ended participants tended to remain near each other's movement frequency Furthermore, the greater the stability of coupling, the more similar the partners' post-interactional frequencies were Proposing that the persistence of behavior in the absence of information exchange was the result of prior frequency adaptation, a mathematical model of human movement was implemented with Haken-Kelso-Bunz oscillators that reproduced the experimental findings, even individual dyadic patterns Parametric manipulations revealed multiple routes to persistence of behavior via the interplay of adaptation and other HKB model parameters The experimental results, the model, and their interpretation form the basis of a proposal for future research and possible therapeutic applications
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Date Issued
2016
PURL
http://purl.flvc.org/fau/fd/FA00004793
Subject Headings
Ergodic theory, Dynamics, Conversation analysis--Social aspects, Social interaction, Social acceptance, Identity (Philosophical concept), Motivation (Psychology), Applied mathematics, Statistical physics
Format
Document (PDF)