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Pages
- Title
- ON SOLUTIONS OF A PERTURBED SCHROEDINGER EQUATION.
- Creator
- ARTERO, AGUSTIN., Florida Atlantic University, Schonbek, Tomas P., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
We study L^2 (R^k) solutions of the equation [..] where [..] and V is a non-negative L^2 function. Our main results are Theorems 1 and 2 of Chapter IV, in which we prove that these solutions depend continuously on V.
- Date Issued
- 1975
- PURL
- http://purl.flvc.org/fcla/dt/13716
- Subject Headings
- Schrödinger equation
- Format
- Document (PDF)
- Title
- 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
- SYMMETRIES IN GOPPA CODES.
- Creator
- SAYRS, BRIAN GEORGE., Florida Atlantic University, Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Properties of Goppa codes are studied. These are "good" codes in the sense that they asymptotically approach the Varshamov-Gilbert bound. E. N. Gilbert and R. R. Varshamov have shown (independently) that it is possible to construct an (n, k) linear code over GF(q) with minimum distance d if [equation] and there are long Goppa codes which achieve this bound [10]. Subclasses of Goppa codes which remain invariant under symmetries are given special attention.
- Date Issued
- 1979
- PURL
- http://purl.flvc.org/fcla/dt/13989
- Subject Headings
- Mathematics--Research
- Format
- Document (PDF)
- Title
- A FORTRAN 77 PREPROCESSOR.
- Creator
- LEACH, JOHN TIMOTHY, Florida Atlantic University, Levow, Roy B., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
This thesis is concerned with the design, construction, and implementation of a FORTRAN 77 preprocessor. It demonstrates how the standard compiler-writing techniques for syntactic and lexical analysis can be greatly simplified in preprocessor construction. The input language is FORTRAN 77. The output language is UNIVAC ASCII FORTRAN Level 8R1.
- Date Issued
- 1980
- PURL
- http://purl.flvc.org/fcla/dt/14022
- Subject Headings
- FORTRAN (Computer program language)
- Format
- Document (PDF)
- Title
- THE MINIMUM K-CENTER PROBLEM FOR GRID GRAPH.
- Creator
- HSUEH, CHI-FU, Florida Atlantic University, Hadlock, Frank O., Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
A study was made of the problem of locating M facilities on a connected grid graph, so that M is the minimum and so that every demand node on the graph is within given distance K of one of these M facilities. We call this problem briefly the G(N,K,M) problem, with N denoting the total number of demand nodes. An algorithm for solving this problem by using backtrack technique is presented in this thesis. A heuristic algorithm is also present; although the resulting M is not always minimum, it...
Show moreA study was made of the problem of locating M facilities on a connected grid graph, so that M is the minimum and so that every demand node on the graph is within given distance K of one of these M facilities. We call this problem briefly the G(N,K,M) problem, with N denoting the total number of demand nodes. An algorithm for solving this problem by using backtrack technique is presented in this thesis. A heuristic algorithm is also present; although the resulting M is not always minimum, it tends to be near minimum. The advantage over the backtrack algorithm is that the heuristic algorithm operates very quickly. Algorithms represented in this thesis are programmed in the Pascal language for the Univac 1100 computer at Florida Atlantic University, Boca Raton, Florida.
Show less - Date Issued
- 1981
- PURL
- http://purl.flvc.org/fcla/dt/14077
- Subject Headings
- Graph theory, Algorithms
- Format
- Document (PDF)
- Title
- A SYNTACTIC APPROACH TO HAND PRINTED CHARACTER RECOGNITION.
- Creator
- KING, ALLAN KAI-CHUNG, Florida Atlantic University, Hadlock, Frank O., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
A study was made on the feasibility of the syntactic approach to the problem of hand printed character recognition. The characters are represented as postfix expressions in Picture Description Language. By comparing them with the prototype expressions, each character is classified as the prototype that is closest to it. Programs written in the Pascal language, which generate the postfix expressions for the characters, and recognize the characters, are presented.
- Date Issued
- 1983
- PURL
- http://purl.flvc.org/fcla/dt/14168
- Subject Headings
- Pattern recognition systems, Character sets (Data processing)
- Format
- Document (PDF)
- Title
- TPL, A TUTORIAL PROGRAMMING LANGUAGE.
- Creator
- Huang, Chien-Jen, Florida Atlantic University, Hadlock, Frank O., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
The object of this reaearch is to define and implement an experimental language, Tutorial Programming Language (TPL). Basic language concepts and definitions are introduced initially to provide the background for defining TPL, which is intended as a means to illustrate language concepts, and has Type-3 grammar as a data type. A formal definition of TPL is given in the form of an SLR(1) grammar. TPL is implemented by a syntax directed compiler and a hypothetical machine for which the compiler...
Show moreThe object of this reaearch is to define and implement an experimental language, Tutorial Programming Language (TPL). Basic language concepts and definitions are introduced initially to provide the background for defining TPL, which is intended as a means to illustrate language concepts, and has Type-3 grammar as a data type. A formal definition of TPL is given in the form of an SLR(1) grammar. TPL is implemented by a syntax directed compiler and a hypothetical machine for which the compiler provides code. The machine is emulated by a Pascal program, making TPL highly portable. It is also possible for the interested user to enhance the power of TPL by writing more functions for practical purposes.
Show less - Date Issued
- 1986
- PURL
- http://purl.flvc.org/fcla/dt/14337
- Subject Headings
- Programming languages (Electronic computers)
- Format
- Document (PDF)
- Title
- Bijections for partition identities.
- Creator
- Lai, Jin-Mei Jeng, Florida Atlantic University, Meyerowitz, Aaron, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
This paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieve--equivalent families. Suppose A1' ... ,An are subsets of a finite set A and B1' ... ,Bn are subsets of a finite set B. Define AS=∩(i∈S) Ai and BS = ∩ (i∈S) Bi for all S⊆N={1,...,n}. Given explicit bijections fS: AS->BS for each S⊆N, A-∪Ai has the same size as B-∪Bi. Several authors have given algorithms for producing an explicit bijection between these...
Show moreThis paper surveys work of the last few years on construction of bijections for partition identities. We use the more general setting of sieve--equivalent families. Suppose A1' ... ,An are subsets of a finite set A and B1' ... ,Bn are subsets of a finite set B. Define AS=∩(i∈S) Ai and BS = ∩ (i∈S) Bi for all S⊆N={1,...,n}. Given explicit bijections fS: AS->BS for each S⊆N, A-∪Ai has the same size as B-∪Bi. Several authors have given algorithms for producing an explicit bijection between these two sets. In certain important cases they give the same result. We discuss and compare algorithms, use Graph Theory to illustrate them, and provide PAS CAL programs for them.
Show less - Date Issued
- 1992
- PURL
- http://purl.flvc.org/fau/fd/FADT14826
- Subject Headings
- Algorithms, Partitions (Mathematics), Sieves (Mathematics)
- Format
- Document (PDF)
- Title
- The Cayley-Dickson algebras.
- Creator
- Khalil, Saidah Hasan, Florida Atlantic University, Yiu, Paul Y., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
This thesis studies the various effects of the nonassociativity of the Cayley-Dickson algebras At, t>3, especially on the structure of their automorphism groups. Beginning with the problem of composition algebra structures on euclidean spaces, we shall explain the origin of the Cayley-Dickson algebras, and give a self-contained exposition on some important results on such algebras. These algebras being nonassociative, we focus on the study of the associators of the form (u,w,v) = (uw)v - u(wv...
Show moreThis thesis studies the various effects of the nonassociativity of the Cayley-Dickson algebras At, t>3, especially on the structure of their automorphism groups. Beginning with the problem of composition algebra structures on euclidean spaces, we shall explain the origin of the Cayley-Dickson algebras, and give a self-contained exposition on some important results on such algebras. These algebras being nonassociative, we focus on the study of the associators of the form (u,w,v) = (uw)v - u(wv). The first main result, that if u and v are elements in a Cayley-Dickson algebra for which (u, w, v) = 0 for all w, then u and v generate a 2-dimensional subalgebra isomorphic to C, was conjectured by P. Yiu, and proved by P. Eakin and A. Sathaye. We shall simplify the proof given by these latter authors. This is then used to give a simple proof of R. D. Schafer's theorem on derivations of Cayley-Dickson algebras, and following also Eakin and Sathaye, a proof of the conjecture by R. B. Brown on the structure of the automorphism groups of these algebras. Two simple proofs are presented for the beautiful characterization by H. Brandt that in the Cayley algebra A3 = K, conjugation by a unit element a is an automorphism if and only if a is a 6th root of unity. We shall present a geometric proof by M. A. Zorn and a purely algebraic one. The zero divisors of the Cayley-Dickson algebra A4 are also analyzed in detail.
Show less - Date Issued
- 1993
- PURL
- http://purl.flvc.org/fcla/dt/14993
- Subject Headings
- Cayley algebras
- Format
- Document (PDF)
- Title
- Time series analysis and correlation dimension estimation: Mathematical foundation and applications.
- Creator
- Jiang, Wangye, Florida Atlantic University, Ding, Mingzhou, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
A time series is a data set of a single quantity sampled at intervals T time units apart. It is widely used to represent a chaotic dynamical system. The correlation dimension measures the complexity of a dynamical system. Using the delay-coordinate map and the extended GP algorithm one can estimate the correlation dimension of an experimental dynamical system from measured time series. This thesis discusses the mathematical foundation of the methods and the corresponding applications. The...
Show moreA time series is a data set of a single quantity sampled at intervals T time units apart. It is widely used to represent a chaotic dynamical system. The correlation dimension measures the complexity of a dynamical system. Using the delay-coordinate map and the extended GP algorithm one can estimate the correlation dimension of an experimental dynamical system from measured time series. This thesis discusses the mathematical foundation of the methods and the corresponding applications. The embedding theorems and their relationship with dimension preservation are reviewed in detail, but more attention is focussed on the concept development.
Show less - Date Issued
- 1995
- PURL
- http://purl.flvc.org/fcla/dt/15213
- Subject Headings
- Time-series analysis--Mathematical models, Chaotic behavior in systems
- Format
- Document (PDF)
- Title
- 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.
Show less - Date Issued
- 1996
- PURL
- http://purl.flvc.org/fcla/dt/15289
- Subject Headings
- Mathematics
- Format
- Document (PDF)
- Title
- New methods for estimating fractal dimensions of coastlines.
- Creator
- Klotzbach, Jonathan David, Florida Atlantic University, Voss, Richard, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
A coastline is an example of a statistically self-similar fractal. A standard characterization walks a ruler of fixed size along the coast and estimates fractal dimension from the power-law relationship between length and ruler size. Multiple intersection can lead to ambiguity in choosing the next step. The standard method always chooses the first intersection along the curve. Variations were developed to choose intersections which highlight geographic properties. The land method measures...
Show moreA coastline is an example of a statistically self-similar fractal. A standard characterization walks a ruler of fixed size along the coast and estimates fractal dimension from the power-law relationship between length and ruler size. Multiple intersection can lead to ambiguity in choosing the next step. The standard method always chooses the first intersection along the curve. Variations were developed to choose intersections which highlight geographic properties. The land method measures accessibility to the coast from land at each size while the water method probes water access. Measurements on sections of the East and West Coasts of the United States typically showed the land length exceeding water. Jumps in water length as step size decreased were often caused by narrow rivers or bays which have few corresponding land features. Simple recursive constructions were inadequate to model this asymmetry.
Show less - Date Issued
- 1998
- PURL
- http://purl.flvc.org/fcla/dt/15545
- Subject Headings
- Fractals, Boundaries, Coasts
- Format
- Document (PDF)
- Title
- Input-to-state stability properties for discrete-time nonlinear systems.
- Creator
- Gao, Kehan, Florida Atlantic University, Wang, Yuan, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
In this thesis, we study the input-to-state stability (scISS) property and related characterizations for discrete-time nonlinear systems. Variations of scISS property were employed in solving particular control problems. The main contribution of this work is to provide a detailed analysis on the relations among various types of notations related to system stability and show that most scISS results for continuous-time nonlinear system can be extended to discrete-time case.
- Date Issued
- 1999
- PURL
- http://purl.flvc.org/fcla/dt/15688
- Subject Headings
- Discrete-time systems, Nonlinear systems, Stability, Control theory
- Format
- Document (PDF)
- Title
- Representation of groups in quantum mechanics.
- Creator
- Paskaleva, Elitza Dimitrova, Florida Atlantic University, Schroeck, Franklin E., Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
In this work, we discuss the conceptual framework of quantum mechanics in the Hilbert space formalism from a group representation point of view. After a brief review of the main results of the theory of groups and their representations, we describe mathematical models of the subject, and show the applications of this theory for getting numerical answers to problems in elementary particle physics.
- Date Issued
- 2000
- PURL
- http://purl.flvc.org/fcla/dt/15758
- Subject Headings
- Quantum theory, Particles (Nuclear physics), Representations of groups, Hilbert space
- Format
- Document (PDF)
- Title
- Computing automorphism groups of projective planes.
- Creator
- Adamski, Jesse Victor, Magliveras, Spyros S., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
The main objective of this thesis was to find the full automorphism groups of finite Desarguesian planes. A set of homologies were used to generate the automorphism group when the order of the plane was prime. When the order was a prime power Pa,a ≠ 1 the Frobenius automorphism was added to the set of homologies, and then the full automorphism group was generated. The Frobenius automorphism was found by using the planar ternary ring derived from a coordinatization of the plane.
- Date Issued
- 2013
- PURL
- http://purl.flvc.org/fau/fd/FA0004000
- Subject Headings
- Combinatorial group theory, Finite geometrics, Geometry, Projective
- Format
- Document (PDF)
- Title
- Simulation study on option pricing under jump diffusion models.
- Creator
- Rodrigues, Justin, Long, Hongwei, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
The main objective of this thesis is to simulate, evaluate and discuss several methods for pricing European-style options. The Black-Scholes model has long been considered the standard method for pricing options. One of the downfalls of the Black-Scholes model is that it is strictly continuous and does not incorporate discrete jumps. This thesis will consider two alternate Levy models that include discretized jumps; The Merton Jump Diffusion and Kou's Double Exponential Jump Diffusion. We...
Show moreThe main objective of this thesis is to simulate, evaluate and discuss several methods for pricing European-style options. The Black-Scholes model has long been considered the standard method for pricing options. One of the downfalls of the Black-Scholes model is that it is strictly continuous and does not incorporate discrete jumps. This thesis will consider two alternate Levy models that include discretized jumps; The Merton Jump Diffusion and Kou's Double Exponential Jump Diffusion. We will use each of the three models to price real world stock data through software simulations and explore the results.Keywords: Levy Processes, Brownian motion, Option pricing, Simulation, Black-Scholes, Merton Jump Diffusion, Kou, Kou's Double Exponential Jump Diffusion.
Show less - Date Issued
- 2013
- PURL
- http://purl.flvc.org/fau/fd/FA0004051
- Subject Headings
- Finance -- Mathematical models, Levy processes, Prices -- Econometric models, Statistical physics, Stochastic processes, Valuation -- Econometric models
- Format
- Document (PDF)
- Title
- Detection of multiple change-points in hazard models.
- Creator
- Zhang, Wei, Qian, Lianfen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Change-point detection in hazard rate function is an important research topic in survival analysis. In this dissertation, we firstly review existing methods for single change-point detection in piecewise exponential hazard model. Then we consider the problem of estimating the change point in the presence of right censoring and long-term survivors while using Kaplan-Meier estimator for the susceptible proportion. The maximum likelihood estimators are shown to be consistent. Taking one step...
Show moreChange-point detection in hazard rate function is an important research topic in survival analysis. In this dissertation, we firstly review existing methods for single change-point detection in piecewise exponential hazard model. Then we consider the problem of estimating the change point in the presence of right censoring and long-term survivors while using Kaplan-Meier estimator for the susceptible proportion. The maximum likelihood estimators are shown to be consistent. Taking one step further, we propose an counting process based and least squares based change-point detection algorithm. For single change-point case, consistency results are obtained. We then consider the detection of multiple change-points in the presence of long-term survivors via maximum likelihood based and counting process based method. Last but not least, we use a weighted least squares based and counting process based method for detection of multiple change-points with long-term survivors and covariates. For multiple change-points detection, simulation studies show good performances of our estimators under various parameters settings for both methods. All methods are applied to real data analyses.
Show less - Date Issued
- 2014
- PURL
- http://purl.flvc.org/fau/fd/FA00004173
- Subject Headings
- Problem solving--Data processing., Process control--Statistical methods., Point processes., Mathematical statistics., Failure time data analysis--Data processing., Survival analysis (Biometry)--Data processing.
- Format
- Document (PDF)
- Title
- Bayesian approach to an exponential hazard regression model with a change point.
- Creator
- Abraha, Yonas Kidane, Qian, Lianfen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
This thesis contains two parts. The first part derives the Bayesian estimator of the parameters in a piecewise exponential Cox proportional hazard regression model, with one unknown change point for a right censored survival data. The second part surveys the applications of change point problems to various types of data, such as long-term survival data, longitudinal data and time series data. Furthermore, the proposed method is then used to analyse a real survival data.
- Date Issued
- 2014
- PURL
- http://purl.flvc.org/fau/fd/FA00004013
- Subject Headings
- Bayesian statistical decision theory, Mathematical statistics, Multivariate analysis -- Data processing
- Format
- Document (PDF)
- Title
- Modeling and simulating interest rates via time-dependent mean reversion.
- Creator
- Dweck, Andrew Jason, Long, Hongwei, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
The purpose of this thesis is to compare the effectiveness of several interest rate models in fitting the true value of interest rates. Up until 1990, the universally accepted models were the equilibrium models, namely the Rendleman-Bartter model, the Vasicek model, and the Cox-Ingersoll-Ross (CIR) model. While these models were probably considered relatively accurate around the time of their discovery, they do not provide a good fit to the initial term structure of interest rates, making...
Show moreThe purpose of this thesis is to compare the effectiveness of several interest rate models in fitting the true value of interest rates. Up until 1990, the universally accepted models were the equilibrium models, namely the Rendleman-Bartter model, the Vasicek model, and the Cox-Ingersoll-Ross (CIR) model. While these models were probably considered relatively accurate around the time of their discovery, they do not provide a good fit to the initial term structure of interest rates, making them substandard for use by traders in pricing interest rate options. The fourth model we consider is the Hull-White one-factor model, which does provide this fit. After calibrating, simulating, and comparing these four models, we find that the Hull-White model gives the best fit to our data sets.
Show less - Date Issued
- 2014
- PURL
- http://purl.flvc.org/fau/fd/FA00004103, http://purl.flvc.org/fau/fd/FA00004103
- Subject Headings
- Game theory, Investment analysis, Options (Finance), Recursive functions, Stochastic differential equations
- Format
- Document (PDF)
- Title
- The triangle of reflections.
- Creator
- Torres, Jesus, Yiu, Paul Y., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
This thesis presents some results in triangle geometry discovered using dynamic software, namely, Geometer’s Sketchpad, and confirmed with computations using Mathematica 9.0. Using barycentric coordinates, we study geometric problems associated with the triangle of reflections T of a given triangle T, yielding interesting triangle centers and simple loci such as circles and conics. These lead to some new triangle centers with reasonably simple coordinates, and also new properties of some...
Show moreThis thesis presents some results in triangle geometry discovered using dynamic software, namely, Geometer’s Sketchpad, and confirmed with computations using Mathematica 9.0. Using barycentric coordinates, we study geometric problems associated with the triangle of reflections T of a given triangle T, yielding interesting triangle centers and simple loci such as circles and conics. These lead to some new triangle centers with reasonably simple coordinates, and also new properties of some known, classical centers. Particularly, we show that the Parry reflection point is the common point of two triads of circles, one associated with the tangential triangle, and another with the excentral triangle. More interestingly, we show that a certain rectangular hyperbola through the vertices of T appears as the locus of the perspector of a family of triangles perspective with T, and in a different context as the locus of the orthology center of T with another family of triangles.
Show less - Date Issued
- 2014
- PURL
- http://purl.flvc.org/fau/fd/FA00004167, http://purl.flvc.org/fau/fd/FA00004167
- Subject Headings
- Geometer's Sketchpad, Geometry -- Study and teaching, Geometry, Hyperbolic, Mathematics -- Computer network resources, Problem solving
- Format
- Document (PDF)