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Pages
 Title
 Wind speed analysis for Lake Okeechobee.
 Creator
 Hu, Mingyan, Florida Atlantic University, Qian, Lianfen, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this thesis, we analyze wind speeds collected by South Florida Water Management District at stations L001, L005, L006 and LZ40 in Lake Okeechobee from January 1995 to December 2000. There are many missing values and outliers in this data. To impute the missing values, three different methods are used: Nearby window average imputation, Jones imputation using Kalman filter, and EM algorithm imputation. To detect outliers and remove impacts, we use ARIMA models of time series. Innovational...
Show moreIn this thesis, we analyze wind speeds collected by South Florida Water Management District at stations L001, L005, L006 and LZ40 in Lake Okeechobee from January 1995 to December 2000. There are many missing values and outliers in this data. To impute the missing values, three different methods are used: Nearby window average imputation, Jones imputation using Kalman filter, and EM algorithm imputation. To detect outliers and remove impacts, we use ARIMA models of time series. Innovational and additive outliers are considered. It turns out that EM algorithm imputation is the best method for our wind speed data set. After imputing missing values, detecting outliers and removing the impacts, we obtain the best models for all four stations. They are all in the form of seasonal ARIMA(2, 0, 0) x (1, 0, 0)24 for the hourly wind speed data.
Show less  Date Issued
 2002
 PURL
 http://purl.flvc.org/fcla/dt/12883
 Subject Headings
 WindsSpeedFloridaOkeechobee, Lake, Okeechobee, Lake (Fla )Environmental conditions
 Format
 Document (PDF)
 Title
 Weakly integrally closed domains and forbidden patterns.
 Creator
 Hopkins, Mary E., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

An integral domain D is weakly integrally closed if whenever there is an element x in the quotient field of D and a nonzero finitely generated ideal J of D such that xJ J2, then x is in D. We define weakly integrally closed numerical monoids similarly. If a monoid algebra is weakly integrally closed, then so is the monoid. A pattern F of finitely many 0's and 1's is forbidden if whenever the characteristic binary string of a numerical monoid M contains F, then M is not weakly integrally...
Show moreAn integral domain D is weakly integrally closed if whenever there is an element x in the quotient field of D and a nonzero finitely generated ideal J of D such that xJ J2, then x is in D. We define weakly integrally closed numerical monoids similarly. If a monoid algebra is weakly integrally closed, then so is the monoid. A pattern F of finitely many 0's and 1's is forbidden if whenever the characteristic binary string of a numerical monoid M contains F, then M is not weakly integrally closed. Any stretch of the pattern 11011 is forbidden. A numerical monoid M is weakly integrally closed if and only if it has a forbidden pattern. For every finite set S of forbidden patterns, there exists a monoid that is not weakly integrally closed and that contains no stretch of a pattern in S. It is shown that particular monoid algebras are weakly integrally closed.
Show less  Date Issued
 2009
 PURL
 http://purl.flvc.org/FAU/199327
 Subject Headings
 Mathematical analysis, Algebra, Homological, Monoids, Categories (Mathematics), Semigroup algebras
 Format
 Document (PDF)
 Title
 Various Approaches on Parameter Estimation in Mixture and NonMixture Cure Models.
 Creator
 Kutal, Durga Hari, Qian, Lianfen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Analyzing lifetime data with longterm survivors is an important topic in medical application. Cure models are usually used to analyze survival data with the proportion of cure subjects or longterm survivors. In order to include the propor tion of cure subjects, mixture and nonmixture cure models are considered. In this dissertation, we utilize both maximum likelihood and Bayesian methods to estimate model parameters. Simulation studies are carried out to verify the nite sample per...
Show moreAnalyzing lifetime data with longterm survivors is an important topic in medical application. Cure models are usually used to analyze survival data with the proportion of cure subjects or longterm survivors. In order to include the propor tion of cure subjects, mixture and nonmixture cure models are considered. In this dissertation, we utilize both maximum likelihood and Bayesian methods to estimate model parameters. Simulation studies are carried out to verify the nite sample per formance of the estimation methods. Real data analyses are reported to illustrate the goodnessof t via Fr echet, Weibull and Exponentiated Exponential susceptible distributions. Among the three parametric susceptible distributions, Fr echet is the most promising. Next, we extend the nonmixture cure model to include a change point in a covariate for right censored data. The smoothed likelihood approach is used to address the problem of a loglikelihood function which is not di erentiable with respect to the change point. The simulation study is based on the nonmixture change point cure model with an exponential distribution for the susceptible subjects. The simulation results revealed a convincing performance of the proposed method of estimation.
Show less  Date Issued
 2018
 PURL
 http://purl.flvc.org/fau/fd/FA00013083
 Subject Headings
 Survival Analysis., Bayesian statistical decision theory., Parameter estimation., Weibull distribution.
 Format
 Document (PDF)
 Title
 Unique decomposition of direct sums of ideals.
 Creator
 Ay, Basak., 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 Rmodule which decomposes into a finite 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. In Chapters 13 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of one...
Show moreWe say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any Rmodule which decomposes into a finite 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. In Chapters 13 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of onedimensional reduced commutative Noetherian rings with the UDI property have the UDI property, also. In Chapter 5 we show that the UDI property implies the KrullSchmidt property for direct sums of torsionfree rank one modules for a reduced local commutative Noetherian onedimensional ring R.
Show less  Date Issued
 2010
 PURL
 http://purl.flvc.org/FAU/2683133
 Subject Headings
 Algebraic number theory, Modules (Algebra), Noetherian rings, Commutative rings, Algebra, Abstract
 Format
 Document (PDF)
 Title
 TPL, A TUTORIAL PROGRAMMING LANGUAGE.
 Creator
 Huang, ChienJen, 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 Type3 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 Type3 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
 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 delaycoordinate 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 delaycoordinate 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
 Timeseries analysisMathematical models, Chaotic behavior in systems
 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)
 Title
 On the minimal logarithmic signature conjecture.
 Creator
 Singhi, Nidhi., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The minimal logarithmic signature conjecture states that in any finite simple group there are subsets Ai, 1 i s such that the size jAij of each Ai is a prime or 4 and each element of the group has a unique expression as a product Qs i=1 ai of elements ai 2 Ai. Logarithmic signatures have been used in the construction of several cryptographic primitives since the late 1970's [3, 15, 17, 19, 16]. The conjecture is shown to be true for various families of simple groups including cyclic groups,...
Show moreThe minimal logarithmic signature conjecture states that in any finite simple group there are subsets Ai, 1 i s such that the size jAij of each Ai is a prime or 4 and each element of the group has a unique expression as a product Qs i=1 ai of elements ai 2 Ai. Logarithmic signatures have been used in the construction of several cryptographic primitives since the late 1970's [3, 15, 17, 19, 16]. The conjecture is shown to be true for various families of simple groups including cyclic groups, An, PSLn(q) when gcd(n; q 1) is 1, 4 or a prime and several sporadic groups [10, 9, 12, 14, 18]. This dissertation is devoted to proving that the conjecture is true for a large class of simple groups of Lie type called classical groups. The methods developed use the structure of these groups as isometry groups of bilinear or quadratic forms. A large part of the construction is also based on the Bruhat and Levi decompositions of parabolic subgroups of these groups. In this dissertation the conjecture is shown to be true for the following families of simple groups: the projective special linear groups PSLn(q), the projective symplectic groups PSp2n(q) for all n and q a prime power, and the projective orthogonal groups of positive type + 2n(q) for all n and q an even prime power. During the process, the existence of minimal logarithmic signatures (MLS's) is also proven for the linear groups: GLn(q), PGLn(q), SLn(q), the symplectic groups: Sp2n(q) for all n and q a prime power, and for the orthogonal groups of plus type O+ 2n(q) for all n and q an even prime power. The constructions in most of these cases provide cyclic MLS's. Using the relationship between nite groups of Lie type and groups with a split BNpair, it is also shown that every nite group of Lie type can be expressed as a disjoint union of sets, each of which has an MLS.
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3172946
 Subject Headings
 Finite groups, Abelian groups, Number theory, Combinatorial group theory, Mathematical recreations, Linear algebraic groups, Lie groups
 Format
 Document (PDF)
 Title
 The Finite Abelian Hidden Subgroup Problem.
 Creator
 Losert, Bernd, Magliveras, Spyros S., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The hidden subgroup problem has been an active topic of research in quantum computing for over the past 10 years. Out of all the literature that is out there on this topic, there are very few survey articles which discuss most or all of the details concerning the Abelian hidden subgroup problem. As a matter of fact , many articles [17, 26 , 22, 45] claim that an efficient quantum algorithm for the Abelian hidden subgroup problem is folklore. To quote Jozsa [21]: " ... the detailed...
Show moreThe hidden subgroup problem has been an active topic of research in quantum computing for over the past 10 years. Out of all the literature that is out there on this topic, there are very few survey articles which discuss most or all of the details concerning the Abelian hidden subgroup problem. As a matter of fact , many articles [17, 26 , 22, 45] claim that an efficient quantum algorithm for the Abelian hidden subgroup problem is folklore. To quote Jozsa [21]: " ... the detailed description of an efficient quantum algorithm for the general abelian hidden subgroup problem seems not to have been described in the literature." Apart from banishing this folklore, the aim of this work is to serve as a monograph about the Abelian hidden subgroup, discussing many of the finer points that are ignored in the literature so as to make it accessible and comprehensible to the mathematically mature reader.
Show less  Date Issued
 2010
 PURL
 http://purl.flvc.org/fau/fd/FA00000790
 Format
 Document (PDF)
 Title
 The Covering Numbers of Some Finite Simple Groups.
 Creator
 Epstein, Michael, Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

A finite cover C of a group G is a finite collection of proper subgroups of G such that G is equal to the union of all of the members of C. Such a cover is called minimal if it has the smallest cardinality among all finite covers of G. The covering number of G, denoted by σ(G), is the number of subgroups in a minimal cover of G. Here we determine the covering numbers of the projective special unitary groups U3(q) for q ≤ 5, and give upper and lower bounds for the covering number of U3(q) when...
Show moreA finite cover C of a group G is a finite collection of proper subgroups of G such that G is equal to the union of all of the members of C. Such a cover is called minimal if it has the smallest cardinality among all finite covers of G. The covering number of G, denoted by σ(G), is the number of subgroups in a minimal cover of G. Here we determine the covering numbers of the projective special unitary groups U3(q) for q ≤ 5, and give upper and lower bounds for the covering number of U3(q) when q > 5. We also determine the covering number of the McLaughlin sporadic simple group, and verify previously known results on the covering numbers of the HigmanSims and Held groups.
Show less  Date Issued
 2019
 PURL
 http://purl.flvc.org/fau/fd/FA00013203
 Subject Headings
 Finite simple groups, Covering numbers
 Format
 Document (PDF)
 Title
 The Circular Restricted Four Body Problem is NonIntegrable: A Computer Assisted Proof.
 Creator
 Kepley, Shane, Kalies, William D., MirelesJames, Jason D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Gravitational Nbody problems are central in classical mathematical physics. Studying their long time behavior raises subtle questions about the interplay between regular and irregular motions and the boundary between integrable and chaotic dynamics. Over the last hundred years, concepts from the qualitative theory of dynamical systems such as stable/unstable manifolds, homoclinic and heteroclinic tangles, KAM theory, and whiskered invariant tori, have come to play an increasingly important...
Show moreGravitational Nbody problems are central in classical mathematical physics. Studying their long time behavior raises subtle questions about the interplay between regular and irregular motions and the boundary between integrable and chaotic dynamics. Over the last hundred years, concepts from the qualitative theory of dynamical systems such as stable/unstable manifolds, homoclinic and heteroclinic tangles, KAM theory, and whiskered invariant tori, have come to play an increasingly important role in the discussion. In the last fty years the study of numerical methods for computing invariant objects has matured into a thriving subdiscipline. This growth is driven at least in part by the needs of the world's space programs. Recent work on validated numerical methods has begun to unify the computational and analytical perspectives, enriching both aspects of the subject. Many of these results use computer assisted proofs, a tool which has become increasingly popular in recent years. This thesis presents a proof that the circular restricted four body problem is nonintegrable. The proof of this result is obtained as an application of more general rigorous numerical methods in nonlinear analysis.
Show less  Date Issued
 2017
 PURL
 http://purl.flvc.org/fau/fd/FA00004997
 Subject Headings
 Dissertations, Academic  Florida Atlantic University, Mathematical physics., Invariants., Dynamical systems
 Format
 Document (PDF)
 Title
 THE CHANGE POINT PROBLEM FOR TWO CLASSES OF STOCHASTIC PROCESSES.
 Creator
 Ball, Cory, Long, Hongwei, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
 Abstract/Description

The change point problem is a problem where a process changes regimes because a parameter changes at a point in time called the change point. The objective of this problem is to estimate the change point and each of the parameters of the stochastic process. In this thesis, we examine the change point problem for two classes of stochastic processes. First, we consider the volatility change point problem for stochastic diffusion processes driven by Brownian motions. Then, we consider the drift...
Show moreThe change point problem is a problem where a process changes regimes because a parameter changes at a point in time called the change point. The objective of this problem is to estimate the change point and each of the parameters of the stochastic process. In this thesis, we examine the change point problem for two classes of stochastic processes. First, we consider the volatility change point problem for stochastic diffusion processes driven by Brownian motions. Then, we consider the drift change point problem for OrnsteinUhlenbeck processes driven by _stable Levy motions. In each problem, we establish the consistency of the estimators, determine asymptotic behavior for the changing parameters, and finally, we perform simulation studies to computationally assess the convergence of parameters.
Show less  Date Issued
 2020
 PURL
 http://purl.flvc.org/fau/fd/FA00013462
 Subject Headings
 Stochastic processes, Changepoint problems, Brownian motion processes, OrnsteinUhlenbeck process, Computer simulation
 Format
 Document (PDF)
 Title
 Techniques in Lattice Basis Reduction.
 Creator
 Khadka, Bal K., Magliveras, Spyros S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The mathematical theory of nding a basis of shortest possible vectors in a given lattice L is known as reduction theory and goes back to the work of Lagrange, Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who created the well known LLL algorithm, and many other researchers such as L. Babai and C. P. Schnorr who created signi cant new variants of basis reduction algorithms. The shortest...
Show moreThe mathematical theory of nding a basis of shortest possible vectors in a given lattice L is known as reduction theory and goes back to the work of Lagrange, Gauss, Hermite, Korkin, Zolotarev, and Minkowski. Modern reduction theory is voluminous and includes the work of A. Lenstra, H. Lenstra and L. Lovasz who created the well known LLL algorithm, and many other researchers such as L. Babai and C. P. Schnorr who created signi cant new variants of basis reduction algorithms. The shortest vector (SVP) and closest vector (CVP) problems, presently considered intractable, are algorithmic tasks that lie at the core of many number theoretic problems, integer programming, nding irreducible factors of polynomials, minimal polynomials of algebraic numbers, and simultaneous diophantine approximation. Lattice basis reduction also has deep and extensive connections with modern cryptography, and cryptanalysis particularly in the postquantum era. In this dissertation we study and compare current systems LLL and BKZ, and point out their strengths and drawbacks. In addition, we propose and investigate the e cacy of new optimization techniques, to be used along with LLL, such as hill climbing, random walks in groups, our lattice di usionsub lattice fusion, and multistage hybrid LDSFHC technique. The rst two methods rely on the sensitivity of LLL to permutations of the input basis B, and optimization ideas over the symmetric group Sm viewed as a metric space. The third technique relies on partitioning the lattice into sublattices, performing basis reduction in the partition sublattice blocks, fusing the sublattices, and repeating. We also point out places where parallel computation can reduce runtimes achieving almost linear speedup. The multistage hybrid technique relies on the lattice di usion and sublattice fusion and hill climbing algorithms. Unlike traditional methods, our approach brings in better results in terms of basis reduction towards nding shortest vectors and minimal weight bases. Using these techniques we have published the competitive lattice vectors of ideal lattice challenge on the lattice hall of fame. Toward the end of the dissertation we also discuss applications to the multidimensional knapsack problem that resulted in the discovery of new large sets of geometric designs still considered very rare. The research introduces innovative techniques in lattice basis reduction theory and provides some space for future researchers to contemplate lattices from a new viewpoint.
Show less  Date Issued
 2016
 PURL
 http://purl.flvc.org/fau/fd/FA00004678
 Subject Headings
 Cryptography., Combinatorial analysis., Group theory.
 Format
 Document (PDF)
 Title
 A SYNTACTIC APPROACH TO HAND PRINTED CHARACTER RECOGNITION.
 Creator
 KING, ALLAN KAICHUNG, Florida Atlantic University, Hadlock, Frank O., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

A study was made on the feasibility of the syntactic approach to the problem of hand printed character recognition. The characters are represented as postfix expressions in Picture Description Language. By comparing them with the prototype expressions, each character is classified as the prototype that is closest to it. Programs written in the Pascal language, which generate the postfix expressions for the characters, and recognize the characters, are presented.
 Date Issued
 1983
 PURL
 http://purl.flvc.org/fcla/dt/14168
 Subject Headings
 Pattern recognition systems, Character sets (Data processing)
 Format
 Document (PDF)
 Title
 SYMMETRIES IN GOPPA CODES.
 Creator
 SAYRS, BRIAN GEORGE., Florida Atlantic University, Hoffman, Frederick, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Properties of Goppa codes are studied. These are "good" codes in the sense that they asymptotically approach the VarshamovGilbert 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
 MathematicsResearch
 Format
 Document (PDF)
 Title
 A study of divisors and algebras on a double cover of the affine plane.
 Creator
 Bulj, Djordje., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

An algebraic surface defined by an equation of the form z2 = (x+a1y) ... (x + any) (x  1) is studied, from both an algebraic and geometric point of view. It is shown that the surface is rational and contains a singular point which is nonrational. The class group of Weil divisors is computed and the Brauer group of Azumaya algebras is studied. Viewing the surface as a cyclic cover of the affine plane, all of the terms in the cohomology sequence of Chase, Harrison and Roseberg are computed.
 Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3355618
 Subject Headings
 Algebraic number theory, Geometry, Data processing, Noncommutative differential geometry, Mathematical physics, Curves, Algebraic, Commutative rings
 Format
 Document (PDF)
 Title
 Stochastic optimal impulse control of jump diffusions with application to exchange rate.
 Creator
 Perera, Sandun C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

We generalize the theory of stochastic impulse control of jump diffusions introduced by Oksendal and Sulem (2004) with milder assumptions. In particular, we assume that the original process is affected by the interventions. We also generalize the optimal central bank intervention problem including market reaction introduced by Moreno (2007), allowing the exchange rate dynamic to follow a jump diffusion process. We furthermore generalize the approximation theory of stochastic impulse control...
Show moreWe generalize the theory of stochastic impulse control of jump diffusions introduced by Oksendal and Sulem (2004) with milder assumptions. In particular, we assume that the original process is affected by the interventions. We also generalize the optimal central bank intervention problem including market reaction introduced by Moreno (2007), allowing the exchange rate dynamic to follow a jump diffusion process. We furthermore generalize the approximation theory of stochastic impulse control problems by a sequence of iterated optimal stopping problems which is also introduced in Oksendal and Sulem (2004). We develop new results which allow us to reduce a given impulse control problem to a sequence of iterated optimal stopping problems even though the original process is affected by interventions.
Show less  Date Issued
 2009
 PURL
 http://purl.flvc.org/FAU/3174308
 Subject Headings
 Management, Mathematical models, Control theory, Stochastic differential equations, Distribution (Probability theory), Optimal stopping (Mathematical statistics), Economics, Mathematical
 Format
 Document (PDF)
 Title
 Stability analysis for singularly perturbed systems with timedelays.
 Creator
 Yang, Yang, Wang, Yuan, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Singularly perturbed systems with or without delays commonly appear in mathematical modeling of physical and chemical processes, engineering applications, and increasingly, in mathematical biology. There has been intensive work for singularly perturbed systems, yet most of the work so far focused on systems without delays. In this thesis, we provide a new set of tools for the stability analysis for singularly perturbed control systems with time delays.
 Date Issued
 2015
 PURL
 http://purl.flvc.org/fau/fd/FA00004423, http://purl.flvc.org/fau/fd/FA00004423
 Subject Headings
 Biology  Mathematical models, Biomathematics, Differentiable dynamical systems, Differential equations, Partial  Numerical solutions, Global analysis (Mathematics), Lyapunov functions, Nonlinear theories
 Format
 Document (PDF)
 Title
 Stability analysis for nonlinear systems with timedelays.
 Creator
 Tiwari, Shanaz, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this work, we investigate inputtostate stability (ISS) and other related stability properties for control systems with timedelays. To overcome the complexity caused by the presence of the delays, we adopt a Razumikhin approach. The underlying idea of this approach is to treat the delayed variables as system uncertainties. The advantage of this approach is that one works in the more familiar territory of stability analysis for delayfree systems in the context of ISS instead of carrying...
Show moreIn this work, we investigate inputtostate stability (ISS) and other related stability properties for control systems with timedelays. To overcome the complexity caused by the presence of the delays, we adopt a Razumikhin approach. The underlying idea of this approach is to treat the delayed variables as system uncertainties. The advantage of this approach is that one works in the more familiar territory of stability analysis for delayfree systems in the context of ISS instead of carrying out stability analysis on systems of functional differential equations. Our first step is to provide criteria on ISS and inputtoinput stability properties based on the Razumikhin approach. We then turn our attention to largescale interconnected systems. It has been well recognized that the smallgain theory is a powerful tool for stability analysis of interconnected systems. Using the Razumikhin approach, we develop smallgain theorems for interconnected systems consisting of two or more subs ystems with timedelays present either in the interconnection channels or within the subsystems themselves. As an interesting application, we apply our results to an existing model for hematopoesis, a blood cell production process,and improve the previous results derived by linear methods. Another important stability notion in the framework of ISS is the integral ISS (iISS) property. This is a weaker property than ISS, so it supplies to a larger class of systems. As in the case of ISS, we provide Razumikhin criteria on iISS for systems with delays. An example is presented to illustrate that though very useful in practice, the Razumikhin approach only provides sufficient conditions, not equivalent conditions. Finally, we address stability of timevarying systems with delays in the framework of ISS., In particular, we consider LyapunovRazumikhin functions whose decay rates are affected by timevarying functions that can be zero or even negative on some sets of nonzero measure. Our motivation is that it is often less demanding to find or construct such a Lyapunov function than one with a uniform decay rate. We also extend our smallgain theorems to the timevarying case by treating the timevarying system as an auxiliary timeinvariant system.
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3352880
 Subject Headings
 Nonlinear systems, Simulation methods, Control theory, Stability, Mathematical models, Mathematical optimization
 Format
 Document (PDF)
 Title
 Sobolev Inequalities.
 Creator
 Kalis, Jan, Florida Atlantic University, Milman, Mario, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Recently a rich theory of Sobolev spaces on metric spaces has been developed. It. turas out that many relevant results from the classical theory have their counterparts in the mcnic setting ( cf. [P. Hajlasz and P. Koskela. Sobokv met Poincare), Mern. Arner. Math. Soc. 145 (2000), no. 6888, x+101pp]). In this thesis we prove sharp Sobolev inequalities in the context of metric spaces. Our approach is ba....,ed on two recent papers, [J. Baster·o and M. Milman and F. Ruiz, A note on L(oc, q)...
Show moreRecently a rich theory of Sobolev spaces on metric spaces has been developed. It. turas out that many relevant results from the classical theory have their counterparts in the mcnic setting ( cf. [P. Hajlasz and P. Koskela. Sobokv met Poincare), Mern. Arner. Math. Soc. 145 (2000), no. 6888, x+101pp]). In this thesis we prove sharp Sobolev inequalities in the context of metric spaces. Our approach is ba....,ed on two recent papers, [J. Baster·o and M. Milman and F. Ruiz, A note on L(oc, q) spaces and Sobolev embeddings, Indiana Univ. Math. J. 52 (2003), no. 5, 1215 1230] and [J. Martfn and M. Milman and E. Pustylnik, Sobolev inequalities: symmetrization and self improvement via truncation, to appear in J. Funct. Anal.]. These authors establish sharp Sobolev embeddings in the Euclidean setting using symmetrization. Using suitable maximal operators and covering lemmas we show that these symmetrization inequalities of BasteroMilmanRuiz remain valid m the metric setting. We also show that the symmetrization by truncation method of MartfnMilmanPustylnik can be implemented in our generalized setting. Furthermore we also show that our methods can be adapted to deal with nondoubling measures.
Show less  Date Issued
 2007
 PURL
 http://purl.flvc.org/fau/fd/FA00000863
 Subject Headings
 Sobolev spaces, Inequalities (Mathematics), Nonlinear theories, Potential theory (Mathematics)
 Format
 Document (PDF)