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- 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 out-liers 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 out-liers 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
- Winds--Speed--Florida--Okeechobee, 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 Non-Mixture Cure Models.
- Creator
- Kutal, Durga Hari, Qian, Lianfen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Analyzing life-time data with long-term survivors is an important topic in medical application. Cure models are usually used to analyze survival data with the proportion of cure subjects or long-term survivors. In order to include the propor- tion of cure subjects, mixture and non-mixture 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 life-time data with long-term survivors is an important topic in medical application. Cure models are usually used to analyze survival data with the proportion of cure subjects or long-term survivors. In order to include the propor- tion of cure subjects, mixture and non-mixture 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 goodness-of- 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 non-mixture 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 log-likelihood function which is not di erentiable with respect to the change point. The simulation study is based on the non-mixture 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 R-module 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 1-3 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 R-module 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 1-3 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of one-dimensional reduced commutative Noetherian rings with the UDI property have the UDI property, also. In Chapter 5 we show that the UDI property implies the Krull-Schmidt property for direct sums of torsion-free rank one modules for a reduced local commutative Noetherian one-dimensional 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, 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
- TOPOLOGICAL DATA ANALYSIS FOR DATA SCIENCE: THE DELAUNAY-RIPS COMPLEX, TRIANGULATION STABILITIES, AND PROTEIN STABILITY PREDICTIONS.
- Creator
- Mishra, Amish, Motta, Francis, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
- Abstract/Description
-
Topological Data Analysis (TDA) is a relatively new field of research that utilizes topological notions to extract discriminating features from data. Within TDA, persistent homology (PH) is a robust method to compute multi-dimensional geometric and topological features of a dataset. Because these features are often stable under certain perturbations of the underlying data, are often discriminating, and can be used for visualization of structure in high-dimensional data and in statistical and...
Show moreTopological Data Analysis (TDA) is a relatively new field of research that utilizes topological notions to extract discriminating features from data. Within TDA, persistent homology (PH) is a robust method to compute multi-dimensional geometric and topological features of a dataset. Because these features are often stable under certain perturbations of the underlying data, are often discriminating, and can be used for visualization of structure in high-dimensional data and in statistical and machine learning modeling, PH has attracted the interest of researchers across scientific disciplines and in many industry applications. However, computational costs may present challenges to effectively using PH in certain data contexts, and theoretical stability results may not hold in practice. In this dissertation, we develop an algorithm that can reduce the computation burden of computing persistent homology on point cloud data. Naming it Delaunay-Rips (DR), we define, implement, and empirically test this computationally tractable simplicial complex construction for computing persistent homology of Euclidean point cloud data. We demonstrate the practical robustness of DR for persistent homology in comparison with other simplical complexes in machine learning applications such as predicting sleep state from patient heart rate. To justify the theoretical stability of DR, we prove the stability of the Delaunay triangulation of a pointcloud P under perturbations of the points of P. Specifically, we impose a notion of genericity on the points of P to ensure stability. In the final chapter, we contribute to the field of computational biology by taking a data-driven approach to learn topological features of designed proteins from their persistence diagrams. We find correlations between the learned topological features and biochemical features to investigate how protein structure relates to features identified by subject-matter experts. We train several machine learning models to assess the performance of incorporating topological features into training with biochemical features. Using cover-tree differencing via entropy reduction (CDER), we identify distinguishing regions of the persistence diagrams of stable/unstable proteins. More notably, we find statistically significant improvement in classification performance (in terms of average precision score) for certain designed secondary structure topologies.
Show less - Date Issued
- 2023
- PURL
- http://purl.flvc.org/fau/fd/FA00014311
- Subject Headings
- Data Science, Data Analysis, Topology--Data processing, Protein Stability
- 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
- 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 BN-pair, 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 eff-icient 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 eff-icient 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 Higman-Sims 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 Non-Integrable: A Computer Assisted Proof.
- Creator
- Kepley, Shane, Kalies, William D., Mireles-James, Jason D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
Gravitational N-body 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 N-body 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 sub-discipline. 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 non-integrable. 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 Ornstein-Uhlenbeck 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, Change-point problems, Brownian motion processes, Ornstein-Uhlenbeck 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 post-quantum 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 usion-sub lattice fusion, and multistage hybrid LDSF-HC 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 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
- 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 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 time-delays.
- 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 time-delays.
- Creator
- Tiwari, Shanaz, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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In this work, we investigate input-to-state stability (ISS) and other related stability properties for control systems with time-delays. 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 delay-free systems in the context of ISS instead of carrying...
Show moreIn this work, we investigate input-to-state stability (ISS) and other related stability properties for control systems with time-delays. 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 delay-free 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 input-to-input stability properties based on the Razumikhin approach. We then turn our attention to large-scale interconnected systems. It has been well recognized that the small-gain theory is a powerful tool for stability analysis of interconnected systems. Using the Razumikhin approach, we develop small-gain theorems for interconnected systems consisting of two or more subs ystems with time-delays 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 time-varying systems with delays in the framework of ISS., In particular, we consider Lyapunov-Razumikhin functions whose decay rates are affected by time-varying functions that can be zero or even negative on some sets of non-zero 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 small-gain theorems to the time-varying case by treating the time-varying system as an auxiliary time-invariant 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)