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Title: VOICE AUTHENTICATIONA STUDY OF POLYNOMIAL REPRESENTATION OF SPEECH SIGNALS.
Creator: Strange, John, Mohapatra, Ram, University of Central Florida
Abstract / Description: A subset of speech recognition is the use of speech recognition techniques for voice authentication. Voice authentication is an alternative security application to the other biometric security measures such as the use of fingerprints or iris scans. Voice authentication has advantages over the other biometric measures in that it can be utilized remotely, via a device like a telephone. However, voice authentication has disadvantages in that the authentication system typically requires a large...
Show moreA subset of speech recognition is the use of speech recognition techniques for voice authentication. Voice authentication is an alternative security application to the other biometric security measures such as the use of fingerprints or iris scans. Voice authentication has advantages over the other biometric measures in that it can be utilized remotely, via a device like a telephone. However, voice authentication has disadvantages in that the authentication system typically requires a large memory and processing time than do fingerprint or iris scanning systems. Also, voice authentication research has yet to provide an authentication system as reliable as the other biometric measures. Most voice recognition systems use Hidden Markov Models (HMMs) as their basic probabilistic framework. Also, most voice recognition systems use a frame based approach to analyze the voice features. An example of research which has been shown to provide more accurate results is the use of a segment based model. The HMMs impose a requirement that each frame has conditional independence from the next. However, at a fixed frame rate, typically 10 ms., the adjacent feature vectors might span the same phonetic segment and often exhibit smooth dynamics and are highly correlated. The relationship between features of different phonetic segments is much weaker. Therefore, the segment based approach makes fewer conditional independence assumptions which are also violated to a lesser degree than for the frame based approach. Thus, the HMMs using segmental based approaches are more accurate. The speech polynomials (feature vectors) used in the segmental model have been shown to be Chebychev polynomials. Use of the properties of these polynomials has made it possible to reduce the computation time for speech recognition systems. Also, representing the spoken word waveform as a Chebychev polynomial allows for the recognition system to easily extract useful and repeatable features from the waveform allowing for a more accurate identification of the speaker. This thesis describes the segmental approach to speech recognition and addresses in detail the use of Chebychev polynomials in the representation of spoken words, specifically in the area of speaker recognition. .
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Date Issued: 2005
Identifier: CFE0000366, ucf:46340
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0000366

Title: MODELING TRANSMISSION DYNAMICS OF TUBERCULOSIS INCLUDING VARIOUS LATENT PERIODS.
Creator: Atkins, Tracy, Mohapatra, Ram, University of Central Florida
Abstract / Description: The systems of equations created by Blower et al. (1995) and Jia et al. (2007) designed to model the dynamics of Tuberculosis are solved using the computer software SIMULINK. The results are first employed to examine the intrinsic transmission dynamics of the disease through two models developed by Blower et al. (1995). The "simple transmission model" was used primarily to give insight to the behavior of the susceptible, latent, and infectious groups of individuals. Then, we consider a more...
Show moreThe systems of equations created by Blower et al. (1995) and Jia et al. (2007) designed to model the dynamics of Tuberculosis are solved using the computer software SIMULINK. The results are first employed to examine the intrinsic transmission dynamics of the disease through two models developed by Blower et al. (1995). The "simple transmission model" was used primarily to give insight to the behavior of the susceptible, latent, and infectious groups of individuals. Then, we consider a more detailed transmission model which includes several additional factors. This model captures the dynamics of not only the susceptible, latent and infectious groups but also the non-infectious cases and the recovered cases. Using the SIMULINK results, it can be shown that the intrinsic dynamics of the disease contribute to the rise and decline of the disease seen in historical accounts. Next, the simulation results are used to study the equilibrium points of the disease which can be obtained by varying the parameters and therefore changing the value for the basic reproduction ratio (R0 ). Our model uses the system of equations developed by Jia et al. (2007). The SIMULINK results are used to visually confirm the hypothesis proposed by Jia et al. (2007) that the equilibrium behavior of the system when R0 > 1 is globally asymptotically stable.
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Date Issued: 2008
Identifier: CFE0002030, ucf:47606
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0002030

Title: PADE APPROXIMANTS AND ONE OF ITS APPLICATIONS.
Creator: fowe, Tame-kouontcho, Mohapatra, Ram, University of Central Florida
Abstract / Description: This thesis is concerned with a brief summary of the theory of Padé approximants and one of its applications to Finance. Proofs of most of the theorems are omitted and many developments could not be mentioned due to the vastness of the field of Padé approximations. We provide reference to research papers and books that contain exhaustive treatment of the subject. This thesis is mainly divided into two parts. In the first part we derive a general expression of the Padé...
Show moreThis thesis is concerned with a brief summary of the theory of Padé approximants and one of its applications to Finance. Proofs of most of the theorems are omitted and many developments could not be mentioned due to the vastness of the field of Padé approximations. We provide reference to research papers and books that contain exhaustive treatment of the subject. This thesis is mainly divided into two parts. In the first part we derive a general expression of the Padé approximants and some of the results that will be related to the work on the second part of the thesis. The Aitken's method for quick convergence of series is highlighted as Padé . We explore the criteria for convergence of a series approximated by Padé approximants and obtain its relationship to numerical analysis with the help of the Crank-Nicholson method. The second part shows how Padé approximants can be a smooth method to model the term structure of interest rates using stochastic processes and the no arbitrage argument. Padé approximants have been considered by physicists to be appropriate for approximating large classes of functions. This fact is used here to compare Padé approximants with very low indices and two parameters to interest rates variations provided by the Federal Reserve System in the United States.
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Date Issued: 2007
Identifier: CFE0001682, ucf:47217
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0001682

Title: A MATHEMATICAL STUDY OF TWO RETROVIRUSES, HIV AND HTLV-I.
Creator: Baxley, Dana, Mohapatra, Ram, University of Central Florida
Abstract / Description: In this thesis, we examine epidemiological models of two different retroviruses, which infect the human body. The two viruses under study are HIV or the human immunodefiency virus and HTLV-I, which is the human T lymphotropic virus type I. A retrovirus is a virus, which injects its RNA into the host, rather than it's DNA. We will study each of the different mathematical models for each of the viruses separately. Then we use MATLAB-SIMULINK to analyze the models by studying the...
Show moreIn this thesis, we examine epidemiological models of two different retroviruses, which infect the human body. The two viruses under study are HIV or the human immunodefiency virus and HTLV-I, which is the human T lymphotropic virus type I. A retrovirus is a virus, which injects its RNA into the host, rather than it's DNA. We will study each of the different mathematical models for each of the viruses separately. Then we use MATLAB-SIMULINK to analyze the models by studying the reproductive numbers in each case and the disease progression by examining the graphs. In Chapter 1, we mention basic ideas associated with HIV and HTLV-I. In Chapter 2 some of the basic mathematical model of epidemiology is presented. Chapter 3 is devoted to a model describing the intra-host dynamics of HIV. Here, we take into account how HIV infects and replicates in the CD4+ T cells. The model studied in this thesis examines the difference between cells, which are susceptible to the virus, and cells, which are not susceptible. Through the graphs associated with this model, we are able to see how this difference affects disease progression. In Chapter 4, we examine the effect of HTLV-I virus on human body. The HTLV-I virus causes a chronic infection in humans and may eventually lead to other diseases. In particular, the development of Adult T-cell Leukemia or ATL is studied in this thesis. The T-cell dynamics and progression to ATL is described using a mathematical model with coupled differential equations. Using mathematical analysis and SIMULINK, we obtain results on stability, asymptotic stability and the manner of progression of the disease. In Chapter 5 and appendices, we mention our inference and the MATLAB-SIMULINK codes used in this thesis, so that a reader can verify the details of the work carried out in this thesis.
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Date Issued: 2007
Identifier: CFE0001886, ucf:47398
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0001886

Title: AN EXAMINATION OF THE EFFECTIVENESS OF THE ADOMIAN DECOMPOSITION METHOD IN FLUID DYNAMIC APPLICATIONS.
Creator: Holmquist, Sonia, Mohapatra, Ram, University of Central Florida
Abstract / Description: Since its introduction in the 1980's, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method...
Show moreSince its introduction in the 1980's, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for fluid dynamic applications. In particular, the ADM has been applied to the Blasius equation, the Falkner-Skan equation, and the Orr-Sommerfeld equation. This study is divided into five Chapters and an Appendix. The first chapter is devoted to an introduction of the Adomian Decomposition method (ADM) with simple illustrations. The Second Chapter is devoted to the application of the ADM to generalized Blasius Equation and our result is compared to other published results when the parameter values are appropriately set. Chapter 3 presents the solution generated for the Falkner-Skan equation. Finally, the Orr-Sommerfeld equation is dealt with in the fourth Chapter. Chapter 5 is devoted to the findings and recommendations based on this study. The Appendix contains details of the solutions considered as well as an alternate solution for the generalized Blasius Equation using Bender's delta-perturbation method.
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Date Issued: 2007
Identifier: CFE0001735, ucf:47318
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0001735

Title: DEGREE OF APROXIMATION OF HÖLDER CONTINUOUS FUNCTIONS.
Creator: Landon, Benjamin, Mohapatra, Ram, University of Central Florida
Abstract / Description: Pratima Sadangi in a Ph.D. thesis submitted to Utkal University proved results on degree of approximation of functions by operators associated with their Fourier series. In this dissertation, we consider degree of approximation of functions in H_(α,p) by different operators. In Chapter 1 we mention basic definitions needed for our work. In Chapter 2 we discuss different methods of summation. In Chapter 3 we define the H_(α,p) metric and present the degree of approximation problem...
Show morePratima Sadangi in a Ph.D. thesis submitted to Utkal University proved results on degree of approximation of functions by operators associated with their Fourier series. In this dissertation, we consider degree of approximation of functions in H_(α,p) by different operators. In Chapter 1 we mention basic definitions needed for our work. In Chapter 2 we discuss different methods of summation. In Chapter 3 we define the H_(α,p) metric and present the degree of approximation problem relating to Fourier series and conjugate series of functions in the H_(α,p) metric using Karamata (K^λ) means. In Chapter 4 we present the degree of approximation of an integral associated with the conjugate series by the Euler, Borel and (e,c) means of a series analogous to the Hardy-Littlewood series in the H_(α,p) metric. In Chapter 5 we propose problems to be solved in the future.
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Date Issued: 2008
Identifier: CFE0002414, ucf:47730
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0002414

Title: FRACTAL INTERPOLATION.
Creator: Ramesh, Gayatri, Mohapatra, Ram, University of Central Florida
Abstract / Description: This thesis is devoted to a study about Fractals and Fractal Polynomial Interpolation. Fractal Interpolation is a great topic with many interesting applications, some of which are used in everyday lives such as television, camera, and radio. The thesis is comprised of eight chapters. Chapter one contains a brief introduction and a historical account of fractals. Chapter two is about polynomial interpolation processes such as Newton's, Hermite, and Lagrange. Chapter three focuses on...
Show moreThis thesis is devoted to a study about Fractals and Fractal Polynomial Interpolation. Fractal Interpolation is a great topic with many interesting applications, some of which are used in everyday lives such as television, camera, and radio. The thesis is comprised of eight chapters. Chapter one contains a brief introduction and a historical account of fractals. Chapter two is about polynomial interpolation processes such as Newton's, Hermite, and Lagrange. Chapter three focuses on iterated function systems. In this chapter I report results contained in Barnsley's paper, Fractal Functions and Interpolation. I also mention results on iterated function system for fractal polynomial interpolation. Chapters four and five cover fractal polynomial interpolation and fractal interpolation of functions studied by Navascués. Chapter five and six are the generalization of Hermite and Lagrange functions using fractal interpolation. As a concluding chapter we look at the current applications of fractals in various walks of life such as physics and finance and its prospects for the future.
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Date Issued: 2008
Identifier: CFE0002472, ucf:47698
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0002472

Title: NEURAL NETWORKS SATISFYING STONE-WEIESTRASS THEOREM AND APPROXIMATING SCATTERED DATABYKOHONEN NEURAL NETWORKS.
Creator: Thakkar, Pinal, Mohapatra, Ram, University of Central Florida
Abstract / Description: Neural networks are an attempt to build computer networks called artificial neurons, which imitate the activities of the human brain. Its origin dates back to 1943 when neurophysiologist Warren Me Cello and logician Walter Pits produced the first artificial neuron. Since then there has been tremendous development of neural networks and their applications to pattern and optical character recognition, speech processing, time series prediction, image processing and scattered data approximation....
Show moreNeural networks are an attempt to build computer networks called artificial neurons, which imitate the activities of the human brain. Its origin dates back to 1943 when neurophysiologist Warren Me Cello and logician Walter Pits produced the first artificial neuron. Since then there has been tremendous development of neural networks and their applications to pattern and optical character recognition, speech processing, time series prediction, image processing and scattered data approximation. Since it has been shown that neural nets can approximate all but pathological functions, Neil Cotter considered neural network architecture based on Stone-Weierstrass Theorem. Using exponential functions, polynomials, rational functions and Boolean functions one can follow the method given by Cotter to obtain neural networks, which can approximate bounded measurable functions. Another problem of current research in computer graphics is to construct curves and surfaces from scattered spatial points by using B-Splines and NURBS or Bezier surfaces. Hoffman and Varady used Kohonen neural networks to construct appropriate grids. This thesis is concerned with two types of neural networks viz. those which satisfy the conditions of the Stone-Weierstrass theorem and Kohonen neural networks. We have used self-organizing maps for scattered data approximation. Neural network Tool Box from MATLAB is used to develop the required grids for approximating scattered data in one and two dimensions.
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Date Issued: 2004
Identifier: CFE0000226, ucf:46262
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0000226

Title: ON MODELING HIV INFECTION OF CD4+ T CELLS.
Creator: Comerford, Amy, Mohapatra, Ram, University of Central Florida
Abstract / Description: We examine an early model for the interaction of HIV with CD4+ T cells in vivo and define possible parameters and effects of said parameters on the model. We then examine a newer, more simplified model for the interaction of HIV with CD4+ T cells that also considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The stability of both the disease free steady state and the endemically infected steady state are examined utilizing...
Show moreWe examine an early model for the interaction of HIV with CD4+ T cells in vivo and define possible parameters and effects of said parameters on the model. We then examine a newer, more simplified model for the interaction of HIV with CD4+ T cells that also considers four populations: uninfected T cells, latently infected T cells, actively infected T cells, and free virus. The stability of both the disease free steady state and the endemically infected steady state are examined utilizing standard methods and the Routh-Hurwitz criteria. We show that if N, the number of infectious virions produced per actively infected T cell, is less than a critical value, , then the uninfected state is the only steady state in the non negative orthant, and this state is stable. We establish an expression for . If , then the uninfected steady state is unstable, and the endemically infected state can be stable or unstable, depending on the value of the parameters utilized.
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Date Issued: 2006
Identifier: CFE0001093, ucf:46769
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0001093

Title: A COMPARATIVE STUDY OF ANT COLONY OPTIMIZATION.
Creator: Becker, Matthew, Mohapatra, Ram, University of Central Florida
Abstract / Description: Ant Colony Optimization (ACO) belongs to a class of biologically-motivated approaches to computing that includes such metaheuristics as artificial neural networks, evolutionary algorithms, and artificial immune systems, among others. Emulating to varying degrees the particular biological phenomena from which their inspiration is drawn, these alternative computational systems have succeeded in finding solutions to complex problems that had heretofore eluded more traditional techniques. Often,...
Show moreAnt Colony Optimization (ACO) belongs to a class of biologically-motivated approaches to computing that includes such metaheuristics as artificial neural networks, evolutionary algorithms, and artificial immune systems, among others. Emulating to varying degrees the particular biological phenomena from which their inspiration is drawn, these alternative computational systems have succeeded in finding solutions to complex problems that had heretofore eluded more traditional techniques. Often, the resulting algorithm bears little resemblance to its biological progenitor, evolving instead into a mathematical abstraction of a singularly useful quality of the phenomenon. In such cases, these abstract computational models may be termed biological metaphors. Mindful that a fine line separates metaphor from distortion, this paper outlines an attempt to better understand the potential consequences an insufficient understanding of the underlying biological phenomenon may have on its transformation into mathematical metaphor. To that end, the author independently develops a rudimentary ACO, remaining as faithful as possible to the behavioral qualities of an ant colony. Subsequently, the performance of this new ACO is compared with that of a more established ACO in three categories: (1) the hybridization of evolutionary computing and ACO, (2) the efficacy of daemon actions, and (3) theoretical properties and convergence proofs.
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Date Issued: 2006
Identifier: CFE0001192, ucf:46844
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0001192

Title: ON PRIME GENERATION THROUGH PRIMITIVE DIVISORS OF RECURRENCE SEQUENCES.
Creator: Russell, Richard, Mohapatra, Ram, University of Central Florida
Abstract / Description: We examine results concerning the generation of primes in certain types of integer sequences. The sequences discussed all have a connection in that each satisfies a recurrence relation. Mathematicians have speculated over many centuries that these sequences contain an infinite number of prime terms, however no proof has been given as such. We examine a less direct method of showing an infinitude of primes in each sequence by showing that the sequences contain an infinite number of terms with...
Show moreWe examine results concerning the generation of primes in certain types of integer sequences. The sequences discussed all have a connection in that each satisfies a recurrence relation. Mathematicians have speculated over many centuries that these sequences contain an infinite number of prime terms, however no proof has been given as such. We examine a less direct method of showing an infinitude of primes in each sequence by showing that the sequences contain an infinite number of terms with primitive divisors.
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Date Issued: 2006
Identifier: CFE0001013, ucf:46833
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0001013

Title: CLIMATE MODELING, OUTGOING LONGWAVE RADIATION, AND TROPICAL CYCLONE FORECASTING.
Creator: Rechtman, Thomas, Mohapatra, Ram N., University of Central Florida
Abstract / Description: Climate modeling and tropical cyclone forecasting are two significant issues that are continuously being improved upon for more accurate weather forecasting and preparedness. In this thesis, we have studied three climate models and formulated a new model with a view to determine the outgoing longwave radiation (OLR) budget at the top of the atmosphere (TOA) as observed by the National Oceanic and Atmospheric Administration's (NOAA) satellite based Advanced Very High Resolution Radiometer ...
Show moreClimate modeling and tropical cyclone forecasting are two significant issues that are continuously being improved upon for more accurate weather forecasting and preparedness. In this thesis, we have studied three climate models and formulated a new model with a view to determine the outgoing longwave radiation (OLR) budget at the top of the atmosphere (TOA) as observed by the National Oceanic and Atmospheric Administration's (NOAA) satellite based Advanced Very High Resolution Radiometer (AVHRR). In 2006, Karnauskas proposed the African meridional OLR as an Atlantic hurricane predictor, the relation was further proven in 2016 by Karnauskas and Li. Here we have considered a similar study for all other tropical cyclone basins.
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Date Issued: 2018
Identifier: CFH2000403, ucf:45775
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFH2000403

Title: INITIAL-VALUE TECHNIQUE FOR SINGULARLY PERTURBED TWO POINT BOUNDARY VALUE PROBLEMS VIA CUBIC SPLINE.
Creator: Negron, Luis, Mohapatra, Ram, University of Central Florida
Abstract / Description: A recent method for solving singular perturbation problems is examined. It is designed for the applied mathematician or engineer who needs a convenient, useful tool that requires little preparation and can be readily implemented using little more than an industry-standard software package for spreadsheets. In this paper, we shall examine singularly perturbed two point boundary value problems with the boundary layer at one end point. An initial-value technique is used for its solution by...
Show moreA recent method for solving singular perturbation problems is examined. It is designed for the applied mathematician or engineer who needs a convenient, useful tool that requires little preparation and can be readily implemented using little more than an industry-standard software package for spreadsheets. In this paper, we shall examine singularly perturbed two point boundary value problems with the boundary layer at one end point. An initial-value technique is used for its solution by replacing the problem with an asymptotically equivalent first order problem, which is, in turn, solved as an initial value problem by using cubic splines. Numerical examples are provided to show that the method presented provides a fine approximation of the exact solution. The first chapter provides some background material to the cubic spline and boundary value problems. The works of several authors and a comparison of different solution methods are also discussed. Finally, some background into the specific singularly perturbed boundary value problems is introduced. The second chapter contains calculations and derivations necessary for the cubic spline and the initial value technique which are used in the solutions to the boundary value problems. The third chapter contains some worked numerical examples and the numerical data obtained along with most of the tables and figures that describe the solutions. The thesis concludes with some reflections on the results obtained and some discussion of the error bounds on the calculated approximations to the exact solutions for the numeric examples discussed.
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Date Issued: 2010
Identifier: CFE0003460, ucf:48398
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0003460

Title: Visionary Ophthalmics: Confluence of Computer Vision and Deep Learning for Ophthalmology.
Creator: Morley, Dustin, Foroosh, Hassan, Bagci, Ulas, Gong, Boqing, Mohapatra, Ram, University of Central Florida
Abstract / Description: Ophthalmology is a medical field ripe with opportunities for meaningful application of computer vision algorithms. The field utilizes data from multiple disparate imaging techniques, ranging from conventional cameras to tomography, comprising a diverse set of computer vision challenges. Computer vision has a rich history of techniques that can adequately meet many of these challenges. However, the field has undergone something of a revolution in recent times as deep learning techniques have...
Show moreOphthalmology is a medical field ripe with opportunities for meaningful application of computer vision algorithms. The field utilizes data from multiple disparate imaging techniques, ranging from conventional cameras to tomography, comprising a diverse set of computer vision challenges. Computer vision has a rich history of techniques that can adequately meet many of these challenges. However, the field has undergone something of a revolution in recent times as deep learning techniques have sprung into the forefront following advances in GPU hardware. This development raises important questions regarding how to best leverage insights from both modern deep learning approaches and more classical computer vision approaches for a given problem. In this dissertation, we tackle challenging computer vision problems in ophthalmology using methods all across this spectrum. Perhaps our most significant work is a highly successful iris registration algorithm for use in laser eye surgery. This algorithm relies on matching features extracted from the structure tensor and a Gabor wavelet (-) a classically driven approach that does not utilize modern machine learning. However, drawing on insight from the deep learning revolution, we demonstrate successful application of backpropagation to optimize the registration significantly faster than the alternative of relying on finite differences. Towards the other end of the spectrum, we also present a novel framework for improving RANSAC segmentation algorithms by utilizing a convolutional neural network (CNN) trained on a RANSAC-based loss function. Finally, we apply state-of-the-art deep learning methods to solve the problem of pathological fluid detection in optical coherence tomography images of the human retina, using a novel retina-specific data augmentation technique to greatly expand the data set. Altogether, our work demonstrates benefits of applying a holistic view of computer vision, which leverages deep learning and associated insights without neglecting techniques and insights from the previous era.
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Date Issued: 2018
Identifier: CFE0007058, ucf:52001
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0007058

Title: Variational inclusions with general over-relaxed proximal point and variational-like inequalities with densely pseudomonotonicity.
Creator: Nguyen, George, Mohapatra, Ram, Han, Deguang, Shuai, Zhisheng, Xu, Mengyu, University of Central Florida
Abstract / Description: This dissertation focuses on the existence and uniqueness of the solutions of variational inclusion and variational inequality problems and then attempts to develop efficient algorithms to estimate numerical solutions for the problems. The dissertation consists a total of five chapters. Chapter 1 is an introduction to variational inequality problems, variational inclusion problems, monotone operators, and some basic definitions and preliminaries from convex analysis. Chapter 2 is a studyof a...
Show moreThis dissertation focuses on the existence and uniqueness of the solutions of variational inclusion and variational inequality problems and then attempts to develop efficient algorithms to estimate numerical solutions for the problems. The dissertation consists a total of five chapters. Chapter 1 is an introduction to variational inequality problems, variational inclusion problems, monotone operators, and some basic definitions and preliminaries from convex analysis. Chapter 2 is a studyof a general class of nonlinear implicit inclusion problems. The objective of this study is to explore how to omit the Lipschitz continuity condition by using an alternating approach to the proximal point algorithm to estimate the numerical solution of the implicit inclusion problems. In chapter 3 we introduce generalized densely relaxed ? ? ? pseudomonotone operators and generalized relaxed ? ? ? proper quasimonotone operators as well as relaxed ? ? ? quasimonotone operators. Using these generalized monotonicity notions, we establish the existence results for the generalized variational-like inequality in the general setting of Banach spaces. In chapter 4, we use the auxiliary principle technique to introduce a general algorithm for solutions of the densely relaxed pseudomonotone variational-like inequalities. Chapter 5 is the chapter concluding remarks and scope for future work.
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Date Issued: 2019
Identifier: CFE0007693, ucf:52410
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0007693

Title: In Quest of Bernstein Inequalities Rational Functions, Askey-Wilson Operator, and Summation Identities for Entire Functions.
Creator: Puwakgolle Gedara, Rajitha, Li, Xin, Mohapatra, Ram, Ismail, Mourad, Xu, Mengyu, University of Central Florida
Abstract / Description: The title of the dissertation gives an indication of the material involved with the connecting thread throughout being the classical Bernstein inequality (and its variants), which provides an estimate to the size of the derivative of a given polynomial on a prescribed set in the complex plane, relative to the size of the polynomial itself on the same set. Chapters 1 and 2 lay the foundation for the dissertation. In Chapter 1, we introduce the notations and terminology that will be used...
Show moreThe title of the dissertation gives an indication of the material involved with the connecting thread throughout being the classical Bernstein inequality (and its variants), which provides an estimate to the size of the derivative of a given polynomial on a prescribed set in the complex plane, relative to the size of the polynomial itself on the same set. Chapters 1 and 2 lay the foundation for the dissertation. In Chapter 1, we introduce the notations and terminology that will be used throughout. Also a brief historical recount is given on the origin of the Bernstein inequality, which dated back to the days of the discovery of the Periodic table by the Russian Chemist Dmitri Mendeleev. In Chapter 2, we narrow down the contents stated in Chapter 1 to the problems we were interested in working during the course of this dissertation. Henceforth, we present a problem formulation mainly for those results for which solutions or partial solutions are provided in the subsequent chapters.Over the years Bernstein inequality has been generalized and extended in several directions. In Chapter \ref{Bern-ineq}, we establish rational analogues to some Bernstein-type inequalities for restricted zeros and prescribed poles. Our inequalities extend the results for polynomials, especially which are themselves improved versions of the classical Erd\"{o}s-Lax and Tur\'{a}n inequalities. In working towards proving our results, we establish some auxiliary results, which may be of interest on their own. Chapters \ref{AW-on-polynomials} and \ref{AW-on-entire} focus on the research carried out with the Askey-Wilson operator applied on polynomials and entire functions (of exponential type) respectively.In Chapter 4, we first establish a Riesz-type interpolation formula on the interval $[-1,1]$ for the Askey-Wilson operator. In consequence, a sharp Bernstein inequality and a Markov inequality are obtained when differentiation is replaced by the Askey-Wilson operator. Moreover, an inverse approximation theorem is proved using a Bernstein-type inequality in $L^2-$space. We conclude this chapter with an overconvergence result which is applied to characterize all $q$-differentiable functions of Brown and Ismail. Chapter \ref{AW-on-entire} is devoted to an intriguing application of the Askey-Wilson operator. By applying it on the Sampling Theorem on entire functions of exponential type, we obtain a series representation formula, which is what we called an extended Boas' formula. Its power in discovering interesting summation formulas, some known and some new will be demonstrated. As another application, we are able to obtain a couple of Bernstein-type inequalities.In the concluding chapter, we state some avenues where this research can progress.
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Date Issued: 2018
Identifier: CFE0007237, ucf:52220
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0007237

Title: Semi-Analytical Solutions of Non-linear Differential Equations Arising in Science and Engineering.
Creator: Dewasurendra, Mangalagama, Vajravelu, Kuppalapalle, Mohapatra, Ram, Rollins, David, Kumar, Ranganathan, University of Central Florida
Abstract / Description: Systems of coupled non-linear differential equations arise in science and engineering are inherently nonlinear and difficult to find exact solutions. However, in the late nineties, Liao introduced Optimal Homotopy Analysis Method (OHAM), and it allows us to construct accurate approximations to the systems of coupled nonlinear differential equations.The drawback of OHAM is, we must first choose the proper auxiliary linear operator and then solve the linear higher-order deformation equation by...
Show moreSystems of coupled non-linear differential equations arise in science and engineering are inherently nonlinear and difficult to find exact solutions. However, in the late nineties, Liao introduced Optimal Homotopy Analysis Method (OHAM), and it allows us to construct accurate approximations to the systems of coupled nonlinear differential equations.The drawback of OHAM is, we must first choose the proper auxiliary linear operator and then solve the linear higher-order deformation equation by spending lots of CPU time. However, in the latest innovation of Liao's " Method of Directly Defining inverse Mapping (MDDiM)" which he introduced to solve a single nonlinear ordinary differential equation has great freedom to define the inverse linear map directly. In this way, one can solve higher order deformation equations quickly, and it is unnecessary to calculate an inverse linear operator.Our primary goal is to extend MDDiM to solve systems of coupled nonlinear ordinary differential equations. In the first chapter, we will introduce MDDiM and briefly discuss the advantages of MDDiM Over OHAM. In the second chapter, we will study a nonlinear coupled system using OHAM. Next three chapters, we will apply MDDiM to coupled non-linear systems arise in mechanical engineering to study fluid flow and heat transfer. In chapter six we will apply this novel method to study coupled non-linear systems in epidemiology to investigate how diseases spread throughout time. In the last chapter, we will discuss our conclusions and will propose some future work. Another main focus is to compare MDDiM with OHAM.
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Date Issued: 2019
Identifier: CFE0007624, ucf:52551
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0007624

Title: Convective Heat Transfer in Nanofluids.
Creator: Schraudner, Steven, Vajravelu, Kuppalapalle, Mohapatra, Ram, Rollins, David, University of Central Florida
Abstract / Description: In recent years, the study of fluid flow with nanoparticles in base fluids has attracted the attention of several researchers due to its various applications to science and engineering problems. Recent investigations on convective heat transfer in nanofluids indicate that the suspended nanoparticles markedly change the transport properties and thereby the heat transfer characteristics. Convection in saturated porous media with nanofluids is also an area of growing interest. In this thesis, we...
Show moreIn recent years, the study of fluid flow with nanoparticles in base fluids has attracted the attention of several researchers due to its various applications to science and engineering problems. Recent investigations on convective heat transfer in nanofluids indicate that the suspended nanoparticles markedly change the transport properties and thereby the heat transfer characteristics. Convection in saturated porous media with nanofluids is also an area of growing interest. In this thesis, we study the effects of radiation on the heat and mass transfer characteristics of nanofluid flows over solid surfaces. In Chapter 2, an investigation is made into the effects of radiation on mixed convection over a wedge embedded in a saturated porous medium with nanofluids, while in Chapter 3 results are presented for the effects of radiation on convection heat transfer about a cone embedded in a saturated porous medium with nanofluids. The resulting governing equations are non-dimensionalized and transformed into a non-similar form and then solved by Keller box method. A comparison is made with the available results in the literature, and the results are found to be in very good agreement. The numerical results for the velocity, temperature, volume fraction, the local Nusselt number and the Sherwood number are presented graphically. The salient features of the results are analyzed and discussed for several sets of values of the pertinent parameters. Also, the effects of the Rosseland diffusion and the Brownian motion are discussed.
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Date Issued: 2012
Identifier: CFE0004214, ucf:49024
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0004214

Title: H(&)#252;ckel Energy of a Graph: Its Evolution From Quantum Chemistry to Mathematics.
Creator: Zimmerman, Steven, Mohapatra, Ram, Song, Zixia, Brigham, Robert, University of Central Florida
Abstract / Description: The energy of a graph began with German physicist, Erich H(&)#252;ckel's 1931 paper, QuantenttheoretischeBeitr(&)#228;ge zum Benzolproblem. His work developed a method for computing thebinding energy of the ?-electrons for a certain class of organic molecules. The vertices of thegraph represented the carbon atoms while the single edge between each pair of distinct verticesrepresented the hydrogen bonds between the carbon atoms. In turn, the chemical graphswere represented by an n (&)#215; n...
Show moreThe energy of a graph began with German physicist, Erich H(&)#252;ckel's 1931 paper, QuantenttheoretischeBeitr(&)#228;ge zum Benzolproblem. His work developed a method for computing thebinding energy of the ?-electrons for a certain class of organic molecules. The vertices of thegraph represented the carbon atoms while the single edge between each pair of distinct verticesrepresented the hydrogen bonds between the carbon atoms. In turn, the chemical graphswere represented by an n (&)#215; n matrix used in solving Schr(&)#246;dinger's eigenvalue/eigenvectorequation. The sum of the absolute values of these graph eigenvalues represented the total?-electron energy. The criteria for constructing these chemical graphs and the chemical interpretationsof all the quantities involved made up the H(&)#252;ckel Molecular Orbital theoryor HMO theory. In this paper, we will show how the chemical interpretation of H(&)#252;ckel'sgraph energy evolved to a mathematical interpretation of graph energy that Ivan Gutmanprovided for us in his famous 1978 definition of the energy of a graph. Next, we will presentCharles Coulson's 1940 theorem that expresses the energy of a graph as a contour integraland prove some of its corollaries. These corollaries allow us to order the energies of acyclicand bipartite graphs by the coefficients of their characteristic polynomial. Following Coulson'stheorem and its corollaries we will look at McClelland's first theorem on the boundsfor the energy of a graph. In the corollaries that follow McClelland's 1971 theorem, we willprove the corollaries that show a direct variation between the energy of a graph and thenumber of its vertices and edges. Finally, we will see how this relationship led to Gutman'sconjecture that the complete graph on n vertices has maximal energy. Although this wasdisproved by Chris Godsil in 1981, we will provide an independent counterexample with thehelp of the software, Maple 13.
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Date Issued: 2011
Identifier: CFE0004184, ucf:49027
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0004184

Title: Applications of Compressive Sensing To Surveillance Problems.
Creator: Huff, Christopher, Mohapatra, Ram, Sun, Qiyu, Han, Deguang, University of Central Florida
Abstract / Description: In many surveillance scenarios, one concern that arises is how to construct an imager that is capable of capturing the scene with high fidelity. This could be problematic for two reasons: first, the optics and electronics in the camera may have difficulty in dealing with so much information; secondly, bandwidth constraints, may pose difficulty in transmitting information from the imager to the user efficiently for reconstruction or realization. In this thesis, we will discuss a mathematical...
Show moreIn many surveillance scenarios, one concern that arises is how to construct an imager that is capable of capturing the scene with high fidelity. This could be problematic for two reasons: first, the optics and electronics in the camera may have difficulty in dealing with so much information; secondly, bandwidth constraints, may pose difficulty in transmitting information from the imager to the user efficiently for reconstruction or realization. In this thesis, we will discuss a mathematical framework that is capable of skirting the two aforementioned issues. This framework is rooted in a technique commonly referred to as compressive sensing. We will explore two of the seminal works in compressive sensing and will present the key theorems and definitions from these two papers. We will then survey three different surveillance scenarios and their respective compressive sensing solutions. The original contribution of this thesis is the development of a distributed compressive sensing model.
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Date Issued: 2012
Identifier: CFE0004317, ucf:49473
Format: Document (PDF)
PURL: http://purl.flvc.org/ucf/fd/CFE0004317

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