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Articles 151 - 180 of 551
Full-Text Articles in Mathematics
Haplotype-Based Statistical Inference For Case-Control Genetic Association Studies With Complex Sampling, Daoying Lin
Haplotype-Based Statistical Inference For Case-Control Genetic Association Studies With Complex Sampling, Daoying Lin
Mathematics Dissertations - Archive
With the advances in human genome research, it is now believed that the risks of many complex diseases are triggered by the interplay of genetic susceptibilities and environmental exposures. The population-based case-control study (PBCCS) is widely used to investigate the role of genetic variants and environmental exposures in the etiology of complex diseases. There are numerous ways to implement the selection process of cases and controls. In its simplest form, a simple random sampling (SRS) design is used to choose cases and controls from diseased and disease-free population, respectively. Though SRS is easy to conduct and relevant statistical methodologies are …
The Polynomial Chaos Method With Applications To Random Differential Equations, Juan Antonio Licea Salazar
The Polynomial Chaos Method With Applications To Random Differential Equations, Juan Antonio Licea Salazar
Mathematics Dissertations - Archive
The role of randomness in mathematical models is of paramount importance, with emphasis placed upon the accuracy and reliability of predictions a rational approach is the use of differential equations with random parameters to describe natural phenomena. Well known methods such as Monte Carlo methods and the method of moments have been implemented to approximate the solutions to random differential equations in the last few decades. In this work, analytic solutions to a particular Riccati type dierential equation and discrete delay dierential equation with random coefficients are derived, also, due to its spectral rate of convergence and simplicity, the polynomial …
Numerical Studies For M-Matrix Algebraic Riccati Equations, Weichao Wang
Numerical Studies For M-Matrix Algebraic Riccati Equations, Weichao Wang
Mathematics Dissertations - Archive
A new doubling algorithm - Alternating-Directional Doubling Algorithm (ADDA) - is developed for computing the unique minimal nonnegative solution of an M-Matrix Algebraic Riccati Equation (MARE). It is argued by both theoretical analysis and numerical experiments that ADDA is always faster than two existing doubling algorithms - SDA of Guo, Lin, and Xu (Numer. Math., 103 (2006), pp. 393-412) and SDA-ss of Bini, Meini, and Poloni (Numer. Math., 116 (2010), pp. 553-578) for the same purpose. A deflation technique is then presented for an irreducible singular M-matrix Algebraic Riccati Equation (MARE). The technique improves the rateof convergence of a doubling …
Dns Study For The Origin Of The Chaos In Late Boundary Layer Transition Over A Flat Plate, Manoj Kumar Thapa
Dns Study For The Origin Of The Chaos In Late Boundary Layer Transition Over A Flat Plate, Manoj Kumar Thapa
Mathematics Dissertations - Archive
This dissertation is devoted to the investigation of the origin and mechanism of chaos ( asymmetric or disorganized flow) in late boundary layer transition over a flat plate without pressure gradient. This kind of flow not only exists at the very late stage of transition but also is a crucial component for turbulence formation- still not well understood. According to existing theories, the formation of the chaos in late boundary layer transition was considered due to big background disturbances (noises) and use of non-periodic spanwise boundary condition during numerical simulations. It was further assumed that universal coherent structures (ring-like vortices) …
Resolutions And Tor Algebra Structures For Trivariate Monomial Ideals, Jared Lafayette Painter
Resolutions And Tor Algebra Structures For Trivariate Monomial Ideals, Jared Lafayette Painter
Mathematics Dissertations - Archive
In this manuscript we explore properties of minimal free resolutions and their relationship to the Tor-algebra structure for trivariate monomial ideals. We begin with an in-depth analysis of minimal free resolutions of S = R / I, where R = k[x; y; z] is a polynomial ring over a field k, and I is a monomial ideal that is primary to the homogeneous maximal ideal m of R. We will de ne a special form of the minimal free resolution of S, and then determine when we get nonzero elements from I as entries in the matrices of the resolution. …
High Order Dns For Late Flow Transition, Ping Lu
High Order Dns For Late Flow Transition, Ping Lu
Mathematics Dissertations - Archive
In this report, a new high order scheme for boundary points is introduced when calculating the derivative of smooth functions by Compact Scheme. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the Compact Scheme. Meanwhile, modified compact scheme is developed by using an effective shock detector to block upwinding compact scheme to cross the shock, a control function, and an adaptive scheme which uses some WENO flux near the shock. The new scheme makes the original upwinding compact scheme able to capture the shock sharper than WENO and, more important, keep high …
From Discrete To Continuous Models Of Cell Movement: An Application To Medical Implants, Alicia Prieto Langarica
From Discrete To Continuous Models Of Cell Movement: An Application To Medical Implants, Alicia Prieto Langarica
Mathematics Dissertations - Archive
Mathematical modeling of cell movement is needed to aid in the deeper understanding of vital processes such as embryogenesis, angiogenesis, tumor metastasis, and immune reactions to foreign bodies. In this work, cell movement and growth in response to external stimulus and the interactions between cells and the stimulus are considered. In order to model the random nature of the movement, a discrete model is created to simulate cells moving in the presence of a growing and moving stimulus distribution. The model also includes the depletion of the stimulus under the presence of cells. The discrete model is then upscaled, based …
A Study On The Two Component Periodic Shallow Water Systems, Caixia Chen
A Study On The Two Component Periodic Shallow Water Systems, Caixia Chen
Mathematics Dissertations - Archive
In this dissertation we study the generalized periodic two-component Camassa-Holm system and the generalized periodic two-component Dullin-Gottwald-Holm system, which can be derived from the Euler equation with nonzero constant vorticity in shallow water waves moving over a linear shear flow. The precise blow-up scenarios of strong solutions and several results of blow-up solutions with certain initial profiles are described in detail. The exact blow-up rates are also determined. Finally, the sufficient conditions for global solutions are established.
Nonlinear Dynamics And Stochasticity Of Core Genetic Regulation, Hongguang Xi
Nonlinear Dynamics And Stochasticity Of Core Genetic Regulation, Hongguang Xi
Mathematics Theses - Archive
Bacillus subtilis is one of the very well-studied organisms in biology. Recent results show that an alternative competence regulation circuit for this bacterium, differing only in the order of the composite negative feedback loop onto the master competence regulator gene comK, despite presenting equivalent functionality, exhibits physiologically important differences.It is not clear why Nature only selects a specific gene regulation circuit other than a plethora of equivalent others. Here, we hope, from the point of view of reverse engineering, to discover the fundamental reasons for natural selection of a particular circuit structure over another. Based on the wild-type Bacillus subtilis …
On Primitivity And Dimension Of Finite Semifields And Their Planes, Linlin Chen
On Primitivity And Dimension Of Finite Semifields And Their Planes, Linlin Chen
Mathematics Dissertations - Archive
The study of semifields was originated by L.E. Dickson in 1905 and was greatly developed in the 1960s by Albert, Knuth, Walker, Kleinfeld among others. Two problems of interest in this area are the primitivity of semifields and the dimension of semifields.For the first problem, we provide an equivalent condition for the right (or left) primitivity of finite semifields and with this result, we find that the classical Knuth binary semifields of order 2^{15}, 2^{17} and 2^{19} are all right and left primitive; the Albert semifields of order 2^i, where i=7, 9, 11, 13 are all primitive. Also we prove …
New Results In Finite Geometries Pertaining To Albert-Like Semifields, Angela Michelle Brown
New Results In Finite Geometries Pertaining To Albert-Like Semifields, Angela Michelle Brown
Mathematics Dissertations - Archive
One of the most widely studied class of semifields are the generalized twisted fields defined by Albert in the 50s and 60s. The collineation groups of generalized twisted field planes have been completely described. In a series of papers Cordero and Figueroa studied semifields with an autotopism that acts transitively on one side of the autotopism triangle, equivalently the plane admits an autotopism which induces a permutation on a side of the autotopism triangle of order a p-primitive divisor of pr - 1. They showed that with some minor exceptions the plane is a generalized twisted field plane. These planes …
High Order Les For Supersonic Ramp Flow Control With Mvg, Yonghua Yan
High Order Les For Supersonic Ramp Flow Control With Mvg, Yonghua Yan
Mathematics Dissertations - Archive
An implicitly implemented large eddy simulation by using the fifth order bandwidth-optimized WENO scheme is applied to make comprehensive studies on ramp flows with and without control at Mach 2.5 and Re=5760. Flow control in the form of microramp vortex generators (MVG) is applied. The results show that MVG can distinctly reduce the separation zone at the ramp corner and lower the boundary layer shape factor under the condition of the computation. A series of new findings are obtained about the MVG-ramp flow including the three-dimensional vortex structure generated by MVG. The mechanism about the formation vortex ring structure and …
Effects Of Vector Migration On Sylvatic Trypanosoma Cruzi Transmission, Britnee A. Crawford
Effects Of Vector Migration On Sylvatic Trypanosoma Cruzi Transmission, Britnee A. Crawford
Mathematics Dissertations - Archive
Vector-borne diseases have had a major impact on global health concerns since their discovery in the 1800's. A vector-borne disease is one transmitted to human or animal host via an invertebrate vector (usually an insect). Chagas' disease, caused by the parasite Trypanosoma cruzi, is transmitted via insect vectors from the Triatoma family. Although human infection with Chagas' is of importance, the disease is maintained in sylvatic (in the wild) transmission cycles. This study examines the effects of vector migration on the spread of T. cruzi in certain sylvatic cycles in the southeastern U.S. and Mexico from several angles. First, a …
High Order Compact Scheme For Discontinuous Differential Equations, James Louis Thompson
High Order Compact Scheme For Discontinuous Differential Equations, James Louis Thompson
Mathematics Dissertations - Archive
A high order implicit second derivative compact method is given which is similar the Adams-Moulton method, but requiring only two steps for sixth order. This method is used in both predictor-corrector and Newton's method formulations, and although the compact scheme is not A-stable or stiffly stable, it's region of stability is over six times greater than the Sixth order Adams-Moulton method. This compact method has a small truncation error coefficient, and is more accurate than Enright's method within the region of stability. Fourth and sixth order explicit compact methods are derived as well, and the three step sixth order explicit …
A Mathematical Model For Swine Flu 2009 With Vaccination, Irfan Turk
A Mathematical Model For Swine Flu 2009 With Vaccination, Irfan Turk
Mathematics Theses - Archive
H1N1 influenza is one of the deadliest diseases in human's history. Swine Flu 2009 is the same virus and it was named in 2009. Vaccination is of the most common ways to control a disease. We offer a new vaccination model with recommendations from the US Centers for Disease Control and Prevention (CDC). The entire population is divided into 4 different age groups: one group with no vaccination, one group with 2 doses of vaccination, and two groups with 1 dose of vaccination. We establish that higher levels of vaccination lead to greater savings of life. We also consider the …
Some Problems Of Integral Geometry In Advanced Imaging, Rim Gouia
Some Problems Of Integral Geometry In Advanced Imaging, Rim Gouia
Mathematics Dissertations - Archive
During the past decade, our society has become dependent on advanced mathematics for many of our daily needs. Mathematics is at the heart of the 21st century technologies and more specifically the emerging imaging technologies from thermoacoustic tomography (TAT) and ultrasound computed tomography (UCT) to non-destructive testing (NDT). All of these applications reconstruct the internal structure of an object from external measurements without damaging the entity under investigation. The basic mathematical idea common to such reconstruction problems is often based upon Radon integral transform.The Radon integral transform Rf puts into correspondence to agiven function f its integrals over certain subsets. …
On The Existence Of Totally Reflexive Modules, Kristen Ann Beck
On The Existence Of Totally Reflexive Modules, Kristen Ann Beck
Mathematics Dissertations - Archive
In this manuscript, we investigate the existence of non-free totally reflexive modules over two classes of commutative local (Noetherian) rings.First, we demonstrate existence over a class of local rings which are defined by a Gorenstein homomorphism. Among the corollaries to this result, we recover a theorem of Avramov, Gasharov, and Peeva (1997) concerning the existence of non-free totally reflexive modules over local rings with embedded deformations. We also give a general construction for a class of local rings which satisfy the hypotheses of our theorem, and we show it is able to produce rings without embedded deformations.The second focus of …
Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension, Manizheh Nafari
Regular Algebras Related To Regular Graded Skew Clifford Algebras Of Low Global Dimension, Manizheh Nafari
Mathematics Dissertations - Archive
M. Artin, W. Schelter, J. Tate, and M. Van den Bergh introduced the notion of non-commutative regular algebras, and classified regular algebras of global dimension 3 on degree-one generators by using geometry (i.e., point schemes) in the late 1980s. Recently, T. Cassidy and M. Vancliff generalized the notion of a graded Clifford algebra and called it a graded skew Clifford algebra.In this thesis, we prove that all classes of quadratic regular algebras of global dimension 3 contain graded skew Clifford algebras or Ore extensions of graded skew Clifford algebras of global dimension 2. We also prove that some regular algebras …
An Investigation Of The Conceptual Understanding Of Continuity And Derivatives In Calculus Of Emerging Scholars Versus Non-Emerging Scholars Program Students, Susan Lai Chan
Mathematics Theses - Archive
The Emerging Scholars Program (ESP) has been adapted at colleges and universities across the nation in efforts to increase student access to Science, Technology, Engineering and Mathematics (STEM) disciplines. This study uses a written assessment to gain insight regarding conceptual knowledge on continuity and derivatives for ESP students versus non-ESP students in the same lecture course in first semester calculus at large urban university in the southwest. We analyze the assessment results of 22 ESP and 48 non-ESP students and discuss findings, particularly, those that indicate statistically significant differences regarding continuity over an interval.
A Snapshot Of Advanced High School Students' Understanding Of Continuity, Melissa Jo Vela
A Snapshot Of Advanced High School Students' Understanding Of Continuity, Melissa Jo Vela
Mathematics Theses - Archive
We report on a study of sixteen high school calculus and seven precalculus students' concept image and concept definition of continuity after one-trimester of instruction at a large suburban high school in the southwestern United States. The researchers developed a questionnaire based upon the work of Tall and Vinner (1981) to determine if calculus students had developed a more sophisticated concept image and concept definition of continuity than students in pre-calculus after a typical treatment in both courses. Using data from the written assessment it was not evident that calculus students demonstrated a more sophisticated concept image and concept definition …
Predictive Model For Bigheaded Carps In Mississippi River, Jitendra K. Shrestha
Predictive Model For Bigheaded Carps In Mississippi River, Jitendra K. Shrestha
Mathematics Theses - Archive
Bigheaded carps refer to two species of fish called Silver carp and Bigheaded carp which have invaded the Upper Mississippi River System and are causing nuisance to the native fish like catfish, paddlefish and gizzard Shad by encroaching their habitat. The exponential growth of their population due to their overwhelming reproduction capability and adaptation features calls for a careful study of their population dynamics. In this study, we offer a mathematical model with artificial excessive fishing effort to reduce the population of Bigheaded carps. We numerically observe the correlation among growth rate, fishing rate and the future population of the …
Cuspidal Modules Of The Lie Superalgebras Osp(1|2n), Alekzander J. Malcom
Cuspidal Modules Of The Lie Superalgebras Osp(1|2n), Alekzander J. Malcom
Mathematics Theses - Archive
The classification of all bounded weight modules for the classical Lie superalgebras is an open question. Only recently, in fact, has the question been closed for the Lie algebras (see Mathieu). We give a differential algebra isomorphic to osp(1|2n), which is one of the remaining Lie superalgebras to have its modules classified. We also conjecture, following the results for the Lie algebra sp(2n), a method to finalize the classification for osp(1|2n).
Conditional Confidence Intervals Of Process Capability Indices Following Rejection Of Preliminary Tests, Jianchun Zhang
Conditional Confidence Intervals Of Process Capability Indices Following Rejection Of Preliminary Tests, Jianchun Zhang
Mathematics Dissertations - Archive
Finding an ordinary confidence interval of an unknown parameter is well known, but finding a conditional confidence interval following rejection of a preliminary test is not so noted, especially for finding a conditional confidence interval of the process capability indices Cp or Cpk following rejection of some preliminary tests. This dissertation will provide some basic theories and computational methods for finding such conditional confidence intervals of the two process capability indices. The most basic method used in this dissertation is the general method for finding a confidence interval of an unknown parameter. Numerical methods are also used for finding the …
The Uniqueness Of Minimal Acyclic Complexes, Meri Trema Hughes
The Uniqueness Of Minimal Acyclic Complexes, Meri Trema Hughes
Mathematics Dissertations - Archive
In this paper, we discuss conditions for uniqueness among minimal acyclic complexes of finitely generated free modules over a commutative local ring which share a common syzygy module. Although such uniqueness occurs over Gorenstein rings, the question has been asked whether two minimal acyclic complexes in general can be isomorphic to the left and non-isomorphic to the right. We answer the question in the negative for certain cases, including periodic complexes, sesqui-acyclic complexes, and certain rings with radical cube zero. In particular, we investigate the question for graded algebras with Hilbert series $H_R(t)=1+et+(e-1)t^2$, and such monomial algebras possessing a special …
High-Order Numerical Schemes For High-Speed Flows, Maria Luisa Bambozzi Oliveira
High-Order Numerical Schemes For High-Speed Flows, Maria Luisa Bambozzi Oliveira
Mathematics Dissertations - Archive
A numerical scheme with high order of accuracy is necessary to resolve small length scales in flow transition and turbulence processes. However, numerical simulation for shock-boundary layer interaction, shock-acoustic interaction, porous media flow and multiple phase flow, among others, also require a numerical scheme that can successfully capture discontinuities. To accomplish this, it is essential that an effective shock/discontinuity detector is implemented to reduce damping of physically important high-frequency waves.In this work, two high-order shock capturing schemes - the Weighted Essentially Non-Oscillatory (WENO) scheme and the Weighted Compact Scheme (WCS) - are investigated. Based on this analysis, a shock/discontinuity detector …
Multiple Linear Regression Model Of Visceral Leishmaniasis In Bihar, India, Darren Sheets
Multiple Linear Regression Model Of Visceral Leishmaniasis In Bihar, India, Darren Sheets
Mathematics Theses - Archive
Visceral Leishmaniasis (VL) is one of the world's worst parasitic killers, second only to Malaria, claiming nearly 500,000 lives each year. The disease attacks the spleen, liver, and bone marrow, and if left untreated is nearly always fatal. Whilst the disease is found all around the world, it is primarily prevalent in developing countries, in particular India. The most affected state in India is Bihar, where the disease is endemic. While other research has been conducted with emphasis on the effect of climate variables on the disease incidence rate, this analysis focuses on socio-economic variables such as literacy rate, housing …
A New Method For Non-Rigid Registration Of 3d Images, Mehmet Ali Akinlar
A New Method For Non-Rigid Registration Of 3d Images, Mehmet Ali Akinlar
Mathematics Dissertations - Archive
In this dissertation we present a novel method for the nonrigid registration of 3D images using a well-established mathematical framework mostly known as the deformation based grid generation method. The deformation based grid generation method is able to generate a grid with desired grid density distribution that is free from grid folding. This method gives direct control over the cell size of the adaptive grid and determines the node velocities directly. The adaptive grid system naturally distributes more grids to deprived areas. The positive monitor function disallows grid folding and provides a mean to control the ratio of the areas …
Non-Traditional Socio-Mathematical Norms In Undergraduate Real Analysis, Paul Christian Dawkins
Non-Traditional Socio-Mathematical Norms In Undergraduate Real Analysis, Paul Christian Dawkins
Mathematics Dissertations - Archive
This study builds upon the framework of classroom norms (Cobb, Wood, & Yackel, 1993) and socio-mathematical norms (Cobb & Yackel, 1996) to understand how non-traditional socio-mathematical norms influence student reasoning and transitions to advanced mathematical thinking in undergraduate real analysis. The research involves a qualitative investigation of classroom instruction and interactions, student and instructor interviews, and class exams. The study explores the roles of each norm as the students constructed understanding of advanced mathematics and transitioned to advanced mathematical thinking. I define "non-traditional" according to research accounts of traditional instruction in proof-based mathematics courses and considerations on the culture of …
Large Deviation Principle For Functional Limit Theorems, Adina Oprisan
Large Deviation Principle For Functional Limit Theorems, Adina Oprisan
Mathematics Dissertations - Archive
We study a family of stochastic additive functionals of Markov processes with locally independent increments switched by jump Markov processes in an asymptotic split phase space. Based on an averaging limit theorem, we obtain a large deviation result for this stochastic evolutionary system using a weak convergence approach. Examples, including compound Poisson processes, illustrate cases in which the rate function is calculated in an explicit form.We prove also a large deviation principle for a class of empirical processes associated with additive functionals of Markov processes that were shown to have a martingale decomposition. Functional almost everywhere central limit theorems are …
Logistic Regression With Misclassified Covariates Using Auxiliary Data, Nathan N. Dong
Logistic Regression With Misclassified Covariates Using Auxiliary Data, Nathan N. Dong
Mathematics Dissertations - Archive
When standard regression methods are used, measurement errors cause a bias in parameters estimation. In dealing with discrete covariates, such measurement errors are known as misclassification and the corresponding discrete covariate is said to be misclassified. Even though the collected data may not be fully reliable, it may be possible to collect some sub-data with full precision called auxiliary data and the remaining data called primary data may contain misclassification. In this paper, in order to improve predictions from the primary data with misclassification, we propose a method based on the maximum likelihood approach; by using the prediction with auxiliary …