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Articles 91 - 120 of 550
Full-Text Articles in Mathematics
Simple Weight Modules Of The Lie Algebra Of Vector Fields Of C2, Andrew Cavaness
Simple Weight Modules Of The Lie Algebra Of Vector Fields Of C2, Andrew Cavaness
Mathematics Dissertations - Archive
Classification of the weight modules of the Lie algebra Wn of vector fields on C n has been a long-standing problem in the area of representation theory. In this thesis, a classification of all simple weight modules of W2 with a uniformly bounded set of weight multiplicities is provided, and much of the theory that will be needed to classify all simple weight modules of Wn with a uniformly bounded set of weight multiplicities will also be developed. To achieve this classification, a new family of generalized tensor Wn-modules is introduced, and a twisted localization functor is applied.
High Order Dns For Vortex Structure In Late Flow Transition, Yong Yang
High Order Dns For Vortex Structure In Late Flow Transition, Yong Yang
Mathematics Dissertations - Archive
Turbulence is still a world puzzle after over one hundred years research, and the current and classical theories brim with self-contradictions. C. Liu proposed a new theory on turbulence generation and structure after 28 years research, which are consistent without self-contradictions and well explain turbulence generation and structure. Based on this new theory, this dissertation (1) gives some mathematical explanations for new vortex identify method – Ω method; (2) analyzes the instability of shear layer by applying Chebyshev spectrum method to solve Orr-Sommerfeld eigenvalue equation; (3) investigates the vortex structure development in late flow transition; (4) utilizes the proper orthogonal …
Characterizing College Algebra Students' Mathematical Problem Solving, R. Cavender Campbell
Characterizing College Algebra Students' Mathematical Problem Solving, R. Cavender Campbell
Mathematics Dissertations - Archive
This study examines the mathematical problem solving (MPS) practices of students enrolled in College Algebra at a large urban university in the southwestern United States. The primary research question explores how to characterize the MPS techniques, strategies or orientations used by College Algebra students. In addition, this study documents MPS approaches that appear to be most prevalent and examines how these approaches relate to student performance. A grounded theory approach is used to formulate a theory for characterizing the MPS of students in College Algebra. Data analysis shows that multiple student-held orientations identified in this theory correlate with improved performance …
Mathematical Methods For Vortex Identification With Application On Shock Wave Vortex Ring Interaction, Yinlin Dong
Mathematical Methods For Vortex Identification With Application On Shock Wave Vortex Ring Interaction, Yinlin Dong
Mathematics Dissertations - Archive
Vortices are seen everywhere in nature, from smoke rings to tornadoes. Vortical structures play an essential role in the turbulence dynamics such as turbulence generation, kinetic energy production and dissipation, enhancement of transport of mass, heat and momentum and so on. In this dissertation, we present several vortex identification methods and compare them by the visualization of the examples studied by direct numerical simulation for flows with different speeds. The comparisons show the Omega method is much close to give vortex a mathematical definition and better visualization for vortical structures. We apply our method on the Micro Vortex Generator (MVG) …
A Mathematical Model Of Hepatitis C Virus Infection Incorporating Immune Responses And Cell Proliferation, Huda Amer Hadi
A Mathematical Model Of Hepatitis C Virus Infection Incorporating Immune Responses And Cell Proliferation, Huda Amer Hadi
Mathematics Theses - Archive
This thesis introduces a mathematical model of differential equations for the chronic hepatitis C virus (HCV) infection, which is a contagious disease that infects the liver cells. Firstly, we present the early mathematical models for the basic dynamics of virus infection that developed and analyzed to understand the dynamics of human immunodeficiency virus (HIV), hepatitis B virus (HBV), and some other viruses. Next, we present the extended model of the basic HCV virus dynamics that incorporate the effectiveness of a treatment. After that, the mathematical model that includes proliferation terms for both infected and uninfected hepatocytes is discussed. Lastly, the …
Normalized Cut Problems With Generalized Linear Constraints, Ivan Ruiz
Normalized Cut Problems With Generalized Linear Constraints, Ivan Ruiz
Mathematics Dissertations - Archive
Several methods are used to process images in many fields, including clustering, image segmentation and medical imaging. The so-called graph-cut methods in graph theory are widely used for image segmentation. In these methods graphs determining the relation between several objects are divided into one or more pieces in order to solve a variety of problems. Most of these methods are unsupervised, which means there is no information known about the data objects. In some of the applications listed above some prior knowledge may be known. Using this prior knowledge can be the key to designing better methods. A novel algorithm …
A Study On The Nonlocal Shallow-Water Model Arising From The Full Water Waves With The Coriolis Effect, Junwei Sun
A Study On The Nonlocal Shallow-Water Model Arising From The Full Water Waves With The Coriolis Effect, Junwei Sun
Mathematics Dissertations - Archive
The Equatorial Undercurrent is a significant feature of the geophysical waves near the equator, which is one of the key factors to explain El Niño phenomenon. However, based on β-plane approximation, the classical theory of geophysical waves ignored the vertical structure of the Equatorial Undercurrent. To obtain a better description of the equatorial waves, in this dissertation, I study the rotational-Camassa-Holm (R-CH) equation, which is a mathematical model of long-crested water waves near the equator, propagating mainly in one direction with the effect of Earth's rotation under the f-plane approximation. R-CH equation can be derived by following the formal asymptotic …
Weighted Upwinding Compact Scheme For Shock Capturing, Hassan Abd Al-Dujaly
Weighted Upwinding Compact Scheme For Shock Capturing, Hassan Abd Al-Dujaly
Mathematics Dissertations - Archive
The Weighted Upwinding Compact Scheme in this dissertation has been constructed due to dissipation and dispersion analysis at each stencil. The new scheme is applied to many one-dimensional typical problems involving discontinuities and shock waves, and it maintains a 7th order of accuracy in smooth areas. Additionally, when using the technology of decoupling the system of WUCS, the global dependency problem of the compact scheme is transferred to a local dependency problem in shock regions. As a result of the decoupling method, the shocks are captured sharply with fewer points compared to the related schemes. Furthermore, high order, high resolution, …
Nonparametric Adaptive Distribution-Free Procedure For Crossover Design With Repeated Measures, Afshan Boodhwani
Nonparametric Adaptive Distribution-Free Procedure For Crossover Design With Repeated Measures, Afshan Boodhwani
Mathematics Dissertations - Archive
We propose to apply adaptive nonparametric procedures (Hill, Padmanabhan, & Puri, 1988) on 2x2 crossover design with repeated measures. We will derive the test-statistics (based on function of ranks) and find their asymptotic distributions. These test-statistics will be used to test (a) equality of carryover effects; (b) equality of direct treatment effects; (c) equality of carryover effects over time (repeated measures); and (d) equality of direct treatment effects over time (repeated measures), as suggested by Johnson and Grender (Johnson & Grender, 1993). We will be testing these hypotheses using modified versions of the test statistics derived by Johnson and Grender …
Existence Of Exact Zero Divisors And Totally Reflexive Modules In Artinian Rings, Basanti Sharma Poudyal
Existence Of Exact Zero Divisors And Totally Reflexive Modules In Artinian Rings, Basanti Sharma Poudyal
Mathematics Dissertations - Archive
In this dissertation, we consider commutative local Artinian rings (A, m, k), which are rings that satisfy the descending chain condition on ideals. First, we investigate the existence of exact zero divisors in Artinian Gorenstein rings. We say that a pair of elements (a, b) in m is an exact pair of zero divisors in A if ann(a) = (b) and ann(b) = (a). It is known that a generic Artinian Gorenstein ring of socle degree 3 contains at least one pair of exact zero divisors. We are interested in the existence of exact pairs of zero divisors in the …
Use Of Generalized Gamma Distribution In Modeling, Hongbo Yu
Use Of Generalized Gamma Distribution In Modeling, Hongbo Yu
Mathematics Theses - Archive
In this study, we have considered analysis of lifetime or survival data with right censoring, which is the most common form of censoring encountered in practice. Assuming a fully parametric setup, the main objective is to consider a wider family of distributions for the lifetime and then find the maximum likelihood estimates of the model parameters using some optimization technique available in R statistical software. In this work, the generalized gamma distribution is considered as the distribution for the lifetime which is flexible in the sense that it contains some of the commonly used lifetime distributions, such as Weibull, gamma, …
A Snapshot Of The Alignment Of University Students’ Mathematical Problem Solving Practices To A Likert Scale Assessment Of Mathematical Problem Solving, Duy Phan
Mathematics Theses - Archive
This study investigates the alignment of students' actual problem-solving practices and compares them to the outcomes on a Likert scale mathematical problem solving (MPS) assessment. The Likert scale survey items developed by the Mathematical Problem Solving Item Development Project (MPSI) to gather information on undergraduate's MPS in five domains: sense-making, representing/connecting, reviewing, justifying, and challenge (Epperson, Rhoads, and Campbell, 2016). This snapshot investigation analyzes two individual undergraduate student interviews to characterize the students' MPS practices. Data analysis suggests a promising alignment between the MPSI survey results and students' actual practices. The analysis also establishes preliminary reliability of the MPSI survey …
Functionality And Robustness Of Injured Connectomic Dynamics In C. Elegans: Linking Behavioral Deficits To Neural Circuit Damage, James M. Kunert, Pedro D. Maia, J. Nathan Kutz
Functionality And Robustness Of Injured Connectomic Dynamics In C. Elegans: Linking Behavioral Deficits To Neural Circuit Damage, James M. Kunert, Pedro D. Maia, J. Nathan Kutz
Mathematics Faculty Publications - Archive
Using a model for the dynamics of the full somatic nervous system of the nematode C. elegans, we address how biological network architectures and their functionality are degraded in the presence of focal axonal swellings (FAS) arising from neurodegenerative disease and/or traumatic brain injury. Using biophysically measured FAS distributions and swelling sizes, we are able to simulate the effects of injuries on the neural dynamics of C. elegans, showing how damaging the network degrades its low-dimensional dynamical responses. We visualize these injured neural dynamics by mapping them onto the worm’s low-dimensional postures, i.e. eigenworm modes. We show that a diversity …
Expectation Maximization-Based Likelihood Inference For Com-Poisson Cure Rate Model With Interval Censored Data, Piyachart Wiangnak
Expectation Maximization-Based Likelihood Inference For Com-Poisson Cure Rate Model With Interval Censored Data, Piyachart Wiangnak
Mathematics Dissertations - Archive
A cure rate or long-term survival model is a model for survival data with the presence of a cure fraction. In this study, we consider the analysis of a cure rate model with interval-censored data, which is one of the most practical censoring scheme in survival study. A competing cause scenario has been considered and the number of competing causes is assumed to follow a flexible Conway-Maxwell Poisson (COM-Poisson) distribution which can handle both over- and under-dispersion that is usually encountered in discrete data and also includes some of the well-known discrete distributions as special cases. In addition, a logistic …
Three Dimensional Image Reconstruction (3direct) Of Sparse Signals With Mri Application, Melinda M. Au
Three Dimensional Image Reconstruction (3direct) Of Sparse Signals With Mri Application, Melinda M. Au
Mathematics Dissertations - Archive
Sparse signal reconstruction has been steadily gaining tremendous attention, specifically in applications of compressed sensing as well as feature selection in signal processing methods [IEEE Signal Processing, Vol. 25 (2008) pp.21-30]. Standard techniques to solve these problems such as the nonlinear Conjugate Gradient method have been used successfully on small and medium sized problems. However, as the desire to collect more data becomes the trend, and the need to process information more quickly and reliably becomes more prevalent than before, these standard meth- ods become inadequate. In this thesis, we present a new approach for sparse signal reconstruction called the …
A Harmonic Function Method For Eeg Source Reconstruction, Hongguang Xi
A Harmonic Function Method For Eeg Source Reconstruction, Hongguang Xi
Mathematics Dissertations - Archive
Neuronal activities generate the electrical current in the brain, and further result in the potential changes over the scalp. Electroencephalography (EEG) is a technique used to record the potential changes on the scalp. Even though fMRI, PET, MEG and other brain-imaging tools are widely used in brain research, they are limited by low spatial/temporal resolution, cost, mobility and suitability for long-term monitoring. In contrast, EEG signals have been successfully used to obtain useful diagnostic information (neural oscillations and response times) in clinical contexts. Further, they present the advantage to be highly portable, inexpensive, and can be acquired at the bedside …
Reproductive Numbers For Periodic Epidemic Systems, Christopher David Mitchell
Reproductive Numbers For Periodic Epidemic Systems, Christopher David Mitchell
Mathematics Dissertations - Archive
When using mathematics to study epidemics, often times the goal is to deter- mine when an infection can invade and persist within a population. This can be done in a variety of ways but the most common is to use threshold quantities called reproductive numbers. For models with only one infection, the basic reproductive number (BRN) is used to determine the stability of the disease-free equilibrium. For many years this was done solely for autonomous systems; however, many diseases exhibit seasonal behavior. If this seasonality is incorporated into models, it gives nonautonomous systems, which while more accurate in their description, …
Numerical Construction Of Diffeomorphism And The Applications To Grid Generation And Image Registration, Xi Chen
Mathematics Dissertations - Archive
Diffeomorphism is an active research topic in differential geometry. In this area, the existence and construction of diffeomorphism under certain constraints is an interesting and meaningful task. J. Moser first proved the existence of diffeomorphism under a Jacobian determinant constraint. Later, Dr. Liao along with his co-authors, proposed the deformation method to construct diffeomorphisms. A div-curl system is created in the construction of diffeomorphisms. Since the Jacobian determinant has a direct physical meaning in grid generation, i.e. the grid cell size, the deformation method was applied successfully to grid generation and adaptation problems. In this dissertation, we review the deformation …
Support And Rank Varieties Of Totally Acyclic Complexes, Nathan Thomas Steele
Support And Rank Varieties Of Totally Acyclic Complexes, Nathan Thomas Steele
Mathematics Dissertations - Archive
Support and rank varieties of modules over a group algebra of an elementary abelian p-group have been well studied. In particular, Avrunin and Scott showed that in this setting, the rank and support varieties are equivalent. Avramov and Buchweitz proved an analogous result for pairs of modules over arbitrary commutative local complete intersection rings. In this dissertation we study support and rank varieties in the triangulated category of totally acyclic chain complexes over a complete intersection ring and show that these varieties are also equivalent. We also show that any homogeneous affine variety is realizable as the support of some …
Representations Of The Extended Poincare Superalgebras In Four Dimensions, John David Griffis
Representations Of The Extended Poincare Superalgebras In Four Dimensions, John David Griffis
Mathematics Dissertations - Archive
Eugene Wigner used the Poincare group to induce representations from the fundamental internal space-time symmetries of (special) relativistic quantum particles. Wigner’s students spent considerable amount of time translating passages of this paper into more detailed and accessible papers and books. In 1975, R. Haag et al. investigated the possible extensions of the symmetries of relativistic quantum particles. They showed that the only consistent (super)symmetric extensions to the standard model of physics are obtained by using super charges to generate the odd part of a Lie superalgebra whos even part is generated by the Poincare group; this theory has become known …
A Bisection Method For The Banded Hyperbolic Quadratic Eigenvalue Problem, Ahmed T. Ali
A Bisection Method For The Banded Hyperbolic Quadratic Eigenvalue Problem, Ahmed T. Ali
Mathematics Dissertations - Archive
It is well-known that the eigenvalues of a Hermitian matrix in a given interval can be approximated within a predefined error tolerance using the bisection method as a direct application of the Sylvester's Law of Inertia. In this thesis, we will develop a bisection method for the hyperbolic quadratic eigenvalue problem (HQEP) which is guaranteed to have 2n real eigenvalues for a problem of size n. A number of numerical methods are available to solve HQEPs. Matlab's polyeig uses the QZ algorithm on the problem after linearizing it to a pencil of size 2n. Another approach is by finding a …
Stochastic Reliability Models For A General Server And Related Networks, Rachel Traylor
Stochastic Reliability Models For A General Server And Related Networks, Rachel Traylor
Mathematics Dissertations - Archive
There are many types of systems which can be dubbed servers, i.e. a retail checkout counter, a shipping company, a web server, or a customer service hotline. All of these systems have common general behavior: requests or customers arrive via a stochastic process, the service times vary randomly, and each request increases the stress on the server for some interval of time. A general stochastic model that describes the reliability of a server can provide the necessary informationfor optimal resource allocation and efficient task scheduling, leading to significant cost savings and improved performance metrics. In this work, we consider several …
On The Quantum Spaces Of Some Quadratic Regular Algebras Of Global Dimension Four, Richard Gene Chandler
On The Quantum Spaces Of Some Quadratic Regular Algebras Of Global Dimension Four, Richard Gene Chandler
Mathematics Dissertations - Archive
A quantum $\mathbb{P}^3$ is a noncommutative analogue of a polynomial ring on four variables, and, herein, it is taken to be a regular algebra of global dimension four. It is well known that if a generic quadratic quantum $\mathbb{P}^3$ exists, then it has a point scheme consisting of exactly twenty distinct points and a one-dimensional line scheme. In this thesis, we compute the line scheme of a family of algebras whose generic member is a candidate for a generic quadratic quantum $\mathbb{P}^3$. We find that, as a closed subscheme of $\mathbb{P}^5$, the line scheme of the generic member is the …
Tensor Products Of A Finite-Dimensional Representation And An Infinite-Dimensional Representation, Felicia Dewanaga
Tensor Products Of A Finite-Dimensional Representation And An Infinite-Dimensional Representation, Felicia Dewanaga
Mathematics Theses - Archive
In this project, we explicitly find the decomposition of the tensor product of a Verma module $Z(\lambda)$ and the standard module ${\mathbb C}^n$ of the Lie algebras $\mathfrak{sl}(n)$, $n=2,3$. The result provides an explicit description of the translation functor introduced by Bernstein and Gelfand.
Number Sense In High School Mathematics Students, Vi Le Nguyen
Number Sense In High School Mathematics Students, Vi Le Nguyen
Mathematics Theses - Archive
Understanding the real number system plays a very important role in each student’s mathematical achievement. The Texas Essential Knowledge and Skills (TEKS) for Mathematics Subchapter A. Elementary states, “For students to become fluent in mathematics, students must develop a robust sense of number” (TEKS Subchapter A Elementary, 2012). Knowledge of the real number system and number sense develops over several years. Once students get to high school, they are expected to have a large amount of knowledge about the real number system and number sense in order to effectively start and complete their high school math courses. However, many high …
Cognitive And Behavioral Deficits Arising From Neurodegeneration And Traumatic Brain Injury: A Model For The Underlying Role Of Focal Axonal Swellings In Neuronal Networks With Plasticity, Samuel Rudy, Pedro D. Maia, J. Nathan Kutz
Cognitive And Behavioral Deficits Arising From Neurodegeneration And Traumatic Brain Injury: A Model For The Underlying Role Of Focal Axonal Swellings In Neuronal Networks With Plasticity, Samuel Rudy, Pedro D. Maia, J. Nathan Kutz
Mathematics Faculty Publications - Archive
Neurodegenerative diseases and traumatic brain injury, whose hallmark features are the presence of focal axonal swellings (FAS), are leading causes of cognitive dysfunction. By leveraging biophysical observations of FAS statistics, we develop a theoretical model of functional neural network activity driven by adaptive changes from plasticity. Based upon the FORCE model of Sussillo and Abbott [1], our innovations highlight the role of plasticity in overcoming injuries and degeneration of neurons in a network architecture. We provide a quantitative measure, on a network level, of cognitive deficits arising from injury. We demonstrate that plasticity is capable of overcoming mild injuries while …
Host Switching Vs. Host Sharing In Overlapping Sylvatic Trypanosoma Cruzi Transmission Cycles, Christopher Kribs, Christopher Mitchell
Host Switching Vs. Host Sharing In Overlapping Sylvatic Trypanosoma Cruzi Transmission Cycles, Christopher Kribs, Christopher Mitchell
Mathematics Faculty Publications - Archive
The principle of competitive exclusion is well established for multiple populations competing for the same resource, and simple models for multistrain infection exhibit it as well when cross-immunity precludes coinfections. However, multiple hosts provide niches for different pathogens to occupy simultaneously. This is the case for the vector-borne parasite Trypanosoma cruzi in overlapping sylvatic transmission cycles in the Americas, where it is enzootic. This study uses cycles in the USA involving two different hosts but the same vector species as a context for the study of the mechanisms behind the communication between the two cycles. Vectors dispersing in search of …
Property D Cyclic Neofields, Scott Lacy
Property D Cyclic Neofields, Scott Lacy
Mathematics Dissertations - Archive
In 1948 L. J. Paige introduced the notion of a neofield (N,\oplus,\cdot) as a set N with two binary operations, generally referred to as addition (\oplus) and multiplication (\cdot) such that (N,\oplus) is a loop with identity 0 and (N-\{0\},\cdot) is a group, with both left and right distribution of multiplication over addition. The neofield was considered a generalization of a field and its application was for the coordinatizing of projective planes and related geometry problems. In 1967 A.D. Keedwell introduced the notion of property D cyclic neofields in relation to his study of latin squares and their application to …
On M-Inverse Loops And Quasigroups Of Order N With A Long Inverse Cycle., Carl Edward Looney
On M-Inverse Loops And Quasigroups Of Order N With A Long Inverse Cycle., Carl Edward Looney
Mathematics Dissertations - Archive
In 2002, A.D Keedwell and V.A Sherbacov introduced the concept of finite m-inverse quasigroups with long inverse cycles. Keedwell and Sherbacov observed that finite m-inverse loops and quasigroups with a long inverse cycle could be useful in the study of cryptology. Keedwell and Sherbacov studied the existence of these algebraic structures by determining if a Cayley table of the elements of such structures could be constructed. They showed that m-inverse loops of order 9 with a long inverse cycle do not exist for m = 2; 4 and 6; thus, there do not exist 2,4, or 6 inverse-quasigroups of order …
Numerical Methods For Spontaneous And Evoked Glutamate Release, Justin Shane Blackwell
Numerical Methods For Spontaneous And Evoked Glutamate Release, Justin Shane Blackwell
Mathematics Dissertations - Archive
As synapses are responsible for the majority of neuron communications in the brain, the events of evoked and spontaneous synaptic vesicle release/fusion are key features of all synaptic current. These release events typically activate receptors within a single postsynaptic site and give rise to miniature postsynaptic currents through activations of $N$-methyl-$D$-asparate (NMDA) and $\alpha$-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors, and therefore, they have been extremely instrumental in neurotransmissions. In this paper we will use a mathematical model to simulate spontaneous and evoked neurotransmission resulted from glutamate release within a synapse. Among several issues that modeling can provide quantitative assessment, the issue of …