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Articles 31 - 60 of 550
Full-Text Articles in Mathematics
Liutex Analysis By Pod And Dmd In Turbulent Flow After/ In Micro Vortex Generator, Xuan My Trieu
Liutex Analysis By Pod And Dmd In Turbulent Flow After/ In Micro Vortex Generator, Xuan My Trieu
Mathematics Dissertations - Archive
Although vortex has been studied more than one hundred year, we still have not had universally accepted definition. A few well-known vortex identification methods are introduced ��,∆, ��2,������ criteria to identify coherent vortex structures the last three decades. A new Omega vortex identification method, which is defined as a ratio of the vorticity tensor norm squared over the sum of the vorticity tensor norm squared and deformation norm squared, was proposed in 2016. Two year later, the new vortex vector named Liutex (previously called Rotex) was proposed by Liu et al. with direction of local rotation axis (an eigenvector of …
A Novel Supervised Dimensionality Reduction Method: Integrating Pca With Svm, Faezeh Soleimani
A Novel Supervised Dimensionality Reduction Method: Integrating Pca With Svm, Faezeh Soleimani
Mathematics Dissertations - Archive
Data curation and storage methods have changed over the past few decades with the use of new technologies, and gathering data on a huge number of features (dimensions) is now very common among diverse scientific and engineering fields. Prior to classification or regression, dimensionality reduction is necessary to eliminate irrelevant features and to deal with data with high dimensions. A number of numerical methods have already been proposed to reduce the dimension of data, for example, Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Supervised Principal Component Analysis (SPCA). In this dissertation, we will introduce a novel way of …
Liutex-Based Vortex Identification Methods And Their Application In Dns Study Of Flat Plate Boundary Layer Transition, Pushpa Shrestha
Liutex-Based Vortex Identification Methods And Their Application In Dns Study Of Flat Plate Boundary Layer Transition, Pushpa Shrestha
Mathematics Dissertations - Archive
Vortices are intuitively known as the rotational motion of fluid particles, however, unambiguous and universally accepted methods of vortex definition and identification are not available to date in the literature. First-generation vortex identification methods, also known as vorticity-based vortex criterion, were first proposed by Helmholtz. But these methods have their own problems. These methods have a shear contamination problem, and these methods did not accurately show the direction of fluid rotation. So, to overcome these problems, eigenvalues based second-generation vortex identification methods like Q, Δ, λ_(2 ), λ_(ci ), and Ω have been proposed. Most of these second-generation methods are …
The Natural Middle Of A Complete Resolution, Rebekah J. Aduddell
The Natural Middle Of A Complete Resolution, Rebekah J. Aduddell
Mathematics Dissertations - Archive
It is widely known that minimal free resolutions of a module over a complete intersection ring have nice patterns that arise in their Betti sequences. In the late 1990's Avramov, Gasharov and Peeva defined a new class of R-modules that would exhibit similar patterns in their free resolutions. In doing so, they additionally defined the notion of critical degree for an R-module, which serves as a “flag” for when such patterns arise in the module’s Betti sequence. The main purpose of this thesis is to present an extension of critical degree to the category of totally acyclic complexes, Ktac(R), where …
Compressive Deconvolution Of Mri Imaging Via ℓ1 − ℓ2 Regularization, Talon Johnson
Compressive Deconvolution Of Mri Imaging Via ℓ1 − ℓ2 Regularization, Talon Johnson
Mathematics Dissertations - Archive
The evolution of technology has drastically impacted the imaging field, particularly magnetic resonance imaging (MRI). Compared to other imaging technologies, MRI offers multiple contrasting mechanisms to distinguish tissues and fat, is radiation-free, and provides anatomical and molecular information about the tissue in question. However, data acquisition times to produce those images require a patient to lie still for a relatively long time. Consequently, it may lead to the voluntary or involuntary movement of the patient due to discomfort. Combined with the underlying issue of inherent noise, MRI is often blurry and contains artifacts. Mathematically, one can describe this behavior as …
On A Cubic Nonlinear Equation Model Arising In Shallow Water Theory, Osama Salameh Alkhazaleh
On A Cubic Nonlinear Equation Model Arising In Shallow Water Theory, Osama Salameh Alkhazaleh
Mathematics Dissertations - Archive
The shallow water waves theory produces numerous integrable equations with cubic non- linearity as asymptotic models. We began our work by formally deriving a model equation for the free surface elevation η with higher-order terms from shallow water in the Euler equation for an incompressible fluid with the simplest bottom and surface conditions. This model equation is truncated at the order O(ε3,εμ) and contains higher-order terms, which are useful for deriving a class of unidirectional wave equations including cubic nonlinear terms. Next, we derived an equation with cubic nonlinearity as the asymptotic method from the classical shallow-water theory by employing …
Deconvolving Kernel Regression Function Estimation Based On Right Censored Data, Erol Ozkan
Deconvolving Kernel Regression Function Estimation Based On Right Censored Data, Erol Ozkan
Mathematics Dissertations - Archive
In this study, we propose a new regression function estimator when the observa- tion is contaminated in the convolution model with error in independent variable. We want to examine the e ect of the error variables when the data is right censored. The tail behavior of the characteristic function of the error distribution is used to describe the optimum local and global rates of convergence of these kernel estimators. We show that depending on the error is either ordinary smooth or super smooth, there are two sorts of convergence rates in adjusted mean square error for the regression function estimator. …
A Study On Approximations Of Totally Acyclic Complexes, Tyler Dean Anway
A Study On Approximations Of Totally Acyclic Complexes, Tyler Dean Anway
Mathematics Dissertations - Archive
Let $R$ be a commutative local ring to which we associate the subcategory $\Ktac(R)$ of the homotopy category of $R$-complexes, consisting of totally acyclic complexes. Further suppose there exists a surjection of Gorenstein local rings $Q \xrightarrowdbl{\varphi} R$ such that $R$ can be viewed as a $Q$-module with finite projective dimension. Under these assumptions, Bergh, Jorgensen, and Moore define the notion of approximations of totally acyclic complexes. In this dissertation we make extensive use of these approximations and define several novel applications. In particular, we extend Auslander-Reiten theory from the category of $R$-modules over a Henselian Gorenstein ring and show …
Mathematical Approach Of Liutex Core Line And Liutex Core Tube For Vortex Structure Visualization, Dalal Khalid B Almutairi
Mathematical Approach Of Liutex Core Line And Liutex Core Tube For Vortex Structure Visualization, Dalal Khalid B Almutairi
Mathematics Dissertations - Archive
During the past decades, many vortex identification methods have been published to present a clear definition and identification of the vortex. However, all these methods are failed to offer a unique identification method, and they also cannot answer the six essential issues for vortex identification methods, which are: 1) absolute strength, 2) relative strength, 3) rotational axis, 4) vortex core center location, 5) vortex core size, and 6) vortex boundary. In this work, two vortex identification methods, which are never affected by the threshold, will be proposed. Moreover, this study will address two critical questions: 1) Where is the rotational …
Liutex And Statistical Analysis For Fluid Transition, Charles Matthew Nehemiah Nottage
Liutex And Statistical Analysis For Fluid Transition, Charles Matthew Nehemiah Nottage
Mathematics Dissertations - Archive
A vortex can be intuitively recognized as the rotational swirling motion of the fluids. The fascination of this phenomenon brought about many years of research to define, classify, and identify the vortical structure. Throughout the decades, many vortex identification methods were developed and can be characterized into three generations. The generational methods are vorticity-based, eigenvalue-based such as Q, ��_ci, and ��_2, and Liutex-based. Before the development of Liutex, there was no mathematical definition for vortex. Is Liutex superior to vorticity and the eigenvalue-based methods? Is the vorticity vector the local rotational axis? Should vorticity be considered vortex? In this dissertation, …
On Different Computational Aspects For Box-Cox Transformation Cure Rate Model, Pei Wang
On Different Computational Aspects For Box-Cox Transformation Cure Rate Model, Pei Wang
Mathematics Dissertations - Archive
Cure rate modeling is an emerging area of research not only in biomedical science but also in other disciplines such as sociology, criminal justice, economics and engineering reliability. In the first part of this thesis, use of the wider class of generalized gamma distributions is proposed as the distribution of the lifetime for a particular transformation cure rate model, known as the Box-Cox transformation cure rate model. The maximum likelihood estimation of the Box-Cox transformation cure model parameters is studied through the calculated bias, mean square error and coverage probabilities of the asymptotic confidence intervals. The flexibilities of both generalized …
Some Quadratic Quantum P³S With A Linear One-Dimensional Line Scheme, Ian Christopher Lim
Some Quadratic Quantum P³S With A Linear One-Dimensional Line Scheme, Ian Christopher Lim
Mathematics Dissertations - Archive
It is believed that quadratic Artin-Shelter regular (AS-regular) algebras of global dimension four (sometimes called quadratic quantum P3s can be classified using a geometry similar to that developed in the 1980’s by Artin, Tate, and Van den Bergh. Their geometry involved studying a scheme (later called the point scheme) that parametrizes the point modules over a graded algebra. The notion of line scheme (which parametrizes line modules) was introduced later by Shelton and Vancliff. It is known that “generic” quadratic quantum P3s have a finite point scheme and one-dimensional line scheme. A family of algebras with these properties is presented …
Option Pricing With Investment Strategy Under Stochastic Interest Rates, Niloofar Ghorbani
Option Pricing With Investment Strategy Under Stochastic Interest Rates, Niloofar Ghorbani
Mathematics Dissertations - Archive
Equity options are the most common types of financial derivatives that give an investor the right but not the obligation to buy or sell shares of stock at a given price in the future for a premium (option price) paid at present. The Classical Black- Scholes Formula solved a longstanding mathematical problem of finding no arbitrage option price by means of stochastic Ito calculus based on Geometric Brownian Motion dynamics of the stock price and a fixed interest rate over the option time horizon. We extend the Black-Scholes Model by adding a component of investor’s buying and selling strategies for …
Assessing The Impact Of Vaccination And Behavior Change On Outbreaks Of Emerging Respiratory Diseases, Mohammed Hameed Alharbi
Assessing The Impact Of Vaccination And Behavior Change On Outbreaks Of Emerging Respiratory Diseases, Mohammed Hameed Alharbi
Mathematics Dissertations - Archive
The purpose of this dissertation is to use mathematical models to evaluate the impact of characteristics of respiratory diseases like influenza and COVID-19 either alone or co-circulating and how might influenza vaccine affect this interplay. First, we assess the effects of matching and mismatching between vaccine strains and circulating strains during the Hajj. Then we evaluate the impact of the proportion of asymptomatic COVID- 19 infections on the magnitude of an epidemic under three different behavior change scenarios. Finally, we model the co-circulation of influenza and COVID-19 to investigate whether the influenza vaccine increases the combined disease burden of influenza …
Exploring Development Of Problem Solving Strategies In Emerging Mathematicians, Andrew Charles Kercher
Exploring Development Of Problem Solving Strategies In Emerging Mathematicians, Andrew Charles Kercher
Mathematics Dissertations - Archive
To solve an unfamiliar mathematics problem, students of the subject must know more than the appropriate prerequisite content knowledge. They must also know how best to strategically apply their knowledge, how to monitor and gauge the effectiveness of their work, and how to respond (both cognitively and emotionally) to unanticipated results. Expanding current research on the types of experiences that foster these skills is the objective of this study. In a sequence of two task-based interviews, eight graduate and four upper-division undergraduate mathematics students solved non-traditional mathematics problems, used their work on these problems as a basis to comment on …
Stochastic Risk Measures For The Lundberg Model With Reinsurance And Investment, Benie Justine N'Gozan
Stochastic Risk Measures For The Lundberg Model With Reinsurance And Investment, Benie Justine N'Gozan
Mathematics Dissertations - Archive
Risk measures emerge in fields such as economics, insurance, finance and are concerned with a stochastic representation of uncertainties stemming from the unpredictability of the real world events. In essence, risk analysis amounts to quantifying the chances of undesirable events and developing a model that limits the impact of potential losses. Assets and liabilities in the Insurance industry, as well as financial goals of Investment companies rely on calculating the probability that their respective portfolios satisfy the preset constraints. On the flip side, risk measures serve both industries by providing optimal strategies for minimizing losses. Our research is concerned with …
New Development Of Grid Generation And Image Analysis, Ben Hildebrand
New Development Of Grid Generation And Image Analysis, Ben Hildebrand
Mathematics Dissertations - Archive
Image segmentation and registration are indispensable tools for the aid in medical diagnoses by experts. The current gold-standard for image segmentation is manual labeling of pixels by experts which is cumbersome and inefficient. In a paper by Zhu et. al. grids are generated through the deformation method for grid generation and differential properties of these grids are used in a deep learning algorithm for image segmentation. In this dissertation, we develop a new method for generating grid images based on the Variational Method. This new grid generation method generates grids based on image pixel intensities which improves upon the deformation …
Asymptotic Normality Of The Deconvolution Kernel Density Estimators Based On Independent As Well As Strong Mixing Right Censored Data, Wenqing Zhu
Mathematics Dissertations - Archive
We consider estimation of a density when observed lifetime from the convolution model contaminated by additive measurement errors. A kernel type deconvolution density estimator of the unknown distribution based on right censored data is proposed by using the Inverse-Probability-of-Censoring Weighted Average. Further, we discuss the asymptotic normality of the deconvolution kernel density estimators for independent and strong mixing vectors when the error distribution function is either ordinary smooth or supersmooth. Our method is applied to the study conducted by UTSW medical center. The research team at UTSW collected the data of women who underwent cystoscopy fulguration for recurrent urinary tract …
Inverse Problems And Forward Propagation Of Optical Flow, John Montalbo
Inverse Problems And Forward Propagation Of Optical Flow, John Montalbo
Mathematics Dissertations - Archive
Optical flow is a concept originally introduced in computer vision that quantifies, and aids in the presentation of, motion (flow field) between two or more images. In essence, it is a solution of an inverse problem recovering a vector field between images through optimization techniques. This work studies the possibility of using optical flow and various techniques of forward propagation of the recovered flow field for a pair of image processing tasks in magnetic resonance imaging (MRI). It is shown that the proposed framework can be efficient in approximating missing image layers, as well as in generation of deliberately modified …
Likelihood Inference For Flexible Cure Rate Models In The Context Of Infectious Diseases With Multiple Exposures, Zachry Joseph Engel
Likelihood Inference For Flexible Cure Rate Models In The Context Of Infectious Diseases With Multiple Exposures, Zachry Joseph Engel
Mathematics Dissertations - Archive
Cure rate models are mostly used to study data arising from cancer clinical trials. Its use in the context of infectious diseases has not been explored well. In 2007, Tournoud and Ecochard rst proposed a mechanistic formulation of cure rate model in the context of infectious diseases with multiple exposures to infection. However, they assumed a simple Poisson distribution to capture the unobserved number of pathogens at each exposure time. In this thesis, we propose a new exible cure rate model to study infectious diseases with discrete multiple exposures to infection. This new model uses the Conway-Maxwell Poisson (COM-Poisson) distribution …
Optimizing L1 Loss Regularizer And Its Application To Eeg Inverse Problem, Kiran Kumar Mainali
Optimizing L1 Loss Regularizer And Its Application To Eeg Inverse Problem, Kiran Kumar Mainali
Mathematics Dissertations - Archive
Sparse reconstruction occurs frequently in science and engineering and real-world applications, including statistics, finance, imaging, biological system, compressed sensing, and, today more than ever, machine learning and data science in general. Mathematically, they are often modeled as l1-minimization problems. There are a number of existing numerical methods that can efficiently solve such l1-minimization problems, such as Alternating Direction Methods of Multipliers (ADMM), Fast Iterative Shrinkage Thresholding Algorithm (FISTA), and Homotopy algorithm. In this dissertation, we will introduce a special type of l1-minimization problem called the Sylvester Least Absolute Shrinkage and Selection Operator (SLASSO) problem. In theory, an SLASSO problem can …
Mathematical Modeling Of Scavengers And Zebras On The African Savanna With Disease Dynamics, Crystal Dawn Mackey
Mathematical Modeling Of Scavengers And Zebras On The African Savanna With Disease Dynamics, Crystal Dawn Mackey
Mathematics Dissertations - Archive
The purpose of this dissertation is to use mathematical models to see how anthrax in the zebra population in Etosha National Park (ENP) interacts with scavenger populations and disease dynamics. First, we study if scavengers can save zebras from anthrax. Then we introduce a disease in the jackal population to see if anthrax in zebras can help propagate rabies in jackals. Finally, the last two models we develop describe the interaction between competing scavengers: jackals and vultures, with exploitative and interference competition. ENP is home to many different animals such as lions, jackals, hyenas, zebras, elephants, etc. Each year grazing …
Optimal Bandwidth Selection For Deconvoluted Kernel Density Estimation Using Bootstrap Method, Souad Sosa
Optimal Bandwidth Selection For Deconvoluted Kernel Density Estimation Using Bootstrap Method, Souad Sosa
Mathematics Dissertations - Archive
To estimate an unknown density when observed measurements are from the convolution model contaminated by additive measurement errors, Stefanski and Carroll (1990) proposed using Fourier inversion on the product of Fourier transform of a kernel function and the characteristic function of the error variable. One important element in constructing such a density estimator is the bandwidth. The goal of this research is to establish an optimal bandwidth so that the mean integrated squared error of the estimator is minimized. The bootstrap method is used to accomplish this goal. The simulation results show that the estimated optimal bandwidths provide adequate estimation …
Origins Of Atrophy In Parkinson Linked To Early Onset And Local Transcription Patterns, Pedro D. Maia, Sneha Pandya, Benjamin Freeze, Justin Torok, Ajay Gupta, Yashar Zeighami, Ashish Raj
Origins Of Atrophy In Parkinson Linked To Early Onset And Local Transcription Patterns, Pedro D. Maia, Sneha Pandya, Benjamin Freeze, Justin Torok, Ajay Gupta, Yashar Zeighami, Ashish Raj
Mathematics Faculty Publications - Archive
There is enormous clinical value in inferring the brain regions initially atrophied in Parkinson disease for individual patients and understanding its relationship with clinical and genetic risk factors. The aim of this study is to leverage a new seed-inference algorithm demonstrated for Alzheimer’s disease to the Parkinsonian context and to cluster patients in meaningful subgroups based on these incipient atrophy patterns. Instead of testing brain regions separately as the likely initiation site for each patient, we solve an L1-penalized optimization problem that can return a more predictive heterogeneous, multi-locus seed patterns. A cluster analysis of the individual seed patterns reveals …
Network Mediation Of Pathology Pattern In Sporadic Creutzfeldt–Jakob Disease, Benjamin Freeze, Pedro Maia, Sneha Pandya, Ashish Raj
Network Mediation Of Pathology Pattern In Sporadic Creutzfeldt–Jakob Disease, Benjamin Freeze, Pedro Maia, Sneha Pandya, Ashish Raj
Mathematics Faculty Publications - Archive
Sporadic Creutzfeldt–Jakob disease is a rare fatal rapidly progressive dementia caused by the accumulation and spread of pathologically misfolded prions. Evidence from animal models and in vitro experiments suggests that prion pathology propagates along neural connectivity pathways, with the transmission of misfolded prions initiating a corruptive templating process in newly encountered brain regions. Although particular regional patterns of disease have been recognized in humans, the underlying mechanistic basis of these patterns remains poorly understood. Here, we demonstrate that the spatial pattern of disease derived from publicly available human diffusion-weighted MRI data demonstrates stereotypical features across patient cohorts and can be …
Precision Medicine: Gene And Clinical Data Analysis Of Renal Cancer, Sumeyye Su
Precision Medicine: Gene And Clinical Data Analysis Of Renal Cancer, Sumeyye Su
Mathematics Dissertations - Archive
Recent advances in biotechnology led to generation of large complex biological and clinical data sets that can be used to infer the underlying mechanism of many diseases and arrive at personalized treatments. One of these data sets are the whole genome profiles, including a good collection of publicly available human gene expression data sets. In the first part of this study, we analyzed gene expression profiles of patients with renal cell carcinoma (RCC). We found that the regulator of G-protein signaling 5 (RGS5) might play a crucial role in initiation and progression of RCC, and it might be prognostic. We …
Optimal Treatment Strategies For Cancer Patients In Terms Of Survival Months And Socio-Economic Factors, Omer Mogultay
Optimal Treatment Strategies For Cancer Patients In Terms Of Survival Months And Socio-Economic Factors, Omer Mogultay
Mathematics Dissertations - Archive
One of the main challenges of cancer patients and their healthcare providers is making decisions regarding choosing the best treatment option. In the first part of thesis, we analyze breast cancer patients’ data to discover characteristics of patients who would benefit from each breast cancer surgical procedure in terms of increasing survival months. Since the outcome of breast cancer treatments strongly depends on the tumor subtypes, several studies investigated the outcome of surgical procedures for each of these subtypes. On the other hand, it has been shown that the outcome of breast cancer treatments is significantly different between black and …
Examining The Concept Images Of Function Held By Preservice Secondary Mathematics Teachers With Varying Levels Of Prior Mathematical Experience, Janessa Michele Beach
Examining The Concept Images Of Function Held By Preservice Secondary Mathematics Teachers With Varying Levels Of Prior Mathematical Experience, Janessa Michele Beach
Mathematics Dissertations - Archive
This multiple case study examines the function concept images of preservice secondary mathematics teachers (PSMTs) enrolled in a mathematics content course designed specifically for PSMTs at a large urban university in the southwestern United States. The primary research question explores the changes in PSMTs’ function concept images when they engage with research-based explorations designed to elicit function-related cognitive conflicts. Furthermore, this study explores the extent to which there are differences in the function concept images of advanced undergraduate mathematics majors and those with the minimum prerequisite knowledge. Thematic analysis is applied to identify PSMTs function-related associations and characterize their function …
Impact Of Domestic Animals On Prevalence Of Vector-Borne Diseases In Humans, Md Mondal Hasan Zahid
Impact Of Domestic Animals On Prevalence Of Vector-Borne Diseases In Humans, Md Mondal Hasan Zahid
Mathematics Dissertations - Archive
Vector-borne infectious diseases are one of the leading problems for public health worldwide, particularly in underdeveloped and developing countries. These diseases infect humans through the bite of infected vectors. The effect of host diversity on disease persistence, well studied in ecological literature, is examined here in a domestic setting. Some additional hosts dilute infection, while others amplify certain disease infections. Domestic animals can play an important role, as an additional host, in the disease dynamics by affecting host-pathogen interactions. However, the effect of additional hosts is not always straightforward since their presence impacts negatively by helping the vector population grow …
Bases Of Infinite-Dimensional Representations Of Orthosymplectic Lie Superalgebras, Dwight Anderson Williams Ii
Bases Of Infinite-Dimensional Representations Of Orthosymplectic Lie Superalgebras, Dwight Anderson Williams Ii
Mathematics Dissertations - Archive
We provide explicit bases of representations of the Lie superalgebra osp(1|2n) obtained by taking tensor products of infinite-dimensional representation and the standard representation. This infinite-dimensional representation is the space of polynomials C[x₁,...,xn]. Also, we provide a new differential operator realization of osp(1|2n) in terms of differential operators of n commuting variables x₁,...,xn and 2n anti-commuting variables ξ1; : : : ; ξ2n.