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Weighted Inequalities For Dyadic Operators Over Spaces Of Homogeneous Type, David Edward Weirich
Weighted Inequalities For Dyadic Operators Over Spaces Of Homogeneous Type, David Edward Weirich
Mathematics & Statistics ETDs
A so-called space of homogeneous type is a set equipped with a quasi-metric and a doubling measure. We give a survey of results spanning the last few decades concerning the geometric properties of such spaces, culminating in the description of a system of dyadic cubes in this setting whose properties mirror the more familiar dyadic lattices in R^n . We then use these cubes to prove a result pertaining to weighted inequality theory over such spaces. We develop a general method for extending Bellman function type arguments from the real line to spaces of homogeneous type. Finally, we uses this …
Which Factors Influence Student Success In Intermediate Algebra, Math 101-102-103?, Linh T. Ward
Which Factors Influence Student Success In Intermediate Algebra, Math 101-102-103?, Linh T. Ward
Mathematics & Statistics ETDs
At The University of New Mexico (UNM), Intermediate Algebra (MATH 120 and MATH 101-102-103) has historically been a so-called “killer course”, with very low pass rates: approximately 40% in Fall 2009 to Spring 2011 and about 50% from Fall 2011 to Spring 2013. Furthermore, many students failed the class multiple times. Since 2013, a computer system called ALEKS has been used to teach the course and, along with some additional interventions, on Albuquerque/Main campus success rates for MATH 101 have increased to roughly 80% and MATH 102 to about 70%. This thesis provides a strategy to identify those 20-30% as-risk …
Trace Formulas For Perturbations Of Operators With Hilbert-Schmidt Resolvents, Bishnu Prasad Sedai
Trace Formulas For Perturbations Of Operators With Hilbert-Schmidt Resolvents, Bishnu Prasad Sedai
Mathematics & Statistics ETDs
In this dissertation, we study Taylor approximations of functions of operators with Hilbert-Schmidt resolvents. We obtain integral representations for traces of the respective Taylor remainders that are analogous to trace formulas obtained in the case of Schatten perturbations in [10, 11, 16].
High Order Hermite And Sobolev Discontinuous Galerkin Methods For Hyperbolic Partial Differential Equations, Adeline Kornelus
High Order Hermite And Sobolev Discontinuous Galerkin Methods For Hyperbolic Partial Differential Equations, Adeline Kornelus
Mathematics & Statistics ETDs
Many real-world problems involving dynamics of solid or fluid bodies can be modeled by hyperbolic partial differential equations (PDEs). Up to this point, only solutions to selected PDEs are available. Many PDEs are physically or geometrically complex, resulting in difficulties computing the analytical solutions. In this thesis, we focus on numerical methods for approximating solutions to hyperbolic PDEs. Long-term simulation for the motion of the body described by the PDE requires a method that is not only robust and efficient, but also produces small error because the error will be propagated and accumulated over the course of the simulation. Therefore, …
Comparison Of Two Methods In Estimating Standard Error Of Simulated Moments Estimators For Generalized Linear Mixed Models, Danielle K. Duran
Comparison Of Two Methods In Estimating Standard Error Of Simulated Moments Estimators For Generalized Linear Mixed Models, Danielle K. Duran
Mathematics & Statistics ETDs
We consider standard error of the method of simulated moment (MSM) estimator for generalized linear mixed models (GLMM). Parametric bootstrap (PB) has been used to estimate the covariance matrix, in which we use the estimates to generate the simulated moments. To avoid the bias introduced by estimating the parameters and to deal with the correlated observations, (Lu, 2012) proposed a multi-stage block nonparametric bootstrap to estimate the standard errors. In this research, we compare PB and nonparametric bootstrap methods (NPB) in estimating the standard errors of MSM estimators for GLMM. Simulation results show that when the group size is large, …
Optimal Experimental Design To Characterize A Wave Source Using Dosimeter Measurements, Renee L. Gooding
Optimal Experimental Design To Characterize A Wave Source Using Dosimeter Measurements, Renee L. Gooding
Mathematics & Statistics ETDs
When modeling physical phenomena we want to solve the inverse problem by estimating the parameters that characterize the source model that we are interested in. In this thesis, we focus on the optimal placement of a finite number of individual sensors, called dosimeters, in two and three dimensions with a time dependent Gaussian wave source. Using a computational model along with experimental data, we design an iterative process to determine the optimal placement of an additional sensor such that the noise in the measurements has a minimal effect on the parameter estimation. First, we estimate the parameters that characterize the …
Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci
Deterministic And Probabilistic Methods For Seismic Source Inversion, Juan Pablo Madrigal Cianci
Mathematics & Statistics ETDs
The national Earthquake Information Center (NEIC) reports an occurrence of about 13,000 earthquakes every year, spanning different values on the Richter scale from very mild (2) to "giant earthquakes'' (8 and above). Being able to study these earthquakes provides useful information for a wide range of applications in geophysics. In the present work we study the characteristics of an earthquake by performing seismic source inversion; a mathematical problem that, given some recorded data, produces a set of parameters that when used as input in a mathematical model for the earthquake generates synthetic data that closely resembles the measured data. There …
Cancer Modeling: From Optimal Cell Renewal To Immunotherapy, Cesar L. Alvarado
Cancer Modeling: From Optimal Cell Renewal To Immunotherapy, Cesar L. Alvarado
Mathematics & Statistics ETDs
Cancer is a disease caused by mutations in normal cells. According to the National Cancer Institute, in 2016, an estimated 1.6 million people were diagnosed and approximately 0.5 million people died from the disease in the United States. There are many factors that shape cancer at the cellular and organismal level, including genetic, immunological, and environmental components. In this thesis, we show how mathematical modeling can be used to provide insight into some of the key mechanisms underlying cancer dynamics. First, we use mathematical modeling to investigate optimal homeostatic cell renewal in tissues such as the small intestine with an …
Modeling Trait Evolutionary Processes With More Than One Gene, Huan Jiang
Modeling Trait Evolutionary Processes With More Than One Gene, Huan Jiang
Mathematics & Statistics ETDs
Phylogenetic comparative methods have been used to test evolutionary signals through trait evolutionary processes. Traditionally, biologists use one phylogenetic tree as a tool to handle dependent data for the traits of interest and hence utilize one gene only. However, it is more informative if the evolutionary processes of a trait are presented by phylogenetic trees reconstructed by the DNA alignments from more than one gene. In this work, we explain and develop two methods involving modeling the trait evolutionary processes: (a) two gene trees via the Brownian motion (BM) model; and (b) two gene trees via the Ornstein-Uhlenbeck (OU) model. …
The Effects Of Different Teaching Methods On Student Attitude And Achievement In Calculus Recitations, Jocelyn Noelle Rios
The Effects Of Different Teaching Methods On Student Attitude And Achievement In Calculus Recitations, Jocelyn Noelle Rios
Mathematics & Statistics ETDs
Many universities offer recitation sections in their calculus sequences; however, little research has been conducted on TA best practices in the recitations.This study first aimed to observe the different teaching methods that TAs employed in their recitations and then measure their efficacy in improving student course attitudes and achievement, focusing on student-centered and concept-based instruction. In addition, this study aimed to assess the quality of professional development offered to recitation leaders. Using a quantitative-dominant mixed methods design, 12 TAs were observed throughout the semester and TAs and calculus students were surveyed. This study found that student-centered instruction was positively correlated …