Physical Sciences and Mathematics Commons^™

An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). The experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory …

Analyzing Suicidal Text Using Natural Language Processing, Cassandra Barton

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Using Natural Language Processing (NLP), we are able to analyze text from suicidal individuals. This can be done using a variety of methods. I analyzed a dataset of a girl named Victoria that died by suicide. I used a machine learning method to train a different dataset and tested it on her diary entries to classify her text into two categories: suicidal vs non-suicidal. I used topic modeling to find out unique topics in each subset. I also found a pattern in her diary entries. NLP allows us to help individuals that are suicidal and their family members and close …

Report: Spatial Facilitation-Inhibition Effects On Vegetation Distribution And Their Associated Patterns, Daniel D'Alessio

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Changes in the spatial distribution of vegetation respond to variations in the production and transportation mechanisms of seeds at different locations subject to heterogeneities, often because of soil characteristics. In semi-arid environments, the competition for water and nutrients pushes the superficial plant’s roots to obtain scarce resources at long ranges. In this report, we assume that vegetation biomass interacts with itself in two different ways, facilitation and inhibition, depending on the relative distances. We present a 1-dimensional Integro-difference model to represent and study the emergence of patterns in the distribution of vegetation.

Optimal Control Of Algae Biofilm Growth In Wastewater Treatment Using Computational Mathematical Models, Gerald Benjamin Jones

Undergraduate Honors Capstone Projects

Microalgal biofilms are comprised of a syntrophic consortium of microalgae and other microorganisms embedded within an extracellular matrix. Despite significant processes in the application of microalgal biofilms in wastewater treatment, mechanistic understanding and optimization of microalgal biomass yield and productivity under environmental constraints is still lacking. This paper identifies theoretical insights on this challenging biological problem by leveraging novel mathematical and computational tools. In particular, through a computational mathematical model to advance the understanding of microalgal biofilm growth kinetics under environmental constraints through a systematic parameter study. Moreover, design of algae biofilm reactors for optimal biomass yield and productivity in …

Numerical Approximations Of Phase Field Equations With Physics Informed Neural Networks, Colby Wight

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Designing numerical algorithms for solving partial differential equations (PDEs) is one of the major research branches in applied and computational mathematics. Recently there has been some seminal work on solving PDEs using the deep neural networks. In particular, the Physics Informed Neural Network (PINN) has been shown to be effective in solving some classical partial differential equations. However, we find that this method is not sufficient in solving all types of equations and falls short in solving phase-field equations. In this thesis, we propose various techniques that add to the power of these networks. Mainly, we propose to embrace the …

Methods In Modeling Wildlife Disease From Model Selection To Parameterization With Multi-Scale Data, Ian Mcgahan

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The effects of emerging wildlife diseases are global and profound, resulting in loss of human life, economic and agricultural impacts, declines in wildlife populations, and ecological disturbance. The spread of wildlife diseases can be viewed as the result of two simultaneous processes: spatial spread of wildlife populations and disease spread through a population. For many diseases these processes happen at different timescales, which is reflected in available data. These data come in two flavors: high-frequency, high-resolution telemetry data (e.g. GPS collar) and low-frequency, low-resolution presence-absence disease data. The multi-scale nature of these data makes analysis of such systems challenging. Mathematical …

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms …

Examining Teacher Perceptions When Utilizing Volunteers In School-Based Agricultural Education Programs, Ashley B. Cromer

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

There has been little research conducted related to how school-based agricultural (SBAE) teachers perceive the utilization of volunteers in the classroom. The United States is facing a shortage of SBAE teachers, and with turnover rates that are not sustainable, solutions for support and reduction of the SBAE teachers’ workload must be sought with diligence. There is potential for volunteers to reduce some of the responsibilities that the SBAE teacher is faced with. The purposes of this study are to determine the demographic characteristics of the volunteers being utilized and of the SBAE teachers, determine the perceived benefits, barriers and beliefs …

Prediction Of Stress Increase In Unbonded Tendons Using Sparse Principal Component Analysis, Eric Mckinney

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

While internal and external unbonded tendons are widely utilized in concrete structures, the analytic solution for the increase in unbonded tendon stress, Δ���, is challenging due to the lack of bond between strand and concrete. Moreover, most analysis methods do not provide high correlation due to the limited available test data. In this thesis, Principal Component Analysis (PCA), and Sparse Principal Component Analysis (SPCA) are employed on different sets of candidate variables, amongst the material and sectional properties from the database compiled by Maguire et al. [18]. Predictions of Δ��� are made via Principal Component Regression models, and the method …

A Stochastic Model For Water-Vegetation Systems And The Effect Of Decreasing Precipitation On Semi-Arid Environments, Shannon A. Dixon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Current climate change trends are affecting the magnitude and recurrence of extreme weather events. In particular, several semi-arid regions around the planet are confronting more intense and prolonged lack of precipitation, slowly transforming these regions into deserts. Many mathematical models have been developed for purposes of analyzing vegetation-water interactions, particularly in semi-arid landscapes. Most models are based on the average behavior of the system as a whole, and how it is influenced by external changes. These models may be termed "macro-scale" models. Other models have concerned themselves with the interactions between individuals, in this case the interactions between individual plants …

On The Propagation Of Atmospheric Gravity Waves In A Non-Uniform Wind Field: Introducing A Modified Acoustic-Gravity Wave Equation, Ahmad Talaei

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Atmospheric gravity waves play fundamental roles in a broad-range of dynamical processes extending throughout the Earth’s neutral atmosphere and ionosphere. In this paper, we present a modified form for the acoustic-gravity wave equation and its dispersion relationships for a compressible and non-stationary atmosphere in hydrostatic balance. Importantly, the solutions have been achieved without the use of the well-known Boussinesq approximation which have been used extensively in previous studies.

We utilize the complete set of governing equations for a compressible atmosphere with non-uniform airflows to determine an equation for vertical velocity of possible atmospheric waves. This intricate wave equation is simplified …

Modeling Phloem Temperatures Relative To Mountain Pine Beetle Phenology, Matthew Jared Lewis

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We explore a variety of methods to estimate phloem temperatures from ambient air temperatures suitable for the mountain pine beetle, Dendroctonus ponderosae. A model's ability to induce the same phenology generated from observed phloem temperatures measures its effectiveness rather than a simple reconstruction of phloem temperatures. From a model's phenology results we are able to ascertain whether the model produces a similar amount of developmental energy exhibited by observed phloem temperatures.

Three models performed best: Newton, Newton South and Matching. The Newton model uses Newton's Law of Cooling to effectively estimate northern aspect phloem temperatures. The Newton South model …

Dietary Patterns And Cognitive Decline In Aged Populations, Austin J. Bowles

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In this paper, we discuss distinctive features of longitudinal studies, and illustrate two regression-based methods for the analysis of longitudinal data. A study of dietary patterns and cognitive decline (Cache County Memory Study) is used to motivate our discussion and analysis. Cognitive decline is a risk factor for Alzheimer’s disease, the sixth leading cause of all deaths among Americans. The study attempted to identify dietary patterns associated with reduced risk of age-related cognitive decline in elderly populations. Higher levels of adherence to the Dietary Approaches to Stop Hypertension (DASH) and/or Mediterranean diets were found to be associated with increased cognitive …

Grading Practice Influence On The Value Of An Assigned Grade, Carrie Bala

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This article presents results of a study of grading practice influence on the value of an assigned grade. The value of an assigned grade, as an indication of student achievement of learning goals, was measured using the Utah Criterion-Referenced Test (CRT) in the subjects of Geometry and Algebra 2. The grading policies of six mathematics teachers at the same high school were categorized according to grading practice and their combined 587 students' scores on the Utah CRT were collected and analyzed. The findings suggest that certain grading practices , such as the use of a 1-4 scale and a criterion-referenced …

Statistical Analysis Of Wastewater Remediation And Bio-Fuels Production Of Algae, Jay D. Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The Logan city wastewater treatment system consists of a series of seven large aerated ponds (460 acres) that biologically treats 15 million gallons per day of wastewater from Logan city and six other communities. Tighter regulations of allowed phosphorus levels in the effluent have recently been implemented due to environmental concerns of a downstream reservoir. The Biological Engineering program at Utah State University, the Bio-fuels Center, the Utah Water Research Laboratory (UWRL) and the city of Logan are working together to remediate the wastewater treatment system using microalgae. Algal growth requires the uptake of phosphorus. Thus, phosphorus in the effluent …

Intermediate-Complexity Biological Modeling Framework For Nutrient Cycling In Lakes Based On Physical Structure, Michael Clay Rigley

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Mathematical models for the change in concentration of total dissolved nitrogen (TDN) in mountain lakes are developed based on the dynamics of coupled, well-mixed containers. Each includes a stratified lake structure without the complexity of a full fluid model. A lake is divided into a suite of compartments based on physical structure: warm upper layer (epilimnion), cold inflow and insertion layer (metalimnion), cold lower layer (hypolimnion), and a warm shallow shelf. With the compartments as the framework and literature values for uptake rates, death rates, half-saturation constants, and sinking rates, systems of equations are written for three models. The first …

Heritability Of Cognition Subscales In The Cache County Memory Study Cohort And Methods For Estimating Heritability, Colette Kelly Childs

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The rapid improvement of genotyping technology holds the promise of better understanding the genetic causes of complex disease. While traits of interest often include the presence or absence of disease, there is growing interest in intermediate phenotypes (or so-called endophenotypes) that may yield more information about disease onset or course. In particular, changes over time with respect to an investigative ordinal measure often contain significant predictive power, and rate-of-change phenotypes are becoming important in their own right when studying genetic association. Initial steps in assessing the potential genetic determinants of a continuous trait often involve estimating the degree of the …

Capstone Mathematics And Technology: A Collection Of Mathematical Technology Enhanced Activities For Students And Teachers, Heidi Eastman

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this project is to provide an introduction to how technology can be used in the mathematical classroom to enhance students' learning of mathematics, while at the same time leading students to a richer and deeper understanding of those mathematical concepts. The topics were selected based on their relevance to the Utah State Core Curriculum for middle and secondary mathematics courses. It was intended that each lesson plan would challenge a preservice mathematics educator to build relationships between different areas of mathematics and/or to create deeper understandings of specific mathematical concepts. At the same time many of the …

Nonlinear Schrödinger Type Equations With Asymptotically Linear Terms, Francois A. Van Heerden

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We study the nonlinear Schrödinger type equation

–Δu + (λg(x) + 1)u = f(u)

on the whole space R^N. The nonlinearity f is assumed to be asymptotically linear and g(x) ≥ 0 has a potential well. We do not assume a limit for g(x) as |x| → ∞ . Using variational techniques, we prove the existence of a positive solution for λ large. In the case where f is odd we obtain multiple pairs of solutions. The limiting behavior of solutions as λ → ∞ is also considered.

Tournament Matrices An Overview, Russel O. Carlson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The results of a round robin tournament can be represented as a matrix of zeros and ones, by ordering the players and placing a one in the (i,j) position if player i beat player j, and zeros otherwise. These matrices, called tournament matrices, can be represented by graphs, called tournament graphs. They have been the subject of much research and study, yet there have been few attempts to give a wide exposition on the subject. Those that have been done tend to focus on the graph theoretical aspects of tournaments. S. Ree and Y. Koh did write a brief …

A Recommendation For Determining The Efficacy Of Weight Removal Estimates For The Pacific Cod Longline Cdq Fishery, Anna L. Furniss

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In January 2000, the Alaska Department of Community and Economic Development contacted the National Marine Fisheries Service (NMFS) regarding concerns over the methods used to determine catch estimates for the Pacific Cod Community Development Quota (CDQ) fishery. Currently, NMFS determines catch estimates for the Pacific Cod CDQ fishery based on the data collected by observers from the North Pacific Groundfish Observer Program (NPGOP).

Observer estimates for catch are based on the random sampling methods for a longline fishing vessel as described in the North Pacific Groundfish Observer Manual. These sampling methods provide an official total catch (OTC) estimate for each …

Incorporating Technology In Mathematics Education: A Suite Of E-Activities For The Modem Mathematics Classroom, Jennifer E. Youngberg

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

National studies indicate major deficiencies in students' understanding of mathematics. Research suggests that students tend to view mathematics as a set of computational rules rather than a process of discovery and a tool for problem-solving. Most students fail to grasp the concepts behind the computations.

Technology provides a partial solution to this problem. Over the past decade, computers have emerged as a powerful tool in education. Computers place the control of action in the learning process with the student. They allow students to experiment with, explore, and discover mathematics at their own pace. With computers, students can consider more examples …

Algebraic Properties Of Endomorphisms Of Abelian Groups And Rings, Johnnie George Slagle

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The main objective of the thesis was to extend the definition of an M-Group to what is called an M-Ring. From this extension a system called an expanded ring follows naturally. To facilitate the development of the expanded ring, chapter I is devoted to developing properties on systems that are not quite rings where many interesting examples are constructed. In chapter II the definition of an M-Ring is given and some of its properties are derived. In chapter III some of the properties of expanded rings are proved, and examples of expanded rings are given to show their existence.

Measure Theory And Lebesgue Integration, Evan S. Brossard

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The Lebesgue integral is a generalization of the Riemann integral which extends the collection of functions which are integrable.

Lebesgue integration differs from Riemann integration in the way the approximations to the integral are taken. Riemann approximations use step functions which have a constant value on any given interval of the domain corres­ponding to some partition. Lebesgue approximations use what are called simple functions which, like the step functions, take on only a finite number of values. However, these values are not necessarily taken on by the function on intervals of the domain, but rather on arbitrary subsets of the …

Tests Of Methods That Control Round-Off Error, Dale M. Rasmuson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Methods of controlling round-off error in one-step methods in the numerical solution of ordinary differential equations are compared. A new Algorithm called theoretical cumulative rounding is formulated. Round-off error bounds are obtained for single precision, and theoretical cumulative rounding. Limits of these bounds are obtained as the step length approaches zero. It is shown that the limit of the bound on the round-off error is unbounded for single precision and double precision, is constant for theoretical partial double precision, and is zero for theoretical cumulative rounding.

The limits of round-off bounds are not obtainable in actual practice. The round-off error …

Principal Component Factor Analysis, Herbert H. Jolliff

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Factor analysis came into being around 1900 in the field f psychology to explain theories of human ability. Several methods of factor analysis exist; but according to Harman (1967) principal component factor analysis is unique in the mathematical sense, therefore, quite often the preferred method. The centroid method is computationally easier, and it gives close approximations to the principal component method on some data sets. An example of this is shown in Appendixes B and F by comparison.

Factor analysis is being used in many fields. A few of the fields are sociology, meteorology, political science, medicine, geography, business, economics, …

Linear Coordinate Systems And Statistical Independence And Vector Spaces And Linear Statistical Models, James B. Mcdonald

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The object of this report is an investigation of statistical independence and linear coordinate systems. It is hoped that this report will give some background for an ultimate investigation of independence and non­linear coordinate systems using tensor analysis.

An additional basic objective is to obtain explicit algebraic expressions for different types of linear trans- formations.

The first concepts to be covered are arbitrary linear transformations, various ways of looking at linear transformations, and the effects of a linear transformation on a vector of normally distributed random variables.

Next orthogonal transformations to independence, and then oblique transformations to independence will be …

Estimation Of Parameters Of Normal Populations From Truncated Samples, Kuo-Chung Liang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In statistical experiments, if a random sample of items drawn from a population is tested until all items fail, conventional statistical techniques may be employed but normal frequency distributions may not be satisfied. Failure of the data to satisfy the assumption of normality may lead to an invalid result. Some statistical results, however, have been shown to be robust to the failure of the data to meet normality. When using conventional experimental methods, considerable time and money are required to produce failure of all samples. To be economical, many experiments are concluded before all test items fail. A sample obtained …

An Exposition On Bayesian Inference, John Laffoon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The Bayesian approach to probability and statistics is described, a brief history of Bayesianism is related, differences between Bayesian and Frequentist schools of statistics are defined, protential applications are investigated, and a literature survey is presented in the form of a machine-sort card file.

Bayesian thought is increasing in favor among statisticians because of its ability to attack problems that are unassailable from the Frequentist approach. It should become more popular among practitioners because of the flexibility it allows experimenters and the ease with which prior knowledge can be combined with experimental data.

Topics In Semigroups, Merlin Ray Jenson

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The semigroup theories of fundamental importance were discovered in 1928 with the publication of a paper by A. K. Suschkewitsch. The paper is included in the only book published prior to 1961 dealing primarily with the algebraic theory of semigroups. The book written by the above author and published in 1937 is entitles "The Theory of Generalized Groups."

Since 1940 the number of papers on semigroups has increased to approximately 30 per year. Thus we find ourselves in the midst of a new and expanding area of mathematics. Our interest centers around the structure of semigroups and their representation by …