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2021

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Gas Phase Reactions Of Cyclopentadiene With Ch And Oh Radicals, Kacee Lynn Caster Jan 2021

Gas Phase Reactions Of Cyclopentadiene With Ch And Oh Radicals, Kacee Lynn Caster

Graduate Theses, Dissertations, and Problem Reports (ETD)

The formation of polycyclic aromatic hydrocarbons (PAHs) and carbon-based nanoparticles in combustion environments is driven by the pyrolysis and oxidation of abundant fuel molecules. The subsequent growth of these pyrolytic byproducts is then propagated by reactions with small free radical species like OH, CH, O atoms, and C2H. Cyclopentadiene (C5H6) is a significant five-member combustion intermediate that has been detected in many high temperature reactions, such as in the pyrolysis of jet fuels like JP-10. Experimental and theoretical investigations in the reactions of cyclopentadiene with these small free radical species are necessary towards understanding …


Effects Of Multiple Stressors On Aquatic Macroinvertebrate Communities In A Mixed-Land-Use Watershed, Joellen Stivala Jan 2021

Effects Of Multiple Stressors On Aquatic Macroinvertebrate Communities In A Mixed-Land-Use Watershed, Joellen Stivala

Graduate Theses, Dissertations, and Problem Reports (ETD)

As urbanization continues, there is a need to identify and understand environmental stressors that impact stream condition in mixed-land-use watersheds. This study analyzed four years of aquatic macroinvertebrate community and environmental data collected from ten sites located at the mouths of first-order tributaries and along the main stem creek of a 23-km2, mixed-land-use watershed in central Appalachia. The main objectives were to 1) determine stream ecological integrity by analyzing stream macroinvertebrate taxonomic and trait-based composition and 2) assess which of 23 environmental variables explained significant variability in common community composition metrics (WVSCI, GLIMPSS, Biotic Index, % clingers, etc.). …


Evaluation Of A Low-Cost Uas And Phenocams For Measuring Grapevine Greenness, Timothy J. Hoheneder Jan 2021

Evaluation Of A Low-Cost Uas And Phenocams For Measuring Grapevine Greenness, Timothy J. Hoheneder

Graduate Theses, Dissertations, and Problem Reports (ETD)

Unpersoned aerial systems (UAS) could provide winegrowers with the potential to monitor vineyard productivity with ultra-high-resolution imagery and low operational costs. This ability could prove particularly valuable in the challenging cool-climate viticultural areas of Appalachia. Especially in this mountainous region of increasingly variable microclimates, there could be of great value from an ability to use UAS-measured greenness to monitor wine grape phenology and predict harvest quality and quantity. In this study, I assess how UAS-measured greenness relates to three complementary measures of field-based: leaf angle measurements, phenocam measured greenness, and leaf spectral measurements of greenness. After correlating these field-based measures …


Non-Monetary Economies: A Study On Different Governing Principles, Richard Perry Vest Ii Jan 2021

Non-Monetary Economies: A Study On Different Governing Principles, Richard Perry Vest Ii

Graduate Theses, Dissertations, and Problem Reports (ETD)

This thesis examines a new economic system with a focus on non-monetary (primarily automation) aspects. Currency has been used in exchange for goods and services and this exchange has often resulted in benefits gained by any given individual. What if that wasn’t the case? How might society function if it was not influenced by currency? This thesis explores this hypothetical concept of an economy without currency with a focus given to automation. Using utility and production functions, discussion is given on how supply and demand functions behave in a non-monetary economy, how governing policy could be handled, and how society …


The Origin Of Novel Trait Inferred From Transcriptomic Analysis And A Targeted Gene Approach In The Beetle Horns., Naureen Fatima Jan 2021

The Origin Of Novel Trait Inferred From Transcriptomic Analysis And A Targeted Gene Approach In The Beetle Horns., Naureen Fatima

Graduate Theses, Dissertations, and Problem Reports (ETD)

The origin of the evolutionary new trait (evolutionary novelty) and its subsequent evolution is of great interest for biologists in various fields, and beetle horns have been used to address this fundamental biological question. Previous studies on one of the horned beetle species, Onthophagus taurus, that utilized comparative gene expression analyses, suggested legs to be a strong candidate of the origin of horns. At the same time, their horns are secondary sexual traits whose development is regulated by the same gene (doublesex) as genitalia, which also originates from paired appendages such as legs. However, little is known …


Learning And Workers In Transition (Wit), Jeffrey Burgazzoli Jr Jan 2021

Learning And Workers In Transition (Wit), Jeffrey Burgazzoli Jr

Graduate Theses, Dissertations, and Problem Reports (ETD)

This study utilized autoethnography to generate new understandings about learning and workplace transitions. I journaled the first 90 days in a new job, writing about the notable learning events that occurred and collecting work artifacts to create a rich storyboard of the transition scene. Qualitative analysis of the storyboard revealed four broader dimensions of learning that must be considered: 1) knowledge growth and development, 2) cognition, 3) situational context, and 4) emotion. The results of the study illuminated key inflection points that happened during the transition process, conceptualized how my learning changed over time, and showed how I processed and …


Process Modeling And Techno-Economic Analysis Of Micro- Encapsulated Carbon Sorbents (Mecs) For Co2 Capture In A Fixed Bed And Moving Bed Reactors, Goutham Kotamreddy Jan 2021

Process Modeling And Techno-Economic Analysis Of Micro- Encapsulated Carbon Sorbents (Mecs) For Co2 Capture In A Fixed Bed And Moving Bed Reactors, Goutham Kotamreddy

Graduate Theses, Dissertations, and Problem Reports (ETD)

Carbon capture, utilization, and storage (CCUS) is seen as a suite of technologies to curb the carbon dioxide emissions from the atmosphere and plays a crucial role to meet the net zero emissions target for many countries by 2050. One of the major sources for CO2 emissions is combustion of fossil fuels. Various innovative capture technologies are being explored because the state-of-the-art monoethanolamine (MEA) based carbon capture technology has drawbacks such as corrosion, energy penalty. There are several potential solvents that have lower energy penalty, but they are highly viscous or may turn into solid phase in the absorber …


Ensemble Encoder-Decoder Models For Predicting Land Transformation, Pariya Pourmohammadi Jan 2021

Ensemble Encoder-Decoder Models For Predicting Land Transformation, Pariya Pourmohammadi

Graduate Theses, Dissertations, and Problem Reports (ETD)

In studying dynamic and complex processes which are influenced by a system of inter-connected driving variables, it is crucial to apply models that can learn the complexity of the interactions. Land transformation is one of such complex processes, prediction of which can help to mitigate severe climate situations and improve the resiliency of communities. In this study, a multi-spectral set of data cubes is used to capture various characteristics of a geographic region. Based on the data cube, a feature space is constructed using socio-economic attributes, terrain characteristics, and landscape traits of the study region. Two-dimensional and three-dimensional convolutional neural …


An Equest Based Building Energy Modeling Analysis For Energy Efficiency Of Buildings, Saroj Lamichhane Jan 2021

An Equest Based Building Energy Modeling Analysis For Energy Efficiency Of Buildings, Saroj Lamichhane

Graduate Theses, Dissertations, and Problem Reports (ETD)

Building energy performance is a function of numerous building parameters. In this study, sensitivity analysis on twenty parameters is performed to determine the top three parameters which have the most significant impact on the energy performance of buildings. Actual data from two fully operational commercial buildings were collected and used to develop a building energy model in eQUEST. The model is calibrated using Normalized Mean Bias Error (NMBE) and Coefficient of Variation of Root Mean Square Error (CV(RMSE)) method. The model satisfies the NMBE and CV(RMSE) criteria set by the American Society of Heating, Refrigeration, and Air-Conditioning (ASHRAE) Guideline 14, …


Sustainability Assessment Of Direct Energy Deposition (Ded) Based Hybrid Manufacturing Using Life Cycle Assessment (Lca) Method, Faujia Islam Jan 2021

Sustainability Assessment Of Direct Energy Deposition (Ded) Based Hybrid Manufacturing Using Life Cycle Assessment (Lca) Method, Faujia Islam

Graduate Theses, Dissertations, and Problem Reports (ETD)

As sustainability has emerged as a highlight for almost every field over the last few decades, the manufacturing field is no exception. Generally, additive manufacturing performs better than traditional manufacturing in terms of sustainability because of its lean energy- and material usage. Previous studies have compared the sustainability performance between traditional and additive manufacturing, but hybrid manufacturing was not focused upon much. In this paper, the life cycle assessment method is used to analyze and compare the energy consumption and environmental impact of direct energy deposition (DED) based hybrid manufacturing and traditional manufacturing “CNC milling” process for a turbine blade. …


Harnessing Acoustic Streaming For Bioanalysis In Microfluidics, Xiaojun Li Jan 2021

Harnessing Acoustic Streaming For Bioanalysis In Microfluidics, Xiaojun Li

Graduate Theses, Dissertations, and Problem Reports (ETD)

In the past few decades, microfluidic technology has been developed rapidly in both fabrication methods and multifunctionality integrations, making it a powerful tool for a wider variety of biological applications. The device fabrication method has expanded from conventional polymer-based micro devices to 3D-printed micro devices, and allows multiple functions such as electric, optic, magnetic and acoustic to be integrated on a single platform. This dissertation focuses on method development of acoustic streaming-based microfluidics in bioanalysis such as immunoassay, enzyme kinetics and DNA fragmentation analysis. In this dissertation, a micromixer was developed based on acoustic streaming generated from sharp-edge structure vibration …


Prioritization Framework For Advanced Systems Of Urban Roads In The Context Of Smart Cities, Jinwoong Lee Jan 2021

Prioritization Framework For Advanced Systems Of Urban Roads In The Context Of Smart Cities, Jinwoong Lee

Graduate Theses, Dissertations, and Problem Reports (ETD)

The concept of a smart city has emerged as a solution to resolve various urban challenges by applying advanced systems for the functions of the city (e.g., environment, economy, infrastructure, governance, and people). Urban infrastructure with the use of modern technologies, such as Information Communication Technology and the Internet of Things, plays an essential role in enhancing the capability of the city to resolve the challenges. Particularly, urban roads supported by advanced systems with modern technologies serve as a principal bedrock to establish a smart city. Witnessing the benefits from intelligent urban roads has promoted city stakeholders to make investment …


Employing Exoglycosidase And Transferase Enzymes In Capillary Nanogel Electrophoresis For The Determination Of N-Glycan Linkages And Enzyme Michaelis-Menten Constants., Lloyd Bwanali Jan 2021

Employing Exoglycosidase And Transferase Enzymes In Capillary Nanogel Electrophoresis For The Determination Of N-Glycan Linkages And Enzyme Michaelis-Menten Constants., Lloyd Bwanali

Graduate Theses, Dissertations, and Problem Reports (ETD)

As a post translational modification protein glycosylation plays a crucial role in protein signaling, binding, kinetics and folding. In disease diagnosis and prognosis, monitoring glycosylation has been identified as a biomarker. Sialylation and sialic acid linkage in N-glycans are markers of cancers including liver, pancreatic and kidney cancer. Quantification of sialic acid linkage is analytically challenging because of the diverse linkages and the presence of heterogenous branching. A capillary electrophoresis method is reported that integrates a unique combination of enzymes and lectins to modify sialylated asparagine-linked glycans (N-glycans) in real time in the capillary so that N-glycan structures containing α2–6-linked …


Grouping Algorithms For Informative Array Testing In Disease Surveillance, David Sokolov Jan 2021

Grouping Algorithms For Informative Array Testing In Disease Surveillance, David Sokolov

Graduate Theses, Dissertations, and Problem Reports (ETD)

In order to maintain normal operations and prevent unnecessary morbidity and mortality during times of disease outbreak, institutions find a need to conduct frequent and widespread testing of their constituents, often under significantly limited testing resource constraints. Faced with the challenge of how best to allo- cate these limited resources to maximum effect, institutions are increasingly turning to group (or “pooled”) testing, which involves testing strategically-chosen groups of patient samples rather than individual samples, producing significant testing resource savings under certain regimes of disease prevalence. While group test- ing can be conducted without any a priori knowledge of individual disease …


Analyzing Applied Calculus Student Understanding Of Definite Integrals In Real-Life Applications, Cody Hood Jan 2021

Analyzing Applied Calculus Student Understanding Of Definite Integrals In Real-Life Applications, Cody Hood

Graduate Theses, Dissertations, and Problem Reports (ETD)

An individual’s knowledge of definite integrals can range from rote memorization to a strong foundational connection harkening back to its Riemann sum limit definition. In my research, I conducted seven task-based face-to-face interviews with Applied Calculus students. Through the use of real-life examples and guided reinvention, I analyzed ways in which these students, who all initially demonstrated rote memorization, could exhibit a Riemann sum based level of comprehension. This research was conducted in the confines of a student population with definite integral experience, but no formal instruction on limits. My results show that the lack of computational emphasis in class …


Using Zebrafish To Elucidate The Expression And Gene Regulatory Network Of The Genomic Screen Homeobox Transcription Factors And Bring Innovative Science Learning Experiences To West Virginia, Rebecca Ann Coltogirone Jan 2021

Using Zebrafish To Elucidate The Expression And Gene Regulatory Network Of The Genomic Screen Homeobox Transcription Factors And Bring Innovative Science Learning Experiences To West Virginia, Rebecca Ann Coltogirone

Graduate Theses, Dissertations, and Problem Reports (ETD)

Central nervous system (CNS) development requires a code of regionally expressed transcription factors that impart initial neuronal cell identity, connectivity, and function. The absence of a transcription factor code would eliminate the neurodevelopmental logic producing diverse cell types in the CNS. Furthermore, early disruptions in transcription factor expression can affect later connectivity and function of neuronal circuits mediating sensory processing, defects in which are often observed as comorbid with various neurodevelopmental disorders (NDDs). Characterizing transcription factor expression and function is therefore an essential step in discerning the molecular mechanisms underlying human NDDs. genomic screen homeobox 1 and 2 (gsx1 …


Using Molecular Dynamics To Characterize The Relationship Between Membrane Components And Dynamics And Supramolecular Organization Of Membrane Proteins, Eric Sefah Jan 2021

Using Molecular Dynamics To Characterize The Relationship Between Membrane Components And Dynamics And Supramolecular Organization Of Membrane Proteins, Eric Sefah

Graduate Theses, Dissertations, and Problem Reports (ETD)

Molecular dynamics (MD) simulations have gained impetus as a technique for elucidating structural and dynamical information about membrane proteins (MP). In particular, coarse-grained (CG) MD simulations have provided valuable information about the relationship between membrane components and supramolecular organization of MPs. In this work MD simulations are used to characterize the effects of hopanoids on bacterial membrane dynamics and association in a model protein proteorhodopsin (PR), as well as the role of the extended C-terminus of the human adenosine receptor (A2AR) on its dimerization. PR is found to dimerize in a manner that is dependent on both the …


Arrow Spaces: A Unified Algebraic Approach To Euclidean Geometry And Inner Product Spaces, Hussin M. Albahboh Jan 2021

Arrow Spaces: A Unified Algebraic Approach To Euclidean Geometry And Inner Product Spaces, Hussin M. Albahboh

Graduate Theses, Dissertations, and Problem Reports (ETD)

Given a postulated set of points, an algebraic system of axioms is proposed for an ``arrow space". An arrow is defined to be an ordered set of two points (T,H), named respectively Tail and Head. The set of arrows is an arrow space. The arrow space is axiomatically endowed with an arrow space ``pre-inner product" which is analogous to the inner product of an inner product vector space over R. Using this arrow space pre-inner product, various properties of the arrow space are derived and contrasted with the properties of a vector space over R. The axioms …


Algebraic, Analytic, And Combinatorial Properties Of Power Product Expansions In Two Independent Variables., Mohamed Ammar Elewoday Jan 2021

Algebraic, Analytic, And Combinatorial Properties Of Power Product Expansions In Two Independent Variables., Mohamed Ammar Elewoday

Graduate Theses, Dissertations, and Problem Reports (ETD)

Let $F(x,y)=I+\hspace{-.3cm}\sum\limits_{\substack{p=1\\m+n=p}}^{\infty}\hspace{-.3cm}A_{m,n}x^my^n$ be a formal power series, where the coefficients $A_{m,n}$ are either all matrices or all scalars. We expand $F(x,y)$ into the formal products $\prod\limits_{\substack{p=1\\m+n=p}}^{\infty}\hspace{-.3cm}(I+G_{m,n}x^m y^n)$, $\prod\limits_{\substack{p=1\\m+n=p}}^{\infty}\hspace{-.3cm}(I-H_{m,n}x^m y^n)^{-1}$, namely the \textit{ power product expansion in two independent variables} and \textit{inverse power product expansion in two independent variables} respectively. By developing new machinery involving the majorizing infinite product, we provide estimates on the domain of absolute convergence of the infinite product via the Taylor series coefficients of $F(x,y)$. This machinery introduces a myriad of "mixed expansions", uncovers various algebraic connections between the $(A_{m,n})$ and the $(G_{m,n})$, and uncovers various algebraic …


Magnetic Properties Of Lsmo/Sto Thin Films: Magnetocaloric, Spin Dynamics And Magnetic Viscosity Investigations, Navid Mottaghi Jan 2021

Magnetic Properties Of Lsmo/Sto Thin Films: Magnetocaloric, Spin Dynamics And Magnetic Viscosity Investigations, Navid Mottaghi

Graduate Theses, Dissertations, and Problem Reports (ETD)

While other films are discussed, this dissertation will focus on detailed studies of the dc and ac bulk magnetometry in a characteristic 7.6 nm thin film of La0.7Sr0.3MnO3 grown on SrTiO3 (001). The dc bulk magnetometry measurements show that the sample is magnetically inhomogeneous. Temperature variation of magnetization (M vs. T) was measured in zero-field-cooled and field-cooled protocols to determine the blocking temperature TB in different applied magnetic fields. The field variation of TB is interpreted as the presence of embedded spin clusters of 1.4 nm. Moreover, the M vs. …


Transform Based Approaches For The Detection Of Astrophysical Signals, Marwan Mahfud Alkhweldi Jan 2021

Transform Based Approaches For The Detection Of Astrophysical Signals, Marwan Mahfud Alkhweldi

Graduate Theses, Dissertations, and Problem Reports (ETD)

Development of new algorithms for the detection of isolated astrophysical pulses is of interest to radio astronomers. Both Fast Radio Bursts (FRBs) and several Rotating Radio Transients (RRATs) were detected through the application of a single pulse search algorithm. The conventional approach to detect astronomical pulses requires an exhaustive search for the correct dispersion measure. Its accelerated versions involve signal processing in Fourier transform space.

In this dissertation, we present several new transform-based approaches for the detection and analysis of astrophysical signals with the latest being the most effective and advanced of all. It is implemented in several steps. First, …


Huntingtin Aggregation At Interfaces Associated With Membranes And Organelles, Adewale Vincent Adegbuyiro Jan 2021

Huntingtin Aggregation At Interfaces Associated With Membranes And Organelles, Adewale Vincent Adegbuyiro

Graduate Theses, Dissertations, and Problem Reports (ETD)

Huntington’s Disease (HD) is a genetic neurodegenerative disease caused by the expansion of polyglutamine (polyQ) domain within the first exon (exon1) of the huntingtin (htt) protein. Due to this mutation within the polyQ domain, htt aggregates into various toxic species such as oligomers, fibrils, and other amorphous aggregates. While the aggregation of htt strongly correlates with polyQ length, other factors, e.g. interaction with membranes or organelles and posttranslational modifications (PTMs), modulate aggregation. The first 17 N-terminal amino acids (Nt17) that precede the polyQ in htt-exon1 enhances aggregation and facilitated binding of htt to membranous organelles, promoting morphological changes and disfunction. …


Heterogeneous Generalizations Of Vertex Coloring, Lucia Ciletti Mazza Jan 2021

Heterogeneous Generalizations Of Vertex Coloring, Lucia Ciletti Mazza

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation proves a collection of results in some heterogeneous generalizations of vertex coloring, i.e. generalizations in which the relationship between the colors of two adjacent vertices may differ throughout the graph. For the most part, the results are from group coloring, group list coloring, and DP coloring. The main results are as follows: a group list coloring analogue of Brooks' Theorem for multigraphs, a result linking group structure (rather than only group size) with group coloring, some results involving coloring edge-disjoint unions, and an examination of the relationship between the group and DP coloring numbers of a multigraph and …


Effects Of Nonexamples On Concept Formation, Catherine Louise Williams Jan 2021

Effects Of Nonexamples On Concept Formation, Catherine Louise Williams

Graduate Theses, Dissertations, and Problem Reports (ETD)

Concept formation is affected by the examples and nonexamples provided during training, but the degree to which examples and nonexamples should differ is unknown. Two experiments compared concept formation when different kinds of nonexamples were used during training. Both experiments included a within-subject comparison of concept formation following three training conditions: a) nonexamples that were more similar to the examples, b) nonexamples that are less similar to the examples, and c) no nonexamples. Arbitrary concepts were trained in Experiment 1 and concepts akin to those that could be taught in a classroom were trained in Experiment 2. Before and after …


Characterization Of Modern Ammunition And Background Profiles: A Novel Approach And Probabilistic Interpretation Of Inorganic Gunshot Residue, Korina Layli Menking-Hoggatt Jan 2021

Characterization Of Modern Ammunition And Background Profiles: A Novel Approach And Probabilistic Interpretation Of Inorganic Gunshot Residue, Korina Layli Menking-Hoggatt

Graduate Theses, Dissertations, and Problem Reports (ETD)

Gunshot residue (GSR) can provide essential clues in gun-related investigations. The standard practice for GSR analysis uses SEM-EDS, with the capability for single particle elemental and morphological analysis. However, the method is time-consuming and based on categorical classification models without considering case circumstances. Therefore, complementary and more encompassing methods are needed to improve evidence interpretation of modern ammunition. This research aims to fill these demands by developing standard materials and alternative methods to characterize and interpret IGSR.

This study developed primer GSR (pGSR) standards from sixty discharged primers that were fully characterized by three techniques. The number of GSR particles, …


Identifying Self-Determined Learning Practices Within Social Media For Teacher Professional Development, Leah Mcjilton Jan 2021

Identifying Self-Determined Learning Practices Within Social Media For Teacher Professional Development, Leah Mcjilton

Graduate Theses, Dissertations, and Problem Reports (ETD)

The collective increase of learner-centered teaching and substantial technology use in the classroom has given instructors potential opportunities to support students in developing lifelong learning skills. The ability to manage one’s own learning is an essential skill for lifelong learners in today’s workforce. Heutagogy, or self-determined learning, suggests that individuals have agency with respect to how, what, and when they learn. Heutagogy provides a framework for making the most of these developments, drawing on established learner-centered education theories. The key principles of heutagogy provide a foundation for designing and developing learning environments using social media. In order for teachers to …


Feminist Mentorship: Women Leading Men In Counselor Education, Erin Rachel Hagen Jan 2021

Feminist Mentorship: Women Leading Men In Counselor Education, Erin Rachel Hagen

Education

This Interpretative Phenomenological Study was initiated to explore the lived experiences of mentorship pairs in counselor education doctoral studies. The research question guiding this study was: what are the qualities of the mentoring relationship between female, cisgender, feminist-oriented counselor education mentors and their male cisgender traditionally-oriented doctoral counselor education mentees? This pair was identified for exploration by noting a gap in mentorship literature that recognizes the unique relational qualities and mentorship outcomes with cross-gender pairs, and the specific influence of feminist orientation on male mentees and the mentorship process. Cross-gender mentorship is addressed in literature but dominantly refers to men …


Comparing The Content And Pedagogical Knowledge Of Alternatively And Traditionally Certified Agricultural Educators, Kristi Marie Tonnessen Jan 2021

Comparing The Content And Pedagogical Knowledge Of Alternatively And Traditionally Certified Agricultural Educators, Kristi Marie Tonnessen

Education

The purpose of this research study is to determine and describe in-service SBAE teachers’ perceived Pedagogical Content Knowledge (PCK) and challenges with non-content related classroom material. In general, PCK is the point where knowledge of teaching meets agricultural content knowledge. With the rising number of alternatively certified agricultural educators across the country, it is important to examine PCK in both traditionally and alternatively certified teachers as well as the differences between the two. Since successful classroom management is crucial to teacher retention, it is necessary to look at the differences in difficulty of implementation of various strategies. Agricultural education is …


Does Mattering Really Matter To Graduate Students?, Jodi Colleen Ost Jan 2021

Does Mattering Really Matter To Graduate Students?, Jodi Colleen Ost

Education

As graduate student attrition hovers around 50%, scholars are beginning to study what is leading to these high attrition rates (Wao, 2010). As there has been little theoretical work done on graduate student retention, a review of the literature related to undergraduate student engagement and retention provides a starting point for developing theories of graduate student engagement and retention. One theory of undergraduate student engagement and retention relates to feelings of mattering. Mattering is a sense that other people care about you as it involves facets of feeling important to others, being noticed by others, that others are proud of …


C4-Face-Magic Toroidal Labelings On CM × CN, Stephen J. Curran, Richard M. Low, Stephen C. Locke Jan 2021

C4-Face-Magic Toroidal Labelings On CM × CN, Stephen J. Curran, Richard M. Low, Stephen C. Locke

Faculty Research, Scholarly, and Creative Activity

For a graph G = (V, E) naturally embedded in the torus, let F(G) denote the set of faces of G. Then, G is called a Cn-face-magic toroidal graph if there exists a bijection f : V (G) → {1, 2, . . ., |V (G)|} such that for every F ∈ F(G) with F ∼= Cn, the sum of all the vertex labels along Cn is a constant S. Let xv = f(v) for all v ∈ V (G). We call {xv : v ∈ V (G)} a Cn-face-magic toroidal labeling on G. We show that, for all m, …