Rigorous Analysis Of An Edge-Based Network Disease Model,
2019
University of Central Florida
Rigorous Analysis Of An Edge-Based Network Disease Model, Sabrina Mai
Honors Undergraduate Theses
Edge-based network disease models, in comparison to classic compartmental epidemiological models, better capture social factors affecting disease spread such as contact duration and social heterogeneity. We reason that there should exist infinitely many equilibria rather than only an endemic equilibrium and a disease-free equilibrium for the edge-based network disease model commonly used in the literature, as there do not exist any changes in demographic in the model. We modify the commonly used network model by relaxing some assumed conditions and factor in a dependency on initial conditions. We find that this modification still accounts for realistic dynamics of disease spread …
Comparison Of Green's Functions For A Family Of Boundary Value Problems For Fractional Difference Equations,
2019
University of Dayton
Comparison Of Green's Functions For A Family Of Boundary Value Problems For Fractional Difference Equations, Paul W. Eloe, Catherine Kublik, Jeffrey T. Neugebauer
Mathematics Faculty Publications
In this paper, we obtain sign conditions and comparison theorems for Green's functions of a family of boundary value problems for a Riemann-Liouville type delta fractional difference equation. Moreover, we show that as the length of the domain diverges to infinity, each Green's function converges to a uniquely defined Green's function of a singular boundary value problem.
On The Time Evolution Of Resonant Triads In Rotational Capillary-Gravity Water Waves,
2019
Technological University Dublin
On The Time Evolution Of Resonant Triads In Rotational Capillary-Gravity Water Waves, Rossen Ivanov, Calin Martin
Articles
We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes, and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero, we recover the well known integrable three-wave system.
Effects Of Advective-Diffusive Transport Of Multiple Chemoattractants On Motility Of Engineered Chemosensory Particles In Fluidic Environments,
2019
Trinity University
Effects Of Advective-Diffusive Transport Of Multiple Chemoattractants On Motility Of Engineered Chemosensory Particles In Fluidic Environments, D. King, H. Başağaoğlu, Hoa Nguyen, Frank G. Healy, Melissa Whitman, Sauro Succi
Mathematics Faculty Research
Motility behavior of an engineered chemosensory particle (ECP) in fluidic environments is driven by its responses to chemical stimuli. One of the challenges to understanding such behaviors lies in tracking changes in chemical signal gradients of chemoattractants and ECP-fluid dynamics as the fluid is continuously disturbed by ECP motion. To address this challenge, we introduce a new multiscale numerical model to simulate chemotactic swimming of an ECP in confined fluidic environments by accounting for motility-induced disturbances in spatiotemporal chemoattractant distributions. The model accommodates advective-diffusive transport of unmixed chemoattractants, ECP-fluid hydrodynamics at the ECP-fluid interface, and spatiotemporal disturbances in the chemoattractant …
Use Of Symmetries In Economics: An Overview,
2019
The University of Texas at El Paso
Use Of Symmetries In Economics: An Overview, Vladik Kreinovich, Olga Kosheleva, Nguyen N. Thach, Nguyen Duc Trung
Departmental Technical Reports (CS)
In this paper, we show that many semi-heuristic econometric formulas can be derived from the natural symmetry requirements. The list of such formulas includes many famous formulas provided by Nobel-prize winners, such as Hurwicz optimism-pessimism criterion for decision making under uncertainty, McFadden's formula for probabilistic decision making, Nash's formula for bargaining solution -- as well as Cobb-Douglas formula for production, gravity model for trade, etc.
Why Bilingualism Helps Autistic Children Function: A Symmetry-Based Explanation,
2019
The University of Texas at El Paso
Why Bilingualism Helps Autistic Children Function: A Symmetry-Based Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
One of the main problems of autistic children is that it is very difficult for them to switch to a different state, to a different activity -- and such switches are often needed. Researchers have recently shown that bilingualism helps autistic children function: namely, it is somewhat easier for bilingual children to switch to a new activity. In this paper, we provide a possible explanation for this empirical phenomenon. Namely, we show that, in general terms, autism means difficulty with breaking symmetries of a state, and we describe how this general reformulation indeed explains the above recently discovered phenomenon.
Applications Of Geometric And Spectral Methods In Graph Theory,
2019
University of Denver
Applications Of Geometric And Spectral Methods In Graph Theory, Lauren Morey Nelsen
Electronic Theses and Dissertations
Networks, or graphs, are useful for studying many things in today’s world. Graphs can be used to represent connections on social media, transportation networks, or even the internet. Because of this, it’s helpful to study graphs and learn what we can say about the structure of a given graph or what properties it might have. This dissertation focuses on the use of the probabilistic method and spectral graph theory to understand the geometric structure of graphs and find structures in graphs. We will also discuss graph curvature and how curvature lower bounds can be used to give us information about …
Decidability For Residuated Lattices And Substructural Logics,
2019
University of Denver
Decidability For Residuated Lattices And Substructural Logics, Gavin St. John
Electronic Theses and Dissertations
We present a number of results related to the decidability and undecidability of various varieties of residuated lattices and their corresponding substructural logics. The context of this analysis is the extension of residuated lattices by various simple equations, dually, the extension of substructural logics by simple structural rules, with the aim of classifying simple equations by the decidability properties shared by their extensions. We also prove a number of relationships among simple extensions by showing the equational theory of their idempotent semiring reducts coincides with simple extensions of idempotent semirings. On the decidability front, we develop both semantical and syntactical …
Bottle Filling Task Reasoning: A Comparison Of Matching Versus Constructed Student Responses,
2019
Boise State University
Bottle Filling Task Reasoning: A Comparison Of Matching Versus Constructed Student Responses, Dominique Banner, Laurie Overman Cavey
Mathematics Faculty Publications and Presentations
In this paper, we compare the levels of reasoning elicited during the completion of three versions of a bottle filling task: high school level matching; middle school level matching and constructed response. The goal of the tasks was to make visible secondary students covariational reasoning methods. Video of students completing the task while explaining their reasoning during one-onone interviews were analyzed. Analysis demonstrated a wide range of reasoning when provided a matching version with a greater incidence of accuracy with students who exhibited lower levels of reasoning. Conversely, the constructed response task demonstrated higher levels of reasoning more consistently with …
Mathematics Of The Infinite God In The Works Of Nicholas Of Cusa,
2019
Calvin University
Mathematics Of The Infinite God In The Works Of Nicholas Of Cusa, Lauren Henderson
Beets Paper Contest
The geometrical analyses of infinity exemplified in the work of Nicholas of Cusa can aid in understanding the complex nature of God’s attributes, specifically the perceived tension between his simplicity and his quality of encompassing and upholding all things.
Ua84 Sigma Chi,
2019
Western Kentucky University
Ua84 Sigma Chi, Wku Archives
WKU Archives Collection Inventories
Records created by and about the WKU chapter of Sigma Xi.
Student Help-Seeking Behaviors And Teacher Instructional Practices: Examining Their Relationship With U.S. Student Mathematics Achievement,
2019
University of Kentucky
Student Help-Seeking Behaviors And Teacher Instructional Practices: Examining Their Relationship With U.S. Student Mathematics Achievement, Michael C. Osborne
Theses and Dissertations--Curriculum and Instruction
Even though the United States (U.S.) spends, on average, more money per student than most Organisation for Economic Co-operation and Development (OECD) countries, it continues to lag behind its international peers in mathematics achievement. This study, which responded to the call for educational reforms that improve the mathematics achievement of U.S. students, aimed to examine the issue of student help-seeking behaviors and teacher instructional practices as they interact to affect student mathematics achievement. The Programme for International Student Assessment (PISA) defines student help-seeking behaviors as the ways in which students have a propensity to depend on the knowledge and intellect …
L(2, 1)-Labeling Of Circulant Graphs,
2019
Fort Hays State University
L(2, 1)-Labeling Of Circulant Graphs, Sarbari Mitra, Soumya Bhoumik
Mathematics Faculty Publications
An L(2, 1)-labeling of a graph Γ is an assignment of non-negative integers to the vertices such that adjacent vertices receive labels that differ by at least 2, and those at a distance of two receive labels that differ by at least one. Let λ12(Γ) denote the least λ such that Γ admits an L(2, 1)-labeling using labels from {0, 1, . . ., λ}. A Cayley graph of group G is called a circulant graph of order n, if G = Zn. In this paper initially we investigate the upper bound for the span of the L(2, 1)-labeling for …
Using A Discursive Framework To Analyze Geometric Learning And Instruction,
2019
Eastern Illinois University
Using A Discursive Framework To Analyze Geometric Learning And Instruction, Peter Wiles, Rick Anderson
Faculty Research and Creative Activity
In this study we applied a discursive perspective of learning (Sfard, 2008) to a sequence of 21 geometry mini-lessons taught in a fourth grade classroom. From this perspective, learning is defined as changes in mathematical discourse. We first characterize and then compare discourse from the beginning and the end of the mini-lesson sequence. We identify shifts in the discourse that occurred during the sequence. We then discuss how the characteristics of the st geometric discourse informed task design and instruction. This perspective provided a useful means for linking instruction to student learning in an operationalized manner.
A Second Order Bdf Numerical Scheme With Variable Steps For The Cahn-Hilliard Equation,
2019
Missouri University of Science and Technology
A Second Order Bdf Numerical Scheme With Variable Steps For The Cahn-Hilliard Equation, Wenbin Chen, Xiaoming Wang, Yue Yan, Zhuying Zhang
Mathematics and Statistics Faculty Research & Creative Works
We present and analyze a second order in time variable step BDF2 numerical scheme for the Cahn-Hilliard equation. the construction relies on a second order backward difference, convex-splitting technique and viscous regularizing at the discrete level. We show that the scheme is unconditionally stable and uniquely solvable. in addition, under mild restriction on the ratio of adjacent time-steps, an optimal second order in time convergence rate is established. the proof involves a novel generalized discrete Gronwall-type inequality. as far as we know, this is the first rigorous proof of second order convergence for a variable step BDF2 scheme, even in …
Automating The Calculation Of The Hilbert–Kunz Multiplicity And F-Signature,
2019
University of Mississippi
Automating The Calculation Of The Hilbert–Kunz Multiplicity And F-Signature, Gabriel Johnson, Sandra Spiroff
Faculty and Student Publications
© 2018 The Authors The Hilbert–Kunz multiplicity and F-signature are important invariants for researchers in commutative algebra and algebraic geometry. We provide software, and describe the automation, for the calculations of the two invariants in the case of intersection algebras over polynomial rings.
Ua66/10/2 Ogden College Of Science & Engineering Mathematics Publications,
2019
Western Kentucky University
Ua66/10/2 Ogden College Of Science & Engineering Mathematics Publications, Wku Archives
WKU Archives Collection Inventories
Publications created by and about the Mathematics department.
Enhancing The Quandle Coloring Invariant For Knots And Links,
2019
Claremont Colleges
Enhancing The Quandle Coloring Invariant For Knots And Links, Karina Elle Cho
HMC Senior Theses
Quandles, which are algebraic structures related to knots, can be used to color knot diagrams, and the number of these colorings is called the quandle coloring invariant. We strengthen the quandle coloring invariant by considering a graph structure on the space of quandle colorings of a knot, and we call our graph the quandle coloring quiver. This structure is a categorification of the quandle coloring invariant. Then, we strengthen the quiver by decorating it with Boltzmann weights. Explicit examples of links that show that our enhancements are proper are provided, as well as background information in quandle theory.
Radial Solutions To Semipositone Dirichlet Problems,
2019
Claremont Colleges
Radial Solutions To Semipositone Dirichlet Problems, Ethan Sargent
HMC Senior Theses
We study a Dirichlet problem, investigating existence and uniqueness for semipositone and superlinear nonlinearities. We make use of Pohozaev identities, energy arguments, and bifurcation from a simple eigenvalue.
Bounding The Number Of Compatible Simplices In Higher Dimensional Tournaments,
2019
University of Kentucky
Bounding The Number Of Compatible Simplices In Higher Dimensional Tournaments, Karthik Chandrasekhar
Theses and Dissertations--Mathematics
A tournament graph G is a vertex set V of size n, together with a directed edge set E ⊂ V × V such that (i, j) ∈ E if and only if (j, i) ∉ E for all distinct i, j ∈ V and (i, i) ∉ E for all i ∈ V. We explore the following generalization: For a fixed k we orient every k-subset of V by assigning it an orientation. That is, every facet of the (k − 1)-skeleton of the ( …
