Mathematics Commons^™

Stochastic Games Of Parental Vaccination Decision Making And Bounded Rationality, Andras Balogh, Tamer Oraby

School of Mathematical & Statistical Sciences Faculty Publications

Vaccination is an effective strategy to prevent the spread of diseases. However, hesitancy and rejection of vaccines, particularly in childhood immunizations, pose challenges to vaccination efforts. In that case, according to rational decision-making and classical utility theory, parents weigh the costs of vaccination against the costs of not vaccinating their children. Social norms influence these parental decision-making outcomes, deviating their decisions from rationality. Additionally, variability in values of utilities stemming from stochasticity in parents' perceptions over time can lead to further deviations from rationality. In this paper, we employ independent white noises to represent stochastic fluctuations in parental perceptions of …

Asymptotic Matrix Behaviors And Iterative Algorithms, Tin-Yau Tam

Mathematics Colloquium Series

This presentation examines the asymptotic behavior of matrix iterations, focusing on the QR and LR algorithms and their significance in eigenvalue computation. It highlights foundational developments by Rutishauser, Francis, and Kublanovskaya and modern refinements by Huang and Tam, particularly on matrix decompositions and spectral properties. Extensions of Yamamoto’s theorem, including recent works by Nayak and Shekhawat, and Huang and Tam, are discussed, connecting iterative processes to spectral radius formulas and Jordan decompositions. This is a joint work with Huajun Huang of Auburn University.

Weak Solutions Of Spdes In The Space Of Tempered Distributions, Suprio Bhar, Barun Sarkar

Journal of Stochastic Analysis

No abstract provided.

Optimized Hiv/Aids Resource Allocation In Ohio: A Linear Programming Approach, Godfred Ahenkroa Kesse

Data Science and Data Mining

This study employs a linear and integer programming approach to optimize HIV resource allocation in Ohio, aiming to minimize new infections and enhance the impact of limited resources. With the advances in HIV prevention and treatment, Ohio faces challenges in addressing disparities in access to healthcare, particularly among high-risk populations. The proposed model integrates data on infection rates, transmission patterns, demographic factors, and cost-effectiveness to provide a decision-support framework for policymakers. Using epidemiological data and equity constraints, the model prioritizes high-risk regions and populations while ensuring fair resource distribution. Results indicate that increased funding allocations significantly enhance the potential to …

Ultrathin-Layer Strain-Based Electronic Devices: From-First-Principles Derivation Of The Corresponding Equation, Julio C. Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

Most information about the world comes from sensors -- and from the results of processing sensor data. In many practical situations -- e.g., in biomedical applications -- it is desirable to make sure that the sensors are as "invisible" as possible, in particular, that they are as small as possible. One way to achieve such small size is to use ultrathin-layer materials such as graphene. It is known that for such materials, strain causes electromagnetic effects -- which can be used to detect small strains. Interestingly, it turned out that the same equation describes the relation between strain and electric …

A Natural Extension Of F-Transform To Triangular And Triangulated Domains Necessitates The Use Of Triangular Membership Functions, Hana Zámečiková, Irina Perfilieva, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations when we process 1-D data, the method of F-transform turned out to be very useful. In this method, we can use either triangular membership functions or more complex ones. Because this method has been so successful in 1-D applications, a natural idea is to extend it to functions defined on 2-D and higher-dimensional domains -- e.g., to images. This method allows natural generalization to rectangular domains, where it indeed turned out to be very effective. A recent paper showed that it can extended to more general domains -- e.g., to triangular domains and to more general …

Fourier Series For Singular Measures In Higher Dimensions, Chad Berner, John E. Herr, Palle E.T. Jorgensen, Eric S. Weber

Mathematics and Statistics Faculty Research & Creative Works

For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal L2 Fourier expansions. Our results hold for probability measures μ with finite support in Rd that satisfy a certain disintegration condition that we refer to as "slice-singular". In this general framework, we present explicit L2(μ)-Fourier expansions, with Fourier exponentials having positive Fourier frequencies in each of the d coordinates. Our Fourier representations apply to every f∈L2(μ), are based on an extended Kaczmarz algorithm, and use a new recursive μ Rokhlin disintegration representation. In detail, our Fourier series expansion for f is in terms of the …

Unconditionally Optimal Convergent Zero-Energy-Contribution Scheme For Two Phase Mhd Model, Jinjin Yang, Shipeng Mao, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

This paper focuses on the unconditionally optimal error estimates of a fully discrete decoupled scheme for two-phase magnetohydrodynamic (MHD) model with different viscosities and electric conductivities, by using the zero-energy-contribution (ZEC) method for the temporal discretization and mixed finite elements for the spatial discretization. Based on the ZEC property of the nonlinear and coupled terms of the model, an ordinary differential equation is designed to introduce a nonlocal scalar auxiliary variable which will play a key role in the design and the energy stability of the decoupled scheme. Combining fully explicit treatment on the nonlinear and coupled terms with the …

Analytical Method For Solving Systems Of Fractional Initial Value Problems Using The Modified Atangana-Baleanu Derivative, Lana Mohammad Aref

Theses

This thesis presents an analytical method to solve systems of fractional initial value problems using the Modified Atangana-Baleanu Fractional Derivative. The proposed approach leverages an improved operational matrix method, incorporating an iterative, direct computation technique to simplify the solution process and reduce computational costs. Foundational concepts in fractional calculus and block pulse functions are introduced, followed by the derivation of operational matrices tailored for fractional systems. Theoretical analysis establishes the existence and uniqueness of solutions, along with uniform convergence and error estimates. Practical examples and applications are presented that demonstrate the efficiency, accuracy, and versatility of the method in solving …

Project Title: Maximizing The Volume Of A Cardboard Box To Save Trees– An Application Of Polynomial Functions To Address Global Issues [Mathematics], Lucie Mingla

Open Educational Resources

MAT 115 College Algebra & Trigonometry/Precalculus

Project Title: Maximizing the Volume of a Cardboard Box to Save Trees– An Application of Polynomial Functions to Address Global Issues

Reflective Narrative:

This project was inspired by my participation in the "Designing and Implementation of STEM Co-Curricular Activities" CTL seminar in Spring 2023. I am grateful to Drs. Bukurie Gjoci, Daniel Gertner, Ingrid Veras, and Midas Tsai, along with fellow participants, for their invaluable feedback that helped shape its development. The project was implemented in two College Algebra and Trigonometry courses. I participated in two seminars to further develop this project. The Community …

Order-2 Delaunay Triangulations Optimize Angles, Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian

School of Mathematical & Statistical Sciences Faculty Publications

The local angle property of the (order-1) Delaunay triangulations of a generic set in R2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">R2R2 asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">R2R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations …

For Chow Variety Try This New Dessert Recipe, Jane P. Sheldon

Journal of Humanistic Mathematics

A positive addition to any dinner table or social function, this baked good can be served plane or à la mode.

Integration Bar, Erik Talvila

Journal of Humanistic Mathematics

In this humourous story, the narrator is dragged by their friend to a crazy bar for a late night of wild drinking and dancing. Except, the drinking is replaced with computing integrals.

Constanto Mysterium - A Paradise Of Shifting Constants, Vijay Fafat

Journal of Humanistic Mathematics

Mathematicians speak of constants of mathematics. Some of these constants are known to high-heavens. Some remain hidden in the obscurity of erudition. And to be frank, while every real number is a mathematical constant, we don’t know much about most of them (is not the set of transcendental numbers incommensurable without us knowing or understanding very many of them?).

So what elevates some constants above others? Is this elevation just a measure of the ignorance of mathematicians who have explored but a small patch of an infinite quilt, a case of six wise men trumpeting the – well, the trumpet …

Welcome 2025—The Year Of A Magical Number, Md Sadikur Rahman

Journal of Humanistic Mathematics

This is a poem to welcome the new year 2025 and note its relevance to mathematics.

A Ramsey Theory Essay: The Dinner Party, Ryan Coghill

Journal of Humanistic Mathematics

This is a poem inspired by Ramsey’s theorem. Its main characters are; Frank Ramsey, Issai Schur, Richard Rados, Bertel van der Waarden, Ronald Graham and Paul Erdos, some of the pioneers of the field of Ramsey theory. There has been care put into each paragraph so that it’s lines can be viewed as though they were nodes on a graph which share traits with each other of rhyme, theme and length which can be paired in 2 states, sharing and unique in such a way that one might find coloured graph edges when working in the field of Ramsey theory.

Math Is A Tiger And A Pecan, William Cocke

Journal of Humanistic Mathematics

Using perfect secrecy and the ability to identify gibberish in a given language, we encode two poems in one. This allows for a single cipherpoem to have multiple plainpoems associated with it. The result is a form of superposition where neither poem is the more correct interpretation than the other.

The poem presented is about two distinct aspects of mathematics: the tiger to be sought after and hunted; or a pecan that we have surrounded but cannot crack open.

My Academic Life -- A Poem, Sonja Petrovic

Journal of Humanistic Mathematics

No abstract provided.

Belonging, Lawrence M. Lesser

Journal of Humanistic Mathematics

No abstract provided.

What Happened When I Took Calculus For The First Time At Age 47, Britt Kaufmann

Journal of Humanistic Mathematics

These five poems are inspired by being in high school math classes and could be used in the classroom for cross-curricular enrichment.