Digital Commons Network^™

Fractional Derivative-Based Analysis Of The Heat Transfer Properties Of Fluid Flow Over A Contracting Permeable Infinite-Length Cylinder, Anas Saeb Alhasan

Theses

Understanding the complex interplay between the contracting behavior of the cylinder and the fluid flow dynamics has implications for the design of porous structures for heat exchange and filtration systems. In this study, we investigate the dynamics and thermal behavior of fluid flow past a contracting permeable infinite cylinder. First, we developed a mathematical model based on the Navier-Stokes equations to describe the fluid dynamics around the contracting permeable infinite cylinder. A new simple well-behaved definition of fractional derivative called conformable fractional derivative introduced by authors Khalil et al. [3] is employed to generalize the PDE’s of momentum and energy. …

Learners’ Mathematics Identity And Achievement: Where Does The Teacher Come In?, Luis M. Fernandez, Ursula Nguyen, Rebecca Callahan

School of Mathematical & Statistical Sciences Faculty Publications

In response to recent interest in K-12th students’ mathematics identity formation and its implications for achievement, the present study examines the relationship between learners’ mathematics identity and student achievement while simultaneously accounting for teacher-enacted instructional practices in mathematics. Drawing from HSLS:2009, a nationally representative dataset of 9th–12th students within the United States, we use multiple linear regression analyses to examine how teachers’ mathematical pedagogies and 9th grade students’ perceptions of teacher equity are associated, first, with students’ mathematics identity, and, subsequently, math achievement after accounting for students’ mathematics identity. Ultimately, results from our models reveal a statistically significant relationship between …

A Micromagnetic Study Of Skyrmions In Thin-Film Multilayered Ferromagnetic Materials, Nicholas J. Dubicki

Dissertations

Magnetic skyrmions are topologically protected, localized, nanoscale spin textures in non-centrosymmetric thin ferromagnetic materials and heterostructures. At present they are of great interest to physicists for potential applications in information technology due to their particle-like properties and stability. In a system of multiple thin ferromagnetic layers, the stray field interaction was typically treated with various simplifications and approximations. It is shown that extensive analysis of the micromagnetic equations leads to an exact representation of the stray field interaction energy in the form of layer interaction kernels, a so-called 'finite thickness' representation. This formulation reveals the competition between perpendicular magnetic anisotropy …

Oer Textbook Review For Calculus - Openstax Calculus, Jing Hu Ph.D.

Open Educational Resources Publications

This OER textbook review provides a comprehensive evaluation of the "Calculus" textbook series published by OpenStax. The reviewer, Jing Hu, an adjunct lecturer at Bentley University, highlights the textbook's strengths, including its thorough coverage of essential calculus topics, accurate and well-established mathematical principles, practical relevance, and user-friendly design. The open-access nature of the resource is seen as a significant advantage, contributing to its long-term utility and accessibility for both students and educators. Overall, the review concludes that the OpenStax Calculus textbook is a high-quality, comprehensive, and freely available resource that effectively supports the learning and teaching of calculus.

Graph And Group Theoretic Properties Of The Soma Cube And Somap, Kyle Asbury, Ben Glancy

Mathematical Sciences Technical Reports (MSTR)

The SOMA Cube is a puzzle toy in which seven irregularly shaped blocks must be fit together to build a cube. There are 240 distinct solutions to the SOMA Cube. One rainy afternoon, Conway and Guy created a graph of all the solutions by manually building each solution. They called their graph the SOMAP. We studied how the geometric structure of the SOMA Cube pieces informs the graph theoretic properties of the SOMAP, such as subgraphs that can or cannot appear and vertex centrality. We have also used permutation group theory to decipher notation used by Knuth in previous work …

A Quotient Of Fomin-Kirillov Algebra And Q-Lucas Polynomial, Sirous Homayouni

Mathematics Faculty Publications

We introduce a quotient of the Fomin-Kirillov algebra F K(n) denoted by F KCn (n), over the ideal generated by the edges of a complete graph on n vertices that are missing in the n-cycle graph Cn. In this quotient algebra, we establish a one-to-one correspondence between the basis elements and the set of matchings in an n-cycle graph. We prove that the Hilbert series of F KCn (n) corresponds to the q-Lucas polynomials, and the dimension of this quotient algebra is equal to the Lucas number Ln. We also find the character map of this quotient algebra over the …

On Blow-Up And Explicit Soliton Solutions For Coupled Variable Coefficient Nonlinear Schrödinger Equations, Jose M. Escorcia, Erwin Suazo

School of Mathematical & Statistical Sciences Faculty Publications

This work is concerned with the study of explicit solutions for a generalized coupled nonlinear Schrödinger equations (NLS) system with variable coefficients. Indeed, by employing similarity transformations, we show the existence of rogue wave and dark–bright soliton-like solutions for such a generalized NLS system, provided the coefficients satisfy a Riccati system. As a result of the multiparameter solution of the Riccati system, the nonlinear dynamics of the solution can be controlled. Finite-time singular solutions in the 𝐿∞ norm for the generalized coupled NLS system are presented explicitly. Finally, an n-dimensional transformation between a variable coefficient NLS coupled system and a …

New Class Function In Dual Soft Topological Space, Maryam Adnan Al-Ethary, Maryam Sabbeh Al-Rubaiea, Mohammed H. O. Ajam

Al-Bahir

In this paper we introduce a new class of maps in the dual Soft topological space and study some of its basic properties and relations among them, then we study and mapping.

Dynamic Optimization With Timing Risk, Erin Cottle Hunt, Frank N. Caliendo

Economics and Finance Faculty Publications

Timing risk refers to a situation in which the timing of an economically important event is unknown (risky) from the perspective of an economic decision maker. While this special class of dynamic stochastic control problems has many applications in economics, the methods used to solve them are not easily accessible within a single, comprehensive survey. We provide a survey of dynamic optimization methods under comprehensive assumptions about the nature of timing risk. We also relax the assumption of full information and summarize optimization with limited information, ambiguity, imperfect hedging, and dynamic inconsistency. Our goal is to provide a concise user …

Math Developmental Models Examined: Pass Rate, Duration For Completion, Enrollment Consistency And Racial Disparity, Xixi Wang, Annie Childers, Lianfang Lu

Journal of Access, Retention, and Inclusion in Higher Education

No abstract provided.

Diagrams In Involutive Residuated Lattices, Isis A. Gallardo

Electronic Theses and Dissertations

First, we show that every distributive lattice-ordered pregroup can be embedded into a functional algebra over an integral chain, thereby improving the existing Cayley/Holland style embedding theorem. Using this result, we demonstrate that the variety of all dis tributive lattice-ordered pregroups is generated by the functional algebra on the integers. Additionally, we prove that the equational theory of this variety is decidable.

Next, we establish that DLP is equal to the join of its subvarieties LP_n, where 𝑛 ∈ ℤ⁺, consisting of 𝑛-periodic ℓ-pregroups. We also prove that every algebra in LP_n can be embedded …

Developing A Comprehensive Cognitive Model Of Math Achievement, Nina Anderson

Electronic Theses and Dissertations

Recently, downward trends have been reported in U.S. children’s math performance following school disruptions during COVID-19 amidst longstanding concerns for instruction and curricula within the subject. In support of efforts to remedy these declines, the current work presents two studies dedicated to identifying cognitive factors that are most strongly related to math performance, and which therefore offer promising potential targets for assessment and intervention. Both studies use data from the Colorado Learning Disabilities Research Center, which includes participants ages 8 - 16 and multiple well-validated measures of all constructs of interest. Study 1 tests three alternative latent cognitive models of …

Soft Sets Extensions: Innovating Healthcare Claims Analysis, Daniela Gifu, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the dynamic arena of healthcare research, where the complexities of data often rival the intricacies of biological systems, the ability to model and analyze such multifaceted datasets is crucial. This comprehensive review delves into the evolution and application of Soft Sets and their extensions, including HyperSoft Sets, SuperHyperSoft Sets, IndetermSoft Sets, IndetermHyperSoft Sets, and TreeSoft Sets, in healthcare claims data analysis.

The Bicomplex Tensor Product And A Bicomplex Choi Theorem, Daniel Alpay, Antonino De Martino, Kamal Diki, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we extend the concept of tensor product to the bicomplex case and use it to prove the bicomplex counterpart of the classical Choi theorem in the theory of complex matrices and operators. The concept of hyperbolic tensor product is also discussed, and we link these results to the theory of quantum channels in the bicomplex and hyperbolic case.

A Second Homotopy Group For Digital Images, Gregory Lupton, Oleg R. Musin, Nicholas A. Scoville, P. Christopher Staecker, Jonathan Treviño-Marroquín

School of Mathematical & Statistical Sciences Faculty Publications

We define a second (higher) homotopy group for digital images. Namely, we construct a functor from digital images to abelian groups, which closely resembles the ordinary second homotopy group from algebraic topology. We illustrate that our approach can be effective by computing this (digital) second homotopy group for a digital 2-sphere.

Free Energy Differences In Nonequilibrium Thermodynamic Processes, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Systems which may be allowed to go out of equilibrium have been of interest recently. A quantity is formulated whose average over an ensemble of microscopic realizations of the process depends only on the initial and final states. This is so even though the system may not be in equilibrium during the process. A generalization to the case where the initial and final states are not equilibrium states is developed here. Quantum analogues of these relations are derived, and an indication of how this might be applied to study entropy increase in thermodynamics is presented.

Representation Dimensions Of Algebraic Tori And Symmetric Ranks Of G-Lattices, Jason Bailey Heath

Theses and Dissertations

Algebraic tori over a field k are special examples of affine group schemes over k, such as the multiplicative group of the field or the unit circle. Any algebraic torus can be embedded into the group of invertible n x n matrices with entries in k for some n, and the smallest such n is called the representation dimension of that torus. Representation dimensions of algebraic tori can be studied via symmetric ranks of G-lattices. A G-lattice L is a group isomorphic to the additive group Zⁿ for some n, along with an action …

Generalizations Of The Graham-Pollak Tree Theorem, Gabrielle Anne Tauscheck

Theses and Dissertations

Graham and Pollak showed in 1971 that the determinant of a tree’s distance matrix depends only on its number of vertices, and, in particular, it is always nonzero. This dissertation will generalize their result via two different directions: Steiner distance k-matrices and distance critical graphs. The Steiner distance of a collection of k vertices in a graph is the fewest number of edges in any connected subgraph containing those vertices; for k = 2, this reduces to the ordinary definition of graphical distance. Here, we show that the hyperdeterminant of the Steiner distance k-matrix is always zero if …

Modeling, Analysis, Approximation, And Application Of Viscoelastic Structures And Anomalous Transport, Yiqun Li

Theses and Dissertations

(Variable-order) fractional partial differential equations are emerging as a competitive means to integer-order PDEs in characterizing the memory and hereditary properties of physical processes, e.g., anomalously diffusive transport, viscoelastic mechanics and financial mathematics, and thus have attracted widespread attention. In particular, optimal control problems governed by fractional partial differential equations are attracting increasing attentions since they are shown to provide competitive descriptions of challenging physical phenomena. Nevertheless, variable-order fractional models exhibit salient features compared with their constant-order analogues and introduce mathematical difficulties that are not typical encountered in the context of integer-order and constant-order fractional partial differential equations.

This dissertation …

Erlang-Distributed Seir Epidemic Models With Cross-Diffusion, Victoria Chebotaeva

Theses and Dissertations

We examine the effects of cross-diffusion dynamics in epidemiological models. Using reaction-diffusion dynamics to model the spread of infectious diseases, we focus on situations in which the movement of individuals is affected by the concentration of individuals of other categories. In particular, we present a model where susceptible individuals move away from large concentrations of infected and infectious individuals.

Our results show that accounting for this cross-diffusion dynamics leads to a noticeable effect on epidemic dynamics. It is noteworthy that this leads to a delay in the onset of epidemics and an increase in the total number of people infected. …

Global Well-Posedness Of Nonlocal Differential Equations Arising From Traffic Flow, Thomas Joseph Hamori

Theses and Dissertations

Macroscopic traffic flow models describe the evolution of a function ρ(t, x), which represents the traffic density at time t and location x according to a differential equation (typically a conservation law). Numerous models have been introduced over the years which capture the phenomenon of shock formation in which the solution develops a discontinuity. This presents difficulties from the standpoint of mathematical analysis, necessitating the consideration of weak solutions. At the same time, this undesirable mathematical behavior corresponds to unsafe driving conditions on real roadways, in which the heaviness of traffic may vary abruptly and dramatically. This thesis introduces and …

Traveling Wave Phenomena Of Inhomogeneous Half-Wave Equation, Zhaosheng Feng, Yu Su

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we are concerned with traveling wave phenomena of the inhomogeneous half-wave equation, which models the energy of a spin zero particle in the Coulomb field. We study the Gagliardo-Nirenberg and critical Hardy-Sobolev inequalities with velocity 0 < | v | < 1 and obtain the estimates for the best constants and optimizers of inequalities. Moreover, we establish the non-scattering results with small traveling wave for energy subcritical and critical cases.

An Introduction To Category Theory, Joseph Kopp

Electronic Proceedings of Undergraduate Mathematics Day

Category theory is a relatively new field of mathematics that has grown much in popularity in recent years. It is a general theory of mathematical structure that lends itself to making overarching, yet deep, connections between many branches of mathematics. This power to make such wide-reaching statements is what has drawn many to study it. However, category theory has also been criticized for being "abstract nonsense," in that some believe the theory to be too abstract to carry meaning, much less be applied to the real world. The goal of this paper is to introduce the main ideas of category …

Derivation Of The Sliding Catenary Curve Via Calculus Of Variations, Ethan Shade

Electronic Proceedings of Undergraduate Mathematics Day

Using the calculus of variations this paper derives the general equation for the "sliding catenary curve" — a hanging chain with terminal links free to slide along two poles, one tilted and one vertical. By applying physical assumptions along with the Euler-Lagrange equation, the Beltrami identity, the Legendre-Clebsch condition, the transversality condition, Lagrange multipliers, and the isoperimetric constraint, we derive the general equation for the sliding catenary curve through a functional that measures the potential energy of the hanging chain. This general equation is then compared to a real-life construction of a sliding catenary curve. Additionally the paper explores a …

Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer

CODEE Journal

This paper aims to develop a mathematical model to study the dynamics of addiction as individuals go through their detox journey. The motivation for this work is three fold. First, there has been a significant increase in drug overdose and drug addiction following the COVID-19 pandemic, and addiction may be interpreted as a infectious disease. Secondly, the dynamics of infectious disease could be modeled via compartmental models described by differential equations and one can therefore leverage the existing analytical and numerical methods to model addiction as a disease. Finally, the work helps to inform how mathematical models governed by differential …

Bernoulli Convolution Of The Depth Of Nodes In Recursive Trees With General Affinities, Toshio Nakata, Hosam Mahmoud

Journal of Stochastic Analysis

No abstract provided.

Frames And Spaces For Distributive Quasi Relation Algebras And Distributive Involutive Fl-Algebras, Andrew Craig, Peter Jipsen, Claudette Robinson

Mathematics, Physics, and Computer Science Faculty Articles and Research

Analogous to atom structures for relation algebras, we define partially ordered frames and prove they are duals for complete perfect distributive quasi relation algebras and distributive involutive FL-algebras. We then extend this dual representation to all algebras and their corresponding frames with a Priestley topology.

For relation algebras up to size 16 it has been determined which algebras are representable by binary relations. We compute all finite distributive quasi relation algebras up to 8 elements and provide representations for some of them.

An Em-Based Likelihood Inference For Degradation Data Analysis Using Gamma Process, Lochana Palayangoda, N. Balakrishnan

Mathematics Faculty Publications

The gamma process is widely used for the lifetime estimation of highly reliable products that degrade over time. Typically, incomplete likelihood is used to estimate the model parameters and the reliability estimates for the first passage time distribution of the gamma process; however, it (i.e., pseudo method) does not consider interval censoring and right censoring information of the degradation data. In this work, the expectation-maximization algorithm-based method (EM method) is developed for the estimation of the gamma process model parameters and the reliability estimates incorporating interval censoring and right censoring. The asymptotic variance–covariance matrix and the asymptotic confidence intervals for …

On The Structure Of Balanced Residuated Partially Ordered Monoids, Stefano Bonzio, José Gil-Férez, Peter Jipsen, Adam Přenosil, Melissa Sugimoto

Mathematics, Physics, and Computer Science Faculty Articles and Research

A residuated poset is a structure ⟨A,⩽, ·, \, /, 1⟩ where ⟨A,⩽⟩ is a poset and ⟨A, ·, 1⟩ is a monoid such that the residuation law x · y ⩽ z ⇐⇒ x ⩽ z/y ⇐⇒ y ⩽ x\z holds. A residuated poset is balanced if it satisfies the identity x\x ≈ x/x. By generalizing the well-known construction of Płonka sums, we show that a specific class of balanced residuated posets can be decomposed into such a sum indexed by the set of positive idempotent elements. Conversely, given a semilattice directed system of residuated posets equipped with two …

Waves In Cosmological Background With Static Schwarzschild Radius In The Expanding Universe, Karen Yagdjian

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we prove the existence of global in time small data solutions of semilinear Klein–Gordon equations in space-time with a static Schwarzschild radius in the expanding universe.