Digital Commons Network^™

Exploring Topological And Game-Theoretic Properties Of Selective Covering Bispaces, Selma Özçağ

Turkish Journal of Mathematics

This paper considers set selectively star countable chain condition in a bitopological setting, exploring its fundamental topological properties and its relationships with the existing selective covering properties. Furthermore we investigate a game-theoretic characterizations of the selectively countable chain condition property in bitopological spaces.

The Killing Magnetic Curves In The Anti-De Sitter Space H31, Uğur Dursun

Turkish Journal of Mathematics

In this paper, we study space-like, time-like and light-like Killing magnetic curves derived from Killing magnetic vector fields of the anti-de Sitter space H³₁ by using the half-space model H³₁ of H³₁. We find the first integrals of the system of nonlinear differential equations that describe the Killing magnetic curves corresponding to some Killing vector fields of H³₁, and then we give some particular solutions to obtain space-like, time-like and light-like magnetic curves of H³₁. Also, we calculate the curvature and torsion of some space-like and time-like …

A Non-Newtonian Approach To Screw Motion And Dual Numbers, Esra Parlak, Zehra Özdemi̇r

Turkish Journal of Mathematics

In this paper, we define multiplicative dual numbers, multiplicative dual vectors, scalars, and vector products associated with the multiplicative dual numbers. We give the base elements of multiplicative dual elliptic quaternions and their operational properties. We explain the rotation and translation motions in multiplicative dual elliptical quaternions. We provide the matrix representations of the screw motion using multiplicative dual elliptical quaternions. Thanks to these multiplicative dual elliptical quaternions, we explain the screw motion along with rotation and translation with theorems and proofs. We visualize this screw motion with mathematical programs by applying screw-ruled surfaces.

Cover And Contents

Turkish Journal of Mathematics

No abstract provided.

Predicting Tart Cherry Stem Water Potential Using Uav Multispectral Imagery And Environmental Data Via Symbolic Regression, Anderson L. S. Safre, Alfonso Torres-Rua, Kurt Wedegaertner, Brent Black, Brennan Bean, Burdette Barker, Matt Yost

Civil and Environmental Engineering Faculty Publications

Tart cherry is an important fruit crop in Utah, where irrigation is essential due to arid conditions. Precision irrigation requires reliable indicators of plant water status, and stem water potential (Ψ_stem), is among the most sensitive though labor-intensive and spatially limited. This study develops Ψ_stem estimation models using high-resolution multispectral Unmanned Aerial Vehicle (UAV) imagery combined with meteorological and soil moisture data, applying Symbolic Regression (SR). Results show a stronger correlation between optical bands and Ψ_stem during the pre-harvest period. Among 85 vegetation indices, the Red Chromatic Coordinate (RCC) index performed best (R² = 0.67). …

Measuring What Matters: Specifications Grading And Latin* Students’ Mathematics Identity, Luis Miguel Fernández, Mayra Ortiz Galarza, Cristina Villalobos, Martha Asare

School of Mathematical & Statistical Sciences Faculty Publications

This study examined Specifications Grading, an alternative grading system emphasizing clearly defined learning outcomes and revision, and mathematics identity among 846 Latin* Calculus I students at a Hispanic-Serving Institution. Mathematics identity, comprising competence/performance, recognition, and interest, was measured at the beginning and end of the semester. Repeated-measures analyses indicated stable competence/performance and recognition alongside declines in interest. Specifications Grading was associated with increased mathematics identity, and multilingual students experienced smaller declines than their peers overall.

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Este estudio examinó la calificación por especificaciones, un sistema de evaluación alternativo que enfatiza resultados de aprendizaje claramente definidos y oportunidades estructuradas de revisión, …

Numerals And Other Means Of Expressing Plurality In Language And Thought: A Developmental Perspective Across Cultures., Giovanni Giuseppe G.G. Nicosia Prof.

Numeracy

Several ancient languages use linguistic structures to differentiate between singular, dual, and plural forms that are used when one, two, or many objects are referenced. (Some languages go further, adding a trial form to differentiate two from three.) In many modern languages, numerals are used to convey precise number. After reviewing a range of ways languages express number (including the interesting case of Pirahã which does not express precise number), the paper concludes with a proposed developmental path for the expression of quantity in languages.

Mckinsey-Tarski Algebras And Raney Extensions, G. Bezhanishvili, R. Raviprakash, A. L. Suarez, Joanne Walters-Wayland

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce the notion of Raney morphism between MT-algebras and show that the resulting category is equivalent to the category of Raney extensions. This is done by generalizing the construction of the Funayama envelope of a frame. The resulting notion of the T₀-hull of a Raney extension generalizes that of the T_D-hull of a frame.

How Euler Could Have Done It: Euler And A Heuristic Derivation Of The Prime Number Theorem, Alexander Aycock

Euleriana

We present an argument that leads to the formulation of the Prime Number Theorem that Euler could have given.

The Modern History Of The Basel Problem, John Campbell, Paul Levrie

Euleriana

The \emph{Basel problem} refers to the problem of determining a closed form for the infinite series $\frac{1}{1^2} + \frac{1}{2^2} + \cdots$. If we consider what mathematical results have the most peer-reviewed papers devoted to new ways of proving such results, Euler's formula $\frac{1}{1^2} + \frac{1}{2^2} + \cdots = \frac{\pi^2}{6}$ is certainly among the top of such results. This motivates our historical study of peer-reviewed papers based on proofs of Euler's formula, and we introduce what appears to be the most comprehensive and up-to-date and exhaustive catalogue of peer-reviewed, published papers in the 20th and 21st centuries devoted to or mainly …

Even Repdigits Are Not Perfect: Conclusions From Triangular Numbers, Uwe Hassler

Euleriana

Are there nontrivial repdigits that are perfect numbers? This note gives an answer: not for numbers smaller than $10^{1500}$. This finding follows from results for triangular numbers. Passing by, I review Euler's contributions on polygonal numbers.

Euler And Gauss On The Hypergeometric Function -- A Comparison, Alexander Aycock

Euleriana

We present several results stated by Euler on what is today called the Gaussian hypergeometric function. For this purpose, we compare the results found by Gauss to Euler's results.

The Extent To Which The Earth's Motion Is Perturbed By The Moon, More Accurately Investigated: An English Translation Of E139, Patrick T. Headley

Euleriana

In Tabulae astronomicae solis et lunae (Solar and lunar astronomical tables) (E87), published in 1746, Euler made a first attempt to correct his astronomical tables for the gravitational attraction of the Earth toward the Moon, simply by accounting for the difference between the position of the Earth and the center of gravity of the Earth-Moon system. In this article Euler revisited the problem, noting that this center of gravity would not itself take an elliptical path around the Sun. To model the motion more accurately, Euler considered the separate gravitational attractions of the Sun and Moon acting on the Earth. …

About Infinite Algebraic Curves Whose Indefinite Lengths Equal An Elliptic Arc: An English Translation Of E780, Derek R. Aoki

Euleriana

Euler continues his study of algebraic curves with equal arc length, a subject to which he returned several times. After a brief review, he introduces an infinite family of curves with the same indefinite length as a given ellipse. However, this first family is by his own admission poorly motivated, so he derives directly a different but related family of curves with the same indefinite length as a given ellipse.

Historical Beginnings To Modern Results, Christopher Goff, Erik Tou

Euleriana

An introduction to the contents in Volume 6 (Issue 1) of Euleriana.

Averaging Principle For A General Class Of Periodic Functions In Discrete Spaces, Martin Bohner, Jaqueline G. Mesquita, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

In this work, we develop a periodic averaging principle for arbitrary discrete time domains, leveraging a novel definition of periodicity. This definition does not rely on the classical requirement for the time domain itself to be periodic. We implement this averaging principle across diverse discrete time domains and explore a range of periodic functions within this extended context. The paper contains several examples with numerical simulations, providing visual demonstrations of our results. This highlights the versatility of our averaging principle and its potential to understand dynamics of nonautonomous recurrences with complex temporal patterns.

Controllability Of The Semilinear Benjamin–Bona–Mahony Dynamic Equation On Homogeneous Time Scales, Martin Bohner, Cosme Duque, Hugo Leiva

Mathematics and Statistics Faculty Research & Creative Works

This work investigates the approximate controllability and free-time approximate controllability of a generalized semi linear Benjamin–Bona–Mahony type dynamic equation defined on homogeneous time scales, subject to homogeneous Dirichlet boundary conditions. To accomplish this, the problem is framed within an abstract setting, employing the -semigroup theory on time scales. Moreover, we apply a technique introduced by Bashirov et al. [1, 2], which enables us to avoid relying on fixed point theorems.

(Si16-04) Some Fixed Point Theorems On Chatterjea Type Contractions, Irom Shashikanta Singh, Y. Mahendra Singh

Applications and Applied Mathematics: An International Journal (AAM)

This paper establishes the existence of fixed points related to strict Chatterjee contractive mappings by relaxing the compactness of the underlying spaces and the continuity of the mapping involved, using altering distance functions and comparison functions in the general setting of metric spaces. Several non-trivial and illustrative examples are provided to demonstrate, support, and validate the obtained theoretical results. In addition, a theorem that can characterize the completeness of metric spaces through the existence of fixed points is rigorously proven and discussed. Furthermore, a theorem on strict Chatterjea-type modulus contractive mappings without continuity assumptions and with relaxed compactness conditions is …

(Si16-06) Equations Of Geodesics In Two-Dimensional Finsler Manifold With A Special Cubic (Α, Β)-Metric, Sejal Prajapati, Brijesh Kumar Tripathi, V. K. Chaubey

Applications and Applied Mathematics: An International Journal (AAM)

Geodesics represent the shortest path between two points in curved spacetime and are vital in the study of Finsler manifolds. Matsumoto and Park first derived the geodesic equation as a secondorder differential equation in a two-dimensional Finsler manifold with Randers, Kropina, and Matsumoto metrics. Building on this foundation, our paper presents the geodesic differential equation for a two-dimensional Finsler manifold using a special cubic power metric. In this two-dimensional setting, this work also looks at certain well-known geometric curves and analyzes their variants as solutions to the geodesic differential equation. Additionally, this work examines the geometric applications of the geodesic’s …

(Si16-07) Computing The Kirchhoff Index And The Wiener Index Of Spiro Para Hexagonal Cylinder Chain, Md Selim Reja, Sk. Md. Abu Nayeem

Applications and Applied Mathematics: An International Journal (AAM)

In graph theory, the Kirchhoff index serves as a metric to evaluate the complexity of a graph. It is determined by adding up the resistance distances between every pair of vertices in the graph. In a network created from the given graph by substituting each edge by a unit resistor, the resistance distance between a pair of specified vertices is equivalent to the electrical resistance between them in the constructed network. Basically, it measures the convenience with which data or flow can move between various locations in a network that the graph represents. In terms of graph matrices, the Kirchhoff …

A Diffuse Interface Model And Fully Decoupled, Energy-Stable Scheme For The Two-Phase Ferrofluid Flows In Porous Media, Guo Dong Zhang, Shuai Zhou, Yunqing Huang, Xiaoming He, Xiaofeng Yang

Mathematics and Statistics Faculty Research & Creative Works

We propose a new diffuse interface model for two-phase porous media ferrofluid flows, employing the phase-field method and establishing an associated energy law. This thermodynamically consistent multi-physics model integrates the Cahn-Hilliard equations, Darcy equations, the magnetostatic equation, and magnetization equations. To efficiently solve the system by addressing its inherent nonlinearities, coupling, and saddle-point structure, we incorporate several advanced techniques, including the SAV-ZEC method to handle nonlinearities and couplings, a reformulated approach to decouple the linear coupling of the magnetic potential and magnetization, and the pressure projection method to decouple velocity and pressure. This results in a numerical scheme that is …

An Seir Model On Time Scales With Discrete Applications To Tuberculosis, E. Akın, G. Yeni, D. Konur, S. R. Işık, M. R. Işık

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we propose a novel dynamical model on time scales consisting of new parameters to investigate the transmission dynamics of tuberculosis (TB), one of the deadliest infectious diseases worldwide, characterized by a long latency stage. The dynamical TB model, governed by the Susceptible–Exposed–Infected–Recovered (SEIR) framework within a unified form, yields a continuous model with a non-saturated incidence rate on the real numbers and discrete models with saturated incidence rates when different time domains are chosen. We analyze the stability of the equilibrium points of both the continuous TB model on the set of real numbers and the discrete …

Pointwise Self-Homeomorphic Generalized Inverse Limits, Ali H. Ali, Faruq A. Mena, Robert Paul Roe

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we find uncountable families of generalized inverse sequences on intervals, where the bonding functions consist of a finite number of line segments, such that the inverse limit spaces of these sequences are pointwise self-homeomorphic continua. We give several examples of pointwise self-homeomorphic continua obtained in this manner including the dendrite D3 and a dendrite containing Dω. The dendrite D3 was obtained previously, by others, as a generalized inverse limit but the bonding function in that example contained infinitely many line segments. We show that the techniques we use on intervals can be extended to inverse limits where …

Time-Dependent Amplification Of Growth Rates In A Plankton-Oxygen Model, Rapha Coutin

Master's Theses

Near-bottom hypoxia occurs when dissolved oxygen levels drop to a level that is harmful to marine biology, creating biological dead zones along the ocean floor. Recent years have seen a dramatic increase in the percentage of coastal, near-bottom, hypoxic water, with the average in 2021 nearly double that of the average from 2009 to 2018 and about twenty-eight times the average from 1950 to 1980. Recent literature has linked this increase in oceanic hypoxia to the increase in upwelling-favorable winds caused by climate change. Upwelling brings low-oxygen, nutrient-rich water up to the surface, leading to plankton blooms and mass consumption …

Molecular Lung Imaging Following Exposure To Radiation Predicts Long-Term Survival In Rats, Anne V. Clough, Kathrina Mpala, Taheri Pardis, Laura Norwood Toro, Andreas M. Beyer, Tracy Gasperetti, Ming Zhao, Sarah Kerns, Heather A. Himburg, Said H. Audi

Mathematical and Statistical Science Faculty Research and Publications

Delayed effects of acute radiation exposure (DEARE), including radiation pneumonitis (lung-DEARE), develop weeks to months after radiation exposure. Pathway-targeted biomarkers that capture early oxidative stress and cell death could improve risk stratification and provide objective measures of mitigator efficacy. The objective was to test whether molecular lung imaging predicts long-term survival and mitigator response after irradiation. Rats received 13.5 Gy leg-out partial-body irradiation with a subset treated with the radiation-injury mitigator lisinopril. Rats underwent lung imaging at weeks 2 and 4 post-irradiation with ^99mTc-duramycin (cell death) and ^99mTc-HMPAO (oxidative stress). Plasma mitochondrial damage-associated molecular patterns (mtDAMPs) were also …

Demystifying Hardware Formal Verification For Undergraduate Education: A Risc-V Processor Case Study With Coursework Implementation, Riley A. Peters

Master's Theses

Hardware verification engineers apply formal methods to prove that a digital device always behaves according to its specification. This differs from traditional functional verification, in which engineers establish correctness by repeatedly sending test inputs to the device and comparing the outputs against a reference model. With the growing complexity of integrated circuits, the demand for digital verification engineers with formal methods experience has continued to increase. However, California Polytechnic State University: San Luis Obispo's current curriculum lacks dedicated material to prepare students for these roles.

This thesis seeks to address the lack of formal methods material through two efforts. First, …

Vaccination Games Of Boundedly Rational Parents Toward New Childhood Immunization, Wei Yin, Martial L. Ndeffo-Mbah, Tamer Oraby

School of Mathematical & Statistical Sciences Faculty Publications

Infectious diseases harm societies through disease-induced morbidity, mortality, loss of productivity, and inequality. Thus, controlling and preventing them is critical for public health and societal well-being. However, societies can hinder efforts to control the spread of diseases by failing to adhere to public health recommendations, such as through vaccine hesitancy. Various disease-transmission models have been utilized to help policymakers respond to (re)emerging outbreaks. The usefulness of such models in assessing the effectiveness of public health policies is significantly dependent on human behavior. This paper introduces a new model of parental behavior toward a new childhood immunization. The model incorporates societal …

Identical Vanishing Of Coefficients In The Series Expansion Of Eta Quotients, Modulo 4, 9 And 25, Tim Huber, James Mclaughlin, Dongxi Ye

School of Mathematical & Statistical Sciences Faculty Publications

Let A(q)=:∑∞n=0anqn and B(q)=:∑∞n=0bnqn be two eta quotients. In some previous papers, the present authors considered the problem of when

an=0⟺bn=0.

In the present paper we consider the “mod m” version of this problem, i.e. for which eta quotients A(q) and B(q) and for which integers m>1 do we have (non-trivially) that

an≡0(modm)⟺bn≡0(modm)?

(We say “non-trivially” as there are trivial situations where an≡bn(modm) for all n≥0). The m for which we found non-trivial (in the sense just mentioned) results were m=p2, p=2,3 and 5. For m=4 and m=9, we found results which …

Mat1500 Calculus I Syllabus, Xinlong Dong

Open Educational Resources

No abstract provided.

Accessibility For Mathematical Documents, Xinlong Dong

Open Educational Resources

No abstract provided.