Applied Mathematics Commons^™

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Modeling The Population Dynamics And Movement Of Zebra Mussels, Alexanderia Lacy, Yu Jin, David Strayer, Suzanne Lenhart

Department of Mathematics: Faculty Publications

Zebra mussels have caused significant damage in many lakes and rivers. By using a hybrid population model with discrete-time equations and ordinary differential equations, we represent the zebra mussel’s life cycle, growth, and population movement. The dynamics of the larvae (unsettled and settled larvae) are represented during the summer months in a system of two ordinary differential equations, while the juvenile, small adult, and large adult stages are represented by a discrete model with yearly time steps. The goal is to investigate the effects of zebra mussel movement between three different spatial locations and possible control measures. Zebra mussel data …

Simulation Of Multi-Variable Converters Using The Linear Interpolation Method, Miraziz Vorisovich Sagatov

Chemical Technology, Control and Management

In this work, based on the theory of barycentric coordinates and simplexes, a linear interpolation method is proposed for modeling and controlling the operation of multiparameter converters. It has been determined that the linear interpolation method minimizes the structural diagram of a computing device, which makes it possible to more accurately determine the metrological characteristics of multiparameter measuring transducers and offer effective methods and means for processing primary measurement information. A theorem has been proven about a linear interpolating polynomial of a function of many variables, which will allow us to judge the property of linearization of multidimensional quantities from …

Regular Ideals, Ideal Intersections, And Quotients, Jonathan H. Brown, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff

Department of Mathematics: Faculty Publications

Let B ⊆ A be an inclusion of C^∗ -algebras. We study the relationship between the regular ideals of B and regular ideals of A.We show that if B ⊆ A is a regular C^∗ -inclusion and there is a faithful invariant conditional expectation from A onto B, then there is an isomorphism between the lattice of regular ideals of A and invariant regular ideals of B. We study properties of inclusions preserved under quotients by regular ideals. This includes showing that if D ⊆ A is a Cartan inclusion and J is a regular ideal in A, …

Tikaram And Chandrakala Dhananjaya: A Collaborative Couple In Mathematics From Nepal, Deepak Basyal, Brigitte Stenhouse

Mathematics and Statistics

Within the history of mathematics and mathematics education in Nepal, Tikaram and Chandrakala Dhananjaya are relatively well-known figures for their two books Śiśubodha Taraṅgiṇī and Līlāvatī. This is despite there being almost no archival or manuscript materials offering a window into their lives: we have no letters, notebooks, diaries, or school records. Rather than focusing on either individual in isolation, in this article we present an argument for considering the Dhananjayas as an analytically indivisible collaborative couple in mathematics. Of the two aforementioned books, one is attributed to Chandrakala and the other to Tikaram; but in fact, both are translations …

A Mathematical Model For Frogeye Leaf Spot Epidemics In Soybean, Chayu Yang, Jin Wang

Department of Mathematics: Faculty Publications

We propose a new mathematical model based on differential equations to investigate the transmission and spread of frogeye leaf spot, a major soybean disease caused by the fungus Cercospora sojina. The model incorporates the primary and secondary transmission routes of the disease as well as the intrinsic dynamics of the pathogen in the contaminated soil. We conduct detailed equilibrium and stability analyses for this model using theories of dynamical systems. We additionally conduct numerical simulations to verify the analytical predictions and to implement the model for a practical application.

Renormalized Stress-Energy Tensor For Scalar Fields In Hartle-Hawking, Boulware, And Unruh States In The Reissner-Nordström Spacetime, Julio Arrechea, Cormac Breen, Adrian Ottewill, Peter Taylor

Articles

In this paper, we consider a quantum scalar field propagating on the Reissner-Nordström black hole spacetime. We compute the renormalized stress-energy tensor for the field in the Hartle-Hawking, Boulware and Unruh states. When the field is in the Hartle-Hawking state, we renormalize using the recently developed “extended coordinate” prescription. This method, which relies on Euclidean techniques, is very fast and accurate. Once, we have renormalized in the Hartle-Hawking state, we compute the stress-energy tensor in the Boulware and Unruh states by leveraging the fact that the difference between stress-energy tensors in different quantum states is already finite. We consider a …

Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine

Honors Program Theses and Research Projects

Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …

(R2066) New Results Of Ulam Stabilities Of Functional Differential Equations Of First Order Including Multiple Retardations, Merve Şengün, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

In this study, we pay attention to a functional differential equation (FDE) of first order including N-variable delays. We construct new sufficient conditions in relation to the Hyers-Ulam stability (HUS) and the generalized Hyers-Ulam-Rassias stability (GHURS ) of the FDE of first order including N-variable delays. By using Banach contraction principle (BCP), Picard operator and Gronwall lemma, we confirm two new theorems in relation to the HUS and the GHURS. The results of this study are new and extend, improve some earlier results of the HUS and the GHURS.

(R2055) Magnetic Effects On Unsteady Non-Newtonian Blood Flow Through A Tapered And Overlapping Stenotic Artery, Abiodun J. Babatunde, Moses S. Dada

Applications and Applied Mathematics: An International Journal (AAM)

This study aims to investigating the effect of magnetic field and porosity on non-Newtonian flow of blood through a tapered, and overlapping stenosed artery. The Casson fluid model represents the rheological character of blood. A tapered and overlapping stenosed artery influences the hemodynamic behavior of the blood flow. The problem is solved by using analytical techniques with the help of boundary conditions, and results are displayed graphically for different flow characteristics like pressure drop, shear stress, velocity profile and stream function. It is realized that rises in Darcy number and Womersley number accelerates the velocity profile and reduces the radial …

(R2058) Mhd Stagnation Point Flow Of Nanofluid With Buoyancy Effect Through A Porous Shrinking Sheet, Timothy L. Oyekunle, Mojeed T. Akolade, Samson A. Agunbiade, Paul O. Adeniran

Applications and Applied Mathematics: An International Journal (AAM)

The current investigation seeks to identify the response of buoyancy and heat source mechanisms on chemically reacting and magnetized nanofluid. The stagnation point flows through the shrinking porous surface assumed as an air-based fluid conveying nanoparticles under Buongiorno’s model. This article contributes to the existing literature with the introduction of nonlinear convection of the nanofluid, triggered by the heat source, which accelerates the temperature of the fluid particles, thus resulting in airflow upstream. Subject to these conditions, the mathematical model is presented in PDE systems. An approach of similarity variable is employed to arrive at the ODE systems, which is …

Motion Simulation And Risk Assessment Of Dropped Objects In Offshore Operations, Hanqi Yu

LSU New Orleans Theses and Dissertations

Subsea pipelines are a cost-effective and reliable way to transport hydrocarbons in offshore oil and gas development. However, dropped objects can pose hazards and cause damage to pipelines. This dissertation briefly introduces the hazards and hidden dangers caused by dropped containers, discusses motion simulation methods for different object shapes, and reviews risk assessment procedures for handling dropped objects in offshore operations. Ongoing research at the University of New Orleans' towing tank on dropped container models is also discussed. Using ANSYS Fluent, we simulate trajectories of container models and calculate relevant hydrodynamic coefficients for different dropped angles. We then apply risk …

Game-Theoretic Approaches To Optimal Resource Allocation And Defense Strategies In Herbaceous Plants, Molly R. Creagar

Department of Mathematics: Dissertations, Theses, and Student Research

Empirical evidence suggests that the attractiveness of a plant to herbivores can be affected by the investment in defense by neighboring plants, as well as investment in defense by the focal plant. Thus, allocation to defense may not only be influenced by the frequency and intensity of herbivory but also by defense strategies employed by other plants in the environment. We incorporate a neighborhood defense effect by applying spatial evolutionary game theory to optimal resource allocation in plants where cooperators are plants investing in defense and defectors are plants that do not. We use a stochastic dynamic programming model, along …

Statistical Analysis Of Health Habits For Incoming College Students, Wendy Isamara Lizarraga Noriega

Electronic Theses, Projects, and Dissertations

Health habits among college students are commonly overseen, especially for students transitioning from high school right into college. These students are becoming independent young adults, and learning how to adapt to a different scenery when it comes to their learning environment. As these young adults transition into college, this is the perfect time for the students to become more vulnerable and comfortable with their independence, and their weight begins to fluctuate. Many variables come into consideration when increasing weight as an incoming first-year student. Students are more likely to live alone, get a job, and rely on fast food and …

(R2059) Modeling The Spread Of Coronavirus With Self-Protection And Quarantine Effect, Dileep Sharma, Agraj Tripathi, Ram Naresh Tripathi

Applications and Applied Mathematics: An International Journal (AAM)

A nonlinear mathematical model to study the effect of transmission dynamics of COVID-19 virus in a population with variable size structure is proposed and analyzed. The model divides the total human population into five subclasses: susceptibles, self-protected susceptibles, infectives, quarantined infectives, and recovered population including a class representing cumulative density of coronavirus in the environmental reservoir. The model exhibits two equilibria, namely, the diseasefree and the endemic equilibrium. Model analysis reveals the global dynamics of the spread of COVID-19 is completely determined by the basic reproduction number. If basic reproduction number is greater than one, the endemic equilibrium is locally …

(R2061) Differential Equations Involving A New Definition Of Complex Number Derivatives, Mehmet Pakdemirli

Applications and Applied Mathematics: An International Journal (AAM)

The recently proposed complex number differential operator is used in formulating ordinary differential equations for the first time. The differential operator definition is totally different than the real number differentiation of complex valued functions. The basic definitions and properties of the differential operator are given first. Various linear differential equations are treated containing the new differential operator. Associated theorems with the differential equations are given. Then the nonlinear differential equations of complex valued functions are treated. In separated form, the complex differential operator equations lead to nonlinear coupled real valued equations. Various nonlinear differential equations with complex number derivatives are …

Controlled Manipulation And Transport By Microswimmers In Stokes Flows, Jake Buzhardt

All Dissertations

Remotely actuated microscale swimming robots have the potential to revolutionize many aspects of biomedicine. However, for the longterm goals of this field of research to be achievable, it is necessary to develop modelling, simulation, and control strategies which effectively and efficiently account for not only the motion of individual swimmers, but also the complex interactions of such swimmers with their environment including other nearby swimmers, boundaries, other cargo and passive particles, and the fluid medium itself. The aim of this thesis is to study these problems in simulation from the perspective of controls and dynamical systems, with a particular focus …

Exploration And Statistical Modeling Of Profit, Caleb Gibson

Undergraduate Honors Theses

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability.

In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based …

(R2056) Convergence Criteria For Solutions Of A System Of Second Order Nonlinear Differential Equations, Akinwale Olutimo

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate the convergence of solutions of certain nonlinear system of two differential equations using a suitable Lyapunov functional with sufficient conditions to establish our new result. An example is given to demonstrate the effectiveness of the result obtained and geometric argument to show that the solutions of the system are better rapidly converging under the criteria obtained.