Applied Mathematics Commons^™

Incorporating Interventions To An Extended Seird Model With Vaccination: Application To Covid-19 In Qatar, Elizabeth Amona

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Population Dynamics Of Imperiled Guzmania Monostachia Populations, Erin N. Bodine, Helen E. Pennington, Pranay Lingareddy

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modularity In Gene Regulatory Networks, Mehak Kapoor, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Dynamics Of A Diffusive Vaccination Model With Therapeutic Impact And Non-Linear Incidence Rates, Md Shahriar Mahmud

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

An Agent-Based Model Of Covid-19 Transmission At Lewis University, Austin Kind, Brittany Stephenson Phd

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Covid-19 And Challenges To The Classical Theory Of Epidemics, Simon Levin

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Functional Data Analysis Of Covid-19, Nichole L. Fluke

Mathematics & Statistics ETDs

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1^st, 2020 and goes through March 31^st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …

Music Genre Classification By Convolutional Neural Networks, Usame Suud

Mathematics & Statistics ETDs

In today’s world, deep learning models are widely used in a variety of fields. Audio

applications include speech recognition, audio classification, and music information

retrieval. In this paper, we will focus on the classification of music genres using an

artificial neural network. The development of audio machine learning techniques has

created an independence from traditional, more time-consuming signal processing

techniques. Starting with raw audio data, we will gain an understanding of what

audio is and its digital representation. Then, the focus will be on obtaining frequency

information from audio signals through the use of spectrograms. Transforming the

spectrograms into the …

Minimizers Of Nonlocal Polyconvex Energies In Nonlocal Hyperelasticity, José C. Bellido, Javier Cueto, Carlos Mora-Corral

Department of Mathematics: Faculty Publications

We develop a theory of existence of minimizers of energy functionals in vectorial problems based on a nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics model and is also applicable to nonlocal solid mechanics, especially nonlinear elasticity. This nonlocal gradient was introduced in an earlier work, inspired by Riesz’ fractional gradient, but suitable for bounded domains. The main assumption on the integrand of the energy is polyconvexity. Thus, we adapt the corresponding results of the classical case to this nonlocal context, notably, Piola’s identity, the integration by parts of the determinant and the weak …

Math 57: Applied Differential Equations I, John Mayberry

Pacific Open Texts

This book is designed for the fourth semester, “capstone” course in a calculus sequence with an emphasis on modeling with linear differential equations. Students will learn to translate verbal descriptions of physical problems into differential equation models, solve and visualize solutions to differential equations using MATLAB, calculate and investigate the behavior of analytic solutions to linear differential equations, discuss how solutions to differential equations depend on parameters, and interpret solutions to differential equations in the context of applications.

Manufacturability And Analysis Of Topologically Optimized Continuous Fiber Reinforced Composites, Jesus A. Ferrand

Doctoral Dissertations and Master's Theses

Researchers are unlocking the potential of Continuous Fiber Reinforced Composites for producing components with greater strength-to-weight ratios than state of the art metal alloys and unidirectional composites. The key is the emerging technology of topology optimization and advances in additive manufacturing. Topology optimization can fine tune component geometry and fiber placement all while satisfying stress constraints. However, the technology cannot yet robustly guarantee manufacturability. For this reason, substantial post-processing of an optimized design consisting of manual fiber replacement and subsequent Finite Element Analysis (FEA) is still required.

To automate this post-processing in two dimensions, two (2) algorithms were developed. The …

Compilación De Procesos Investigativos En Educación Matemática, Martha Lidia Barreto Moreno, Yeferson Castellanos Novoa, María Alejandra Mayorga Henao, Diana Marcela Contento Sarmiento, Jesús Antonio Villarraga Palomino, Andrés Alberto Gutiérrez Morales, Juan David Firigua Bejarano, Yineth Marleidy Parra Ubaque, Lady Johanna Silva Marín

Educación

En el libro Compilación de procesos de investigación en educación matemática, consta de cuatro capítulos donde se presentan los procesos desarrollados en el marco de proyectos de investigación a nivel de pregrado y postgrado en Educación.

El primer capítulo consiste en la sistematización de la acción docente desarrollada en el marco de los Talleres Itinerantes de Alfabetización Computacional en la provincia de Sumapaz, propuesta de innovación para implementar procesos didácticos que contribuyan al desarrollo del pensamiento matemático computacional en educación básica primaria rural.

El segundo capítulo contiene el proceso investigativo que dio continuidad al trabajo realizado en la Fase1, sobre …

Improved Operational Matrices Of Dp-Ball Polynomials For Solving Singular Second Order Linear Dirichlet-Type Boundary Value Problems, Ahmed Kherd, Salim F. Bamsaoud, Omar Bazighifan, Mobarek A. Assabaai

Hadhramout University Journal of Natural & Applied Sciences

Solving Dirichlet-type boundary value problems (BVPs) using a novel numerical approach is presented in this study. The operational matrices of DP-Ball Polynomials are used to solve the linear second-order BVPs. The modification of the operational matrix eliminates the BVP's singularity. Consequently, guaranteeing a solution is reached. In this article, three different examples were taken into consideration in order to demonstrate the applicability of the method. Based on the findings, it seems that the methodology may be used effectively to provide accurate solutions.

(Si10-003) Some New Fixed Point Theorem Via Shifting Distance Functions, Bhuban Chandra Deuri

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a new fixed point theorem involving non-compactness measures and shifting distance functions. This paper provides a generalization of the famous fixed point theorem of Banach. A fixed point theory is a gorgeous blend of mathematical analysis that explains the conditions under which maps provide excellent solutions. Numerous mathematicians later used this theory to prove their results; see, for example, the Schauder fixed point theorem, the Darbo fixed point theorem, the nonexpansive fixed point theorem, etc. Additionally, we hypothesized that a large number of known fixed point theorems can be simply deduced from the Banach theorem. …

(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we concentrated to study the controllability of fuzzy solution for nonlinear impulsive functional neutral integrodifferential equations with nonlocal condition in n-dimensional vector space. Moreover, we obtained controllability of fuzzy result for the normal, convex, upper semi-continuous and compactly supported interval fuzzy number. Finally, an example was provided to reveal the application of the result.

(Si10-067) Numerical Study Of The Time Fractional Burgers’ Equation By Using Explicit And Implicit Schemes, Swapnali Doley, A. Vanav Kumar, L. Jino

Applications and Applied Mathematics: An International Journal (AAM)

The study discusses the numerical solution for a time fractional Burgers’ equation using explicit (scheme 1) and implicit scheme (scheme 2), respectively. The approximation of the differential equation is discretized using the finite difference method (FDM). A non-linear term present in the Burgers’ equation is approximated using the time-averaged values. The Von-Neumann analysis shows that the Scheme 1 is conditionally stable and Scheme 2 is unconditionally stable. The numerical solutions are compared with the exact solutions and are good in agreement. Also, the error is estimated between exact and numerical solutions.

(Si10-083) Approximate Controllability Of Infinite-Delayed Second-Order Stochastic Differential Inclusions Involving Non-Instantaneous Impulses, Shobha Yadav, Surendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This manuscript investigates a broad class of second-order stochastic differential inclusions consisting of infinite delay and non-instantaneous impulses in a Hilbert space setting. We first formulate a new collection of sufficient conditions that ensure the approximate controllability of the considered system. Next, to investigate our main findings, we utilize stochastic analysis, the fundamental solution, resolvent condition, and Dhage’s fixed point theorem for multi-valued maps. Finally, an application is presented to demonstrate the effectiveness of the obtained results.

(Si10-057) Effect Of Time-Delay On An Sir Type Model For Infectious Diseases With Saturated Treatment, R. P. Gupta, Arun Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This study presents the complex dynamics of an SIR epidemic model incorporating a constant time-delay in incidence rate with saturated type of treatment rate. The system is studied to observe the effect of time lag in the asymptotic stability of endemic equilibrium states. We also establish global asymptotic stability of both disease-free and endemic equilibrium states by Lyapunov direct method with the help of suitable Lyapunov functionals. The existences of periodic solutions are ensured for the suitable choice of delay parameter. Finally, we perform numerical simulations supporting the analytical findings as well as to observe the effect of time-delay. The …

(Si10-056) Fear Effect In A Three Species Prey-Predator Food-Web System With Harvesting, R. P. Gupta, Dinesh K. Yadav

Applications and Applied Mathematics: An International Journal (AAM)

Some recent studies and field experiments show that predators affect their prey not only by direct capture; they also induce fear in prey species, which reduces their reproduction rate. Considering this fact, we propose a mathematical model to study the fear effect of a middle predator on its prey in a three-species food web system with harvesting. The ecological feasibility of solutions to the proposed system is guaranteed in terms of positivity and boundedness. The local stability of stationary points in the proposed system is derived. Multiple co-existing stationary points for the proposed system are observed, which makes the problem …

Bounds On Cohomological Support Varieties, Benjamin Briggs, Eloisa Grifo, Josh Pollitz

Department of Mathematics: Faculty Publications

Over a local ring R, the theory of cohomological support varieties attaches to any bounded complex M of finitely generated R-modules an algebraic variety VR(M) that encodes homological properties of M. We give lower bounds for the dimension of VR(M) in terms of classical invariants of R. In particular, when R is Cohen-Macaulay and not complete intersection we find that there are always varieties that cannot be realized as the cohomological support of any complex. When M has finite projective dimension, we also give an upper bound for dimVR(M) in terms of the dimension of the radical of the homotopy …