Applied Mathematics Commons^™

The “Knapsack Problem” Workbook: An Exploration Of Topics In Computer Science, Steven Cosares

Open Educational Resources

This workbook provides discussions, programming assignments, projects, and class exercises revolving around the “Knapsack Problem” (KP), which is widely a recognized model that is taught within a typical Computer Science curriculum. Throughout these discussions, we use KP to introduce or review topics found in courses covering topics in Discrete Mathematics, Mathematical Programming, Data Structures, Algorithms, Computational Complexity, etc. Because of the broad range of subjects discussed, this workbook and the accompanying spreadsheet files might be used as part of some CS capstone experience. Otherwise, we recommend that individual sections be used, as needed, for exercises relevant to a course in …

On Higher-Order Duality In Nondifferentiable Minimax Fractional Programming, S. Al-Homidan, Vivek Singh, I. Ahmad

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a nondifferentiable minimax fractional programming problem with continuously differentiable functions and formulate two types of higher-order dual models for such optimization problem. Weak, strong and strict converse duality theorems are derived under higher- order generalized invexity.

Hybrid Algorithm For Singularly Perturbed Delay Parabolic Partial Differential Equations, Imiru T. Daba, Gemechis F. Duressa

Applications and Applied Mathematics: An International Journal (AAM)

This study aims at constructing a numerical scheme for solving singularly perturbed parabolic delay differential equations. Taylor’s series expansion is applied to approximate the shift term. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is an ε−uniformly convergent accuracy of order one. Some test examples are considered to testify …

A Stochastic Knapsack Game: Revenue Management In Competitions, Yingdong Lu

Applications and Applied Mathematics: An International Journal (AAM)

We study a mathematical model for revenue management under competitions with multiple sellers. The model combines the stochastic knapsack problem, a classic revenue management model, with a non-coorperative game model that characterizes the sellers’ rational behavior. We are able to establish a dynamic recursive procedure that incorporate the value function with the utility function of the games. The formalization of the dynamic recursion allows us to establish some fundamental structural properties.

A Family Of Householder Matrices, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

A Householder transformation, or Householder reflection, or Household matrix, is a reflection about a hyperplane with a unit normal vector. Not only have the Household matrices been used in QR decomposition efficiently but also implicitly and successfully applied in other areas. In the process of investigating a family of unitary filterbanks, a new family of Householder matrices are established. These matrices are produced when a matrix filter is required to preserve certain order of 2d digital polynomial signals. Naturally, they can be applied to image and signal processing among others.

Memory Response Of Magneto-Thermoelastic Problem Due To The Influence Of Modified Ohm’S Law, Latika C. Bawankar, Ganesh D. Kedar

Applications and Applied Mathematics: An International Journal (AAM)

In this article, in the form of the heat conduction equation with memory-dependent-derivative (MDD), a new model in magneto-thermoelasticity was developed with modified Ohm’s law. To obtain the solutions, normal mode analysis is used. The obtained solution is then exposed to time- dependent thermal shock and stress-free boundary conditions. The effect of the modified Ohm’s law coefficient, time-delay, and different kernel functions under the magnetic field effect on different quantities are evaluated and observed graphically on all field variables.

Effect Of Magnetic And Perturbation Parameters On Blood Flow Distribution Through An Artery, Sultan Ahmad, A. F. Al-Johani, Subratakumar Sahu

Applications and Applied Mathematics: An International Journal (AAM)

The motion of the blood inside an artery is investigated under the transverse magnetic field. The velocity and temperature variation of the blood flow motion are solved by perturbation technique. We considered the magnetic field is constant and viscosity of the fluid distribution depends on temperature. We derived flow rate and wall shear stress during the flow of blood through the human artery. We analyzed the effect of temperature profiles, flow rate and wall shear stress during the propagation of blood. It is observed that the human will die with respect to the increase temperature in the blood flow distribution.

Demailly's Conjecture And The Containment Problem, Sankhaneel Bisui, Eloisa Grifo, Huy Tài Hà, Thái Thành Nguyên

Department of Mathematics: Faculty Publications

We investigate Demailly’s Conjecture for a general set of sufficiently many points. Demailly’s Conjecture generalizes Chudnovsky’s Conjecture in providing a lower bound for the Waldschmidt constant of a set of points in projective space. We also study a containment between symbolic and ordinary powers conjectured by Harbourne and Huneke that in particular implies Demailly’s bound, and prove that a general version of that containment holds for generic determinantal ideals and defining ideals of star configurations.

Novel And Fast Peridynamic Models For Material Degradation And Failure, Siavash Jafarzadeh

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Fracture is one of the main mechanisms of structural failure. Corroded surfaces with chemically-induced damage are, notably, potential sites for crack initiation and propagation in metals, which can lead to catastrophic failure of structures. Despite some progress in simulating fracture and damage using classical models, realistic prediction of complex damage progression and failure has been out of reach for many decades. Peridynamics (PD), a nonlocal theory introduced in 2000, opened up new avenues in modeling material degradation and failure. Existing numerical methods used to discretize PD equations, however, are quite expensive as the PD nonlocal interactions make them unaffordable for …

Correlated Positron-Electron Orbital (Cpeo): A Novel Method That Models Positron-Electron Correlation In Virtual Ps At The Mean-Field Level, Kevin E. Blaine

Theses and Dissertations

The Correlated Positronic-Electronic Orbital (CPEO) method was developed and implemented to capture correlation effects at between the positron and electron in the modeling of systems that involve a bound positron. Methods that effectively model these systems require many hundred basis functions and use a mean field approach as the beginning step. CPEO builds an orbital for virtual Positronium (Ps) that contains a positron in a bound state along with an accompanying electron to the larger system. Assigning the virtual Ps orbital allows for the two particle variational optimization in conjunction with the other particles that compose the whole system. This …

Intermittent Dynamics Of Dense Particulate Matter, Chao Cheng

Dissertations

Granular particle systems are scattered around the universe, and they can behave like solids when there exist strong force-bearing networks, so that the granular system can resist certain stress without deformation. When such a network is not present, particles yield to small stress and behave like a fluid. A wide range of systems exhibit intermittent dynamics as they are slowly loaded, with different dynamical regimes governing many industrial and natural phenomena. While a significant amount of research on exploring intermittent dynamics of granular systems has been carried out, not much is known about the connection between particle-scale response and the …

Eigenvalue Problems For Fully Nonlinear Elliptic Partial Differential Equations With Transport Boundary Conditions, Jacob Lesniewski

Dissertations

Fully nonlinear elliptic partial differential equations (PDEs) arise in a number of applications. From mathematical finance to astrophysics, there is a great deal of interest in solving them. Eigenvalue problems for fully nonlinear PDEs with transport boundary conditions are of particular interest as alternative formulations of PDEs that require data to satisfy a solvability condition, which may not be known explicitly or may be polluted by noisy data. Nevertheless, these have not yet been well-explored in the literature. In this dissertation, a convergence framework for numerically solving eigenvalue problems for fully nonlinear PDEs is introduced. In addition, existing two-dimensional methods …

An Examination Of Fontan Circulation Using Differential Equation Models And Numerical Methods, Vanessa Maybruck

Honors Student Research

Certain congenital heart defects can lead to the development of only a single pumping chamber, or ventricle, in the heart instead of the usual two ventricles. Individuals with this defect undergo a corrective, three-part surgery, the third step of which is the Fontan procedure, but as the patients age, their cardiovascular health will likely deteriorate. Using computational fluid dynamics and differential equations, Fontan circulation can be modeled to investigate why the procedure fails and how Fontan failure can be maximally prevented. Borrowing from well-established literature on RC circuits, the differential equation models simulate systemic blood flow in a piecewise, switch-like …

Stock Markets Performance During A Pandemic: How Contagious Is Covid-19?, Yara Abushahba

Theses and Dissertations

Background and Motivation: The coronavirus (“COVID-19”) pandemic, the subsequent policies and lockdowns have unarguably led to an unprecedented fluid circumstance worldwide. The panic and fluctuations in the stock markets were unparalleled. It is inarguable that real-time availability of news and social media platforms like Twitter played a vital role in driving the investors’ sentiment during such global shock.

Purpose:The purpose of this thesis is to study how the investor sentiment in relation to COVID-19 pandemic influenced stock markets globally and how stock markets globally are integrated and contagious. We analyze COVID-19 sentiment through the Twitter posts and investigate its …

Finite Element Modeling Of Underwater Acoustic Environments And Domain Decomposition Methods, General Ozochiawaeze

Theses

Underwater acoustic scattering problems have several important applications ranging from sonar imaging in target detection to providing information for sediment classification and geoacoustic inversion. This work presents numerical methods for time-harmonic acoustic scattering problems, specifically, finite element methods for the Helmholtz equation. Furthermore, an iterative domain decomposition formulation is introduced for acoustic scattering problems where the physical domain consists of multiple layers of different materials.

Compare And Contrast Maximum Likelihood Method And Inverse Probability Weighting Method In Missing Data Analysis, Scott Sun

Mathematical Sciences Technical Reports (MSTR)

Data can be lost for different reasons, but sometimes the missingness is a part of the data collection process. Unbiased and efficient estimation of the parameters governing the response mean model requires the missing data to be appropriately addressed. This paper compares and contrasts the Maximum Likelihood and Inverse Probability Weighting estimators in an Outcome-Dependendent Sampling design that deliberately generates incomplete observations. WE demonstrate the comparison through numerical simulations under varied conditions: different coefficient of determination, and whether or not the mean model is misspecified.

Access To Higher Education: Do Schools “Grant” Success?, Nathaniel Jones

Symposium of Student Scholars

University education can lead to upward income mobility for low-income students. Being exposed to other student’s life experiences that are different from their own may highlight activities and actions that they may want to consider aiding their success. According to the U.S. Bureau of Labor Statistics, the median weekly earnings in 2019 for all workers in the U.S. was $969. Of those, U.S. workers who held bachelor’s degrees earned $1,248. In 2016, the Brookings Institute found that Pell Grant recipients and first-generation student loan borrowers attended universities that had lower graduation rates and higher loan default rates in comparison to …

Environmental Impact On Competition In Ecological Communities, Isabel Ouko

Symposium of Student Scholars

We study the effects of environmental feedback on the ecological competition by analyzing the classic Lotka-Volterra model coupled with a simple model of the environment. In particular, we look for ways in which feedback between competing populations and the environment stabilizes or destabilizes coexistence between the species. To do so, we use a combination of mathematical analysis and computer software such as Matlab.

KEYWORDS; mathematical modeling, Lotka-Volterra, ecological competition, environmental feedback

Characterizing The Northern Hemisphere Circumpolar Vortex Through Space And Time, Nazla Bushra

LSU Doctoral Dissertations

This hemispheric-scale, steering atmospheric circulation represented by the circumpolar vortices (CPVs) are the middle- and upper-tropospheric wind belts circumnavigating the poles. Variability in the CPV area, shape, and position are important topics in geoenvironmental sciences because of the many links to environmental features. However, a means of characterizing the CPV has remained elusive. The goal of this research is to (i) identify the Northern Hemisphere CPV (NHCPV) and its morphometric characteristics, (ii) understand the daily characteristics of NHCPV area and circularity over time, (iii) identify and analyze spatiotemporal variability in the NHCPV’s centroid, and (iv) analyze how CPV features relate …

Computational Design Of Nonlinear Stress-Strain Of Isotropic Materials, Askhad M.Polatov, Akhmat M. Ikramov, Daniyarbek Razmukhamedov

Chemical Technology, Control and Management

The article deals with the problems of numerical modeling of nonlinear physical processes of the stress-strain state of structural elements. An elastoplastic medium of a homogeneous solid material is investigated. The results of computational experiments on the study of the process of physically nonlinear deformation of isotropic elements of three-dimensional structures with a system of one- and double-periodic spherical cavities under uniaxial compression are presented. The influence and mutual influence of stress concentrators in the form of spherical cavities, vertically located two cavities and a horizontally located system of two cavities on the deformation of the structure are investigated. Numerical …