Applied Mathematics Commons^™

A Chebyshev Spectral Collocation Method For Solving Kdv-Burgers Equation, Mubarak Awadh Assabaai

Hadhramout University Journal of Natural & Applied Sciences

A mixed spectral/ Runge-Kutta method is used to obtain numerical solutions of Kortewege–de Vries–Burgers’ (KdVB) equation. The suggested method based on Chebyshev spectral collocation is used with Runge-Kutta method of order four. This technique is accomplished by starting with a Chebyshev approximation for the higher order derivatives in the x -direction and generating approximations to the lower derivatives through successive integrations of the highest-order derivative. The proposed technique reduces the problem to a system of ordinary differential equations in the t -direction. The Runge-Kutta method of order four is used to solve this system. Excellent numerical results have been obtained …

Computer Program Simulation Of A Quantum Turing Machine With Circuit Model, Shixin Wu

Mathematical Sciences Technical Reports (MSTR)

Molina and Watrous present a variation of the method to simulate a quantum Turing machine employed in Yao’s 1995 publication “Quantum Circuit Complexity”. We use a computer program to implement their method with linear algebra and an additional unitary operator defined to complete the details. Their method is verified to be correct on a quantum Turing machine.

Final Project Report Nsf Award 1744490: Nsf Includes Ddlp: Leadership And Isteam For Females In Elementary School (Life): An Integrated Approach To Increase The Number Of Women Pursuing Careers In Stem, Bruce G. Bukiet, James Lipuma, Nancy Steffen-Fluhr

STEM for Success Resources

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.

The LiFE project created and studied a comprehensive program bringing together iSTEAM, holistic student growth, modern technologies, and other supports to engage girls in STEM experiences through a collective impact approach.

LiFE supported STEAM clubs with role models and utilized research-based best …

An Analysis Of Comparison-Based Sorting Algorithms, Jacob M. Gomez, Edgar Aponte, Brad Isaacson

Publications and Research

Our names are Edgar Aponte and Jacob Gomez and we are Applied Mathematics students at City Tech. Our mentor is Prof. Isaacson and we conducted an analysis of comparison-based sorting algorithms, meaning that they can sort items of any type for which a “less-than” relation is defined. We implemented 24 comparison-based sorting algorithms and elaborated on 6 for our poster. We analyzed the running times of these sorting algorithms with various sets of unsorted data and found that introspective sort and timsort were the fastest and most efficient, with introspective sort being the very fastest.

(R1491) Numerical Solution Of The Time-Space Fractional Diffusion Equation With Caputo Derivative In Time By A-Polynomial Method, Saeid Abbasbandy, Jalal Hajishafieiha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a novel type of polynomial is defined which is equipped with an auxiliary parameter a. These polynomials are a combination of the Chebyshev polynomials of the second kind. The approximate solution of each equation is assumed as the sum of these polynomials and then, with the help of the collocation points, the unknown coefficients of each polynomial, as well as auxiliary parameter, is obtained optimally. Now, by placing the optimal value of a in polynomials, the polynomials are obtained without auxiliary parameter, which is the restarted step of the present method. The time discretization is performed …

(R1480) Heat Transfer In Peristaltic Motion Of Rabinowitsch Fluid In A Channel With Permeable Wall, Mahadev M. Channakote, Dilipkumar V. Kalse

Applications and Applied Mathematics: An International Journal (AAM)

This paper is intended to investigate the effect of heat transfer on the peristaltic flow of Rabinowitsch fluid in a channel lined with a porous material. The Navier -Stokes equation governs the channel's flow, and Darcy's law describes the permeable boundary. The Rabinowitsch fluid model's governing equations are solved by utilizing approximations of the long-wavelength and small number of Reynolds. The expressions for axial velocity, temperature distribution, pressure gradient, friction force, stream function are obtained. The influence on velocity, pressure gradient, friction force, and temperature on pumping action of different physical parameters is explored via graphs.

(R1497) On The Invariant Subspaces Of The Fractional Integral Operator, Mehmet Gürdal, Anar Adiloglu Nabiev, Meral Ayyıldız

Applications and Applied Mathematics: An International Journal (AAM)

In operator theory, there is an important problem called the invariant subspace problem. This important problem of mathematics has been clear for more than half a century. However the solution seems to be nowhere in sight. With this motivation, we investigate the invariant subspaces of the fractional integral operator in the Banach space with certain conditions in this paper. Also by using the Duhamel product method, unicellularity of the fractional integral operator on some space is obtained and the description of the invariant subspaces is given.

(R1468) Global Analysis Of An Seirs Model For Covid-19 Capturing Saturated Incidence With Treatment Response, David A. Oluyori, Helen O. Adebayo, Ángel G.C. Pérez

Applications and Applied Mathematics: An International Journal (AAM)

In this work, a new SEIRS model with saturated incidence rate and piecewise linear treatment response is proposed to describe the dynamics of COVID-19. It is assumed that the treatment response is proportional to the number of infected people as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceeds the carrying capacity of the available medical facilities. Thus, the basic reproduction number of the model is obtained. It is proved that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number …

(R1056) Effect Of Rotation On Plane Waves Of Generalized Magneto-Thermoelastic Medium With Voids Under Thermal Loading Due To Laser Pulse, Mohamed I.A. Othman, Ezaira R.M. Edeeb

Applications and Applied Mathematics: An International Journal (AAM)

The investigation in this paper deals with the rotation of the magneto-thermoelastic solid and with voids subjected to thermal loading due to laser pulse. The problem is studied in the context of three theories of generalized magneto thermoelasticity: Lord-Schulman (L-S), Green-Lindsay (G-L) and the coupled theory (CD) with the effect of rotation, magnetic field, thermal loading and voids. The methodology applied here is using the normal mode analysis to solve the physical problem to obtain the exact expressions for the displacement components, the stresses, the temperature, and the change in the volume fraction field have been shown graphically by comparison …

(R1513) The Dynamical Study Of Variable Mass Test Particle In Nonlinear Sense Of Restricted 3-Body Problem With Heterogeneous Primaries, Sada Nand Prasad, Kumari Shalini, Abdullah A. Ansari

Applications and Applied Mathematics: An International Journal (AAM)

The main idea of this paper is to study the non-linear stability property of the motion of the test particle which is moving under the influence of heterogeneous primaries having N-layers with different densities as well as varying its mass according to Jeans law. The system is also perturbed by the small perturbations in Coriolis as well as centrifugal forces. We evaluate the equations of motion of the test particle under the influence of the above said perturbations. From this system of equations of motion, we reveal analytically the locations of stationary points as well as the non-linear stability.

(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat

Applications and Applied Mathematics: An International Journal (AAM)

The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal …

(R1508) Stability And Zero Velocity Curves In The Perturbed Restricted Problem Of 2 + 2 Bodies, Rajiv Aggarwal, Dinesh Kumar, Bhavneet Kaur

Applications and Applied Mathematics: An International Journal (AAM)

The present study investigates the existence and linear stability of the equilibrium points in the restricted problem of 2+2 bodies including the effect of small perturbations epsilon-1 and espilon-2 in the Coriolis and centrifugal forces respectively. The less massive primary is considered as a straight segment and the more massive primary a point mass. The equations of motion of the infinitesimal bodies are derived.We obtain fourteen equilibrium points of the model, out of which six are collinear and rest non-collinear with the centers of the primaries. The position of the equilibrium points are affected by the small perturbation in centrifugal …

(R1493) Discussion On Stability And Hopf-Bifurcation Of An Infected Prey Under Refuge And Predator, Moulipriya Sarkar, Tapasi Das

Applications and Applied Mathematics: An International Journal (AAM)

The paper deals with the case of non-selective predation in a partially infected prey-predator system, where both the susceptible prey and predator follow the law of logistic growth and some preys avoid predation by hiding. The disease-free preys get infected in due course of time by a certain rate. However, the carrying capacity of the predator population is considered proportional to the sum-total of the susceptible and infected prey. The positivity and boundedness of the solutions of the system are studied and the existence of the equilibrium points and stability of the system are analyzed at these points. The effect …

(R1506) Generalized Cr3b Problem With Heterogeneous Primary And Secondary As Finite Straight Segment, Abdullah A. Ansari, K. R. Meena, K. Shalini

Applications and Applied Mathematics: An International Journal (AAM)

The existence and stability of stationary points are investigated under the effects of heterogeneous primary having N-layers with different densities, radiating finite straight segment and the Coriolis as well as centrifugal forces in the frame of cr3bp. The equations of motion are determined with the help of which we evaluate five stationary points analytically as well as graphically, and examine their stability.

(R1494) Approximate Solutions Of The Telegraph Equation, Ilija Jegdić

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the initial boundary value problems for the linear telegraph equation in one and two space dimensions are considered. To find approximate solutions, a recently proposed optimization-free approach that utilizes artificial neural networks with one hidden layer is used, in which the connecting weights from the input layer to the hidden layer are chosen randomly and the weights from the hidden layer to the output layer are found by solving a system of linear equations. One of the advantages of this method, in comparison to the usual discretization methods for the two-dimensional linear telegraph equation, is that this …

(R1471) Mhd Reiner-Rivlin Liquid Flow Through A Porous Cylindrical Annulus, Satya Deo, Satish Kumar

Applications and Applied Mathematics: An International Journal (AAM)

The present work concerns the steady and unsteady flow of an incompressible Reiner- Rivlin liquid in the porous annular region of two concentric rotating cylinders, which is moving parallel to their axis, about the common axis of these cylinders under uniform magnetic field acted in perpendicular direction of the axis. The electrically conducting flow of Reiner-Rivlin liquid in the annular porous region is governed by the Brinkman equation with the consideration that the effective viscosity of liquid is same as viscosity of the liquid. Analytical expressions for velocity components, pressure gradient and volumetric flow rate are established. Effects of the …

(R1523) Abundant Natural Resources, Ethnic Diversity And Inclusive Growth In Sub-Saharan Africa: A Mathematical Approach, Juliet I. Adenuga, Kazeem B. Ajide, Anthonia T. Odeleye, Abayomi A. Ayoade

Applications and Applied Mathematics: An International Journal (AAM)

The sub-Saharan African region is blessed with abundant natural resources and diverse ethnic groups, yet the region is dominated by the largest number of poor people worldwide due to inequitable distribution of national income. Existing statistics forecast decay in the quality of lives over the years compared to the continent of Asia that shares similar history with the region. In this paper, a-five dimensional first-order nonlinear ordinary differential equations was formulated to give insight into various factors that shaped dynamics of inclusive growth in sub-Saharan Africa. The validity test was performed based on ample mathematical theorems and the model was …

A Practical Extension To The Ab/Ba Design, My T.A Nguyen

Electronic Theses and Dissertations

In this work, we take a close look at a general extension to the traditional AB/BA
crossover design that is commonly used in clinical trials to determine the effectiveness
of new candidate drugs. While the traditional crossover design requires each patient
in the study to be measured on both treatment A and treatment B, we consider the
possibility of additional measurements being available on each patient. This produces
designs such as the AABB/BBAA design which has been used in previous studies.
A general test statistic will be derived to test for treatment effects as well as its
corresponding power function …

An Algorithm For Biobjective Mixed Integer Quadratic Programs, Pubudu Jayasekara Merenchige

All Dissertations

Multiobjective quadratic programs (MOQPs) are appealing since convex quadratic programs have elegant mathematical properties and model important applications. Adding mixed-integer variables extends their applicability while the resulting programs become global optimization problems. Thus, in this work, we develop a branch and bound (BB) algorithm for solving biobjective mixed-integer quadratic programs (BOMIQPs). An algorithm of this type does not exist in the literature.

The algorithm relies on five fundamental components of the BB scheme: calculating an initial set of efficient solutions with associated Pareto points, solving node problems, fathoming, branching, and set dominance. Considering the properties of the Pareto set of …

On The P-Inner Functions Of ℓPA, James G. Dragas

Mathematics & Statistics Theses & Dissertations

Define ℓ^p_A as the space of all functions holomorphic over the unit disk whose Taylor coefficients are p-summable. Despite their classical origins and simple definition, these spaces are not as well understood as one might expect. This is particularly true when compared with the Hardy spaces, which provide a useful road map for the types of questions we might consider reasonable. In this work we examine the zero sets of ℓ^p_A, p ∈ (1;∞), as well as a notion of inner function that is consistent with the approach taken on numerous other function spaces. …

Grid Homology Invariants For Singular Legendrian Links, Richard Michael Shumate

Graduate Theses and Dissertations

If $\Lambda_{1}^{\ast}$ and $\Lambda_{2}^{\ast}$ are two oriented singular Legendrian links that are Legendrian isotopic, we first construct front diagram representations of $\Lambda_{1}^{\ast}$ and $\Lambda_{2}^{\ast}$ that have a natural allowable singular gird diagram associated to them. These allowable singular grid diagrams will always correspond to singular Legendrian links. The grid Legendrian invariants, $\lambda^{\pm}$, in the nonsingular grid homology theory have a natural extension to the singular grid theory, and are natural under the newly defined singular grid moves. This gives an invariant of singular Legendrian links, and in fact, a broader class of singular links.

Modeling Cherenkov Light Detection Timing For The Very Energetic Radiation Imaging Telescope Array System, Keilan Finn Ramirez

Physics

The Very Energetic Radiation Imaging Telescope Array System (VERITAS) is an array of four 12-meter telescopes which use the Imaging Atmospheric Cherenkov Technique to conduct high-energy gamma-ray astronomy. VERITAS detects magnitude and location information associated with Cherenkov light, and uses this information to indirectly observe gamma-rays through a software reconstruction process. VERITAS also records timing information corresponding to Cherenkov light detection, and this additional information could theoretically be incorporated into the reconstruction process to improve the accuracy of gamma-ray observations. The first step to including timing information is to understand when Cherenkov light detection would be expected from a known …

(R1524) The Existence And Uniqueness Of Solution For Fractional Newel-Whitehead-Segel Equation Within Caputo-Fabrizio Fractional Operator, Ali Khalouta

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce and study the existence and uniqueness theorem of the solution for the fractional Newell-Whitehead-Segel equation within Caputo-Fabrizio fractional operator. Also, we propose a new numerical method known as natural reduced differential transform method (NRDTM) for solving this equation. We confirm our theoretical discussion with two numerical examples in order to achieve the validity and accuracy of the proposed method. The computations, associated with these examples, are performed by MATLAB software package.

(R1464) Stability Of The Artificial Equilibrium Points In The Low-Thrust Restricted Three-Body Problem With Variable Mass, Amit Mittal, Krishan Pal, Pravata Kumar Behera, Deepak Mittal

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we have investigated the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem with variable mass. In this model of the low-thrust restricted three-body problem, we have considered both the primaries as point masses. The mass of the spacecraft varies with time according to Jeans’ law (1928). We have introduced a new concept for creating the AEPs in the restricted three-body problem with variable mass using continuous constant acceleration. We have derived the equations of motion of the spacecraft after using the space-time transformations of Meshcherskii. The AEPs have been created …

(R1412) Stability And Bifurcation Of A Cholera Epidemic Model With Saturated Recovery Rate, Huda Abdul-Satar, Raid K. Naji

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound …

(R1454) On Reducing The Linearization Coefficients Of Some Classes Of Jacobi Polynomials, Waleed Abd-Elhameed, Afnan Ali

Applications and Applied Mathematics: An International Journal (AAM)

This article is concerned with establishing some new linearization formulas of the modified Jacobi polynomials of certain parameters. We prove that the linearization coefficients involve hypergeometric functions of the type ₄F₃(1). Moreover, we show that the linearization coefficients can be reduced in several cases by either utilizing certain standard formulas, and in particular Pfaff-Saalschütz identity and Watson’s theorem, or via employing the symbolic algebraic algorithms of Zeilberger, Petkovsek, and van Hoeij. New formulas for some definite integrals are obtained with the aid of the developed linearization formulas.

(R1504) Second-Order Modified Nonstandard Runge-Kutta And Theta Methods For One-Dimensional Autonomous Differential Equations, Madhu Gupta, John M. Slezak, Fawaz K. Alalhareth, Souvik Roy, Hristo V. Kojouharov

Applications and Applied Mathematics: An International Journal (AAM)

Nonstandard finite difference methods (NSFD) are used in physical sciences to approximate solutions of ordinary differential equations whose analytical solution cannot be computed. Traditional NSFD methods are elementary stable but usually only have first order accuracy. In this paper, we introduce two new classes of numerical methods that are of second order accuracy and elementary stable. The methods are modified versions of the nonstandard two-stage explicit Runge-Kutta methods and the nonstandard one-stage theta methods with a specific form of the nonstandard denominator function. Theoretical analysis of the stability and accuracy of both modified NSFD methods is presented. Numerical simulations that …

(R1496) Impact Of Electronic States Of Conical Shape Of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots, Md. Fayz-Al-Asad, Md. Al-Rumman, Md. Nur Alam, Salma Parvin, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

Semiconductor quantum dots (QDs) have unique atom-like properties. In this work, the electronic states of quantum dot grown on a GaAs substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing eigen value equation has been solved, thereby obtaining the dependence of ground state energy on radius and height of the cone-shaped -dots. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). We discovered that the eigen functions and energies are nearly associated with the GaAs …

(R1458) A New Finite Difference Scheme For High-Dimensional Heat Equation, Jafar Biazar, Roxana Asayesh

Applications and Applied Mathematics: An International Journal (AAM)

In this research‎, ‎a new second-order finite difference scheme is proposed to solve two and three- dimensional heat equation‎. Finite difference equations are determined via a discretization approach in which spatial second order partial derivatives in x and y directions are approximated simultaneously‎ while in the classic method, each spatial partial derivative is replaced by a central finite difference approximation, separately. By this new discretization scheme and also using the forward difference to the first-order time derivative, a finite difference equation is obtained for the parabolic equation. This approach is explicit and similar to other explicit approaches, an interval for …

On A Class Of Critical N-Laplacian Problems, Tsz Chung Ho

Theses and Dissertations

We establish some existence results for a class of critical N-Laplacian problems in a bounded domain in R^N. In the absence of a suitable direct sum decomposition, we use an abstract linking theorem based on the Z₂-cohomological index to obtain a nontrivial critical point.