Numerical Analysis and Computation Commons^™

The Potentials Of Faecal Sludge Treatment Using Local Conditioners In Tanzania: A Review, Doglas Benjamin1

Tanzania Journal of Engineering and Technology (TJET)

Worldwide, every day human beings generate millions of tons of Faecal Sludge (FS), which is rich in water, nutrients, energy, and organic compounds. Yet FS is not being managed in a way that permits us to derive value from its reuse, while at the same time, millions of farmers struggle with depleted soils and lack of water. In most of the developing countries, energy for cooking is mainly derived from cutting of trees, either as wood or charcoal. Resource recovery and reuse from FS can create livelihoods, enhance food security, support green economies, reduce waste and contribute to cost recovery …

Personalized Detection Of Anxiety Provoking News Events Using Semantic Network Analysis, Jacquelyn Cheun Phd, Luay Dajani, Quentin B. Thomas

SMU Data Science Review

In the age of hyper-connectivity, 24/7 news cycles, and instant news alerts via social media, mental health researchers don't have a way to automatically detect news content which is associated with triggering anxiety or depression in mental health patients. Using the Associated Press news wire, a semantic network was built with 1,056 news articles containing over 500,000 connections across multiple topics to provide a personalized algorithm which detects problematic news content for a given reader. We make use of Semantic Network Analysis to surface the relationship between news article text and anxiety in readers who struggle with mental health disorders. …

A Data Driven Approach To Forecast Demand, Hannah Kosinovsky, Sita Daggubati, Kumar Ramasundaram, Brent Allen

SMU Data Science Review

Abstract. In this paper, we present a model and methodology for accurately predicting the following quarter’s sales volume of individual products given the previous five years of sales data. Forecasting product demand for a single supplier is complicated by seasonal demand variation, business cycle impacts, and customer churn. We developed a novel prediction using machine learning methodology, based upon a Dense neural network (DNN) model that implicitly considers cyclical demand variation and explicitly considers customer churn while minimizing the least absolute error between predicted demand and actual sales. Using parts sales data for a supplier to the oil and gas …

Determinism Of Stochastic Processes Through The Relationship Between The Heat Equation And Random Walks, Gurmehar Singh Makker

Publications and Research

We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.

Individual Based Model To Simulate The Evolution Of Insecticide Resistance, William B. Jamieson

Department of Mathematics: Dissertations, Theses, and Student Research

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory.

Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual …

An (S - 1; S) Inventory System With Negative Arrivals And Multiple Vacations, Kathiresan Jothivel, Anbazhagan Neelamegam

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we consider a continuous review one-to-one ordering policy inventory system with multiple vacations and negative customers. The maximum storage capacity is S. The customers arrive according to a Poisson process with finite waiting hall. There are two types of customers: ordinary and negative. An ordinary customer, on arrival, joins the queue and the negative customer does not join the queue and takes away any one of the waiting customers. When the waiting hall is full, the arriving primary customer is considered to be lost. The service time and lead time are assumed to have independent exponential distribution. …

Non-Standard Finite Difference Schemes For Investigating Stability Of A Mathematical Model Of Virus Therapy For Cancer, A. R. Yaghoubi, H. S. Najafi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a special case of finite difference method called non-standard finite difference (NSFD) method was studied to compute the numerical solutions of the nonlinear mathematical model of the interaction between tumor cells and oncolytic viruses. The global stability of the equilibrium points of the discrete model is investigated by using the Lyapunov stability theorem. Some conditions were gained for the local asymptotical stability of the equilibrium points of the system. Finally, numerical simulations are carried out to illustrate the main theoretical results. The discrete system is dynamically consistent with its continuous model, it preserves essential properties, such as …

Solutions Of The Generalized Abel’S Integral Equation Using Laguerre Orthogonal Approximation, N. Singha, C. Nahak

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a numerical approximation is drafted for solving the generalized Abel’s integral equation by practicing Laguerre orthogonal polynomials. The proposed approximation is framed for the first and second kinds of the generalized Abel’s integral equation. We have utilized the properties of fractional order operators to interpret Abel’s integral equation as a fractional integral equation. It offers a new approach by employing Laguerre polynomials to approximate the integrand of a fractional integral equation. Given examples demonstrate the simplicity and suitability of the method. The graphical representation of exact and approximate solutions helps in visualizing a solution at discrete points, …

An Admm-Factorization Algorithm For Low Rank Matrix Completion, Rahman Taleghani, Maziar Salahi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose an Alternating Direction Method of Multipliers (ADMM) based algorithm that is taking advantage of factorization for the fixed rank matrix completion problem. The convergence of the proposed algorithm to the KKT point is discussed. Finally, on several classes of test problems, its efficiency is compared with several efficient algorithms from the literature.

Analysis Of Batch Arrival Single And Bulk Service Queue With Multiple Vacation Closedown And Repair, T. Deepa, A. Azhagappan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we analyze batch arrival single and bulk service queueing model with multiple vacation, closedown and repair. The single server provides single service if the queue size is ‘< a’ and bulk service if the queue size is ‘ ≥ a’. After completing the service (single or bulk), the server may breakdown with probability ξ and then it will be sent for repair. When the system becomes empty or the server is ready to serve after the repair but no one is waiting, the server resumes closedown and then goes for a multiple vacation of random length. Using supplementary variable technique, the steady-state probability generating function (PGF) of …

A Certain Class Of Statistical Deferred Weighted A-Summability Based On (P; Q)-Integers And Associated Approximation Theorems, L. N. Mishra, M. Patro, S. K. Paikray, B. B. Jena

Applications and Applied Mathematics: An International Journal (AAM)

Statistical summability has recently enhanced researchers’ substantial awareness since it is more broad than the traditional (ordinary) convergence. The basic concept of statistical weighted A- summability was introduced by Mohiuddine (2016). In this investigation, we introduce the (presumably new) concept of statistical deferred weighted A-summability and deferred weighted A- statistical convergence with respect to the difference sequence of order r involving (p; q)-integers and establish an inclusion relation between them. Furthermore, based upon the proposed methods, we intend to approximate the rate of convergence and to demonstrate a Korovkin type approximation theorem for functions of two variables defined on a …

An Efficient Computational Method For Solving A System Of Fdes Via Fractional Finite Difference Method, M. M. Khader, Sunil Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This paper aims to provide a numerical method for solving systems of fractional (Caputo sense) differential equations (FDEs). This method is based on the fractional finite difference method (FDM), where we implemented the Grünwald-Letnikov’s approach. This method is computationally very efficient and gives very accurate solutions. In this study, the stability of the obtained numerical scheme is given. The numerical results show that the proposed approach is easy to be implemented and are accurate when applied to system of FDEs. The method introduces promising tool for solving many systems of FDEs. Two examples are given to demonstrate the applicability and …

Numerical Solution Of Fractional Partial Differential Equations With Normalized Bernstein Wavelet Method, Mahsa Entezari, Saeid Abbasbandy, Esmail Babolian

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, normalized Bernstein wavelets are presented. Next, the fractional order integration and Bernstein wavelets operational matrices of integration are derived and finally are used for solving fractional partial differential equations. The operational matrices merged with the collocation method are used in order to convert fractional problems to a number of algebraic equations. In the suggested method the boundary conditions are automatically taken into consideration. An assessment of the error of function approximation based on the normalized Bernstein wavelet is also presented. Some numerical instances are given to manifest the versatility and applicability of the suggested method. Founded numerical …

Analysis Of Two Stage M[X1],M[X2]/G1,G2/1 Retrial G-Queue With Discretionary Priority Services, Working Breakdown, Bernoulli Vacation, Preferred And Impatient Units, G. Ayyappan, B. Somasundaram

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study M^[X₁] , M^[X2] /G₁ ,G₂ /1 retrial queueing system with discretionary priority services. There are two stages of service for the ordinary units. During the first stage of service of the ordinary unit, arriving priority units can have an option to interrupt the service, but, in the second stage of service it cannot interrupt. When ordinary units enter the system, they may get the service even if the server is busy with the first stage of service of an ordinary unit or may enter into the orbit or leave …

Multi-Point Flux Approximations Via The O-Method, Christen Leggett

Master's Theses

When an oil refining company is drilling for oil, much of the oil gets left behind after the first drilling. Enhanced oil recovery techniques can be used to recover more of that oil, but these methods are quite expensive. When a company is deciding if it is worth their time and money to use enhanced oil recovery methods, simulations can be used to model oil flow, showing the behavior and location of the oil. While methods do exist to model this flow, these methods are often very slow and inaccurate due to a large domain and wide variance in coefficients. …

Local Non-Similar Solution Of Powell-Eyring Fluid Flow Over A Vertical Flat Plate, Hemangini Shukla, Hema C. Surati, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

Our objective is to obtain the non-similarity solution of non-Newtonian fluid for Powell-Eyring model by a local non-similarity method. Here, free stream velocity is considered in power-law form (𝑈=𝑥^m). The governing equations are transformed using non-similar transformations and derived equations are treated as ordinary differential equations. Non-similar solutions are obtained for different values of power-law index 𝑚 and stream-wise location 𝜉. Influence of various parameters on velocity and temperature field are presented graphically using MATLAB bvp4c solver.

Inverse Spectral Problems For Spectral Data And Two Spectra Of N By N Tridiagonal Almost-Symmetric Matrices, Bayram Bala, Manaf D. Manafov, Abdullah Kablan

Applications and Applied Mathematics: An International Journal (AAM)

One way to study the spectral properties of Sturm-Liouville operators is difference equations. The coefficients of the second order difference equation which is equivalent Sturm-Liouville equation can be written as a tridiagonal matrix. One investigation area for tridiagonal matrix is finding eigenvalues, eigenvectors and normalized numbers. To determine these datas, we use the solutions of the second order difference equation and this investigation is called direct spectral problem. Furthermore, reconstruction of matrix according to some arguments is called inverse spectral problem. There are many methods to solve inverse spectral problems according to selecting the datas which are generalized spectral function, …

Numerical Solution Of The Lane-Emden Equations With Moving Least Squares Method, Sasan Asadpour, Hassan Hosseinzadeh, Allahbakhsh Yazdani

Applications and Applied Mathematics: An International Journal (AAM)

No abstract provided.

Recover Data In Sparse Expansion Forms Modeled By Special Basis Functions, Abdulmtalb Mohamed Hussen

Dissertations

In data analysis and signal processing, the recovery of structured functions (in terms of frequencies and coefficients) with respect to certain basis functions from the given sampling values is a fundamental problem. The original Prony method is the main tool to solve this problem, which requires the equispaced sampling values.

In this dissertation, we use the equispaced sampling values in the frequency domain after the short time Fourier transform in order to reconstruct some signal expansions, such as the exponential expansions and the cosine expansions. In particular, we consider the case that the phase of the cosine expansion is quadratic. …

Optimal Relaxation Weights For Multigrid Reduction In Time (Mgrit), Masumi Sugiyama

Mathematics & Statistics ETDs

Based on current trends in computer architectures, faster compute speeds must come from increased parallelism rather than increased clock speeds, which are stagnate. This situation has created the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. In this work, we consider the scheme known as multigrid-reduction-in-time (MGRIT), but note that there exist other parallel-in-time methods such as parareal and the parallel full approximation scheme in space and time (PFASST). MGRIT is a full multi-level method applied to the time dimension and …

Sperm Motility In Groups, Julie Simons

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Transient Dynamics Of Infection Transmission In An Intensive Care Unit, Christopher Short, Matthew S. Mietchen, Eric T. Lofgren

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Discrete-Time Disease Model With Population Motion Under The Kolmogorov Equation View And Application, Ye Li

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Collective Migration Of Neural Crest Cells With A Cucker-Smale Velocity Alignment Process, Claire Evensen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling, Analysis, Simulation Of The Opioid Crisis With Prescription And Social Drug Addiction Models, Kirthi Kumar

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Derivation Of Direct Explicit Integrators Of Rk Type For Solving Class Of Seventh-Order Ordinary Differential Equations, Mohammed S. Mechee, Jawad K. Mshachal

Karbala International Journal of Modern Science

The main contribution of this work is the development of direct explicit methods of Runge-Kutta (RK) type for solving class of seventh-order ordinary differential equations (ODEs) to improve computational efficiency. For this purpose, we have generalized RK, RKN, RKD, RKT, RKFD and RKM methods for solving class of first-, second-, third-, fourth-, and fifth-order ODEs. Using Taylor expansion approach, we have derived the algebraic equations of the order conditions for the proposed RKM integrators up to the tenth-order. Based on these order conditions, two RKM methods of fifth- and sixth-order with four- and five-stage are derived. The zero stability of …

Academic Skill Learning And The Problem Of Complexity I: Creational Purposeful Integrated Capability At Skill (Cpics), Martin F. Gardiner

Northeast Journal of Complex Systems (NEJCS)

Physical and mental skills are intended to achieve success at acting purposefully. As capability at any skill increases, the need to adjust details of application to complexity of context and goals will increase as well. It will become more and more important to prepare mentally for what I now term Creational Purposeful Integrated Capability at Skill (CPICS). This paper develops what I mean by CPICS. Theory concerning Complex Dynamical Systems (CDS) such as the brain and other evidence points to the likelihood that the mental operations by which our brain produces any kind of skillful behavior cannot remain constant, …

Being In Uncertainties: An Inquiry-Based Model Leveraging Complexity In Teaching-Learning, Diane Rosen

Northeast Journal of Complex Systems (NEJCS)

Education is traditionally structured as a closed system, privileging result-driven methods that offer control and predictability. In recent decades this reductionist approach has been effectively challenged by interdisciplinary work in complex systems theory, revealing myriad levels of orderly disorder that make either-or, linear instruction an inadequate norm. Narrowing the broad implications of a complexity lens on education, this paper focuses on generative uncertainty in teaching-learning, a paradoxical state of epistemological and creative growth described by English poet John Keats as "the negative capability of being in uncertainties, mysteries, doubts." Opportunities to advance this potentiating capacity are especially abundant in constructivist …

Creativity As An Emergent Property Of Complex Educational System, Ceire Monahan, Mika Munakata, Ashwin Vaidya

Northeast Journal of Complex Systems (NEJCS)

The importance of creativity in education has been discussed often in the literature. While there remains no agreed-upon definition of creativity, the psychological literature points to traits of a creative person. These include the ability to think outside the box, make connections between seemingly disparate ideas, and question norms. The literature provides several examples of classroom experiments to help foster creativity in the classroom. In science and mathematics, we can start by getting students to recognize mathematics and the sciences as being creative endeavors. While these attempts are noteworthy, they are not necessarily aligned with instructional practices. In this article, …