Applied Mathematics Commons^™

Using Fuzzy Linear Regression To Estimate Relationship Between Forest Fires And Meteorological Conditions, Hande G. Akdemir, Fatma Tiryaki

Applications and Applied Mathematics: An International Journal (AAM)

Each year, millions of hectares of forest land are destroyed by fires causing great financial loss and ecological damage. In this paper, our aim is to study the effect of the variation of meteorological conditions on the total burned area in hectares, by using fuzzy linear regression analysis based on Tanaka’s approaches. The total burned area is considered a dependent variable. Air temperature (in ºC), relative humidity (in %), wind speed (in km/h) and rainfall (in mm/m² ) are considered to be independent variables. The relationship between input and output data is estimated using data provided in data mining …

Spread Of Malicious Objects In Computer Network: A Fuzzy Approach, Bimal K. Mishra, Apeksha Prajapati

Applications and Applied Mathematics: An International Journal (AAM)

We propose an e-epidemic fuzzy SEIQRS (Susceptible-Exposed-Infectious-Quarantine- Recovered-Susceptible) model for the transmission of malicious codes in a computer network. We have simulated the result for various parameters and analyzed the stability of the model. The efficiency of antivirus software and crashing of the nodes due to attack of malicious code is analyzed. Furthermore, initial simulation results illustrate the behavior of different classes for minimizing the infection in a computer network. It also reflects the positive impact of anti-virus software on malicious code propagation in a computer network. The basic reproduction number R0 f and its formulation is also discussed.

Exponentially Fitted Variants Of The Two-Step Adams-Bashforth Method For The Numerical Integration Of Initial Problems, Gurjinder Singh, V. Kanwar, Saurabh Bhatia

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we propose new variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods for the numerical integration of ordinary differential equations (ODEs). The methods are constructed geometrically from an exponentially fitted osculating parabola. The accuracy and stability of the proposed variants is discussed and their applicability to some initial value problems is also considered. Numerical experiments demonstrate that the exponentially fitted variants of the two-step Adams-Bashforth and the one-step Adams-Moulton methods outperform the existing classical two-step Adams-Bashforth and one-step Adams- Moulton methods respectively.

A Note On The Qualitative Behavior Of Some Second Order Nonlinear Equation, Juan E. Nápoles Valdes

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present two qualitative results concerning the solutions of some second order nonlinear equations, under suitable assumptions. The first result centers on the boundedness of the solutions while the second discusses the square integrability of the solutions. These results are obtained by extending and improving the current literature through sound mathematical analysis.

Application Of The Optimal Homotopy Asymptotic Method For Solving The Cauchy Reaction-Diffusion Problem, H. Jafari, S. Gharbavy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the optimal homotopy asymptotic method is applied on the Cauchy reaction-diffusion problems to check the effectiveness and performance of the method. The obtained solutions show that the OHAM is more effective, simpler and easier than other methods. Moreover, this technique does not require any discretization or linearization and therefore it reduces significantly the numerical computations. The results reveal that the method is explicit.

Grayscale-Image Encryption Using Random Hill Cipher Over Sln(F) Associated With Discrete Wavelet Transformation, D. C. Mishra, R. K. R. K. Sharma

Applications and Applied Mathematics: An International Journal (AAM)

Image data are highly sensitive and prone to incidental decoding by intruders. The security of image data in an insecure network is therefore a major issue. In this paper, we have presented a novel approach for grayscale-image encryption and decryption using Random Hill cipher over SLn(F) associated with discrete wavelet transformation. Earlier techniques for encryption and decryption of image data discussed missing the keys, but in this approach, both the keys and the arrangement of RHC are emphasized. Additionally, keys multiplication side (pre or post) over a grayscale-image data matrix also inevitable to know, to correctly decrypt the encrypted image …

Stabilized Finite Elements For Compressible Turbulent Navier-Stokes, Jon Taylor Erwin

Masters Theses and Doctoral Dissertations

In this research a stabilized finite element approach is utilized in the development of a high-order flow solver for compressible turbulent flows. The Reynolds averaged Navier-Stokes (RANS) equations and modified Spalart-Almaras (SA) turbulence model are discretized using the streamline/upwind Petrov-Galerkin (SUPG) scheme. A fully implicit methodology is used to obtain steady state solutions or to drive unsteady problems at each time step. Order of accuracy is assessed for inviscid and viscous flows in two and three dimensions via the method of manufactured solutions. Proper treatment of curved surface geometries is of vital importance in high-order methods, especially when high aspect …

Extension Of A High-Order Petrov-Galerkin Implementation Applied To Non-Radiating And Radar Cross Section Geometries, William L. Shoemake

Masters Theses and Doctoral Dissertations

Capabilities of a high-order Petrov-Galerkin solver are expanded to include N-port systems. Tait-Bryan angles are employed to launch electro-magnetic waves in arbitrary directions allowing off axis ports to be driven. The transverse-electric (TE) formulation is added allowing waveguide geometries to be driven directly. A grid convergence study is performed on a coax-driven waveguide system. Physical data are matched to a hybrid-T junction (magic-T) electromagnetic waveguide structure to verify the TE driving formulation along with the Tait-Bryan angles and modified post-processing routines. A simple sphere case is used to exercise the radar cross section (RCS) routines and to examine the benefits …

2-D Cfd Design Of The Cross-Sectional Shape Of Arterial Stents, Kristen Karman

Masters Theses and Doctoral Dissertations

An approach for desigining arterial stents to maximize wall shear stress is presented. A cost equation to maximize wall shear stress is derived and then inverted into a minimization problem for the optimizer. A 2-D mixed-element finite-volume scheme for solving the compressible Navier-Stokes equations is implemented. A paramaterization of the cross- sectional shape of the stent wire using Hicks-Henne functions is described. The strategies used in the commercial optimization software, DAKOTA, to minimize the cost equation are described. The solver is validated using well known fluid flow test cases and is shown to match other published computed results for bloodflow …

A Hybrid Agent-Based And Differential Equations Model For Simulating Antibiotic Resistance In A Hospital Ward, Lester Caudill, Barry Lawson

Department of Math & Statistics Faculty Publications

Serious infections due to antibiotic-resistant bacteria are pervasive, and of particular concern within hospital units due to frequent interaction among health-care workers and patients. Such nosocomial infections are difficult to eliminate because of inconsistent disinfection procedures and frequent interactions among infected persons, and because ill-chosen antibiotic treatment strategies can lead to a growth of resistant bacterial strains. Clinical studies to address these concerns have several issues, but chief among them are the effects on the patients involved. Realistic simulation models offer an attractive alternative. This paper presents a hybrid simulation model of antibiotic resistant infections in a hospital ward, combining …

A Population Model For Walleye In Nebraska Irrigation Reservoirs, Robert A. Kill

School of Natural Resources: Dissertations, Theses, and Student Research

Understanding how and why fish population size changes between years is a central theme in fisheries ecology. Fishery agencies have limited time and financial resources, thus there is a need for a quantitative way to direct the limited time and financial resources so agencies can manage fisheries more efficiently. I developed a tool for fishery managers that synthesizes common population indices and evaluated the relative importance of those indices given varying uncertainty in age-0 walleye Sander vitreus survival. Under most circumstances, I determined that resources are best utilized in reducing age-0 survival uncertainty when understanding walleye population growth. I applied …

Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench

Textbooks Collection

No abstract provided.

Elementary Differential Equations, William F. Trench

Textbooks Collection

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra.

In writing this book I have been guided by the these principles:

An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough.

An …

Introduction To Real Analysis, William F. Trench

Textbooks Collection

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathe- matical maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence …

Computing Curvature And Curvature Normals On Smooth Logically Cartesian Surface Meshes, John Thomas Hutchins

Boise State University Theses and Dissertations

This thesis describes a new approach to computing mean curvature and mean curvature normals on smooth logically Cartesian surface meshes. We begin by deriving a finite-volume formula for one-dimensional curves embedded in two- or three- dimensional space. We show the exact results on curves for specific cases as well as second-order convergence in numerical experiments. We extend this finite-volume formula to surfaces embedded in three-dimensional space. Exact results are again derived for special cases and second-order convergence is shown numerically for more general cases. We show that our formula for computing curvature is an improvement over using the “cotan” formula …

The Underlying Physiology Of Arterial Pulse Wave Morphology In Spatial Domain, Nzerem F. Egenti, Alozie H. Nkechi

Applications and Applied Mathematics: An International Journal (AAM)

Cardio-vascular events are among the world’s leading causes of morbidity and mortality. Most postulates suppose that culinary delights can be implicated in incidences of cardio-vascular diseases. This school of thought holds well in many respects. Much as the truistic value of the said school is acknowledged, we conceived of physiological disposition as an endogenous dominant factor in the events being considered, whereas culinary measures constitute an exogenous contributory factor. In this work we aimed at studying the effects of distance (stature) on pulse waveforms. Certain elements of our study showed that pulse wavelength was dominant in prescribing cardio-vascular physiology.

Some Geometric Properties Of A New Type Metric Space, Muhammed Çınar, Murat Karakaş, Mikail Et

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we define a metric on our new space and then show that this linear metric space is k-nearly uniform convex and has property beta where p = p_k is a bounded sequence of positive real numbers. Finally, we give a result about property (H) by using k-nearly uniform convexity.

Graphic Illustration Of The Transmission Resonances For The Dkp Particles, B. Boutabia-Chéraitia, Abdenacer Makhlouf

Applications and Applied Mathematics: An International Journal (AAM)

We consider the Duffin-Kemmer-Petiau (DKP) equation in the presence of a spatially one-dimensional Woods-Saxon (WS) potential and we show by graphics how the zero-reflection condition on the Klein interval depends on the shape of the potential.

Viscosity Dependence Of Faraday Wave Formation Thresholds, Lisa Michelle Slaughter

Physics

This experiment uses an electromagnetic shaker to produce standing wave patterns on the surface of a vertically oscillating sample of silicon liquid. These surface waves, known as Faraday waves, form shapes such as squares, lines, and hexagons. They are known to be dependent upon the frequency and amplitude of the forcing as well as on the viscosity and depth of the liquid in the dish. At a depth of 4mm and for various silicon liquids having kinematic viscosities of 10, 20, and 38 cSt, we determined the acceleration at which patterns form for frequencies between 10 and 60 Hz. For …

Several New Families Of Jarratt’S Method For Solving Systems Of Nonlinear Equations, V. Kanwar, Sanjeev Kumar, Ramandeep Behl

Applications and Applied Mathematics: An International Journal (AAM)

In this study, we suggest and analyze a new and wide general class of Jarratt’s method for solving systems of nonlinear equations. These methods have fourth-order convergence and do not require the evaluation of any second or higher-order Fréchet derivatives. In terms of computational cost, all these methods require evaluations of one function and two first-order Fréchet derivatives. The performance of proposed methods is compared with their closest competitors in a series of numerical experiments. It is worth mentioning that all the methods considered here are found to be effective and comparable to the robust methods available in the literature.