Applied Mathematics Commons^™

Certain Fractional Integral Operators And The Generalized Incomplete Hypergeometric Functions, H. M. Srivastava, Praveen Agarwal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply a certain general pair of operators of fractional integration involving Appell’s function F₃ in their kernel to the generalized incomplete hypergeometric functions _pΓ_q[z] and _pɣ_q [z], which were introduced and studied systematically by Srivastava et al. in the year 2012. Some interesting special cases and consequences of our main results are also considered.

New Existence Results To Solution Of Fractional Boundary Value Problems, Rahmat Darzi, Bahar Mohammadzadeh

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we verify the existence of solution to boundary value problem of nonlinear fractional differential equation involving Caputo fractional derivatives. We obtain new existence results based on nonlinear alternative of Leray-Schauder type and Krasnoselskiis fixed point theorem. At the end, two illustrative examples have been presented.

A New Approach To The Numerical Solution Of Fractional Order Optimal Control Problems, T. Akbarian, M. Keyanpour

Applications and Applied Mathematics: An International Journal (AAM)

In this article, a new numerical method is proposed for solving a class of fractional order optimal control problems. The fractional derivative is considered in the Caputo sense. This approach is based on a combination of the perturbation homotopy and parameterization methods. The control function u(t) is approximated by polynomial functions with unknown coefficients. This method converts the fractional order optimal control problem to an optimization problem. Numerical results are included to demonstrate the validity and applicability of the method.

Numerical Algorithm For Analysis Of N-Ary Subdivision Schemes, Ghulam Mustafa, Muhammad Zahid

Applications and Applied Mathematics: An International Journal (AAM)

The analysis for continuity of limit curves generated by m-point n-ary subdivision schemes is presented for m, n ≥ 2. The analysis is based on the study of corresponding differences and divided difference schemes. A numerical algorithm is introduced which computes the continuity and higher order divided differences of schemes in an efficient way. It is also free from polynomial factorization and division unlike the well-known Laurent polynomial algorithm for analysis of schemes which depends on polynomial algebraic operations. It only depends on the arithmetic operations.

Exact Traveling Wave Solutions Of Nonlinear Pdes In Mathematical Physics Using The Modified Simple Equation Method, E. M. E. Zayed, A. H. Arnous

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we apply the modified simple equation method to find the exact solutions with parameters of the (1+1)-dimensional nonlinear Burgers-Huxley equation, the (2+1) dimensional cubic nonlinear Klein-Gordon equation and the (2+1)-dimensional nonlinear Kadomtsev- Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The new exact solutions of these three equations are obtained. When these parameters are given special values, the solitary solutions are obtained.

Numerical Solution Of Fuzzy Arbitrary Order Predator-Prey Equations, Smita Tapaswini, S. Chakraverty

Applications and Applied Mathematics: An International Journal (AAM)

This paper seeks to investigate the numerical solution of fuzzy arbitrary order predator-prey equations using the Homotopy Perturbation Method (HPM). Fuzziness in the initial conditions is taken to mean convex normalised fuzzy sets viz. triangular fuzzy number. Comparisons are made between crisp solution given by others and fuzzy solution in special cases. The results obtained are depicted in plots and tables to demonstrate the efficacy and powerfulness of the methodology.

Random Search Models Of Foraging Behavior: Theory, Simulation, And Observation, Ben C. Nolting

Department of Mathematics: Dissertations, Theses, and Student Research

Many organisms, from bacteria to primates, use stochastic movement patterns to find food. These movement patterns, known as search strategies, have recently be- come a focus of ecologists interested in identifying universal properties of optimal foraging behavior. In this dissertation, I describe three contributions to this field. First, I propose a way to extend Charnov's Marginal Value Theorem to the spatially explicit framework of stochastic search strategies. Next, I describe simulations that compare the efficiencies of sensory and memory-based composite search strategies, which involve switching between different behavioral modes. Finally, I explain a new behavioral analysis protocol for identifying the …

Approximation In Multiobjective Optimization With Applications, Lakmali Weerasena

All Dissertations

Over the last couple of decades, the field of multiobjective optimization has received much attention in solving real-life optimization problems in science, engineering, economics and other fields where optimal decisions need to be made in the presence of trade-offs between two or more conflicting objective functions. The conflicting nature of objective functions implies a solution set for a multiobjective optimization problem. Obtaining this set is difficult for many reasons, and a variety of approaches for approximating it either partially or entirely have been proposed.

In response to the growing interest in approximation, this research investigates developing a theory and methodology …

Filter-Based Multiscale Entropy Analysis Of Complex Physiological Time Series, Liang Zhao

Dissertations - ALL

The multiscale entropy (MSE) has been widely and successfully used in analyzing the complexity of physiologic time series. In this thesis, we re-interpret the averaging process in MSE as filtering a time series by a filter of a piecewise constant type. From this viewpoint, we introduce the {\it filter-based multiscale entropy} (FME) which filters a time series by filters to generate its multiple frequency components and then compute the {\it blockwise} entropy of the resulting components. By choosing filters adapted to the feature of a given time series, FME is able to better capture its multiscale information and to provide …

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 …

Comparison Of Mesh And Meshless Methods For Partial Differential Equations Of Galerkin Form, Wallace F. Atterberry

UNLV Theses, Dissertations, Professional Papers, and Capstones

There are two purposes of this research project. The first purpose is to compare two types of Galerkin methods: The finite element mesh method and moving least sqaures meshless Galerkin (EFG) method. The second purpose of this project is to determine if a hybrid between the mesh and meshless method is beneficial.

This manuscript will be divided into three main parts. The first part is chapter one which develops the finite element method. The second part (Chapter two) will be developing the meshless method. The last part will provide a method for combining the mesh and meshless methods for a …

A More General Diffusion Model For Lightning Radiative Transfer, Elliott Paul Saint-Pierre

UNLV Theses, Dissertations, Professional Papers, and Capstones

A more general diffusion model for lightning radiative transfer is presented. The development is based on the work published by Koshak et al (J. Geo. Phys. Res., vol. 99, (D7), 14361-371, (1994). In this thesis, the diffusion coefficient is allowed to vary as a function of the radial component of the cloud and cylindrical geometry is used. Different approximations in the analysis of the resulting radial equation are provided. The method of Frobenius permits the obtention of a complete solution. Possibilities and means for further development of this research are included.

Validation Of Interpolative Interfaces For Rotorcraft Applications, Adam L. Cofer

Masters Theses and Doctoral Dissertations

The study uses computational methods to simulate fluid flow on the NASA ROBIN helicopter model and on a simplified rotor geometry previously tested at Mississippi State. The ROBIN model and the rotor are run using an unstructured grid. Results from the Tenasi flow solver are compared against both simulated and wind tunnel data. Tenasi is an unstructured, Reynolds Averaged Navier-Stokes (RANS) solver developed at the SimCenter: National Center for Computational Engineering, located at the University of Tennessee at Chattanooga. Steady-state results for the isolated ROBIN fuselage and unsteady results for both fuselage and rotor systems are computed. In the unsteady …

Leslie Matrices For Logistic Population Modeling, Bruce Kessler

Mathematics Faculty Publications

Leslie matrices are taught as a method of modeling populations in a discrete-time fashion with more detail in the tracking of age groups within the population. Leslie matrices have limited use in the actual modeling of populations, since when the age groups are summed, it is basically equivalent to discrete-time modeling assuming exponential population growth. The logistic model of population growth is more realistic, since it takes into account a carrying capacity for the environment of the population. This talk will describe an adjustment to the Leslie matrix approach for population modeling that is both takes into account the carrying …

On Closed Subsets Of Non-Commutative Association Schemes Of Rank 6, Jose Vera

Theses and Dissertations - UTB/UTPA

The notion of an association scheme is a generalization of the concept of a group. In fact, the so-called thin association schemes correspond in a well-understood way to groups. In this thesis, we look at the structure of non-commutative association schemes of rank 6. We will show that a non-normal closed subset of a noncommutative association scheme of rank 6, must have rank 2. The so-called Coxeter schemes of rank 6 which we present in Section 4 provide examples of association schemes of rank 6 with non-normal closed subsets of rank 2. It is shown that normal closed subsets of …

The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan

University Faculty Publications and Creative Works

When finding the nonzero eigenvalues for Hamiltonian eigenvalue problems it is especially important to locate not only the unstable eigenvalues (i.e., those with positive real part) but also those which are purely imaginary but have negative Krein signature. These latter eigenvalues have the property that they can become unstable upon collision with other purely imaginary eigenvalues; i.e., they are a necessary building block in the mechanism leading to the so-called Hamiltonian-Hopf bifurcation. In this paper we review a general theory for constructing a meromorphic matrix-valued function, the so-called Krein matrix, which has the property of not only locating the unstable …

The Krein Matrix: General Theory And Concrete Applications In Atomic Bose-Einstein Condensates, Todd Kapitula, Panayotis G. Kevrekidis, Dong Yan

University Faculty Publications and Creative Works

When finding the nonzero eigenvalues for Hamiltonian eigenvalue problems it is especially important to locate not only the unstable eigenvalues (i.e., those with positive real part) but also those which are purely imaginary but have negative Krein signature. These latter eigenvalues have the property that they can become unstable upon collision with other purely imaginary eigenvalues; i.e., they are a necessary building block in the mechanism leading to the so-called Hamiltonian-Hopf bifurcation. In this paper we review a general theory for constructing a meromorphic matrix-valued function, the so-called Krein matrix, which has the property of not only locating the unstable …

Different Types Of Backward Bifurcations Due To Density-Dependent Treatments, Baojun Song, Wen Du, Jie Lou

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A set of deterministic SIS models with density-dependent treatments are studied to understand the disease dynamics when different treatment strategies are applied. Qualitative analyses are carried out in terms of general treatment functions. It has become customary that a backward bifurcation leads to bistable dynamics. However, this study finds that finds that bistability may not be an option at all; the disease-free equilibrium could be globally stable when there is a backward bifurcation. Furthermore, when a backward bifurcation occurs, the fashion of bistability could be the coexistence of either dual stable equilibria or the disease-free equilibrium and a stable limit …

Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey

Doctoral Dissertations

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …

Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems, Ying He

Open Access Dissertations

This dissertation focuses on the development of high-order numerical methods for acoustic and electromagnetic scattering problems, and nonlinear fluid-structure interaction problems.

For the scattering problems, two cases are considered: 1) the scattering from a doubly layered periodic structure; and 2) the scattering from doubly layered, unbounded rough surface. For both cases, we first apply the transformed field expansion (TFE) method to reduce the two-dimensional Helmholtz equation with complex scattering surface into a successive sequence of the transmission problems with a plane interface. Then, we use Fourier-Spectral method in the periodic structure problem and Hermite-Spectral method in the unbounded rough surface …

An Epidemic Model Structured By The Time Since Last Infection, Jorge Alturo Alfaro Murillo

Open Access Dissertations

Epidemiological models structured by time since infection have their origin in the seminal work of 1927 by Kermack and McKendrick. Compared to ordinary differential equations (ODE) models, they are able to capture differences in infectivity of the individuals in a more suitable manner. Their use declined in the second half of the 20th century, probably because the theory for ODE models is more robust, complete and has proved successful in providing insights and predictions for many epidemiological problems. Nevertheless, it is important to understand in what occasions the inclusion of time since infection may alter the outcomes in a significant …

Why In Mayan Mathematics, Zero And Infinity Are The Same: A Possible Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In Mayan mathematics, zero is supposed to be, in some sense, equal to infinity. At first glance, while this statement may have a deep philosophical meaning, it does not seem to make much mathematical sense. In this paper, we show, that this statement may be made mathematically reasonable. Specifically, on a real line, it is often useful to consider both −∞ and +∞ as a single infinity. When we deal with very small and very large numbers, it makes sense to use floating point representation, i.e., in effect, consider logarithms of the original values. In terms of logarithms, the original …

Predicting Unobserved Exposures From Seasonal Epidemic Data, Eric Forgoston, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a low dimensional stochastic model that captures the same timing of disease outbreak and the same amplitude and phase of recurrent behavior seen in the high dimensional model. Given seasonal epidemic data consisting of the number of infectious individuals, our method enables a data-based model prediction of the number of unobserved exposed individuals over very …

Peaklet Analysis: Software For Spectrum Analysis, Bruce Kessler

Mathematics Faculty Publications

This is the presentation I was invited to give at the Kentucky Innovation and Entrepreneurship Conference, regarding the software that I have developed and worked at commercializing with the help of Kentucky Science and Technology Corporation.

On The Performance Of A Hybrid Genetic Algorithm In Dynamic Environments, Quan Yuan, Zhixin Yang

Mathematics Faculty Research Publications

The ability to track the optimum of dynamic environments is important in many practical applications. In this paper, the capability of a hybrid genetic algorithm (HGA) to track the optimum in some dynamic environments is investigated for different functional dimensions, update frequencies, and displacement strengths in different types of dynamic environments. Experimental results are reported by using the HGA and some other existing evolutionary algorithms in the literature. The results show that the HGA has better capability to track the dynamic optimum than some other existing algorithms.

Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, Mikhail Khenner

Mathematics Faculty Publications

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed …

Characterization Of The Drilling Via The Vibration Augmenter Of Rotary-Drills And Sound Signal Processing Of Impacted Pipe As A Potential Water Height Assessment Tool, Nicholas Morris

STAR Program Research Presentations

The focus of the internship has been on two topics: a) Characterize the drilling performance of a novel percussive augmenter – this drill was developed by the JPL’s Advanced Technologies Group and its performance was characterized; and b) Examine the feasibility of striking a pipe as a means of assessing the water height inside the pipe. The purpose of this investigation is to examine the possibility of using a simple method of applying impacts to a pipe wall and determining the water height from the sonic characteristic differences including damping, resonance frequencies, etc. Due to multiple variables that are relevant …

Every Scattered Space Is Subcompact, William Fleissner, Vladimir Tkachuk, Lynne Yengulalp

Mathematics Faculty Publications

We prove that every scattered space is hereditarily subcompact and any finite union of subcompact spaces is subcompact. It is a long-standing open problem whether every Čech-complete space is subcompact. Moreover, it is not even known whether the complement of every countable subset of a compact space is subcompact. We prove that this is the case for linearly ordered compact spaces as well as for ω -monolithic compact spaces. We also establish a general result for Tychonoff products of discrete spaces which implies that dense G_δ-subsets of Cantor cubes are subcompact.