# Applied Mathematics Commons™

## All Articles in Applied Mathematics

1,474 full-text articles. Page 1 of 39.

Intelligent Firefly Algorithm For Global Optimization, 2014 SelectedWorks

#### Intelligent Firefly Algorithm For Global Optimization, Seif-Eddeen K. Fateen, Adrián Bonilla-Petriciolet

##### Seif-Eddeen K Fateen

Intelligent firefly algorithm (IFA) is a novel global optimization algorithm that aims to improve the performance of the firefly algorithm (FA), whichwas inspired by the flashing communication signals among firefly swarms. This chapter introduces the IFA modification and evaluates its performance in comparison with the original algorithm in twenty multi-dimensional benchmark problems. The results of those numerical experiments show that IFA outperformed FA in terms of reliability and effectiveness in all tested benchmark problems. In some cases, the global minimum could not have been successfully identified via the firefly algorithm, except with the proposed modification for FA.

Fast Estimation Of Time-Varying Transmission Rates For Infectious Diseases, 2014 McMaster University

#### Fast Estimation Of Time-Varying Transmission Rates For Infectious Diseases, Michelle S. Dejonge

##### Open Access Dissertations and Theses

Modelling and analysis of recurrent infectious disease epidemics often depends on the reconstruction of a time-varying transmission rate from historical reports of cases or deaths. Statistically rigorous estimation methods for time-varying transmission rates exist but are too computationally demanding to apply to a time series longer than a few decades. We present a computationally ecient estimation method that is suitable for very long data sets. Our method, which uses a discrete-time approximation to the SIR model for infectious diseases, is easy to implement and outperforms the classic Fine and Clarkson estimation method.

Parameter Identification For Ordinary And Delay Differential Equations By Using Flat Inputs, 2014 SelectedWorks

#### Parameter Identification For Ordinary And Delay Differential Equations By Using Flat Inputs, René Schenkendorf, Michael Mangold

##### René Schenkendorf

The concept of differential flatness has been widely used for nonlinear controller design. In this contribution, it is shown that flatness may also be a very useful property for parameter identification. An identification method based on flat inputs is introduced. The treatment of noisy measurements and the extension of the method to delay differential equations are discussed. The method is illustrated by two case studies: the well-known FitzHugh-Nagumo equations and a virus replication model with delays.

One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, 2014 Dublin Institute of Technology

#### One-Dimensional Weakly Nonlinear Model Equations For Rossby Waves, David Henry, Rossen Ivanov

##### Articles

In this study we explore several possibilities for modelling weakly nonlinear Rossby waves in fluid of constant depth, which propagate predominantly in one direction. The model equations obtained include the BBM equation, as well as the integrable KdV and Degasperis-Procesi equations.

Boundary Value Problems Of Nabla Fractional Difference Equations, 2014 University of Nebraska - Lincoln

#### Boundary Value Problems Of Nabla Fractional Difference Equations, Abigail M. Brackins

##### Dissertations, Theses, and Student Research Papers in Mathematics

In this dissertation we develop the theory of the nabla fractional self-adjoint difference equation,

aν(p∇y)(t)+q(t)y(ρ(t)) = f(t),

where 0 < ν < 1.We begin with an introduction to the nabla fractional calculus. In the second chapter, we show existence and uniqueness of the solution to a fractional self-adjoint initial value problem. We find a variation of constants formula for this fractional initial value problem, and use the variation of constants formula to derive the Green's function for a related boundary value problem. We study the Green's function and its properties in several settings. For a simplified boundary value problem, we show that the Green's function is nonnegative and we find its maximum and the maximum of its integral. For a boundary value problem with generalized boundary conditions, we find the Green's function and show that it is a generalization of the first Green's function. In the third chapter, we use the Contraction Mapping Theorem to prove existence and uniqueness of a positive solution to a forced self-adjoint fractional difference equation with a finite limit. We explore modifications to the forcing term and modifications to the space of functions in which the solution exists, and we provide examples to demonstrate the use of these theorems.

Advisers: Lynn Erbe and Allan Peterson

2014 University of Nebraska - Lincoln

#### The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs

##### Dissertations, Theses, and Student Research Papers in Mathematics

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects that encode ...

Options Pricing And Hedging In A Regime-Switching Volatility Model, 2014 Western University

#### Options Pricing And Hedging In A Regime-Switching Volatility Model, Melissa A. Mielkie

##### University of Western Ontario - Electronic Thesis and Dissertation Repository

Both deterministic and stochastic volatility models have been used to price and hedge options. Observation of real market data suggests that volatility, while stochastic, is well modelled as alternating between two states. Under this two-state regime-switching framework, we derive coupled pricing partial differential equations (PDEs) with the inclusion of a state-dependent market price of volatility risk (MPVR) term.

Since there is no closed-form solution for this pricing problem, we apply and compare two approaches to solving the coupled PDEs, assuming constant Poisson intensities. First we solve the problem using numerical solution techniques, through the application of the Crank-Nicolson numerical scheme ...

2014 University of North Florida

#### What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, John Tabak

##### Journal of Interpretation

Courses and seminars in higher mathematics are some of the most challenging assignments faced by academic interpreters. Difficulties interpreting higher mathematics can adversely impact the academic and professional aspirations of deaf mathematics students and professionals. This paper discusses the nature of higher mathematics with the goal of identifying what distinguishes higher mathematics from other subjects; it then reviews the history of attempts to sign/interpret higher mathematics with particular attention to current challenges associated with expressing higher mathematics in sign. The final part of the paper discusses strategies for more effectively expressing higher mathematics in American Sign Language.

Mathematically Modeling Fetal Electrocardiograms, 2014 University of Tennessee, Knoxville

#### Mathematically Modeling Fetal Electrocardiograms, Samuel Estes, Kiersten Utsey, Erick Kalobwe

##### Pursuit - The Journal of Undergraduate Research at the University of Tennessee

Abstract

Some of the most common and fatal birth defects are those related to the heart. In adults, possible heart conditions are often identified through the use of an electrocardiogram (ECG). However, due to the presence of other signals and noise in the recording, fetal eletrocardiography has not yet proven effective in diagnosing these defects. This paper develops a mathematical model of three-dimensional heart vector trajectories, which was used to generate synthetic maternal and fetal ECG signals. The dipole model is a useful simplification in which the electrical activity of the heart is viewed as a single time-varying vector originating ...

Study Of Nonlinear Vibration Of Euler-Bernoulli Beams By Using Analytical Approximate Techniques, 2014 SelectedWorks

#### Study Of Nonlinear Vibration Of Euler-Bernoulli Beams By Using Analytical Approximate Techniques, Saman Bagheri, Ali Nikkar

##### Ali Nikkar

In this paper, nonlinear responses of a clamped-clamped buckled beam are investigated. Two efficient and easy mathematical techniques called He’s Variational Approach and Laplace Iteration Method are used to solve the governing differential equation of motion. To assess the accuracy of solutions, we compare the results with the Runge-Kutta 4th order. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.

2014 Western Oregon University

#### Full Issue

##### PURE Insights

No abstract provided.

Predicting The Cy Young Award Winner, 2014 Western Oregon University

#### Predicting The Cy Young Award Winner, Stephen Ockerman, Matthew Nabity

##### PURE Insights

Here we examine the application of a decision model to predicting the winner of the Cy Young Award. We investigate a current model cast as a linear programming problem and explore its ability to correctly predict award winners for recent seasons of professional baseball. We suggest the addition of another baseball statistic which leads to a new model. We explore the success of both models with numerical experiments and discuss the results.

2014 University of Nebraska - Lincoln

#### An Applied Functional And Numerical Analysis Of A 3-D Fluid-Structure Interactive Pde, Thomas J. Clark

We will present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. In Chapter \ref{ChWellposedness}, the wellposedness of this PDE model is established by means of constructing for it a nonstandard semigroup generator representation; this representation is essentially accomplished by an appropriate elimination of the pressure. This coupled PDE model involves the Stokes system which evolves on a three dimensional domain $\mathcal{O}$ being coupled to a fourth order plate equation, possibly with rotational inertia parameter $\rho >0$, which evolves on a flat portion $\Omega$ of the boundary of $\mathcal{O ... Birkhoff Theorems In General Relativity, 2014 Utah State University #### Birkhoff Theorems In General Relativity, Charles G. Torre ##### Charles G. Torre In the following Maple worksheet I demonstrate three versions of Birkhoff's theorem, which is a characterization of spherically symmetric solutions of the Einstein equations. The three versions considered here correspond to taking the "Einstein equations" to be: (1) the vacuum Einstein equations; (2) the Einstein equations with a cosmological constant (3) the Einstein-Maxwell equations. 2014 Western Kentucky University #### Green's Functions Of Discrete Fractional Calculus Boundary Value Problems And An Application Of Discrete Fractional Calculus To A Pharmacokinetic Model, Sutthirut Charoenphon ##### Masters Theses & Specialist Projects Fractional calculus has been used as a research tool in the fields of pharmacology, biology, chemistry, and other areas [3]. The main purpose of this thesis is to calculate Green's functions of fractional difference equations, and to model problems in pharmacokinetics. We claim that the discrete fractional calculus yields the best prediction performance compared to the continuous fractional calculus in the application of a one-compartmental model of drug concentration. In Chapter 1, the Gamma function and its properties are discussed to establish a theoretical basis. Additionally, the basics of discrete fractional calculus are discussed using particular examples for further ... On Mikhailov's Reduction Group, 2014 Dublin Institute of Technology #### On Mikhailov's Reduction Group, Tihomir I. Valchev ##### Articles We present a generalization of the notion of reduction group which allows one to study in a uniform way certain classes of nonlocal$S\$-integrable equations like Ablowitz-Musslimani's nonlocal Schr\"odinger equation. Another aspect of the proposed generalization is the possibility to derive in a systematic way solutions to S-integrable equations with prescribed symmetries.

2014 Western Kentucky University

#### Analysis Of A Partial Differential Equation Model Of Surface Electromigration, Selahittin Cinar

##### Masters Theses & Specialist Projects

A Partial Differential Equation (PDE) based model combining surface electromigration and wetting is developed for the analysis of the morphological instability of mono-crystalline metal films in a high temperature environment typical to operational conditions of microelectronic interconnects. The atomic mobility and surface energy of such films are anisotropic, and the model accounts for these material properties. The goal of modeling is to describe and understand the time-evolution of the shape of film surface. I will present the formulation of a nonlinear parabolic PDE problem for the height function h(x,t) of the film in the horizontal electric field, followed ...

A Numerical Model For Nonadiabatic Transitions In Molecules, 2014 East Tennessee State University

#### A Numerical Model For Nonadiabatic Transitions In Molecules, Devanshu Agrawal

In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans ...

Modeling Feral Cat Population Dynamics In Knox County, Tn, 2014 University of Tennessee, Knoxville

#### Modeling Feral Cat Population Dynamics In Knox County, Tn, Lindsay E. Lee, Nick Robl, Alice M. Bugman, An T.N. Nguyen, Bridgid Lammers, Teresa L. Fisher, Heidi Weimer, Suzanne Lenhart, John C. New Jr.

##### University of Tennessee Honors Thesis Projects

No abstract provided.

Spatial Scheduling Algorithms For Production Planning Problems, 2014 Virginia Commonwealth University

#### Spatial Scheduling Algorithms For Production Planning Problems, Sudharshana Srinivasan

##### Theses and Dissertations

Spatial resource allocation is an important consideration in shipbuilding and large-scale manufacturing industries. Spatial scheduling problems (SSP) involve the non-overlapping arrangement of jobs within a limited physical workspace such that some scheduling objective is optimized. Since jobs are heavy and occupy large areas, they cannot be moved once set up, requiring that the same contiguous units of space be assigned throughout the duration of their processing time. This adds an additional level of complexity to the general scheduling problem, due to which solving large instances of the problem becomes computationally intractable. The aim of this study is to gain a ...