# Applied Mathematics Commons™

## All Articles in Applied Mathematics

1,192 full-text articles. Page 1 of 20.

Attractors For A Neural Network Equation, 2014 Providence College

#### Attractors For A Neural Network Equation, Joseph L. Shomberg

##### Joseph L. Shomberg

Under consideration is the neural network equation $\frac{\partial v(w,t)}{\partial t} = -v(w,t) + J*(f\circ v)(w,t) + h$ posed on the bounded domain $\mathbb{S}^1$ in $L^2$. Recently it has been shown that the semigroup of solution operators corresponding to the initial value problem admits a family of global attractors that is upper-semicontinuous with respect to the kernel $J$ \cite{Silva2011}. In this paper we provide further information about the upper-semicontinuity of the global attractors; namely, we obtain explicit control over the semidistances in terms of the perturbation parameter. In addition, we ...

2013 University of Nebraska - Lincoln

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

##### Dissertations & Theses in Natural Resources

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 ...

Stabilized Finite Elements For Compressible Turbulent Navier-Stokes, 2013 University of Tennessee at Chattanooga

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

##### Theses and 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 ...

2013 University of Tennessee at Chattanooga

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

##### Theses and 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, 2013 Western Kentucky University

#### Leslie Matrices For Logistic Population Modeling, Bruce Kessler

##### Bruce Kessler

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 ...

Computation Sequences For Series And Polynomials, 2013 Western University

#### Computation Sequences For Series And Polynomials, Yiming Zhang

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

Approximation to the solutions of non-linear differential systems is very useful when the exact solutions are unattainable. Perturbation expansion replaces the system with a sequences of smaller problems, only the first of which is typically nonlinear. This works well by hand for the first few terms, but higher order computations are typically too demanding for all but the most persistent. Symbolic computation is thus attractive; however, symbolic computation of the expansions almost always encounters intermediate expression swell, by which we mean exponential growth in subexpression size or repetitions. A successful management of spatial complexity is vital to compute meaningful results ...

The Dynamical Systems Approach To Macroeconomics, 2013 McMaster University

#### The Dynamical Systems Approach To Macroeconomics, Bernardo Reis Carneiro Da Costa Lima

##### Open Access Dissertations and Theses

The aim of this thesis is to provide mathematical tools for an alternative to the mainstream study of macroeconomics with a focus on debt-driven dynamics.

We start with a survey of the literature on formalizations of Minsky's Financial Instability Hypothesis in the context of stock-flow consistent models.

We then study a family of macro-economical models that date back to the Goodwin model. In particular, we propose a stochastic extension where noise is introduced in the productivity. Besides proving existence and uniqueness of solutions, we show that orbits must loop around a specific point indefinitely.

Subsequently, we analyze the Keen ...

2013 Western University

#### Valuation Of The Peterborough Prison Social Impact Bond, Majid Hasan

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

The Peterborough Prison Bond is a social impact bond (SIB) that was issued by the UK government to reduce recidivism rate in the Peterborough prison. Most of the literature on the SIB so far has been focused on the opportunities, challenges, and the related policy issues (see (Fox), (Strickland), and (Disley)), and little effort has been made to provide a mathematical framework to determine a fair price for such instruments. Here, we aim to provide a pricing framework for the bond. We price the bond both from the issuer's and the buyer's perspective, by adjusting for the bond ...

Why In Mayan Mathematics, Zero And Infinity Are The Same: A Possible Explanation, 2013 University of Texas at El Paso

#### 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 value ...

2013 Western University

#### Sensitivity Analysis Of Minimum Variance Portfolios, Xiaohu Ji

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

The purpose of this thesis is to conduct a sensitivity analysis of the investment allocation decisions made, not within a modern portfolio theory, but within a capital asset pricing model framework. For analytic tractability, we made the simplification (of some current practical interest) that investors have the objective of minimizing the variance of their portfolios without reference to the expected returns to be obtained from these portfolios. Our analytic results reveal how the minimum variance portfolio composition, expected return and risk would change with respect to the changes of the underlying asset correlations and volatilities. We give the investors instructions ...

Peaklet Analysis: Software For Spectrum Analysis, 2013 Western Kentucky University

#### Peaklet Analysis: Software For Spectrum Analysis, Bruce Kessler

##### Bruce Kessler

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.

2013 Western University

#### Pricing And Hedging Index Options With A Dominant Constituent Stock, Helen Cheyne

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

In this paper, we examine the pricing and hedging of an index option where one constituents stock plays an overly dominant role in the index. Under a Geometric Brownian Motion assumption we compare the distribution of the relative value of the index if the dominant stock is modeled separately from the rest of the index, or not. The former is equivalent to the relative index value being distributed as the sum of two lognormal random variables and the latter is distributed as a single lognormal random variable. Since these are not equal in distribution, we compare the two models. The ...

2013 Western University

#### On Evolution Dynamics And Strategies In Some Host-Parasite Models, Liman Dai

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

In this thesis, we use mathematical models to study the problems about the evolution of hosts and parasites. Firstly, we study a within-host age-structured model with mutation and back mutation which is in the form of partial differential equations with double-infections by two strains of viruses. For the case when the production rates of viruses are gamma distributions, the PDE model can be transferred into an ODE one. Then, we analyze our model in two cases: one is without mutation, and the other is with mutation. In the first case, we prove that the two strains of viruses without mutation ...

2013 Western University

#### Topological Properties Of Modular Networks, With A Focus On Networks Of Functional Connections In The Human Brain, Estefania Ruiz Vargas

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

Complex network theory offers useful approaches to analyze the structural and functional properties of real life networks. In this work, we explore some of the mathematical concepts of network theory and study real life systems from a complex network perspective. We pay particular attention to networks of connections within the human brain. We analyze weighted networks calculated from full functional magnetic resonance imaging (fMRI) data acquired during task performance. The first novelty of this study is the fact that we retain all of the connections between all of the voxels in the full brain fMRI data. We then evaluate the ...

2013 Western University

#### Modeling Leafhopper Populations And Their Role In Transmitting Plant Diseases., Ji Ruan

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

This M.Sc. thesis focuses on the interactions between crops and leafhoppers.

Firstly, a general delay differential equations system is proposed, based on the infection age structure, to investigate disease dynamics when disease latencies are considered. To further the understanding on the subject, a specific model is then introduced. The basic reproduction numbers $\cR_0$ and $\cR_1$ are identified and their threshold properties are discussed. When $\cR_0 < 1$, the insect-free equilibrium is globally asymptotically stable. When $\cR_0 > 1$ and $\cR_1 < 1$, the disease-free equilibrium exists and is locally asymptotically stable. When $\cR_1>1$, the disease will persist.

Secondly, we derive another general delay differential equations system to examine how different life stages of leafhoppers affect crops. The basic reproduction numbers $\cR_0$ is determined ...

2013 Western University

#### Ecological Constraints And The Evolution Of Cooperative Breeding, David Mcleod

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

Cooperative breeding is a social behaviour in which certain individuals will opt to delay or forgo their own reproduction in order to help other individuals. Cooperative breeding is one of the most conspicuous examples of cooperation in nature. However, theoretical understanding of why this behaviour occurs is lacking and contradictory. In this thesis, I examine the role played by ecological constraints on the emergence of cooperative breeding. Contrary to previous results, I find that ecological constraints do matter, provided the population dynamics are properly accounted for. I also examine the long-term evolutionary dynamics of cooperative breeding, and obtain the optimal ...

On The Performance Of A Hybrid Genetic Algorithm In Dynamic Environments, 2013 Wayne State University

#### 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.

2013 Western Kentucky University

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

##### Mikhail Khenner

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 ...

2013 Bond University

2013 California Polytechnic State University

#### 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

##### STEM Teacher and Researcher (STAR) Program Posters

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 ...