Applied Mathematics | Open Access Articles | Digital Commons Network™

Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the stability of multiwavelet frames with different matrix dilations and matrix translations by means of operator theory and show that these frames remain stable over some kinds of perturbations of the basic generators.

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A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam

Applications and Applied Mathematics: An International Journal (AAM)

First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing over fitting of data by model. Demonstration shows that the proposed unified frame work can work well for both noise removal and overfitting prevention in subdivision as well as regularization.

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An Ε -Uniform Numerical Method For A System Of Convection-Diffusion Equations With Discontinuous Convection Coefficients And Source Terms, T. Valanarasu, R. M. Priyadharshini, N. Ramanujam, A. Tamilselvan

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a parameter-uniform numerical method is suggested to solve a system of singularly perturbed convection-diffusion equations with discontinuous convection coefficients and source terms subject to the Dirichlet boundary condition. The second derivative of each equation is multiplied by a distinctly small parameter, which leads to an overlap and interacting interior layer. A numerical method based on a piecewise uniform Shishkin mesh is constructed. Numerical results are presented to support the theoretical results.

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Solving Singularly Perturbed Differential Difference Equations Via Fitted Method, Awoke Andargie, Y. N. Reddy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we presented a fitted approach to solve singularly perturbed differential difference equations of second order with boundary at one end (left or right) of the interval. In this approach, with the help of Taylor series expansion, we approximated the terms containing negative and positive shifts and modified the singularly perturbed differential difference equation to singularly perturbed differential equation. A fitting parameter in the coefficient of the highest order derivative of the new equation is introduced and determined its value from the theory of singular perturbation. Finally, we obtained a three term recurrence relation which is solved using …

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Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part I – Problem Investigation, P. Y. C. Lee, W. H. Leong

Applications and Applied Mathematics: An International Journal (AAM)

Designing an experimental apparatus requires considerable amount of planning. Despite proper planning, one can easily overlook a design such as the standard uniform temperature boundary condition applied to all or portion of a wall of an experimental apparatus. Although this boundary condition is mathematically simple and precise, achieving it physically may not be that simple. This paper addresses one such three-dimensional natural convection heat transfer apparatus that was designed to measure benchmark Nusselt numbers at various Rayleigh numbers with uniform temperatures specified at two walls of the enclosure. It was found that the effect of thermal spreading/constriction resistance on one …

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Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we define a new finite element method for numerically approximating solutions of elliptic partial differential equations defined on “arbitrary” smooth surfaces S in RN+1. By “arbitrary” smooth surfaces, we mean surfaces that can be implicitly represented as level sets of smooth functions. The key idea is to first approximate the surface S by a polyhedral surface Sh, which is a union of planar triangles whose vertices lie on S; then to project Sh onto S. With this method, we can also approximate the eigenvalues and eigenfunctions of th Laplace-Beltrami operator on these “arbitrary” surfaces.

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Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part Ii – Problem Solution, P. Y. C. Lee, W. H. Leong

Applications and Applied Mathematics: An International Journal (AAM)

Temperature measurements along one side of the rectangular plate showed severe temperature non-uniformity along one side of a wall of a cubical experimental apparatus where the uniform temperature was physically desired. Despite proper planning and analyses, this non-uniformity was high enough that a benchmark study could not be carried out to the desired accuracy of about one percent error. This paper presents and extends analyses made previously based on the modifications to the original design of the apparatus to reduce the temperature non-uniformity on the wall by adding an auxiliary heater around a wall where the uniform temperature was desired. …

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A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new method based on the generalized Purcell method is proposed to solve the usual least-squares problem arising in the GMRES method. The theoretical aspects and computational results of the method are provided. For the popular iterative method GMRES, the decomposition matrices of the Hessenberg matrix is obtained by using a simple recursive relation instead of Givens rotations. The other advantages of the proposed method are low computational cost and no need for orthogonal decomposition of the Hessenberg matrix or pivoting. The comparisons for ill-conditioned sparse standard matrices are made. They show a good agreement with available …

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Numerical Solution Of Some Nonlinear Volterra Integral Equations Of The First Kind, Leila Saeedi, Abolfazl Tari, Sayyed H. Momeni Masuleh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the solving of a class of the nonlinear Volterra integral equations (NVIE) of the first kind is investigated. Here, we convert NVIE of the first kind to a linear equation of the second kind. Then we apply the operational Tau method to the problem and prove convergence of the presented method. Finally, some numerical examples are given to show the accuracy of the method.

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Solutions Of System Of Fractional Partial Differential Equations, V. Parthiban, K. Balachandran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, system of fractional partial differential equation which has numerous applications in many fields of science is considered. Adomian decomposition method, a novel method is used to solve these type of equations. The solutions are derived in convergent series form which shows the effectiveness of the method for solving wide variety of fractional differential equations.

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Discovering Exoplanets Through Hidden Markov Model Analysis, Jon Drobny

Rose-Hulman Undergraduate Research Publications

The goal for the project is to develop a Hidden Markov Model for the detection and characterization of extrasolar planets through the analysis of light curves.

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Introduction (2013), Eric Gossett

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

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Paper Abstracts (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

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Singular Ergodic Control For Multidimensional Gaussian-Poisson Processes, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

Singular control for multidimensional Gaussian-Poisson processes with a long-run (or ergodic) and a discounted criteria are discussed. The dynamic programming yields the corresponding Hamilton-Jacobi-Bellman equations, which are discussed. Full details on the proofs and further extensions are left for coming works.

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Schedule (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

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Table Of Contents (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

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19th Conference Of The Associations Of Christians In The Mathematical Sciences, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Association of Christians in the Mathematical Sciences 19th Biennial Conference Proceedings, May 29 - June 1, 2011, Bethel University.

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The Neural Ring: An Algebraic Tool For Analyzing The Intrinsic Structure Of Neural Codes, Carina Curto, Vladimir Itskov, Alan Veliz-Cuba, Nora Youngs

Department of Mathematics: Faculty Publications

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stereotyped 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, …

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Eradicating Malaria: Improving A Multiple-Timestep Optimization Model Of Malarial Intervention Policy, Taryn M. Ohashi

Scripps Senior Theses

Malaria is a preventable and treatable blood-borne disease whose complications can be fatal. Although many interventions exist in order to reduce the impacts of malaria, the optimal method of distributing these interventions in a geographical area with limited resources must be determined. This thesis refines a model that uses an integer linear program and a compartmental model of epidemiology called an SIR model of ordinary differential equations. The objective of the model is to find an intervention strategy over multiple time steps and multiple geographic regions that minimizes the number of days people spend infected with malaria. In this paper, …

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Stress Analysis Of Ramberg-Osgood And Hollomon 1-D Axial Rods, Ronald J. Giardina Jr

LSU New Orleans Theses and Dissertations

In this paper we present novel analytic and finite element solutions to 1-D straight rods made of Ramberg-Osgood and Hollomon type materials. These material models are studied because they are a more accurate representation of the material properties of certain metals used often in manufacturing than the simpler composite linear types of stress/strain models. Here, various types of loads are considered and solutions are compared against some linear models. It is shown that the nonlinear models do have manageable solutions, which produce important differences in the results - attributes which suggest that these models should take a more prominent place …

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Peak-End Rule: A Utility-Based Explanation, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, people judge their overall experience by only taking into account the peak and the last levels of pleasantness or unpleasantness. While this peak-end rule is empirically supported by numerous psychological experiments, it seems to contradict our general theoretical ideas about people's preferences. In this paper, we show that, contrary to this impression, the end-peak rule can be justified based on the main ideas of the traditional utility-based decision theory.

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Analyzing And Solving Non-Linear Stochastic Dynamic Models On Non-Periodic Discrete Time Domains, Gang Cheng

Masters Theses & Specialist Projects

Stochastic dynamic programming is a recursive method for solving sequential or multistage decision problems. It helps economists and mathematicians construct and solve a huge variety of sequential decision making problems in stochastic cases. Research on stochastic dynamic programming is important and meaningful because stochastic dynamic programming reflects the behavior of the decision maker without risk aversion; i.e., decision making under uncertainty. In the solution process, it is extremely difficult to represent the existing or future state precisely since uncertainty is a state of having limited knowledge. Indeed, compared to the deterministic case, which is decision making under certainty, the stochastic …

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Floquet Theory On Banach Space, Fatimah Hassan Albasrawi

Masters Theses & Specialist Projects

In this thesis we study Floquet theory on a Banach space. We are concerned about the linear differential equation of the form: y'(t) = A(t)y(t), where t ∈ R, y(t) is a function with values in a Banach space X, and A(t) are linear, bounded operators on X. If the system is periodic, meaning A(t+ω) = A(t) for some period ω, then it is called a Floquet system. We will investigate the existence …

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Minimizing Travel Time Through Multiple Media With Various Borders, Tonja Miick

Masters Theses & Specialist Projects

This thesis consists of two main chapters along with an introduction and
conclusion. In the introduction, we address the inspiration for the thesis, which
originates in a common calculus problem wherein travel time is minimized across two media separated by a single, straight boundary line. We then discuss the correlation of this problem with physics via Snells Law. The first core chapter takes this idea and develops it to include the concept of two media with a circular border. To make the problem easier to discuss, we talk about it in terms of running and swimming speeds. We first address …

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Cooking Up The Optimal Baking Algorithm, Tony Burand, Michael Tetzlaff, Jacob Smith

Math and Computer Science Student Works

Many conventional rectangular baking pans have a problem in that they bake the corners of the batter faster than the rest of the pan. Circular baking pans eliminate this problem, but take up more space in the oven. We propose a solution that given weights for baking consistency and space efficiency based on the importance of each will provide the optimal baking pan shape. We have come up with an algorithm for sorting the pans of area A effectively and formed a model that describes the heat flow into the pan as well as the baking mix itself. The model …

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Analysis Of Time-Dependent Integrodifference Population Models, Taylor J. Mcadam

HMC Senior Theses

The population dynamics of species with separate growth and dispersal stages can be described by a discrete-time, continuous-space integrodifference equation relating the population density at one time step to an integral expression involving the density at the previous time step. Prior research on this model has assumed that the equation governing the population dynamics remains fixed over time, however real environments are constantly in flux. We show that for time-varying models, there is a value Λ that can be computed to determine a sufficient condition for population survival. We also develop a framework for analyzing persistence of a population for …

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Structured Matrices And The Algebra Of Displacement Operators, Ryan Takahashi

HMC Senior Theses

Matrix calculations underlie countless problems in science, mathematics, and engineering. When the involved matrices are highly structured, displacement operators can be used to accelerate fundamental operations such as matrix-vector multiplication. In this thesis, we provide an introduction to the theory of displacement operators and study the interplay between displacement and natural matrix constructions involving direct sums, Kronecker products, and blocking. We also investigate the algebraic behavior of displacement operators, developing results about invertibility and kernels.

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A Comparison And Catalog Of Intrinsic Tumor Growth Models, Elizabeth A. Sarapata

HMC Senior Theses

Determining the dynamics and parameter values that drive tumor growth is of great interest to mathematical modelers, experimentalists and practitioners alike. We provide a basis on which to estimate the growth dynamics of ten different tumors by fitting growth parameters to at least five sets of published experimental data per type of tumor. These timescale tumor growth data are also used to determine which of the most common tumor growth models (exponential, power law, logistic, Gompertz, or von Bertalanffy) provides the best fit for each type of tumor. In order to compute the best-fit parameters, we implemented a hybrid local-global …

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Secret Sharing And Network Coding, Fiona Knoll

All Theses

In this thesis, we consider secret sharing schemes and network coding. Both of these fields are vital in today's age as secret sharing schemes are currently being implemented by government agencies and private companies, and as network coding is continuously being used for IP networks. We begin with a brief overview of linear codes. Next, we examine van Dijk's approach to realize an access structure using a linear secret sharing scheme; then we focus on a much simpler approach by Tang, Gao, and Chen. We show how this method can be used to find an optimal linear secret sharing scheme …

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Editor's Statement, Abby Stocker, Leah Patton, Brad Cox, Jacob Manning, Roberta Fultz, Jared Hedges, Stacie Lewis

Colloquy Undergraduate Research Journal

No abstract provided.

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Full-Text Articles in Applied Mathematics

Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal

Applications and Applied Mathematics: An International Journal (AAM)

A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam

Applications and Applied Mathematics: An International Journal (AAM)

An Ε -Uniform Numerical Method For A System Of Convection-Diffusion Equations With Discontinuous Convection Coefficients And Source Terms, T. Valanarasu, R. M. Priyadharshini, N. Ramanujam, A. Tamilselvan

Applications and Applied Mathematics: An International Journal (AAM)

Solving Singularly Perturbed Differential Difference Equations Via Fitted Method, Awoke Andargie, Y. N. Reddy

Applications and Applied Mathematics: An International Journal (AAM)

Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part I – Problem Investigation, P. Y. C. Lee, W. H. Leong

Applications and Applied Mathematics: An International Journal (AAM)

Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer

Applications and Applied Mathematics: An International Journal (AAM)

Physically-Realizable Uniform Temperature Boundary Condition Specification On A Wall Of An Enclosure: Part Ii – Problem Solution, P. Y. C. Lee, W. H. Leong

Applications and Applied Mathematics: An International Journal (AAM)

A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh

Applications and Applied Mathematics: An International Journal (AAM)

Numerical Solution Of Some Nonlinear Volterra Integral Equations Of The First Kind, Leila Saeedi, Abolfazl Tari, Sayyed H. Momeni Masuleh

Applications and Applied Mathematics: An International Journal (AAM)

Solutions Of System Of Fractional Partial Differential Equations, V. Parthiban, K. Balachandran

Applications and Applied Mathematics: An International Journal (AAM)

Discovering Exoplanets Through Hidden Markov Model Analysis, Jon Drobny

Rose-Hulman Undergraduate Research Publications

Introduction (2013), Eric Gossett

ACMS Conference Proceedings 2013

Paper Abstracts (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Singular Ergodic Control For Multidimensional Gaussian-Poisson Processes, J. L. Menaldi, M. Robin

Mathematics Faculty Research Publications

Schedule (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Table Of Contents (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

19th Conference Of The Associations Of Christians In The Mathematical Sciences, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

The Neural Ring: An Algebraic Tool For Analyzing The Intrinsic Structure Of Neural Codes, Carina Curto, Vladimir Itskov, Alan Veliz-Cuba, Nora Youngs

Department of Mathematics: Faculty Publications

Eradicating Malaria: Improving A Multiple-Timestep Optimization Model Of Malarial Intervention Policy, Taryn M. Ohashi

Scripps Senior Theses

Stress Analysis Of Ramberg-Osgood And Hollomon 1-D Axial Rods, Ronald J. Giardina Jr

LSU New Orleans Theses and Dissertations

Peak-End Rule: A Utility-Based Explanation, Olga Kosheleva, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Analyzing And Solving Non-Linear Stochastic Dynamic Models On Non-Periodic Discrete Time Domains, Gang Cheng

Masters Theses & Specialist Projects

Floquet Theory On Banach Space, Fatimah Hassan Albasrawi

Masters Theses & Specialist Projects

Minimizing Travel Time Through Multiple Media With Various Borders, Tonja Miick

Masters Theses & Specialist Projects

Cooking Up The Optimal Baking Algorithm, Tony Burand, Michael Tetzlaff, Jacob Smith

Math and Computer Science Student Works

Analysis Of Time-Dependent Integrodifference Population Models, Taylor J. Mcadam

HMC Senior Theses

Structured Matrices And The Algebra Of Displacement Operators, Ryan Takahashi

HMC Senior Theses

A Comparison And Catalog Of Intrinsic Tumor Growth Models, Elizabeth A. Sarapata

HMC Senior Theses

Secret Sharing And Network Coding, Fiona Knoll

All Theses

Editor's Statement, Abby Stocker, Leah Patton, Brad Cox, Jacob Manning, Roberta Fultz, Jared Hedges, Stacie Lewis

Colloquy Undergraduate Research Journal