Applied Mathematics Commons^™

Differential Transform Method For Solving The Two-Dimensional Fredholm Integral Equations, F. Ziyaee, A. Tari

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we develop the Differential Transform (DT) method in a new scheme to solve the two-dimensional Fredholm integral equations (2D-FIEs) of the second kind. The differential transform method is a procedure to obtain the coefficients of the Taylor expansion of the solution of differential and integral equations. So, one can obtain the Taylor expansion of the solution of arbitrary order and hence the solution of the given equation can be obtained with required accuracy. Here, we first give some basic definitions and properties about DT from references, and then we prove some theorems to extend the DT method …

Dynamics Of An Sir Model With Nonlinear Incidence And Treatment Rate, Balram Dubey, Preeti Dubey, Uma S. Dubey

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, global dynamics of an SIR model are investigated in which the incidence rate is being considered as Beddington-DeAngelis type and the treatment rate as Holling type II (saturated). Analytical study of the model shows that the model has two equilibrium points (diseasefree equilibrium (DFE) and endemic equilibrium (EE)). The disease-free equilibrium (DFE) is locally asymptotically stable when reproduction number is less than one. Some conditions on the model parameters are obtained to show the existence as well as nonexistence of limit cycle. Some sufficient conditions for global stability of the endemic equilibrium using Lyapunov function are obtained. …

Laminar Boundary Layer Flow Of Sisko Fluid, Manisha Patel, Jayshri Patel, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

The problem of steady two dimensional laminar boundary layer flow of non-Newtonian fluid is analyzed in the present paper. Sisko fluid model, one of the various fluid models of non- Newtonian fluid, is considered for stress-strain relationship. Similarity and numerical solutions obtained for the defined flow problem.

Algorithm For Solving Tri-Diagonal Finite Volume Discretized Linear Systems, J. S. V. R. Krishna Prasad, Parag V. Patil

Applications and Applied Mathematics: An International Journal (AAM)

In this paper we present efficient computational algorithms for solving finite volume discretized tri-diagonal linear systems. The implementation of the algorithm for steady state finite volume structured grids linear system using MS Excel is presented. An example is given in order to illustrate the algorithms.

Computational Analysis Of The Sir Mathematical Model For The Dengue Fever, Joseph Phillip Diaz

Theses and Dissertations

Dengue fever is a disease affecting people in more than 100 countries. Here we consider a host and vector model for the transmission of dengue fever. This SIR model consists of three compartments of susceptible, infective and removed for host (human) and two compartments of susceptible and infective for vector (dengue mosquitos). These five compartments yield five coupled nonlinear ordinary differential equations (ODEs). After non-dimensionalization, we have a system of three nonlinear ODEs. Reproductive number and two equilibrium points are calculated for various cases. Simulation is carried out for susceptible, infective and removed and the results are presented in graphical …

Analysis Of Neuronal Sequences Using Pairwise Biases, Zachary Roth

Department of Mathematics: Dissertations, Theses, and Student Research

Sequences of neuronal activation have long been implicated in a variety of brain functions. In particular, these sequences have been tied to memory formation and spatial navigation in the hippocampus, a region of mammalian brains. Traditionally, neuronal sequences have been interpreted as noisy manifestations of neuronal templates (i.e., orderings), ignoring much richer structure contained in the sequences. This paper introduces a new tool for understanding neuronal sequences: the bias matrix. The bias matrix captures the probabilistic tendency of each neuron to fire before or after each other neuron. Despite considering only pairs of neurons, the bias matrix captures the best …

Applications Of Incomplete Gamma Functions To The Incomplete Normal Distribution, Eric S. Watson

Physics & Astronomy Faculty publications

This paper gives a derivation of a relationship that can be used to estimate the area under a Normal Distribution through the use of Incomplete Gamma Functions.

A Physiologically-Based Pharmacokinetic Model For Vancomycin, Rebekah White

Undergraduate Honors Theses

Vancomycin is an antibiotic used for the treatment of systemic infections. It is given

intravenously usually every twelve or twenty-four hours. This particular drug has a

medium level of boundedness, with approximately fty percent of the drug being free

and thus physiologically eective. A physiologically-based pharmacokinetic (PBPK)

model was used to better understand the absorption, distribution, and elimination of

the drug. Using optimal parameters, the model could be used in the future to test

how various factors, such as BMI or excretion levels, might aect the concentration

of the antibiotic.

Spreading Speeds And Traveling Waves In Some Population Models., Quancheng Meng

Electronic Theses and Dissertations

Virtually every ecosystem has been invaded by exotic organisms with potentially drastic consequences for the native fauna or flora. Studying the forms and rates of invading species has been an important topic in spatial ecology. We investigate two two-species competition models with Allee effects in the forms of reaction-diffusion equations and integro-difference equations. We discuss the spatial transitions from a mono-culture equilibrium to a coexistence equilibrium or a different mono-culture equilibrium in these models. We provide formulas for the spreading speeds based on the linear determinacy and show the results on the existence of traveling waves. We also study a …

An Economic Regression Model To Predict Market Movements, Timothy A. Smith, Andrew Hawkins

Publications

In finance, multiple linear regression models are frequently used to determine the value of an asset based on its underlying traits. We built a regression model to predict the value of the S&P 500 based on economic indicators of gross domestic product, money supply, produce price and consumer price indices. Correlation between the error in this regression model and the S&P’s volatility index (VIX) provides an efficient way to predict when large changes in the price of the S&P 500 may occur. As the true value of the S&P 500 deviates from the predicted value, obtained by the regression model, …

On The Relationship Between Two Notions Of Compatibility For Bi-Hamiltonian Systems, Manuele Santoprete

Mathematics Faculty Publications

Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of compatibility due to Fass`o and Ratiu, that we dub bi-affine compatibility. We present two proofs of this fact. The first one uses the uniqueness of the connection parallelizing all the Hamiltonian vector fields tangent to the leaves of a Lagrangian foliation. …

Stochastic Models For Plant Microtubule Self-Organization And Structure, Ezgi Can Eren, Ram Dixit, Natarajan Gautam

Biology Faculty Research

One of the key enablers of shape and growth in plant cells is the cortical microtubule (CMT) system, which is a polymer array that forms an appropriately-structured scaffolding in each cell. Plant biologists have shown that stochastic dynamics and simple rules of interactions between CMTs can lead to a coaligned CMT array structure. However, the mechanisms and conditions that cause CMT arrays to become organized are not well understood. It is prohibitively time-consuming to use actual plants to study the effect of various genetic mutations and environmental conditions on CMT self-organization. In fact, even computer simulations with multiple replications are …

Existence Of Homoclinic Solutions For Second Order Difference Equations With P-Laplacian, John R. Graef, Lingju Kong, Min Wang

College of Science & Mathematics Departmental Research

Using the variational method and critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation described in the paper.

Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen

SIUE Faculty Research, Scholarship, and Creative Activity

We give a number of explicit matrix-algorithms for analysis/synthesis

in multi-phase filtering; i.e., the operation on discrete-time signals which

allow a separation into frequency-band components, one for each of the

ranges of bands, say N , starting with low-pass, and then corresponding

filtering in the other band-ranges. If there are N bands, the individual

filters will be combined into a single matrix action; so a representation of

the combined operation on all N bands by an N x N matrix, where the

corresponding matrix-entries are periodic functions; or their extensions to

functions of a complex variable. Hence our setting entails …

From Subcompact To Domain Representable, William Fleissner, Lynne Yengulalp

Mathematics Faculty Publications

No abstract provided.

Partial Covariance Based Functional Connectivity Computation Using Ledoit-Wolf Covariance Regularization, Matthew R. Brier, Anish Mitra, John E. Mccarthy, Beau M. Ances, Abraham Z. Snyder

Mathematics Faculty Research

Highlights •We use the well characterized matrix regularization technique described by Ledoit and Wolf to calculate high dimensional partial correlations in fMRI data. •Using this approach we demonstrate that partial correlations reveal RSN structure suggesting that RSNs are defined by widely and uniquely shared variance. •Partial correlation functional connectivity is sensitive to changes in brain state indicating that they contain functional information. Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a …

Local And Distributed Pib Accumulation Associated With Development Of Preclinical Alzheimer's Disease, Matthew R. Brier, John E. Mccarthy, Tammie L.S. Benzinger, Ari Stern, Yi Su, Karl A. Friedrichsen, John C. Morris, Beau M. Ances, Andrei G. Vlassenko

Mathematics Faculty Research

Amyloid-beta plaques are a hallmark of Alzheimer's disease (AD) that can be assessed by amyloid imaging (e.g., Pittsburgh B compound [PiB]) and summarized as a scalar value. Summary values may have clinical utility but are an average over many regions of interest, potentially obscuring important topography. This study investigates the longitudinal evolution of amyloid topographies in cognitively normal older adults who had normal (N = 131) or abnormal (N = 26) PiB scans at baseline. At 3 years follow-up, 16 participants with a previously normal PiB scan had conversion to PiB scans consistent with preclinical AD. We investigated the multivariate …

Algebraic Complexity Theory, Jerzy Weyman

Dalrymple Lecture Series

I will discuss the basic notions related to the complexity theory. The classes of P and NP problems will be defined, with examples given. Besides discussing the statements of the problems, I will talk about the effectiveness of algorithms used in linear algebra (multiplying matrices and solving the systems of linear equations). No previous knowledge of complexity theory will be assumed, however some knowledge of linear algebra (matrices and their multiplication) will be needed.

A Nonlinear Splitting Algorithm For Systems Of Partial Differential Equations With Self-Diffusion, Matthew Beauregard, Joshua L. Padgett, Rana D. Parshad

Faculty Publications

Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular, self-diffusion is a nonlinear term that models overcrowding of a particular species. The nonlinearity complicates attempts to construct efficient and accurate numerical approximations of the underlying systems of equations. In this paper, a new nonlinear splitting algorithm is designed for a partial differential equation that incorporates self diffusion. We present a general model that incorporates self-diffusion and develop a numerical approximation. The numerical analysis of the approximation provides criteria for …

Geometric Approach To Convex Subdifferential Calculus, Boris S. Mordukhovich, Nguyen Mau Nam

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic results of convex subdifferential calculus in full generality and also derive new results of convex analysis concerning optimal value/marginal functions, normals to inverse images of sets under set-valued mappings, calculus rules for coderivatives of single-valued and set-valued mappings, and calculating coderivatives of solution maps to parameterized generalized equations governed by set-valued mappings with convex graphs.