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Physical Sciences and Mathematics Commons™

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East Tennessee State University

2014

Mathematics

Articles 1 - 9 of 9

Full-Text Articles in Physical Sciences and Mathematics

Mathematical Modeling Of Immune Responses To Hepatitis C Virus Infection, Ivan Ramirez Dec 2014

Mathematical Modeling Of Immune Responses To Hepatitis C Virus Infection, Ivan Ramirez

Electronic Theses and Dissertations

An existing mathematical model of ordinary differential equations was studied to better understand the interactions between hepatitis C virus (HCV) and the immune system cells in the human body. Three possible qualitative scenarios were explored: dominant CTL response, dominant antibody response, and coexistence. Additionally, a sensitivity analysis was carried out to rank model parameters for each of these scenarios. Therapy was addressed as an optimal control problem. Numerical solutions of optimal controls were computed using a forward-backward sweep scheme for each scenario. Model parameters were estimated using ordinary least squares fitting from longitudinal data (serum HCV RNA measurements) given in …

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Properties Of Small Ordered Graphs Whose Vertices Are Weighted By Their Degree, Constance M. Blalock Aug 2014

Properties Of Small Ordered Graphs Whose Vertices Are Weighted By Their Degree, Constance M. Blalock

Electronic Theses and Dissertations

Graphs can effectively model biomolecules, computer systems, and other applications. A weighted graph is a graph in which values or labels are assigned to the edges of the graph. However, in this thesis, we assign values to the vertices of the graph rather than the edges and we modify several standard graphical measures to incorporate these vertex weights. In particular, we designate the degree of each vertex as its weight. Previous research has not investigated weighting vertices by degree. We find the vertex weighted domination number in connected graphs, beginning with trees, and we define how weighted vertices can affect …

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Bipartitions Based On Degree Constraints, Pamela I. Delgado Aug 2014

Bipartitions Based On Degree Constraints, Pamela I. Delgado

Electronic Theses and Dissertations

For a graph G = (V,E), we consider a bipartition {V1,V2} of the vertex set V by placing constraints on the vertices as follows. For every vertex v in Vi, we place a constraint on the number of neighbors v has in Vi and a constraint on the number of neighbors it has in V3-i. Using three values, namely 0 (no neighbors are allowed), 1 (at least one neighbor is required), and X (any number of neighbors are allowed) for each of the four constraints, results in 27 distinct types of …

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Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus May 2014

Permutation Groups And Puzzle Tile Configurations Of Instant Insanity Ii, Amanda N. Justus

Electronic Theses and Dissertations

The manufacturer claims that there is only one solution to the puzzle Instant Insanity II. However, a recent paper shows that there are two solutions. Our goal is to find ways in which we only have one solution. We examine the permutation groups of the puzzle and use modern algebra to attempt to fix the puzzle. First, we find the permutation group for the case when there is only one empty slot at the top. We then examine the scenario when we add an extra column or an extra row to make the game a 4 × 5 puzzle or …

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Physiologically-Based Pharmacokinetic Model For Ertapenem, Whitney Forbes May 2014

Physiologically-Based Pharmacokinetic Model For Ertapenem, Whitney Forbes

Electronic Theses and Dissertations

Ertapenem is a carbapenem used to treat a wide range of bacterial infections. What sets ertapenem apart from other carbapenems is its longer half-life which implies it need only be administered once daily. We developed a physiologically-based pharmacokinetic model for the distribution of ertapenem within the body. In the model, parameters such as human body weight and height, age, organ volumes, blood flow rates, and partition coefficients of particular tissues are used to examine the absorption, distribution, metabolism, and excretion of ertapenem. The total and free blood concentrations found were then compared to experimental data. We then examined the sensitivity …

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Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah May 2014

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

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The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Restrictions On The Coefficients, Brett A. Shields Mr. May 2014

The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Restrictions On The Coefficients, Brett A. Shields Mr.

Electronic Theses and Dissertations

In this thesis, we put restrictions on the coefficients of polynomials and give bounds concerning the number of zeros in a specific region. Our results generalize a number of previously known theorems, as well as implying many new corollaries with hypotheses concerning monotonicity of the modulus, real, as well as real and imaginary parts of the coefficients separately. We worked with Enestr\"{o}m-Kakeya type hypotheses, yet we were only concerned with the number of zeros of the polynomial. We considered putting the same type of restrictions on the coefficients of three different types of polynomials: polynomials with a monotonicity``flip" at some …

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Very Cost Effective Domination In Graphs, Tony K. Rodriguez May 2014

Very Cost Effective Domination In Graphs, Tony K. Rodriguez

Electronic Theses and Dissertations

A set S of vertices in a graph G=(V,E) is a dominating set if every vertex in V\S is adjacent to at least one vertex in S, and the minimum cardinality of a dominating set of G is the domination number of G. A vertex v in a dominating set S is said to be very cost effective if it is adjacent to more vertices in V\S than to vertices in S. A dominating set S is very cost effective if every vertex in S is very cost effective. The minimum cardinality of a very cost effective dominating set of …

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A Numerical Model For Nonadiabatic Transitions In Molecules, Devanshu Agrawal May 2014

A Numerical Model For Nonadiabatic Transitions In Molecules, Devanshu Agrawal

Undergraduate Honors Theses

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 …

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