Mathematics Commons^™

Global Resource Management Of Response Surface Methodology, Michael Chad Miller

Dissertations and Theses

Statistical research can be more difficult to plan than other kinds of projects, since the research must adapt as knowledge is gained. This dissertation establishes a formal language and methodology for designing experimental research strategies with limited resources. It is a mathematically rigorous extension of a sequential and adaptive form of statistical research called response surface methodology. It uses sponsor-given information, conditions, and resource constraints to decompose an overall project into individual stages. At each stage, a "parent" decision-maker determines what design of experimentation to do for its stage of research, and adapts to the feedback from that research's potential …

Qualitative Behavior Of Solutions Of Difference Equations With Several Oscillating Coefficients, Martin Bohner, George E. Chatzarakis, Ioannis P. Stavroulakis

Mathematics and Statistics Faculty Research & Creative Works

Sufficient conditions which guarantee the convergence of the non-oscillatory solutions or oscillation of all solutions of a difference equation with several deviating arguments and oscillating coefficients are presented. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given. [Media Object not available: see full text.]

Local Stability Implies Global Stability For The Planar Ricker Competition Model, Eduardo C. Balreira, Saber Elaydi, Rafael Luís

Mathematics Faculty Research

Under certain analytic and geometric assumptions we show that local stability of the coexistence (positive) fixed point of the planar Ricker competition model implies global stability with respect to the interior of the positive quadrant. This result is a confluence of ideas from Dynamical Systems, Geometry, and Topology that provides a framework to the study of global stability for other planar competition models.

Transfer Of Global Measures Of Dependence Into Cumulative Local, Boyan N. Dimitrov, Sahib Esa, Nikolai Kolev, Georgios Pitselis

Mathematics Publications

We explore an idea of transferring some classic measures of global dependence between random variables X1,X2,…,Xn into cumulative measures of dependence relative at any point (X1,X2,…,Xn) in the sample space. It allows studying the behavior of these measures throughout the sample space, and better understanding and use of dependence. Some examples on popular copula distributions are also provided.

Symmetric Periodic Solutions For A Class Of Differential Delay Equations With Distributed Delay, Benjamin B. Kennedy

Math Faculty Publications

We consider a nonlinear distributed delay equation where g and f are smooth, bounded, and odd and satisfy a positive and a negative feedback condition, respectively. Using elementary fixed point theory we prove the existence of a nontrivial periodic solution of period 2 + 2d satisfying certain symmetries, given certain growth conditions on f and g near zero.

Theoretical Analysis And Simulation Of Acute And Chronic Phase Hiv-1 Dynamics, Frank Nani, Mingxian Jin

Math and Computer Science Faculty Working Papers

Aims: The dynamics of HIV-1 induced AIDS is attributed to several biological variables, which characterize the stage, virulence and morbidity of the disease. The aim of this research is to use a necessary and sufficient subset of these immunological variables to construct a clinically plausible mathematical model of the patho-physiological dynamics of HIV-1 induced AIDS during the acute and chronic phases. This model incorporates the interactions between uninfected CD4+ T cells, HIV-1 infected CD4+ T cells, HIV-1 virions in the blood plasma, and specific cytotoxic CD8+ T cells. The major objective is to derive mathematical criteria depicting conditions under which …

John Horton Conway: A Puzzle Game, Jeremiah Farrell, Karen Farrell

Scholarship and Professional Work - LAS

There are 10 different letters in the name JOHN HORTON CONWAY and we use each of these exactly three times each to form the following ten words: JHC, COW, NYC, JAN, RON, WRY, RAT, JOT, HWT, HAY.

Kif11 Dependent Cell Cycle Progression In Radial Glial Cells Is Required For Proper Neurogenesis In The Zebrafish Neural Tube, Kimberly Johnson, Chelsea Moriarty, Nessy Tania, Alissa Ortman, Kristina Dipietrantonio, Brittany Edens, Jean Eisenman, Deborah Ok, Sarah Krikorian, Jessica Barragan, Christophe Golé, Michael J.F. Barresi

Mathematics Sciences: Faculty Publications

Radial glia serve as the resident neural stem cells in the embryonic vertebrate nervous system, and their proliferation must be tightly regulated to generate the correct number of neuronal and glial cell progeny in the neural tube. During a forward genetic screen, we recently identified a zebrafish mutant in the kif11 loci that displayed a significant increase in radial glial cell bodies at the ventricular zone of the spinal cord. Kif11, also known as Eg5, is a kinesin-related, plus-end directed motor protein responsible for stabilizing and separating the bipolar mitotic spindle. We show here that Gfap+ radial glial cells express …

The Itô Calculus And White Noise Theory: A Brief Survey Toward General Stochastic Integration, Hui-Hsiung Kuo

Communications on Stochastic Analysis

No abstract provided.

Stochastic Control Of Itô-Lévy Processes With Applications To Finance, Bernt Øksendal, Agnès Sulem

Communications on Stochastic Analysis

No abstract provided.

Optimal Combined Divided And Proportional Reinsurance Policy, Eriyoti Chikodza, Julius N Esunge

Communications on Stochastic Analysis

No abstract provided.

Expert Opinions And Logarithmic Utility Maximization In A Market With Gaussian Drift, Abdelali Gabih, Hakam Kondakji, Jörn Sass, Ralf Wunderlich

Communications on Stochastic Analysis

No abstract provided.

Portfolio Optimization Under Partial Information With Expert Opinions: A Dynamic Programming Approach, Rüdiger Frey, Abdelali Gabih, Ralf Wunderlich

Communications on Stochastic Analysis

No abstract provided.

Optimal Premium Policy Of An Insurance Firm With Delay And Stochastic Interest Rate, Charles Wilson Mahera, Olivier Menoukeu-Pamen, Moses Mwale

Communications on Stochastic Analysis

No abstract provided.

Modelling Financial Information By Conditioning, Dennis Ikpe, Sure Mataramvura, Ronnie Becker

Communications on Stochastic Analysis

No abstract provided.

Mcdonald Log-Logistic Distribution With An Application To Breast Cancer Data, M. H. Tahir, Muhammad Mansoor, Muhammad Zubair, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to extend the two-parameter log-logistic distribution. Some structural properties of this new distribution such as reliability measures and entropies are obtained. The model parameters are estimated by the method of maximum likelihood using L-BFGS-B algorithm. A useful characterization of the distribution is proposed which does not require explicit closed form of the cumulative distribution function and also connects the probability density function with a solution of a first order differential equation. An application of the new model to real data set shows that it can give consistently better fit …

A Volume Bound For Montesinos Links, Kathleen Arvella Finlinson

Theses and Dissertations

The hyperbolic volume of a knot complement is a topological knot invariant. Futer, Kalfagianni, and Purcell have estimated the volumes of Montesinos link complements for Montesinos links with at least three positive tangles. Here we extend their results to all hyperbolic Montesinos links.

The Irreducible Representations Of D2n, Melissa Soto

Electronic Theses, Projects, and Dissertations

Irreducible representations of a finite group over a field are important because all representations of a group are direct sums of irreducible representations. Maschke tells us that if φ is a representation of the finite group G of order n on the m-dimensional space V over the field K of complex numbers and if U is an invariant subspace of φ, then U has a complementary reducing subspace W .

The objective of this thesis is to find all irreducible representations of the dihedral group D2n. The reason we will work with the dihedral group is because it is one …

Conditional Tests On Basins Of Attraction With Finite Fields, Ian H. Dinwoodie

Mathematics and Statistics Faculty Publications and Presentations

An iterative method is given for computing the polynomials that vanish on the basin of attraction of a steady state in discrete polynomial dynamics with finite field coefficients. The algorithm is applied to dynamics of a T cell survival network where it is used to compare transition maps conditional on a basin of attraction.

The Minimum Rank Of Schemes On Graphs, William Nelson Sexton

Theses and Dissertations

Let G be an undirected graph on n vertices and let S(G) be the class of all real-valued symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let V = {1, 2, . . . , n} be the vertex set of G. A scheme on G is a function f : V → {0, 1}. Given a scheme f on G, there is an associated class of matrices Sf (G) = {A ∈ S(G)|aii = 0 if and only if f(i) = 0}. A scheme f is said …