Physical Sciences and Mathematics Commons^™

On The Miracle Of The Multiplication Of The Loaves And Fishes, Andrew Simoson

ACMS Conference Proceedings 1995

With respect to Jesus’s miracle described in Matthew 14: 15–21, we give whimsical arguments for generating more from what appears to be present—using ideas of set and measure theory and show how to partition the unit interval into two disjoint sets each of whose outer measures is unity; and we go on to discuss the Banach-Tarski paradox showing how to partition the unit sphere into two unit spheres. Note: I do not hold copyrights to Figures 1 and 4.

Improving The Teaching Of Mathematics, David S. Moore

ACMS Conference Proceedings 1995

No one concerned about the teaching of college mathematics--and few mathematicians who are not concerned--can have missed the movement to reform teaching in the mathematical sciences at all levels. The teaching of any active branch of knowledge, like the church, is of course "reforming and ever to be reformed." Calls to modernize what we offer students are always with us. What is striking about the current reform movement is not only its momentum but the fact that it centers on pedagogy rather than on content. We ought, say the reformers, to radically alter our style of teaching. My purpose in …

Introduction (1995), David L. Neuhouser

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Asymptotic Diagonalizations Of A Linear Ordinary Differential System, Feipeng Xie

Dissertations

No abstract provided.

The Mathematics Of Measuring Capabilities Of Artificial Neural Networks, Martha A. Carter

Theses and Dissertations

Researchers rely on the mathematics of Vapnik and Chervonenkis to capture quantitatively the capabilities of specific artificial neural network (ANN) architectures. The quantifier is known as the V-C dimension, and is defined on functions or sets. Its value is the largest cardinality 1 of a set of vectors in Rd such that there is at least one set of vectors of cardinality 1 such that all dichotomies of that set into two sets can be implemented by the function or set. Stated another way, the V-C dimension of a set of functions is the largest cardinality of a set, such …

Probability Polynomials For Cubic Graphs In The Framework Of Random Topological Graph Theory, Esther Joy Tesar

Dissertations

Topological graph theorists study the imbeddings of graphs on surfaces (spheres with handles). Some interesting questions in the field are on w hat surfaces can a graph be 2 -cell imbedded and how m any such imbeddings are there on each surface. The study of these and related questions is called Enumerative Topological Graph Theory. Random Topological Graph Theory uses probability models to study the 2-cell imbeddings. It generalizes the results from Enumerative Topological Graph Theory (which is the uniform case, p= 1/2) to an arbitrary probability p.

We study the model where the sample space consists of all labeled, …

Step Domination In Graphs, Kelly Lynne Schultz

Dissertations

One of the major areas in Graph Theory is domination in graphs. It is this area with which this dissertation deals, with the primary emphasis on step domination in graphs.

In Chapter 1 we present some preliminary definitions and examples. In addition, a background of the area of domination is presented. We then introduce the concepts that lead to step domination.

In Chapter II we formally define the concept of step domination and give several examples. We determine the minimum number of vertices needed in a step domination set for many classes of graphs. We then explore step domination for …

Schedule (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Table Of Contents (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Population Genetics: Estimation Of Distributions Through Systems Of Non-Linear Differential Equations, Nacer E. Abrouk, Robert J. Lopez

Mathematical Sciences Technical Reports (MSTR)

In stochastic population genetics, the fundamental quantity used for describing the genetic composition of a Mendelian population is the gene frequency. The process of change in the gene frequency is generally modeled as a stochastic process satisfying a stochastic differential equation. The drift and diffusion coefficients in this equation reflect such mechanisms as mutation, selection, and migration that affect the population. Except in very simple cases, it is difficult to determine the probability law of the stochastic process of change in gene frequency. We present a method for obtaining approximations of this process, enabling us to study models more realistic …

A Variable Time-Step Midpoint Scheme For Hamiltonian Systems, Yosi Shibberu

Mathematical Sciences Technical Reports (MSTR)

A smooth time-step selection formula for the midpoint method is derived which minimize deviations in the Hamiltonian function along piecewise-linear phase space trajectories of autonomous Hamiltonian systems. The time-step formula is implemented in a second order pre­dictor/corrector scheme and applied to Kepler's problem. The formula significantly improves energy conservation as well as the accuracy of the configuration space trajectory. Peak errors in position and momentum coordinates are not significantly reduced, but the time behavior of the errors is markedly more regular.

Free-Boundary Problems For Potential And Stokes Flows Via Nonsmooth Analysis, Srdjan Stojanovic, Tom Svobodny

Mathematics and Statistics Faculty Publications

A new approach to some free boundary problems of the type of jets and cavities for potential flows is introduced. Both potential and Stokes flows are considered. The variable domain problems are relaxed so that they become nonsmooth optimization problems on fixed domains for somewhat singular state equations. State equations are considered, and multivalued generalized gradients of the variational functionals are studied. The method is constructive.

Distortion And Evolution Of A Localized Vortex In An Irrotational Flow, Joseph F. Lingevitch, Andrew J. Bernoff

All HMC Faculty Publications and Research

This paper examines the interaction of an axisymmetric vortex monopole, such as a Lamb vortex, with a background irrotational flow. At leading order, the monopole is advected with the background flow velocity at the center of vorticity. However, inhomogeneities of the flow will cause the monopole to distort. It is shown that a shear‐diffusion mechanism, familiar from the study of mixing of passive scalars, plays an important role in the evolution of the vorticity distribution. Through this mechanism, nonaxisymmetric vorticity perturbations which do not shift the center of vorticity are homogenized along streamlines on a Re1/3 time scale, much faster …

Descartes And Problem-Solving, Judith V. Grabiner

Pitzer Faculty Publications and Research

What can Descartes' Geometry teach us about problem solving?

Semi-Strongly Regular Graphs And Generalized Cages, Cong Fan

Dissertations

Two well-known classes of graphs, strongly regular graphs and cages, have been studied extensively by many researchers for a long period of time. In this dissertation, we mainly deal with semi-strongly regular graphs, a class of graphs including all strongly regular graphs, and (r, g, t)-cages, a generalization of the usual cage concept.

Chapter I introduces the two new concepts: semi-strongly regular graphs and generalized (r, g, t)-cages, gives necessary conditions for the existence of semi-strongly regular graphs and some interesting properties regarding common neighbors of pairs of vertices, and shows connections between these two new concepts and the old …

Mathematical Models Of Chemotherapy, John Carl Panetta

Mathematics & Statistics Theses & Dissertations

Several mathematical models are developed to describe the effects of chemotherapy on both cancerous and normal tissue. Each model is defined by either a single homogeneous equation or a system of heterogeneous equations which describe the states of the normal and/or cancer cells. Periodic terms are added to model the effects of the chemotherapy. What we obtain are regions, in parameter space (dose and period), of acceptable drug regimens.

The models take into account various aspects of chemotherapy. These include, interactions between the cancer and normal tissue, cell specific chemotherapeutic drug, the use of non-constant parameters to aid in modeling …

Nonlinear Time Series Analysis, James A. Stewart

Theses and Dissertations

This thesis applies neural network feature selection techniques to multivariate time series data to improve prediction of a target time series. Two approaches to feature selection are used. First, a subset enumeration method is used to determine which financial indicators are most useful for aiding in prediction of the S&P 500 futures daily price. The candidate indicators evaluated include RSI, Stochastics and several moving averages. Results indicate that the Stochastics and RSI indicators result in better prediction results than the moving averages. The second approach to feature selection is calculation of individual saliency metrics. A new decision boundary-based individual saliency …

Multipoint Quadratic Approximation For Numerical Optimization, Michael A. Blaylock

Theses and Dissertations

A quadratic approximation for nonlinear functions is developed in order to realize computational savings in solving numerical optimization problems. Function and gradient information accumulated from multiple design points during the iteration history is used in estimating the Hessian matrix. The approximate Hessian matrix is the available for a second order Taylor series approximation to the functions of interest. Several truss and frame models will be used to demonstrate the effectiveness of the new Multipoint Quadratic Approximation (MQA) in solving structural optimization problems.

An Improved Solution Methodology For The Arsenal Exchange Model (Aem), Jeffery D. Weir

Theses and Dissertations

The purpose of this research was to design a solution methodology for the Arsenal Exchange Model (AEM) that is faster and contains less precision error than the current one. The current solution methodology modifies some of the original constraints and uses a computationally slow matrix inverter. The improved methodology uses a revised simplex algorithm to first solve a subproblem having only the weapon constraints generated by the AEM. Given this optimal allocation, hedge constraints and target constraints that are violated by the current solution are added to the original subproblem. A dual simplex algorithm is used to find the optimal …

An Elementary Proof That Finite Groups Lack Unique Product Structures, Matthew Cushman

Mathematical Sciences Technical Reports (MSTR)

We provide an elementary proof that no nontrivial finite group has a unique m-element product structure for any m greater than or equal to 2.

Principal Points And Self-Consistent Points Of Elliptical Distributions, Thaddeus Tarpey, Luning Li, Bernard Flury

Mathematics and Statistics Faculty Publications

In this paper we study principal points and self-consistent points of p-variate elliptical distributions. We also discuss implications of our results for the computation and estimation of principal points.

Computations For A Vibrating System Diagonalize The Variance, J. N. Boyd, P. N. Raychowdhury

Mathematics and Applied Mathematics Publications

The transformations to diagonalize potential energy matrices for coupled harmonic oscillators will also diagonalize the variance when written in matrix form. After a brief review of a geometrical interpretation of the variance, the transformations are described and an example is given.

Alpha+28si Cluster Structure As Solitons On The Nuclear Surface, Andrei Ludu

Andrei Ludu

No abstract provided.

Quasimolecular Resonances In Alpha+20ne Systems, Andrei Ludu

Andrei Ludu

No abstract provided.

Automatic Augmented Galerkin Algorithms For Linear First Kind Integral Equations: Non-Singular And Weak Singular Kernels, S. Abbasbandy, E. Babolian

Saeid Abbasbandy

In this paper we describe some iterative algorithms for computing these paramteres for non-singular and weak-singular first kind integral equations. We give also error estimates which are easily computed. Finally, we give a number of numerical examples showing that these algorithms work well in practice and netter than methods presented in [2],[3] and [8].

Exp For Windows, Version 3.0 A Software Review, Donn E. Miller-Harnish

Mathematics and System Engineering Faculty Publications

No abstract provided.

Optimality Conditions For Systems Driven By Nonlinear Evolution Equations, Nikolaos S. Papageorgiou

Mathematics and System Engineering Faculty Publications

Using the Dubovitskii-Milyutin theory we derive necessary and sufficient conditions for optimality for a class of Lagrange optimal control problems monitored by a nonlinear evolution equation and involving initial and/or terminal constraints. An example of a parabolic control system is also included.

Stability Of Conditionally Invariant Sets And Controlled Uncertain Dynamic Systems On Time Scales, V. Lakshmikantham

Mathematics and System Engineering Faculty Publications

A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built …

Bulk Input Queues With Quorum And Multiple Vacations, Jay Yellen, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The authors study a single-server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less than r and not greater than R(≥r). The server takes vacations each time the queue level falls below r(≥1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics …

Stability Properties And Integrability Of The Resolvent Of Linear Volterra Equations, Muhammad Islam, Paul W. Eloe

Mathematics Faculty Publications

Integrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.