Applied Mathematics Commons^™

Bicyclic Mixed Triple Systems., Benkam Benedict Bobga

Electronic Theses and Dissertations

In the study of triple systems, one question faced is that of finding for what order a decomposition exists. We state and prove a necessary and sufficient condition for the existence of a bicyclic mixed triple system based on the three possible partial orientations of the 3-cycle with twice as many arcs as edges. We also explore the existence of rotational and reverse mixed triple systems. Our principal proof technique applied is the difference method. Finally, this work contains a result on packing of complete mixed graphs on v vertices, M_v, with isomorphic copies of two …

A Limit Theorem In Cryptography., Kevin Lynch

Electronic Theses and Dissertations

Cryptography is the study of encryptying and decrypting messages and deciphering encrypted messages when the code is unknown. We consider Λ_π(Δx, Δy) which is a count of how many ways a permutation satisfies a certain property. According to Hawkes and O'Connor, the distribution of Λ_π(Δx, Δy) tends to a Poisson distribution with parameter ½ as m → ∞ for all Δx,Δy ∈ (Z/qZ)^m - 0. We give a proof of this theorem using the Stein-Chen method: As q^{m …}

Investigation Of Laser Beam Induced Current Techniques For Heterojunction Photodiode Characterization, Weifu Fang, David A. Redfern, Kazufumi Ito, G. Bahir, Charles A. Musca, John M. Dell, Lorenzo Faraone

Mathematics and Statistics Faculty Publications

A reduced model is developed that has significant advantages over the full drift-diffusion model for the simulation of laser beam-induced current (LBIC) signals in the presence of heterojunctions. The model determines the contribution to the LBIC signal that would occur from photogeneration at any position within the semiconductor, and is particularly useful for heterostructures where judicious choice of illumination wavelength can result in photogeneration at different depths within the device structure. The reduced model is used to examine the basic features of LBIC as applied to two types of planar P-n HgCdTe heterojunction photodiode structures. In particular, the question of …

Time-Dependent Thermal Imaging Of Circular Inclusions, Donald L. Brouwn, Mark Hubenthal

Mathematical Sciences Technical Reports (MSTR)

This paper considers the inverse problem of locating one or more circular inclusions in a two-dimensional domain using thermal boundary data, specifically, the input heat flux and measured boundary temperature. The forward problem is governed by the heat equation. We show how the position and size of such defects can be recovered using the boundary data and various approximations of the solution to the forward problem. We also consider the stability of the algorithm involved to recover the defects.

Positive Solutions For The Beam Equation Under Certain Boundary Conditions, Bo Yang

Faculty Articles

We consider a boundary-value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and fastened with a sliding clamp at the other end. Some priori estimates to the positive solutions for the boundary-value problem are obtained. Sufficient conditions for the existence and nonexistence of positive solutions for the boundary-value problem are established

Subdifferential Calculus In Asplund Generated Spaces, Marian Fabian, Philip D. Loewen, Boris S. Mordukhovich

Mathematics Research Reports

We extend the definition of the limiting Frechet subdifferential and the limiting Frechet normal cone from Asplund spaces to Asplund generated spaces. Then we prove a sum rule, a mean value theorem, and other statements for this concept.

Investigation And Applications Of Latin Hypercube Sampling Methods, Prashant K. Patel

Mechanical & Aerospace Engineering Theses & Dissertations

The Latin hypercube sampling method, sometimes called the stratified sampling method, is a commonly used variance reduction method. Recently, the optimal Latin hypercube sampling method (OLH) and the modified optimal Latin hypercube sampling method (MOLH) are introduced in the literature, which use the genetic algorithm to adjust the distance between sampled points.

This paper will compare the basic Latin hypercube, the optimal Latin hypercube and the modified optimal Latin hypercube methods for generating the sample points for statistical application and curve fitting, in te1ms of accuracy and efficiency. Analytical and structural examples are used in this thesis to facilitate the …

Computational Optical Biopsy, Yi Li, Ming Jiang, Ge Wang

Mathematics and Statistics Faculty Publications

Optical molecular imaging is based on fluorescence or bioluminescence, and hindered by photon scattering in the tissue, especially in patient studies. Here we propose a computational optical biopsy (COB) approach to localize and quantify a light source deep inside a subject. In contrast to existing optical biopsy techniques, our scheme is to collect optical signals directly from a region of interest along one or multiple biopsy paths in a subject, and then compute features of an underlying light source distribution. In this paper, we formulate this inverse problem in the framework of diffusion approximation, demonstrate the solution uniqueness properties in …

Object Information Repository In A Christian Theory Of Technology, Longy O. Anyanwu

ACMS Conference Proceedings 2005

It has not been easy to formulate a stable Christian theory of technology. Nonetheless, some ideas and Christian theories of technology have been fielded by a handful of distinguished Christian scientists and technology experts. Although some of these ideas and theories are substantively at variance, others have sizeable common base. Important, though, is the seeming agreement on the visualization of technology as an object with embedded values and information. With object information repository as the primary focus, this study, therefore, attempts to provoke the consideration of a possible synthesis and agreement on the foundational essence of Christian theory of technology …

The Five Orders Of Ignorance: Knowledge, Ignorance, And The Nature Of Software, Phillip Armour

ACMS Conference Proceedings 2005

Software is not a product, it is a medium in which we store knowledge. As simple as this idea seems, the consequences of it are quite significant. If software is not a product, then software development is not a product of production activity, despite the common practice of managing it as such. Most organizations believe that job of software developers is to build a system that we then ship to a customer. It is not. The system we build and ship to the customer is actually the by-product of the real activity which is learning. Software development is the activity …

Mathematics As Poesis: A Preliminary Project Report, Sam Stueckle, Jeremy Case, Ken Constantine, Troy Riggs

ACMS Conference Proceedings 2005

This paper talks about the various viewpoints of mathematics, beginning with classical perspectives and ending with the idea of poesis, or the theology of math as the art of making.

Integrating Catholic And Marianist Historical Perspectives In A Mathematics Coruse For Elementary Education Majors, Mary Wagner-Krankel

ACMS Conference Proceedings 2005

St. Mary's University in San Antonio recently reaffirmed their distinctive nature as a Catholic university promoting the Marianist tradition. This new affirmation is in response to the smaller number of Marianists serving in teaching and administrative positions on campus. Faculty have been encouraged to explore new ways to integrate Catholic and Marianist values and historical perspectives in their teaching and research. I will discuss some major Catholic mathematicians and some classroom activities that I developed for the course MT3304- Mathematics for the Elementary Teacher.

Does The Success Of Mathematics Defeat Naturalism?, Russell W. Howell

ACMS Conference Proceedings 2005

This paper discusses the arguments for and against Intelligent Design from the perspectives of mathematics.

The Artificial Gravity Pitch, Andrew Simoson

ACMS Conference Proceedings 2005

Toss a ball into the air; we analyze and contrast the resultant trajectories when standing both on the Little Prince’s Asteroid B-612 of 1943 and in Arthur C. Clark’s rotating space ship Discovery of 2001.

Explicit Null Space Of Discrete Laplacian, Hanna Vanderzee

ACMS Conference Proceedings 2005

For a given partial differential equation, such as Poisson’s equation in two dimensions, stipulating the null-space component of the solution is sometimes a useful alternative to specifying boundary conditions in order to determine a unique solution. To implement this approach computationally, we need a sparse and well-conditioned representation of the null space of the relevant differential operator. We discuss how the null-space method works and present an explicit formula for generating a sparse null basis for a uniform, finite-difference discretization of Laplacian operator on the unit square. The formula makes use of a triangular array which has the large Schroeder …

Artificial Intelligence: Can We Create Machines In Our Own Image?, Derek C. Shuurman

ACMS Conference Proceedings 2005

The field of Artificial Intelligence (AI) leads to many questions about what it means to be human. Some researchers claim that inevitably computers will reach a certain threshold of complexity that will enable them to “think” and artificial consciousness will emerge. This speculation, taken a step further, leads some to believe that computer technology will eventually set humans free from the frailty of their bodies and enable them to achieve immortality. Underlying these claims is a reductionistic philosophy about what it means to be human and how one approaches the mind-body problem. Ever since the fall people have wanted to …

Integration Of Faith, Learning, And Christian Vocation With First-Year Mathematics Majors, Doug Phillippy, Angela Hare

ACMS Conference Proceedings 2005

The mission of Messiah College is "to educate men and women toward maturity of intellect, character, and Christian faith, in preparation for lives of service, leadership and reconciliation in church and society". Therefore, as faculty in the Mathematical Sciences Department at this college, how we build maturity in our students, not only a mature mathematical intellect, but also maturity of character and Christian faith, reflects our commitment to the mission of the College. Further, our departmental mission statement includes the objective "to challenge students to live out their faith in their vocation as they become servant leaders in society, church, …

Writing Math Lessons That Integrate Christian Beliefs: The Kuyers Institute Grant Project, Dave Klanderman, Gary Talsma

ACMS Conference Proceedings 2005

In this paper, we describe multiple math lessons designed to incorporate a Christian perspective. A total of nine lessons, some with materials for multiple class sessions, will soon be published by the Kuyers Institute. These lessons are appropriate for use at the middle school and high school level.

A Christian Constructivist? The Impact Of Worldview On Learning Theories And The Mathematics Education Research Community, Jeffrey Barrett, Dave Klanderman

ACMS Conference Proceedings 2005

This paper analyzes the role of worldview and its impact on learning theories within the mathematics education research community. The authors propose a scholarly agenda for engaging this issue in future research projects.

Teaching The History Of Mathematics Using Architecture And Art, Maria Zack

ACMS Conference Proceedings 2005

Point Loma Nazarene University (PLNU) is a Christian university deeply committed to teaching in the liberal arts tradition. As a consequence, all of our students take roughly 64 semester hours of “general education” courses as part of the 128 semester hours required for graduation. One of the challenges of teaching at such an institution is helping students to value the core curriculum. I recently taught “Topics in Mathematics: Mathematics, Art and Architecture.” My goal was to help students see, discuss and understand connections between the mathematics that they were studying and some aspects of the general education core that is …

Mathematics From A World View Perspective, Jonathan Zderad

ACMS Conference Proceedings 2005

No abstract provided.