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2005

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Articles 91 - 120 of 422

Full-Text Articles in Mathematics

Mapping The Discrete Logarithm, Daniel R. Cloutier Jul 2005

Mapping The Discrete Logarithm, Daniel R. Cloutier

Mathematical Sciences Technical Reports (MSTR)

The discrete logarithm is a problem that surfaces frequently in the field of cryptog- raphy as a result of using the transformation ga mod n. This paper focuses on a prime modulus, p, for which it is shown that the basic structure of the functional graph is largely dependent on an interaction between g and p-1. In fact, there are precisely as many different functional graph structures as there are divisors of p-1. This paper extracts two of these structures, permutations and binary functional graphs. Estimates exist for the shape of a random permutation, but …

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Elemental T.G. Principles Of Relativistic T-Topos (Presheafification Of Matter, Space, And Time), Goro Kato Jul 2005

Elemental T.G. Principles Of Relativistic T-Topos (Presheafification Of Matter, Space, And Time), Goro Kato

Mathematics

We would like to solve the following problem: find a mathematical model formulating I) quantum entanglement, II) particle-wave duality, III) universal objects (ur-sub-Planck objects): to be defined in terms of direct or inverse limits (defined by universal mapping properties) giving microcosm behaviors of space-time so as to give the smooth macrocosm space-time, and IV) the “curved” space-time associated with particles with mass in microcosm consistent with the notion of a light cone in macrocosm. Problems I) and II) are treated in Kato G., Europhys. Lett., 68 (2004) 467. In this paper, we will focus on III) and IV). As …

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Some Effective Diophantine Results Over Q-Bar, Lenny Fukshansky Jul 2005

Some Effective Diophantine Results Over Q-Bar, Lenny Fukshansky

CMC Faculty Publications and Research

In his 1999 paper D. W. Masser talks about effective search bounds for polynomial equations over integers and rationals. This discussion can also be extended over number fields. Unfortunately, as illustrated by Matiasevich's negative answer to Hilbert's 10-th problem, search bounds in general probably do not exist. Some special cases are understood, but in general very little is known. I will talk about effective search bounds for solutions of polynomial equations over Q-bar with some additional arithmetic conditions. This discussion also naturaly ties into the realm of "absolute" diophantine results, like Siegel's lemma of Roy and Thunder. I will try …

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The Least-Squares Finite Element Method For Grid Deformation And Meshfree Applications, Dionisio Laeber Fleitas Jul 2005

The Least-Squares Finite Element Method For Grid Deformation And Meshfree Applications, Dionisio Laeber Fleitas

Mathematics Dissertations - Archive

Grid adaptation is often needed to improve the numerical solution of a Partial Differential Equation (PDE), due to, for example, shock waves and boundary layers. In moving boundary problems, the grid needs to be regenerated or adapted to fit the new domain. In this work, a LSFEM deformation method is developed for grid generation on fixed or moving domains. The LSFEM is a finite-elements method which seeks to minimize the PDE residual equation through the least-squares method. A new class of numerical methods currently being researched is the meshfree methods, in which the main goal is to numerically solve PDEs …

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Good Measures On Cantor Space, Ethan Akin Jul 2005

Good Measures On Cantor Space, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

While there is, up to homeomorphism, only one Cantor space, i.e. one zero-dimensional, perfect, compact, nonempty metric space, there are many measures on Cantor space which are not topologically equivalent. The clopen values set for a full, nonatomic measure μ is the countable dense subset {μ(U): U is clopen} of the unit interval. It is a topological invariant for the measure. For the class of good measures, it is a complete invariant. A full, nonatomic measure μ is good if whenever U, V are clopen sets with μ(U) < μ(V), there exists W a clopen subset of V such that μ(W) = μ(U). These measures have interesting dynamical properties. They are exactly the measures which arise from uniquely ergodic minimal systems on Cantor space. For some of them there is a unique generic measure-preserving homeomorphism. That is, within the Polish group of such homeomorphisms there is a dense, G δ conjugacy class. ©2004 American Mathematical Society.

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The Reflection Property In Normed Linear Planes With Applications To Generalized Conics, Edward J. O'Neill, Mostafa Ghandehari Jul 2005

The Reflection Property In Normed Linear Planes With Applications To Generalized Conics, Edward J. O'Neill, Mostafa Ghandehari

Mathematics Technical Papers - Archive

The ancient Greek mathematician Heron was the first to solve the problem of finding the shortest path from point A to point B on one side of the line L, subject to the condition that the path goes from A to L and then to B (figure 1). Figure 1. His solution involved going from A to point R on L and then to B such that the line segments AR and BR make equal angles with L. This is exactly the path a light ray from A to B if L were a mirror. Heron included this proposition in …

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Why Are School Districts Abandoning The Core-Plus Mathematics Curriculum, Amber Rae Richgels Jul 2005

Why Are School Districts Abandoning The Core-Plus Mathematics Curriculum, Amber Rae Richgels

Mathematics Graduate Theses

In this paper, the author establishes that high schools are abandoning the Core-Plus Mathematics curriculum and determines the need for curricular reform and the motivation to develop such standards-based programs. She discovers that although Core- Plus is a nationally recognized, exemplary mathematics curriculum, school districts are deciding to discontinue the curricular option of Core-Plus. The author reviewed literature and interviewed teachers from schools that have recently decided to abandon Core-Plus in attempt to determine factors leading to these decisions. This paper discusses those interviews, provides suggestions for the future adoption of Core-Plus, and concludes with recommendations that further study be …

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Subdifferential Calculus In Asplund Generated Spaces, Marian Fabian, Philip D. Loewen, Boris S. Mordukhovich Jul 2005

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.

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A Convergence Theorem For Continued Fractions Of The Form K_{N=1}^{\Infty}A_{N}/1, James Mclaughlin, Nancy Wyshinski Jul 2005

A Convergence Theorem For Continued Fractions Of The Form K_{N=1}^{\Infty}A_{N}/1, James Mclaughlin, Nancy Wyshinski

Mathematics Faculty Publications

In this paper we present a convergence theorem for continued fractions of the form K∞n=1an/1. By deriving conditions on the an which ensure that the odd and even parts of K∞n=1an/1 converge, these same conditions also ensure that they converge to the same limit. Examples will be given.

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On Convergence To The Denjoy-Wolff Point, P. S. Bourdon, Valentin Matache, J. H. Shapiro Jul 2005

On Convergence To The Denjoy-Wolff Point, P. S. Bourdon, Valentin Matache, J. H. Shapiro

Mathematics Faculty Publications

For holomorphic selfmaps of the open unit disc U that are not elliptic automorphisms, the Schwarz Lemma and the Denjoy-Wolff Theorem combine to yield a remarkable result: each such map φ has a (necessarily unique) "Denjoy-Wolff point"...

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Principal Component Regression For Construction Of Wing Weight Estimation Models, Humberto Rocha Jul 2005

Principal Component Regression For Construction Of Wing Weight Estimation Models, Humberto Rocha

Mathematics & Statistics Theses & Dissertations

The multivariate data fitting problem occurs frequently in many branches of science and engineering. It is very easy to fit a data set exactly by a mathematical model no matter how the data points are distributed. But building a response by using a limited number of poorly distributed data points is very unreliable, yet necessary in conceptual design process. This thesis documents the lessons learned from fitting the wing weight data of 41 subsonic transports by three types of interpolation methods---least polynomial interpolation, radial basis function interpolation, and Kriging interpolation. The objective of this thesis is to develop an automatic …

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Maximal Surfaces In Complexes, Allen J. Dickson Jun 2005

Maximal Surfaces In Complexes, Allen J. Dickson

Theses and Dissertations

Cubical complexes are defined in a manner analogous to that for simplicial complexes, the chief difference being that cubical complexes are unions of cubes rather than of simplices. A very natural cubical complex to consider is the complex C(k_1,...,k_n) where k_1,...,k_n are nonnegative integers. This complex has as its underlying space [0,k_1]x...x[0,k_n] subset of R^n with vertices at all points having integer coordinates and higher dimensional cubes formed by the vertices in the natural way. The genus of a cubical complex is defined to be the maximum genus of all surfaces that are subcomplexes of the cubical complex. A formula …

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An Exposition Of The Deterministic Polynomial-Time Primality Testing Algorithm Of Agrawal-Kayal-Saxena, Robert Lawrence Anderson Jun 2005

An Exposition Of The Deterministic Polynomial-Time Primality Testing Algorithm Of Agrawal-Kayal-Saxena, Robert Lawrence Anderson

Theses and Dissertations

I present a thorough examination of the unconditional deterministic polynomial-time algorithm for determining whether an input number is prime or composite proposed by Agrawal, Kayal and Saxena in their paper [1]. All proofs cited have been reworked with full details for the sake of completeness and readability.

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Matrix Representations Of Automorphism Groups Of Free Groups, Ivan B. Andrus Jun 2005

Matrix Representations Of Automorphism Groups Of Free Groups, Ivan B. Andrus

Theses and Dissertations

In this thesis, we study the representation theory of the automorphism group Aut (Fn) of a free group by studying the representation theory of three finite subgroups: two symmetric groups, Sn and Sn+1, and a Coxeter group of type Bn, also known as a hyperoctahedral group. The representation theory of these subgroups is well understood in the language of Young Diagrams, and we apply this knowledge to better understand the representation theory of Aut (Fn). We also calculate irreducible representations of Aut (Fn) in low dimensions and for small n.

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Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff Jun 2005

Statistical Properties Of Thompson's Group And Random Pseudo Manifolds, Benjamin M. Woodruff

Theses and Dissertations

The first part of our work is a statistical and geometric study of properties of Thompson's Group F. We enumerate the number of elements of F which are represented by a reduced pair of n-caret trees, and give asymptotic estimates. We also discuss the effects on word length and number of carets of right multiplication by a standard generator x0 or x1. We enumerate the average number of carets along the left edge of an n-caret tree, and use an Euler transformation to make some conjectures relating to right multiplication by a generator. We describe a computer algorithm which produces …

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Computational Optical Biopsy, Yi Li, Ming Jiang, Ge Wang Jun 2005

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 …

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Classifying Homotopy Types Of One-Dimensional Peano Continua, Mark H. Meilstrup Jun 2005

Classifying Homotopy Types Of One-Dimensional Peano Continua, Mark H. Meilstrup

Theses and Dissertations

Determining the homotopy type of one-dimensional Peano continua has been an open question of some interest. We give a complete invariant of the homotopy type of such continua, which consists of a pair of subspaces together with a relative homology group. Along the way, we describe reduced forms for one-dimensional Peano continua.

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Three Pension Cost Methods Under Varying Assumptions, Linda S. Grizzle Jun 2005

Three Pension Cost Methods Under Varying Assumptions, Linda S. Grizzle

Theses and Dissertations

A pension plan administrator promises certain benefits in the future in exchange for labor today. In order to budget for this expense and create more security for the participant, the administrator uses a pension cost method. Each cost method assigns a portion of the future liability to the current year. This is called the normal cost. We calculate the normal cost under three cost methods using different annuity, interest and inflation assumptions. Then we make comparisons between cost methods as well as between assumption changes. The cost methods considered in this paper are the unit credit cost method, projected unit …

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Object Information Repository In A Christian Theory Of Technology, Longy O. Anyanwu Jun 2005

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 …

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The Five Orders Of Ignorance: Knowledge, Ignorance, And The Nature Of Software, Phillip Armour Jun 2005

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 …

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Mathematics As Poesis: A Preliminary Project Report, Sam Stueckle, Jeremy Case, Ken Constantine, Troy Riggs Jun 2005

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.

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Integrating Catholic And Marianist Historical Perspectives In A Mathematics Coruse For Elementary Education Majors, Mary Wagner-Krankel Jun 2005

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.

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Does The Success Of Mathematics Defeat Naturalism?, Russell W. Howell Jun 2005

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.

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The Artificial Gravity Pitch, Andrew Simoson Jun 2005

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.

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Explicit Null Space Of Discrete Laplacian, Hanna Vanderzee Jun 2005

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 …

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Artificial Intelligence: Can We Create Machines In Our Own Image?, Derek C. Shuurman Jun 2005

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 …

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Integration Of Faith, Learning, And Christian Vocation With First-Year Mathematics Majors, Doug Phillippy, Angela Hare Jun 2005

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, …

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Writing Math Lessons That Integrate Christian Beliefs: The Kuyers Institute Grant Project, Dave Klanderman, Gary Talsma Jun 2005

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.

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A Christian Constructivist? The Impact Of Worldview On Learning Theories And The Mathematics Education Research Community, Jeffrey Barrett, Dave Klanderman Jun 2005

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.

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Teaching The History Of Mathematics Using Architecture And Art, Maria Zack Jun 2005

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 …

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