Applied Mathematics Commons^™

Cost Domination In Graphs, David John Erwin

Dissertations

Let G be a connected graph having order at least 2. A function f : V (G) —> {0 , 1 , . . . , diam G} for which f ( v ) < e(v) for every vertex v of G is a cost function on G. A vertex v with f ( v ) > 0 is an f-dominating vertex, and the set Vj~ = {v 6 V(G) : f(v) > 0} of f-dominating vertices is the f-dominating set. An /-dominating vertex v is said to f-dominate every vertex u with d(n, v) < f(u ), while …

Introduction (2001), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2001

Thirteenth ACMS Conference on Mathematics from a Christian Perspective

Table Of Contents (2001), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2001

Thirteenth ACMS Conference on Mathematics from a Christian Perspective

Schedule (2001), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2001

Thirteenth ACMS Conference on Mathematics from a Christian Perspective

Overview Of Fuzzy Logic, Mohamed Trabia

Mechanical Engineering Faculty Presentations

The presentation includes a brief introduction to fuzzy logic and fuzzy logic controllers. These concepts are illustrated by an example of an autonomous vehicle controller.

Comparison Of Two Distributed Fuzzy Logic Controllers For Flexible-Link Manipulators, Linda Z. Shi, Mohamed Trabia

Mechanical Engineering Faculty Presentations

The paper suggests that fuzzy logic controllers present a computationally efficient and robust alternative to conventional controllers. The paper presents two possible structures for the distributed fuzzy logic controller of a single-link flexible manipulator. A linear quadratic regulator method is used to prove the effectiveness of fuzzy logic controllers.

Design Of Fuzzy Logic Controllers For Optimal Performance, Mohamed Trabia

Mechanical Engineering Faculty Presentations

While fuzzy logic controllers are generally robust, the performance of a system whose behavior is not well understood, or that has a large number of coupled inputs and outputs, may be less than optimal. In this paper, nonlinear programming techniques are used to improve the performance of a fuzzy logic controller for navigating an autonomous vehicle.

Incorporating Technology In Mathematics Education: A Suite Of E-Activities For The Modem Mathematics Classroom, Jennifer E. Youngberg

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

National studies indicate major deficiencies in students' understanding of mathematics. Research suggests that students tend to view mathematics as a set of computational rules rather than a process of discovery and a tool for problem-solving. Most students fail to grasp the concepts behind the computations.

Technology provides a partial solution to this problem. Over the past decade, computers have emerged as a powerful tool in education. Computers place the control of action in the learning process with the student. They allow students to experiment with, explore, and discover mathematics at their own pace. With computers, students can consider more examples …

Separability Of Tilings, Nicholas Baeth, Jason Deblois, Lisa Powell

Mathematical Sciences Technical Reports (MSTR)

A tiling by triangles of an orientable surfaces is called kaleidoscopic if the local reflection in any edge of a triangle extends to a global isometry of the surface. Given such a global reflection the fixed point subset of the reflection consists of embedded circles (ovals) whose union is called the mirror of the reflection. The reflection is called separating if removal of the mirror disconnects the surface into two components. We consider surfaces such that the orientation preserving subgroup of the tiling group generated by the reflection is cyclic or abelian. A complete classification of those surfaces with separating …

A Low Power Application-Specific Integrated Circuit (Asic) Implementation Of Wavelet Transform/Inverse Transform, Daniel N. Harvala

Theses and Dissertations

A unique ASIC was designed implementing the Haar Wavelet transform for image compression/decompression. ASIC operations include performing the Haar wavelet transform on a 512 by 512 square pixel image, preparing the image for transmission by quantizing and thresholding the transformed data, and performing the inverse Haar wavelet transform, returning the original image with only minor degradation. The ASIC is based on an existing four-chip FPGA implementation. Implementing the design using a dedicated ASIC enhances the speed, decreases chip count to a single die, and uses significantly less power compared to the FPGA implementation. A reduction of RAM accesses was realized …

Interstate 69 And The Accessibility Of Indiana's Major Cities, Tracy Blankenship Markert

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Constructing A Large Number Of Nonisomorphic Graphs Of Order, P. O. De Wet

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Stable Matchings In The Couples Problem, Dinielle Bianco, Stephen Hartke, Anne Larimer

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Is Vegas-Style Solitaire Fair?, Missy Dillon, Travis Hall, Patsey Hensley, Kinda Lowder

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

On The Computation Of Viscosity-Shear Rate Temperature Master Curves For Polymeric Liquids, G. T. Helleloid

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.

Geodesics Of Ruled Surfaces, Steven John Ramirez

Theses Digitization Project

The focus of this thesis is on the investigation of the geodesics of ruled surfaces.

Intractability And Undecidability In Small Sets Of Wang Tiles, Adam Delisse

Inquiry: The University of Arkansas Undergraduate Research Journal

Imagine a never-ending checkerboard, red and black squares alternating forever in every direction. Now close your eyes, wait for a second, and open them again. There is still the checkerboard, but is it different? Has somebody moved the checkerboard over two squares? Four squares? One million squares? It still looks the same. This is the nature of periodic tilings. Wang tiles are squares, much like the red and black ones used on a checkerboard, except Wang tiles have colors on their edges instead of on the whole square. Also, Wang tiles can only be put edge-to-edge with each other where …

An Analysis Of Unsolvable Linear Partial Differential Equations Of Order One, Laura J. Fields

Inquiry: The University of Arkansas Undergraduate Research Journal

It is difficult to underestimate the importance of differential equations in understanding the physical world. These equations, involving not just simple variables like temperature, speed or mass, but also the derivatives, i.e. the rate of change of these variables, are found in nearly every branch of science. Until the mid 20th century, all such equations were thought to be solvable. This was based on the discovery by Leonard Euler that certain differential equations, called ordinary differential equations (ODEs), are indeed always solvable. While ODEs deal with simple conditions, under which some quantity changes with some other quantity and its derivatives, …

Theism And Mathematical Realism, John Byl

ACMS Journal 2004

This paper examines connections between theism and mathematical realism. Mathematical realism, which offers the best account of mathematics, strongly supports theism. Theism, in turn, supports mathematical realism. Theism readily explains the intricate relations between mathematics, matter, and mind. The attributes of the biblical God provide a justification for classical mathematics.

Mathematics As Worship, David J. Stucki

ACMS Journal 2004

This paper treats worship in a broad, inclusive sense as the primary and necessary response of human beings to their creator. It provides a brief overview of the relationship between mathematics and theology from the Pythagoreans to the present. It argues that all knowledge is contingent upon faith and thus that contemplation of mathematical insights can lead to worship of God.

Investigation Of Optical Interference Effects In The Generalized Eikonal Formalism, Nyok Fah Thong

Student Works (2000-2009)

In recent studies, the generalized eikonal equation and the equation of continuity had been shown able to describe wave phenomena, which cannot be obtained by simple geometrical optics. The time dependent generalized eikonal equation, derived from the time dependent Maxwell wave equation, is able to describe dispersion and soliton effects. This method was exten4ed to include diffraction, self-trapping and self-focusing in linear and non-linear media for stationary waves. For cases that have no analytical solution, the generalized eikonal equation and the equation of continuity are solved numerically. The solutions are in good agreement with the solutions obtained from the Fresnel-Kirchhoff …

Biharmonic Maps On V-Manifolds, Yuan-Jen Chiang, Hongan Sun

Mathematics Articles

We generalize biharmonic maps between Riemannian manifolds into the case of the domain being V-manifolds. We obtain the first and second variations of biharmonic maps on V-manifolds. Since a biharmonic map from a compact V-manifold into a Riemannian manifold of nonpositive curvature is harmonic, we construct a biharmonic non-harmonic map into a sphere. We also show that under certain condition the biharmonic property of f implies the harmonic property of f. We finally discuss the composition of biharmonic maps on V-manifolds.

Topologically Pure Extensions, Peter Loth

Mathematics Faculty Publications

A proper short exact sequence 0→H →G→K→0 (*) in the category of locally compact abelian groups is said to be topologically pure if the induced sequence 0→nH→nG→nK→0 is proper short exact for all positive integers n. Some characterizations of topologically pure sequences in terms of direct decompositions, pure extensions and tensor products are established. A simple proof is given for a theorem on pure subgroups by Hartman and Hulanickl. Using topologically pure extensions, we characterize those splitting locally compact abelian groups whose torsion part is a direct sum of a compact …

Eddy Structures Induced Within A Wedge By A Honing Circular Arc, C. P. Hills

Articles

In this paper we outline an expeditious numerical procedure to calculate the Stokes flow in a corner due to the rotation of a scraping circular boundary. The method is also applicable to other wedge geometries. We employ a collocation technique utilising a basis of eddy (similarity) functions introduced by Moffatt (1964) that allows us to satisfy automatically the governing equations for the streamfunction and all the boundary conditions on the surface of the wedge. The circular honing problem thereby becomes one-dimensional requiring only the satisfaction of conditions on the circular boundary. The advantage of using the Moffatt eddy functions as …

Eddies Induced In Cylindrical Containers By A Rotating End Wall, Christopher Hills

Articles

The flow generated in a viscous liquid contained in a cylindrical geometry by a rotating end wall is considered. Recent numerical and experimental work has established several distinct phases of the motion when fluid inertia plays a significant role. The current paper, however, establishes the nature of the flow in the thus far neglected low Reynolds number regime. Explicitly, by employing biorthogonality relations appropriate to the current geometry, it is shown that a sequence of exponentially decaying eddies extends outward from the rotating end wall. The cellular structure is a manifestation of the dominance of complex eigensolutions to the homogeneous …

A New Compensating Element For A Femtosecond Photoelectron Gun, Bao-Liang Qian, Hani E. Elsayed-Ali

Electrical & Computer Engineering Faculty Publications

Design and analysis of a new compensating element for improving the electron pulse front and compressing the pulse duration in a femtosecond photoelectron gun are described. The compensating element is a small metallic cylindrical cavity in which an external voltage is applied in such a way that a special electric field forms and interacts with the electron pulse. This electric field reduces the distances between the faster and slower electrons inside the cavity and efficiently compensates for electron pulse broadening caused by the photoelectron energy spread and space charge effects. Poisson's equation and the equation of motion are solved to …

Artin-Schreier Families And 2-D Cycle Codes, Cem Guneri

LSU Doctoral Dissertations

We start with the study of certain Artin-Schreier families. Using coding theory techniques, we determine a necessary and sufficient condition for such families to have a nontrivial curve with the maximum possible number of rational points over the finite field in consideration. This result produces several nice corollaries, including the existence of certain maximal curves; i.e., curves meeting the Hasse-Weil bound.We then present a way to represent two-dimensional (2-D) cyclic codes as trace codes starting from a basic zero set of its dual code. This representation enables us to relate the weight of a codeword to the number of rational …

Bounding The Wild Set (Counting The Minimum Number Of Wild Primes In Hilbert Symbol Equivalent Number Fields), Marius M. Somodi

LSU Doctoral Dissertations

This dissertation makes a contribution to the study of Witt rings of quadratic forms over number fields. To every pair of algebraic number fields with isomorphic Witt rings one can associate a number, called the minimum number of wild primes. The situation is particularly nice when this number is 0; often it is not 0. Earlier investigations have established lower bounds for this number. In this dissertation an analysis is presented that expresses the minimum number of wild primes in terms of the number of wild dyadic primes. This formula not only gives immediate upper bounds, but can be considered …

Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang

Mathematics Faculty Publications

In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a power-law polymer flow in a semi-infinite straight pipe with circular cross section. We show that both models are well-posed and we derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance. We also show estimates for difference between the two solutions in terms of physical data.

Pressure Hallucinations And Patterns In The Brain, Eric Tkaczyk

Morehead Electronic Journal of Applicable Mathematics Archives

No abstract provided.