Physical Sciences and Mathematics Commons^™

Humanistic Mathematics: Personal Evolution And Excavations, Stephen I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

Letters And Comments, Issue 26, 2002, Dick Tahta

Humanistic Mathematics Network Journal

No abstract provided.

Totally Magic Graphs, Geoffrey Exoo, Alan C. H. Ling, John P. Mcsorley, Nicholas C. Phillips, Walter D. Wallis

Articles and Preprints

A total labeling of a graph with v vertices and e edges is defined as a one-to-one map taking the vertices and edges onto the integers 1, 2, · · · , v+e. Such a labeling is vertex magic if the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex, and edge magic if the sum of an edge label and the labels of the endpoints of the edge is constant. In this paper we examine graphs possessing a labeling that is simultaneously …

Mini-Course On Stochastic Systems With Memory (University Of Campinas), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

This is a mini-course consisting of three talks on the theme : ``Stochastic Systems with Memory", given at the Mathematics Institute, University of Campinas, Campinas, Brazil. My visit to Campinas was fully supported by a grant from FAPESP (of the State of Sao Paulo).

Creating Successful Calculus Writing Assignments, Kris H. Green

Mathematical and Computing Sciences Faculty/Staff Publications

I discuss three different writing assignments that I have used in my calculus courses. These assignments are introduced with a discussion of purpose and audience. Defining these qualities of an assignment will ensure that your writing assignments are more successful. The assignments discussed and explored here represent three different purposes: personal, informational and a blend of the two. The audiences for these assignments are diverse and force the students to incorporate particular modes of writing that demonstrate much of their thinking. Assessment of student learning as a result of these assignments is discussed. A fourth writing assignment is developed from …

Computational Geometry Column 43, Joseph O'Rourke

Computer Science: Faculty Publications

The concept of pointed pseudo-triangulations is defined and a few of its applications described.

Nonlinear Interfacial Stability Of Core-Annular Film Flows In The Presence Of Surfactants, Said A. Kas-Danouche

Dissertations

This work is an analytical and computational study of the nonlinear interfacial instabilities found in core-annular flows in the presence of surfactants. Core-annular flows arise when two immiscible fluids (for example water and oil) are caused to flow in a pipe under the action of ail axial pressure gradient. In one typical type of flow regime, the fluids arrange themselves so that the less viscous (e.g. water) lies in the region of high shear near the pipe wall, with the more viscous fluid occupying the core region. Tech nologically, this arrangement provides an advantage since the highly viscous fluid is …

Temporal Synchronization Of Ca1 Pyramidal Cells By High-Frequency, Depressing Inhibition, In The Presence Of Intracellular Noise, Stephen A. Kunec

Dissertations

The Sharp Wave-associated Ripple is a high-frequency, extracellular recording observed in the rat hippocampus during periods of immobility. During the ripple, pyramidal cells synchronize over a short period of time despite the fact that these cells have sparse recurrent connections. Additionally, the timing of synchronized pyramidal cell spiking may be critical for encoding information that is passed on to post-hippocampal targets. Both the synchronization and precision of pyramidal cells is believed to be coordinated by inhibition provided by a vast array of interneurons. This dissertation proposes a minimal model consisting of a single interneuron which synapses onto a network of …

Instability Of Electrified Viscous Films, Knograt Savettaseranee

Dissertations

We examine the stability of a thin two-dimensional liquid film with a regular electric field applied in a direction parallel to an initially flat bounding fluid interface. We study the distinct physical effects of surface tension, van der Waals and electrically induced forces for a viscous incompressible fluid. The film is assumed to be sufficiently thin, and the surface tension and electrically induced forces are large enough that gravity can be ignored to the leading order. Our target is to analyse the nonlinear stability of the flow. We attain this by deriving and numerically solving a set of nonlinear evolution …

Slippage And Change Point Problem With Directional Data., Arnab Kumar Laha Dr.

Doctoral Theses

In this thesis we develop statistical methods for dealing with two problems namely (1) THE SLIPPAGE PROBLEM and (2) THE CHANGE POINT PROB- LEM in the set-up of directional data. In this chapter, we provide an intro- duction to these problems and discuss the importance of the present work. The slippage problem is basically a problem to detect whether any unspecified observation in a given random sample comes from a distribution different from that for all the other remaining observations. This can also be viewed as a problem of outlier detection or that of spuriosity. This problem assumes great importance …

The Mathematics Of T. Benny Rushing, James Keesling, Luis Montejano, Gerard A. Venema

University Faculty Publications and Creative Works

No abstract provided.

Representing Homology Classes Of Simply Connected 4-Manifolds, Vo Thanh Liem, Gerard A. Venema

University Faculty Publications and Creative Works

The main theorem asserts that every 2-dimensional homology class of a compact simply connected PL 4-manifold can be represented by a codimension-0 submanifold consisting of a contractible manifold with a single 2-handle attached. One consequence of the theorem is the fact that every map of S2 into a simply connected, compact PL 4-manifold is homotopic to an embedding if and only if the same is true for every homotopy equivalence. The theorem is also the main ingredient in the proof of the following result: If W is a compact, simply connected, PL submanifold of S4, then each element of H2(W;ℤ) …

Nonorthogonal Polyhedra Built From Rectangles, Melody Donoso, Joseph O'Rourke

Computer Science: Faculty Publications

We prove that any polyhedron of genus zero or genus one built out of rectangular faces must be an orthogonal polyhedron, but that there are nonorthogonal polyhedra of genus seven all of whose faces are rectangles. This leads to a resolution of a question posed by Biedl, Lubiw, and Sun [BLS99].

Local Rings Of Countable Cohen-Macaulay Type, Craig Huneke, Graham J. Leuschke

Mathematics - All Scholarship

We prove (the excellent case of) Schreyer's conjecture that a local ring with countable Cohen-Macaulay type has at most a one-dimensional singular locus. Furthermore we prove that the localization of a Cohen-Macaulay local ring of countable CM type is again of countable CM type.

Communicator-In-Chief: Presidential Use Of Television Past, Present, And Future, Jenna Wasson

Honors Theses

This thesis seeks to determine how television has changed as a communication medium for presidents over the past half century. An evaluation of the evolving ways presidents use television to communicate with and to build support from the American people has been conducted. Presidential communication strategies have been identified by drawing primarily from primary sources written by presidents and White House staff. Television technology and the television audience have changed over the years. Presidents have taken a more pro-active, aggressive role in their efforts to harness television for their own purposes. Why have these changes occurred? What impact have these …

On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li

Yi Li

In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=^N\ω is an exterior domain in ^N, ω⊂^N is a bounded domain with smooth boundary, and N>2. μ⩾0, p>1 are some given constants. K(x) satisfies: K(x)∈C^α_loc(Ω) and ∃C, ϵ, M>0 such that |K(x)|⩽C |x|^l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li

Mathematics and Statistics Faculty Publications

In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=^N\ω is an exterior domain in ^N, ω⊂^N is a bounded domain with smooth boundary, and N>2. μ⩾0, p>1 are some given constants. K(x) satisfies: K(x)∈C^α_loc(Ω) and ∃C, ϵ, M>0 such that |K(x)|⩽C |x|^l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and …

Phase-Space Transport Of Stochastic Chaos In Population Dynamics Of Virus Spread, Lora Billings, Erik M. Bollt, Ira B. Schwartz

Department of Mathematics Facuty Scholarship and Creative Works

A general way to classify stochastic chaos is presented and applied to population dynamics models. A stochastic dynamical theory is used to develop an algorithmic tool to measure the transport across basin boundaries and predict the most probable regions of transport created by noise. The results of this tool are illustrated on a model of virus spread in a large population, where transport regions reveal how noise completes the necessary manifold intersections for the creation of emerging stochastic chaos.

N-Person Cooperative Game Theory Solutions, Coalitions, And Applications, Ragan Nicole Brackin

Masters Theses

This study explores the topic of N-person cooperative game theory. The following paper begins with an introduction to the basic definitions and the- orems of game theory. These definitions and theorems are then used to in- troduce various solution methods and methods of coalition formation. These results are then applied to the airport game, to the supplier-firm-buyer game, and to evolutionary games.

Using The Maple Computer Algebra System As A Tool For Studying Group Theory, Thomas Edmond Cooper, Iii

Masters Theses

The purpose of this study was to show that computers can be powerful tools for studying group theory. Specifically the author examined ways that the computer algebra system Maple can be used to assist in the study of group theory. The study consists of four main parts.

After a brief introduction in chapter one, chapter two discusses simple procedures written by the author to study small finite groups. These procedures rely on the fact that for small finite groups, the elements can all be stored on a computer and tested for various properties. All of the procedures are contained in …

The Uniform Convergence Of Special Standardized Distributions, Marcia Lami

Masters Theses & Specialist Projects

In this thesis, the uniform convergence of two special standardized distributions are examined. The Gamma distribution is standardized, and then the probability density function of the standardized Gamma distribution is shown to converge uniformly to the probability density function of the normal distribution. The F-distribution is standardized, and then the probability density function of the standardized F-distribution is shown to converge uniformly to the probability density function of the normal distribution. Along the way, some other interesting limits are observed.

On Reproducing Kernels And Invariant Subspaces Of The Bergman Shift, George Chailos

Doctoral Dissertations

No abstract provided.

Optimal Control Problems In Pde And Ode Systems, Hem Raj Joshi

Doctoral Dissertations

This dissertation contains three separate optimal control problems involving partial differential equations (PDEs) or ordinary differential equations (ODEs). In each problem, an objective functional representing the goal of the control process is minimized. First, a system of ordinary differential equations which describe the interaction of Human Immunodeficiency Virus (HIV) and CD4+T-cells in the human immune system is studied. Two controls representing drug treatment strategies of this model are explored. Existence and uniqueness results for the optimal control pair are established. The optimality system is derived and then solved numerically using an iterative method with the Runge-Kutta fourth order scheme.

Second, …

Third Order Opial Inequalities, Brandi Michelle Gierhart

Masters Theses

The purpose of the thesis was to find extremals y and constants K for a basic problem and for several variations of the problem. The basic problem was the third order opial inequality. We proved the existence of an extremal of this problem and other related problems. We conjectured that the extremal was a quintic spline with at most one knot, then found the quintic splines and constants for the basic problem and several variations. Maple was an important tool in finding these extremals and constants due to the complexity of the equations. We also proved that these extremals can …

Essays In Indian Corporate Finance., K. V. S. Vinay Dr.

Doctoral Theses

This thesis comprises of three essays in corporate finance focusing on the Indian economy. The first essay contains a theoretical model while the second and the third essays are empirical exercises. In the subsequent paragraphs of this section, we examine the broader issues to which the contents of the thesis contribute.The past few years have seen rising interest in studies of financial insti- tutions and corporate financial policies in countries other than the United States. One of the reasons for such a shift in attention is the diversity in the size and structure of financial arrangements all over the world. …

Boundary Value Problems On The Half Line In The Theory Of Colloids, Ravi P. Agarwal, Donal O'Regan

Mathematics and System Engineering Faculty Publications

No abstract provided.

Modeling And Experimental Verification Of Growth Of An Axisymmetric Cylindrical Rod By Three-Dimensional Laser-Induced Chemical Vapor Deposition, Qing Chen

Doctoral Dissertations

Three-dimensional laser-induced chemical vapor deposition (3D-LCVD) is a recently developed micro-manufacturing process that holds great potential for the production of complex microstructures with high aspect ratio. A laser beam is focused through a vacuum chamber window onto a movable substrate. The heat from the laser at or near the focal spot on the substrate induces the decomposition reaction of precursor gas in the chamber. As a result, solid-phase reaction products are deposited on the substrate to form the microstructure. In this dissertation, a numerical model is developed for simulating kinetically-limited growth of an axisymmetric cylindrical rod by pre-specifying the surface …

A Stirling Encounter With Harmonic Numbers, Arthur T. Benjamin, Gregory O. Preston '01, Jennifer J. Quinn

All HMC Faculty Publications and Research

No abstract provided in this article.

Four-Person Envy-Free Chore Division, Elisha Peterson '00, Francis E. Su

All HMC Faculty Publications and Research

No abstract provided in this article