Physical Sciences and Mathematics Commons^™

Isometries In Three Space And The Seven Solid Crystal Systems, Iris Magee

Theses Digitization Project

No abstract provided.

Stability And Resolution In Thermal Imaging, Lester Caudill, Kurt Bryan

Department of Math & Statistics Faculty Publications

This paper examines an inverse problem which arises in thermal imaging. We investigate the problem of detecting and imaging corrosion in a material sample by applying a heat flux and measuring the induced temperature on the sample's exterior boundary. The goal is to identify the profile of some inaccessible portion of the boundary. We study the case in which one has data at every point on the boundary of the region, as well as the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for …

Analysis On A Hyperplane Of The Quaternions, Pamela Jean Whelchel

Theses Digitization Project

No abstract provided.

Estimating Transition Probabilities From Aggregate Samples Augmented By Haphazard Recaptures, D. L. Hawkins, Jerome Eisenfeld, C. P. Han

Mathematics Technical Papers

Transition probabilities provide a convenient summary of changes in a categorical trait over time in a population. The difficulties of estimating such probabilities based on only aggregate data from repeated sampling are well known. We give here a method for augmenting aggregate data with haphazard recapture data, which can dramatically improve the estimation precision of transition probabilities. The method requires a rather high sampling fraction to provide sufficient numbers of recaptures. It is based on a generalized nonlinear least squares strategy which yields transition probability estimates preserving their natural parameter space, and which are asymptotically efficient. The asymptotic theory is …

A Semiclassical, Dynamical Model Of The Water Molecule, Donald Greenspan

Mathematics Technical Papers

A model of the ground state water molecule is formulated dynamically and studied by computer simulations. Excellent approximations of NMR determined bond angles and bond lengths are achieved through electron pairing and simulation of ice I.

Heron's Problem In The Minkowski Plane, Mostafa Ghandehari

Mathematics Technical Papers

Heron's problem in the Euclidean plane is that of minimizing the length of a path that joins two points on one side of a line and intersects the line. A generalization in the Minkowski plane is given and used to discuss reflection properties of conics.

Computer Modelling Of A Dynamical Water Molecule, Donald Greenspan

Mathematics Technical Papers

A model of a ground state water molecule is formulated dynamically and studied by computer simulations. The enigmatic 104.5° bond angle is approximated by introducing the effects of neighboring molecules in a crystaline state. The numerical methodology used conserves the system energy at all times. Illustrative examples are described and discussed.

A New Method For Approximating Quantum Dynamical Phenomena Over Short (And Sometimes Long) Time Periods, Donald Greenspan

Mathematics Technical Papers

Approximate electron and proton motions are simulated for short time periods for using a special case of the quantum mechanical Ehrenfest equations. Attention is directed only to ground state. A numerical method is employed which conserves the ground state energy at all times. Large proton motions are found, with electron trajectories oscillating between the protons, but concentrating around them.

The Trace Of An Abelian Group:An Application To Digraphs, J. M. Burns, Brendan Goldsmith

Articles

The trace of a finite Abelian group is used to give a short proof of a result of Arlinghaus and Harary on the digraph number of such a group

Fermi Problems: Educated Guesses, John A. Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Nozzle Flow With Vibrational Nonequilibrium, John Gary Landry

Mathematics & Statistics Theses & Dissertations

Flow of nitrogen gas through a converging-diverging nozzle is simulated. The flow is modeled using the Navier-Stokes equations that have been modified for vibrational nonequilibrium. The energy equation is replaced by two equations. One equation accounts for energy effects due to the translational and rotational degrees of freedom, and the other accounts for the affects due to the vibrational degree of freedom. The energy equations are coupled by a relaxation time which measures the time required for the vibrational energy component to equilibrate with the translational and rotational energy components. An improved relaxation time is used in this thesis. The …

A Mathematical Model Of Cycle Chemotherapy, J. C. Panetta, J. Adam

Mathematics & Statistics Faculty Publications

A mathematical model is used to discuss the effects of cycle-specific chemotherapy. The model includes a constraint equation which describes the effects of the drugs on sensitive normal tissue such as bone marrow. This model investigates both pulsed and piecewise-continuous chemotherapeutic effects and calculates the parameter regions of acceptable dose and period. It also identifies the optimal period needed for maximal tumor reduction. Examples are included concerning the use of growth factors and how they can enhance the cell kill of the chemotherapeutic drugs.

Duality On Noncompact Manifolds And Complements Of Topological Knots, Gerard A. Venema

University Faculty Publications and Creative Works

Let be the image of a topological embedding of into. In this paper the homotopy groups of the complement. are studied. In contrast with the situation in the smooth and piecewise-linear categories, it is shown that the first nonstandard homotopy group of the complement of such a topological knot can occur in any dimension in the range 1 through n - 2. If the first nonstandard homotopy group of the complement occurs above the middle dimension, then the end of must have a nontrivial homotopy group in the dual dimension. The complement has the proper homotopy type of if both …

Slow Motion In One-Dimensional Cahn-Morral Systems, Christopher P. Grant

Faculty Publications

In this paper we study one-dimensional Cahn-Morral systems, which are the multicomponent analogues of the Cahn-Hilliard model for phase separation and coarsening in binary mixtures. In particular, we examine solutions that start with initial data close to the preferred phases except at finitely many transition points where the data has sharp transition layers, and we show that such solutions may evolve exponentially slowly; i.e., if ε is the interaction length then there exists a constant C such that in exp(C/ε) units of time the change in such a solution is o(1). This corresponds to extremely slow coarsening of a multicomponent …

On The Relationship Between A Graph And The Cycle Graph Of Its Complement, Christian P. Lopez

Theses: Doctorates and Masters

From an arbitrary graph G, another graph called the cycle graph of G and denoted by C(G) can be derived. The cycle graph C(G) of G has as its vertices the chordless cycles of G and two vertices in C(G) are adjacent if and only if the corresponding chordless cycles have at least one edge in common.

A Spigot Algorithm For The Digits Of Pi, Stan Wagon

Stan Wagon, Retired

No abstract provided.

Shape Criteria Of Bernstein-Bezier Polynomials Over Simplexes, Tian-Xiao He

Tian-Xiao He

This paper discusses the criteria of convexity, monotonicity, and positivity of Bernstein- Bezier polynomials over simplexes.

Calculus In The Operating Room, Stan Wagon, P. Toy

Stan Wagon, Retired

No abstract provided.

Asymptotic Behavior Of Solutions Of Asymptotically Constant Coefficient System Of Linear Differential Equations, William F. Trench

William F. Trench

No abstract provided.

Invertibly Convergent Infinite Products Of Matrices, With Applications To Difference Equations, William F. Trench

William F. Trench

No abstract provided.

Encryption/Decryption Dickwads Of Cipherspace, Raleigh Muns

Raleigh Muns

Model And Design-Based Analysis Of Complex Surveys., Joydip Mitra Dr.

Doctoral Theses

We consider estimating the total Y of a variable y defined on a survey population. The survey is complex only in the sense that we admit sample selection with arbitrary probabilities. Our 'analysis' consists in examining efficacies of conf Idence intervals for the For this we need point estimators and or mean square error (MSE) variance { estimators, respectively say, total. the corresponding e and v. The distribution, resulting from repeated sampling, of the pivotal quantity d = (e-Y)/V 1s supposed to approximate that of standard normal deviate t or of Students t with (n-1) degrees of freedom, assuming large …

Computing Χ² Values, John F. Dooley, Daniel C. St Clair, William E. Bond

Mathematics and Statistics Faculty Research & Creative Works

Textbooks and courses on numerical algorithms contain numerous examples which lead students to believe that the algorithm of choice for computing the zeros of a function f1994 is Newton's algorithm. In many of these courses little or no time is spent in providing students with "real world" experiences where Newton's method fails. The work presented in this paper describes a slow convergence problem encountered while trying to use Newton to estimate values for the 2 distributions. The problem occurred while the authors were trying to implement a well-known machine learning algorithm from the field of artificial intelligence. The function being …

Computer Simplification Of Engineering Systems Formulas, J. W. Helton, Mark Stankus, John Wavrik

Mathematics

Currently, the three most popular commercial computer algebra systems are Mathematica, Maple, and MACSYMA (the 3 M’s). These systems provide a wide variety of symbolic computation facilities for commutative algebra and contain implementations of powerful algorithms in that domain. The Gröbner Basis Algorithm, for example, is an important tool used in computation with commutative algebras and in solving systems of polynomial equations.

On the other hand, most of the computation involved in linear control theory is performed on matrices and these do not commute. A typical issue of IEEE TAC is full of A B C D type linear systems …

Square Roots Of Finite Groups - Ii, Matthew Devos, David Mcadams, Rebecca Rapoport

Mathematical Sciences Technical Reports (MSTR)

A subset R of a finite group G is a square root of G if R² = G. If R is a square root of G for which |R|² = G, then R is referred to as a perfect square root of G. It can be shown using character theory that perfect square roots do not exist. The purpose of this paper is to work toward an elementary proof of this result.

Review Of “Linear Programming And Related Problems” By E. Nering And A. W. Tucker, Stephen B. Maurer

Mathematics & Statistics Faculty Works

No abstract provided.

Topologies Invariant Under A Group Action, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

We study links between faithful group actions on a set and topologies on that set. In one direction, a group action has its invariant topologies (so we may regard members of the action to be homeomorphisms relative to those topologies); in the other direction, a topology has its preserving group actions (i.e., the subgroups of the homeomorphism group of the topology). This two-way passage allows us to discuss topological features of group actions as well as symmetry features of topologies.

Quasireversibility Methods For Non-Well-Posed Problems, Gordon W. Clark, Seth F. Oppenheimer

Faculty Articles

The nal value problem,

ae u t + Au = 0 ; 0 ! t ! T u(T ) = f

with positive self-adjoint unbounded A is known to be ill-posed. One approach to dealing with this has been the method of quasireversibility, where the operator is perturbed to obtain a well-posed problem which approximates the original problem. In this work, we will use a quasi-boundary-value method, where we perturb the nal condition to form an approximate non-local problem depending on a small parameter. We show that the approximate problems are well posed and that their solutions u converge on …

First Passage Processes In Queuing System Mx/Gr/1 With Service Delay Discipline, Lev M. Abolnikov, Jewgeni H. Dshalalow, Alexander M. Dukhovny

Mathematics and System Engineering Faculty Publications

This article deals with a general single-server bulk queueing system with a server waiting until the queue will reach level r before it starts processing customers. If at least r customers are available the server takes a batch of the fixed size r of units for service. The input stream is assumed to be a compound Poisson process modulated by a semi-Markov process and with a multilevel control of service time. The authors evaluate the steady state probabilities of the queueing processes with discrete and continuous time parameter preliminarily establishing necessary and sufficient conditions for the ergodicity of the processes. …

A Characterization Of Sigma-Symmetrically Porous Symmetrical Cantor Sets, M. Evans, P. Humke, Karen Saxe

Karen Saxe

No abstract provided.