Physical Sciences and Mathematics Commons^™

Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller

Mathematics and Statistics Faculty Publications

No abstract provided.

Extension Of The Method Of Quasilinearization For Stochastic Initial Value Problems, Naseer Shahzad, Farzana A. Mcrae

Mathematics and System Engineering Faculty Publications

In this paper we extend the method of quasilinearization to stochastic initial value problems. Further we prove that the iterates converge uniformly almost surely to the unique solution and the convergence is quadratic.

A Note On Reordering Ordered Topological Spaces And The Existence Of Continuous, Strictly Increasing Functions, Joe Mashburn

Mathematics Faculty Publications

The origin of this paper is in a question that was asked of the author by Michael Wellman, a computer scientist who works in artificial intelligence at Wright Patterson Air Force Base in Dayton, Ohio. He wanted to know if, starting with Rn and its usual topology and product partial order, he could linearly reorder every finite subset and still obtain a continuous function from Rⁿ into R that was strictly increasing with respect to the new order imposed on Rⁿ. It is the purpose of this paper to explore the structural characteristics of ordered topological spaces …

Generalized Geynman Integrals: The 𝓛(L2, L2) Theory, Chull Park, David Skough

Department of Mathematics: Faculty Publications

In this paper we develop an 𝓛(L₂(R), L₂(R)) theory for the Feynman integral of functionals of general stochastic processes.

Dynamic Phase Steepening In Alfven Waves, Stephen R. Granade

Honors Theses

Our solar system contains more activity and complexity than can be seen through a telescope. One such "invisible" phenomenon is the solar wind, created by a steady stream of particles blasted away from the sun in all directions. The sun's donut-shaped magnetic field lines channel this stream. Particles moving along the field lines perform an intricate helical dance, with ions winding one way and electrons the other.

The solar wind shapes and is shaped by the magnetic fields of the planets and the sun. If left undisturbed by outside influences, the earth's magnetic field, like the sun's, would resemble a …

Intersecting Self-Similar Cantor Sets, J. J. P. Veerman

Mathematics and Statistics Faculty Publications and Presentations

We define a self-similar set as the (unique) invariant set of an iterated function system of certain contracting affine functions. A topology on them is obtained (essentially) by inducing the C ¹- topology of the function space. We prove that the measure function is upper semi-continuous and give examples of discontinuities. We also show that the dimension is not upper semicontinuous. We exhibit a class of examples of self-similar sets of positive measure containing an open set. If C ₁ and C ₂ are two self-similar sets C ₁ and C ₂ such that the sum of their dimensions …

A Convergent Reconstruction Method For An Elliptic Operator In Potential Form, Lester Caudill

Department of Math & Statistics Faculty Publications

We investigate the problem of recovering a potential q(x) in the equation -∆u + q(x)u = 0 from overspecified boundary data on the unit square in R². The potential is characterized as a fixed point of a nonlinear operator, which is shown to be a contraction on a ball in C^∝. Uniqueness of q(x) follows, as does convergence of the resulting recovery scheme. Numerical examples, demonstrating the performance of the algorithm, are presented.

Metode De Calcul În Analiza Matematică, Florentin Smarandache, C. Dumitrescu

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.

Fixed Points Of Generalized Contractive Multi-Valued Mappings, Peter Z. Daffer, Hideaki Kaneko

Mathematics & Statistics Faculty Publications

In a recent paper N. Mizoguchi and W. Takahashi gave a positive answer to the conjecture of S. Reich concerning the existence of fixed points of multi-valued mappings that satisfy a certain contractive condition. In this paper, we provide an alternative and somewhat more straightforward proof for the theorem of Mizoguchi and Takahashi. Also the problems associated with fixed points of weakly contractive multi-valued mappings are studied. Finally, we make a few comments that improve other results from their paper (J. Math. Anal. Appl. 141 (1989), 177-188).

Error Estimates And Lipschitz Constants For Best Approximation In Continuous Function Spaces, M. Bartelt, W. Li

Mathematics & Statistics Faculty Publications

We use a structural characterization of the metric projection PG(f), from the continuous function space to its one-dimensional subspace G, to derive a lower bound of the Hausdorff strong unicity constant (or weak sharp minimum constant) for PG and then show this lower bound can be attained. Then the exact value of Lipschitz constant for PG is computed. The process is a quantitative analysis based on the Gâteaux derivative of PG, a representation of local Lipschitz constants, the equivalence of local and global Lipschitz constants for lower semicontinuous mappings, and construction …

A Logistic Model Of Periodic Chemotherapy, J. C. Panetta

Mathematics & Statistics Faculty Publications

A logistic differential equation with a time-varying periodic parameter is used to model the growth of cells, in particular cancer cells, in the presences of chemotherapeutic drugs. The chemotherapeutic effects are modeled by a periodic parameter that modifies the growth rate of the cell tissue. A negative growth rate represents the detrimental effects of the drugs. A simple criterion is obtained for the behavior of the chemotherapy.

Linear Time Optimization Algorithms For P4-Sparse Graphs, Beverly Jamison, Stephan Olariu

Computer Science Faculty Publications

Quite often, real-life applications suggest the study of graphs that feature some local density properties. In particular, graphs that are unlikely to have more than a few chordless paths of length three appear in a number of contexts. A graph G is P₄-sparse if no set of five vertices in G induces more than one chordless path of length three. P₄-sparse graphs generalize both the class of cographs and the class of P₄-reducible graphs. It has been shown that P₄-sparse graphs can be recognized in time linear in the size of the …

An Optimal Path Cover Algorithm For Cographs, R. Lin, S. Olariu

Computer Science Faculty Publications

The class of cographs, or complement-reducible graphs, arises naturally in many different areas of applied mathematics and computer science. In this paper, we present an optimal algorithm for determining a minimum path cover for a cograph G. In case G has a Hamiltonian path (cycle) our algorithm exhibits the path (cycle) as well.

Modelling And Risk Analysis Of The Western Rock Lobster (Panulirus Cygnus) Fishery Of Western Australia, C. S. Yap

Theses: Doctorates and Masters

The predictive power for short-term forecasting of selected biomass dynamic models was examined using the standardised catch and effort data from the 1944/45 to 1990/91 season of the western rock lobster. Risk analysis of the fishery based on the predicted fishing efforts with the Deriso-Schnute delay-difference model indicates a high probability of recruitment failure. Some hypothetical management strategies of reducing fishing effort were evaluated by taking into consideration the total catch and biological risk to the fishery.

Transhipment Problem, Salt Exportation, Brian Hogben

Theses : Honours

In order to improve its shipping operations a major salt exporter needs to reduce costs, increase market share and improve customer service. This thesis examines the use of linear (LP) and nonlinear programming (NLP) as a means of solving a nonlinear transhipment problem associated with the export of salt. Tho feasibility of using a LP or NLP approach is explored, taking into consideration the computational time and useability of the models. To meet the demands of their customers the company currently uses heuristic methods to allocate varying size ships to different routes. To remain competitive the shipping options that are …

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.

Distinct Products Of Triples In Finite Groups, Curtis Z. Mitchell

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group and let D_i(G) be the proportion of triples ( x , y , z ) of elements in G such that the cardinality of { xyz , xzy , yxz, yzx , zxy , zyx } is i. In this paper we show that:

i) The average value of D_i is either 1 or at least 53/32.

ii) D₂= 0 ==> D₃ = D₄ = D₅ = D₆ = 0;

iii) D₃= 0 ==> D₄ = D₅ = 0

High Breakdown Rank-Based Estimates For Linear Models, William H. Chang

Dissertations

No abstract provided.

The Theory And Applications Of Stratified Graphs, Reza Rashidi

Dissertations

Physical design is one of several stages in the design of a VLSI chip. In this stage, the specifications of an electrical circuit are converted into a geometrical model. Problems concerning the physical design stage can often be studied by means of graphs. The problems encountered here are routing problems and concern placement of vertices, which represent wires, into layers. All this gives rise to a class of graphs whose vertices are partitioned into classes. Such graphs are called stratified graphs. In this dissertation, we formally define stratified graphs, study their properties, and investigate various algorithmic problems related to these …

Computing Norad Mean Orbital Elements From A State Vector, Dwight E. Andersen

Theses and Dissertations

NORAD maintains and disseminates mean orbital elements on Earth-orbiting satellites in the form of Two-Line Element Sets (TLE). Five mathematical propagator models were developed for NORAD's use to predict the position and velocity using TLEs. This study investigated two approaches, Newton's method and direct iteration, to inverting this process by iterating to obtain NORAD-compatible mean orbital elements from a position and velocity state vector and the drag term. The Newton's iteration method was developed but not tested. The less computationally intensive direct iteration method was developed, coded in FORTRAN, and tested. The initial guess and subsequent corrections in the iterative …

A Bootstrap Method To Analyze An Intervention Model With Autoregressive Error Terms, Scott D. Mcknight

Dissertations

The analysis of a particular time-series intervention model involving lag one autoregressive (AR(1)) error terms is the focus of this dissertation. The method of ordinary least squares, and several two stage procedures that are commonly used to analyze this intervention model are examined. The two stage Cochrane-Orcutte, Durbin, and generalized least squares procedures each requires estimation of the AR(1) parameter in stage one before hypothesis testing about the intervention parameters can be performed in stage two. Using Monte Carlo experiments we show that the AR(1) estimates commonly used in these procedures are poor and consequently the stage two hypothesis tests …

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. …

Series Solutions, Factorials, And The Gamma Function, Steven J. Wilson

Topics in Mathematics

Using a power series to solve an ordinary differential equation will often result in a solution whose general term involves a product of terms from an arithmetic sequence. This paper explores how factorials and the gamma function can be used to rewrite such general terms in a closed form.

An Inverse Problem In Thermal Language, Kurt M. Bryan, Lester Caudill

Mathematical Sciences Technical Reports (MSTR)

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring of the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has of data at every point on the boundary of the region and 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 various experimental configurations.

Rapid Relaxation Of An Axisymmetric Vortex, Andrew J. Bernoff, Joseph F. Lingevitch

All HMC Faculty Publications and Research

In this paper it is argued that a two‐dimensional axisymmetric large Reynolds number (Re) monopole when perturbed will return to an axisymmetric state on a time scale (Re^1/3) that is much faster than the viscous evolution time scale (Re). It is shown that an arbitrary perturbation can be broken into three pieces; first, an axisymmetric piece corresponding to a slight radial redistribution of vorticity; second, a translational piece which corresponds to a small displacement of the center of the original vortex; and finally, a nonaxisymmetric perturbation which decays on the Re^1/3 time scale due to a shear/diffusion …

Perturbations Of Certain Reflexive Algebras, David R. Pitts

Department of Mathematics: Faculty Publications

In this note we use cohomological techniques to prove that if there is a linear map between two CSL algebras which is close to the identity, then the two CSL algebras are similar. We use our result to show that if 2' is a purely atomic, hyperreflexive CSL with uniform infinite multiplicity which satisfies the 4-cycle interpolation condition, then there are constants d, C > 0 such that whenever L is another CSL such that d(Alg2' , AlgL) < d, then there is an invertible operator S such that S Alg2'S-1 = AlgL and IISII liS-III < 1 + Cd(AIg2' , AIgL).

A Numerical Analysis Of Smoothed Particle Hydrodynamics, David A. Fulk

Theses and Dissertations

This dissertation studies the numerical method of Smoothed Particle Hydrodynamics SPH as a technique for solving systems of conservation equations. The research starts with a detailed consistency analysis of the method. Higher dimensions and non-smooth functions are considered in addition to the smooth one dimensional case. A stability analysis is then performed. Using a linear technique, an instability is found. Solutions are proposed to resolve the instability. Also a total variation stability analysis is performed leading to a monotone form of SPH. The concepts of consistency and stability are then used in a convergence proof. This proof uses lemmas derived …

Optimal Pulsed Pumping For Aquifer Remediation When Contaminant Transport Is Affected By Rate-Limited Sorption: A Calculus Of Variation Approach, Richard T. Hartman

Theses and Dissertations

The remediation of groundwater contamination continues to persist as a social and economic problem due to increased governmental regulations and public health concerns. Additionally, the geochemistry of the aquifer and the contaminant transport within the aquifer complicates the remediation process to restore contaminated aquifers to conditions compatible with health-based standards. Currently, the preferred method for aquifer cleanup pump-and-treat has several limitations including, the persistence of sorbed chemicals on soil matrix and the long term operation and maintenance expense. The impetus of this research was to demonstrate that a calculus of variations approach could be applied to a pulsed pumping aquifer …

Applied Mathematics Should Be Taught Mixed, Gary I. Brown

Humanistic Mathematics Network Journal

No abstract provided.

Isospectral Graphs And The Expander Coefficient, Ian Campbell Walters Jr.

Dissertations

The expander coefficient of a graph is a parameter that is utilized to quantify the rate at which information is spread throughout a graph. The eigenvalues of the Lapladan of a graph provide a bound for the expander coefficient of the graph. In this dissertation, we construct many pairs of isospectral graphs with different expander coefficients.

In Chapter I, we define the problem and present some preliminary definitions. We then introduce two constructions that are related to graph composition and that may be employed to produce cospectral and isospectral graphs.

In Chapter II, we investigate the connectivity of and distance …