Applied Mathematics Commons^™

Computations For A Vibrating System Diagonalize The Variance, J. N. Boyd, P. N. Raychowdhury

Mathematics and Applied Mathematics Publications

The transformations to diagonalize potential energy matrices for coupled harmonic oscillators will also diagonalize the variance when written in matrix form. After a brief review of a geometrical interpretation of the variance, the transformations are described and an example is given.

Stability Properties And Integrability Of The Resolvent Of Linear Volterra Equations, Muhammad Islam, Paul W. Eloe

Mathematics Faculty Publications

Integrability of the resolvent and the stability properties of the zero solution of linear Volterra integrodifferential systems are studied. In particular, it is shown that, the zero solution is uniformly stable if and only if the resolvent is integrable in some sense. It is also shown that, the zero solution is uniformly asymptotically stable if and only if the resolvent is integrable and an additional condition in terms of the resolvent and the kernel is satisfied. Finally, the integrability of the resolvent is obtained under an explicit condition.

Mathematical And Theological Beliefs: A Cognitive Science Perspective, Ron Benbow

ACMS Journal 2004

In recent years, research studies have shown that control decisions and processes, beliefs about the nature of mathematics, attitudes, and other affective variables have enormous impact on the mathematical performance of students. This paper gives an overview of the research on mathematical beliefs and reviews some work done in Christian education relating to theological beliefs. It then compares the two.

Mathematics From The Viewpoint Of Science In Context, Johan Deklerk

ACMS Journal 2004

This is the first of a series of papers presented over several years by deKlerk exploring the notion of how mathematics might be taught from a Christian perspective. In this paper, he introduces the notion of context as the basis for such an approach. He then discusses seven contexts a teacher can employ.

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).

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.

Optimality Conditions For Systems Driven By Nonlinear Evolution Equations, Nikolaos S. Papageorgiou

Mathematics and System Engineering Faculty Publications

Using the Dubovitskii-Milyutin theory we derive necessary and sufficient conditions for optimality for a class of Lagrange optimal control problems monitored by a nonlinear evolution equation and involving initial and/or terminal constraints. An example of a parabolic control system is also included.

Bulk Input Queues With Quorum And Multiple Vacations, Jay Yellen, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The authors study a single-server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less than r and not greater than R(≥r). The server takes vacations each time the queue level falls below r(≥1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics …

Exp For Windows, Version 3.0 A Software Review, Donn E. Miller-Harnish

Mathematics and System Engineering Faculty Publications

No abstract provided.

Stability Of Conditionally Invariant Sets And Controlled Uncertain Dynamic Systems On Time Scales, V. Lakshmikantham

Mathematics and System Engineering Faculty Publications

A basic feedback control problem is that of obtaining some desired stability property from a system which contains uncertainties due to unknown inputs into the system. Despite such imperfect knowledge in the selected mathematical model, we often seek to devise controllers that will steer the system in a certain required fashion. Various classes of controllers whose design is based on the method of Lyapunov are known for both discrete [4], [10], [15], and continuous [3–9], [11] models described by difference and differential equations, respectively. Recently, a theory for what is known as dynamic systems on time scales has been built …

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 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.

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 …

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 …

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 …

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.

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.

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.

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.

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 …

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 …

Model For Complete Drawdown Of Floating Solids In Stirred Tank Reactors, J Mmbaga

Tanzania Journal of Engineering and Technology (TJET)

A Semi-empirical model has been developed on the basis of Kolmogoroff's theory of isotropic turbulence to determine the minimum drawdown speed for floating solids in a mechanically agitated vessel. An adjustable pa- rameter in the model is found to be afunction of impeller type and position in a vessel. A simplified representation of macroscopicflow pattern, rep- resenting the circulation flow in a vessel depending on impeller pumping characteristic is developed to account for recirculation pattern.

Optimum Geometrical Parameters For Prismatic Folded Plate Roofs: System- Atic Search Approach, N Mwitta

Tanzania Journal of Engineering and Technology (TJET)

Folded plate structures have unique structural advantages over conven- nonal beam-and-slab structural forms. Selection of optimum geometrical parameters in design would make folded plate roofs more appealing to the national construction industry in terms ofcost. This paper presents a study on shape optimization of prismatic folded plate roofs for minimum weight of the structure per unit covered area. A computer based systematic search approach has been employed.for the optimization study, while the tranyeer matrix method has been used for analysis. Curves opriinum geometrical parameters versus span have been pre sented for three commonly used shapes of prismatic folded plate roofs. …

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

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 …

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 …

Msda A Machinery Selection Decision Aid For Stubble Management Practices, Linda Leonard, Andrew Green

Grain and other field crops published reports

MSDA is a user friendly program developed to help farmers predict stubble outcomes before acting on their management practice. This manual is an accompaniment to a computer program designed on Micorsoft Excel-macros. Its aim is to help farmers assess their current machinery and stubble handling ability and view options that may be adopted as best practice for their properties.

The program is designed with the complete season in mind. Information is gathered on the full complement of machinery used from harvest through to seeding, to allow farmers to see all choices available and enable them to choose the best system …