Applied Mathematics Commons^™

Mathematical Modelling Of Road Bumps, E. S. Massawe

Tanzania Journal of Engineering and Technology (TJET)

In this paper, a general mathematical model that may be used for construction of a road bump on an inclined road is developed. It is shown that if the parameters for the inclination are set to zero, the resulting model reflects the special case of a flat road. Existing experiences are briefly highlighted and a case study was done on different locations along the University Road to demonstrate the developed model.

Application Of Vibrational Techniques In Determination Of Dynamic Properties Of Agricultural Products-State Of The Arton Of Vibrational Techniques In Determination Of Dynamic Properties Of Agricultural Products-State Of The Art, Silas Kajuna

Tanzania Journal of Engineering and Technology (TJET)

Vibration is one of the techniques employed in the determination of dynamic properties of fruits and vegetables. It entails generation of a mechanical or acoustic vibrational signal which is propagated through the flesh of the agricultural material. A transducer is either attached or held close to the specimen to monitor the propagation of the signal through the specimen. The manner in which the signal is transmitted through the material is analyzed, and the dynamic properties of the specimen which relate to its firmness or its internal being are derived. The technique has been around for the past 30 years or …

Self-Consistency Algorithms, Thaddeus Tarpey

Mathematics and Statistics Faculty Publications

The k-means algorithm and the principal curve algorithm are special cases of a self-consistency algorithm. A general self-consistency algorithm is described and results are provided describing the behavior of the algorithm for theoretical distributions, in particular elliptical distributions. The results are used to contrast the behavior of the algorithms when applied to a theoretical model and when applied to finite datasets from the model. The algorithm is also used to determine principal loops for the bivariate normal distribution.

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Mathematics and Statistics Faculty Publications

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …

A Simplified Model Of Wound Healing - Ii: The Critical Size Defect In Two Dimensions, J. S. Arnold, John A. Adam

Mathematics & Statistics Faculty Publications

Recently, a one-dimensional model was developed which gives a reasonable explanation for the existence of a Critical Size Defect (CSD) in certain animals [1]. In this paper, we examine the more realistic two-dimensional model of a circular wound of uniform depth to see what modifications are to be found, as compared with the one-dimensional model, in studying the CSD phenomenon. It transpires that the range of CSD sizes for a reasonable estimate of parameter values is 1 mm-1 cm. More realistic estimates await the appropriate experimental data.

Evaporation Of Jet Fuels, Charles Eric Hack

Theses and Dissertations

Determining the fate and transport of JP-8 jet fuel is a complex and important problem. As part of the startup procedures for jet engines, fuel is passed through aircraft engines before combustion is initiated. Because of the extremely low temperatures at northern tier Air Force bases, the unburned fuel does not evaporate readily and may come into contact with ground crew. To determine the amount and duration of contaminant contact, the evaporation of the emitted fuel must be modeled. The amount and composition of the fuel upon reaching the ground crew may be determined by droplet evaporation models that have …

A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler

Mathematics Faculty Publications

This paper will provide the general construction of the continuous, orthogonal, compactly-supported multiwavelets associated with a class of continuous, orthogonal, compactly-supported scaling functions that contain piecewise linears on a uniform triangulation of $\R^2$. This class of scaling functions is a generalization of a set of scaling functions first constructed by Donovan, Geronimo, and Hardin. A specific set of scaling functions and associated multiwavelets with symmetry properties will be constructed.

Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.

Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder

Mathematics and Statistics Faculty Publications

In this paper, we examine a random version of the lattice point problem.

Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li

Mathematics and Statistics Faculty Publications

Image resolution is the primary parameter for performance characterization of any imaging system. In this work, we present an axiomatic approach for quantification of image resolution, and demonstrate that a good image resolution measure should be proportional to the standard deviation of the point spread function of an imaging system.

Three-Dimensional Reconstructions Of Tadpole Chondrocrania From Histological Sections, Gary P. Radice, Mary Kate Boggiano, Mark Desantis, Peter M. Larson, Joseph Oppong, Matthew T. Smetanick, Todd M. Stevens, James Tripp, Rebecca A. Weber, Michael Kerckhove, Rafael O. De Sá

Biology Faculty Publications

Reconstructing three dimensional structures (3DR) from histological sections has always been difficult but is becoming more accessible with the assistance of digital imaging. We sought to assemble a low cost system using readily available hardware and software to generate 3DR for a study of tadpole chondrocrania. We found that a combination of RGB camera, stereomicroscope, and Apple Macintosh PowerPC computers running NIH Image, Object Image, Rotater. and SURFdriver software provided acceptable reconstructions. These are limited in quality primarily by the distortions arising from histological protocols rather than hardware or software.

Stability Of Self-Similar Solutions For Van Der Waals Driven Thin Film Rupture, Thomas P. Witelski, Andrew J. Bernoff

All HMC Faculty Publications and Research

Recent studies of pinch-off of filaments and rupture in thin films have found infinite sets of first-type similarity solutions. Of these, the dynamically stable similarity solutions produce observable rupture behavior as localized, finite-time singularities in the models of the flow. In this letter we describe a systematic technique for calculating such solutions and determining their linear stability. For the problem of axisymmetric van der Waals driven rupture (recently studied by Zhang and Lister), we identify the unique stable similarity solution for point rupture of a thin film and an alternative mode of singularity formation corresponding to annular “ring rupture.”

Codes Over Rings From Curves Of Higher Genus, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

We construct certain error-correcting codes over finite rings and estimate their parameters. These codes are constructed using plane curves and the estimates for their parameters rely on constructing “lifts” of these curves and then estimating the size of certain exponential sums.

THE purpose of this paper is to construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools; notably, an estimate for the dimension of trace codes over rings (generalizing work of van der Vlugt over fields and some results on lifts of affin curves from field of characteristic p …

Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald

Mathematics and Statistics Faculty Publications

Let D be a smoothly bounded domain in Euclidean space and let X_t be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from D of a particle driven by X_t, where the average is taken overall starting points in D.

A Simplified Model Of Wound Healing (With Particular Reference To The Critical Size Defect), J. A. Adam

Mathematics & Statistics Faculty Publications

This paper is an attempt to construct a simple mathematical model of wound healing/tissue regeneration which reproduces some of the known qualitative features of those phenomena. It does not address the time development of the wound in any way, but does examine conditions (e.g., wound size) under which such healing may occur. Two related one-dimensional models are examined here. The first, and simpler of the two corresponds to a "swath" of tissue (or more realistically in this case, bone) removed from an infinite plane of tissue in which only a thin band of tissue at the wound edges takes part …

Multiple Comparison Pruning Of Neural Networks, Donald E. Duckro

Theses and Dissertations

Reducing a neural network's complexity improves the ability of the network to be applied to future examples. Like an overfitted regression function, neural networks may miss their target because of the excessive degrees of freedom stored up in unnecessary parameters. Over the past decade, the subject of pruning networks has produced non-statistical algorithms like Skeletonization, Optimal Brain Damage, and Optimal Brain Surgery as methods to remove connections with the least salience. There are conflicting views as to whether more than one parameter can be removed at a time. The methods proposed in this research use statistical multiple comparison procedures to …

Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Development And Application Of Adaptive Dynamic Grids For Wake Vortex/Ground Interaction, Ilker Emin Türkgeldi

Mechanical & Aerospace Engineering Theses & Dissertations

An adaptive and dynamic grid approach is developed for the numerical computations of wake vortex flow problems with ground interaction. The unnecessary grid points at the far field of the original, large, single zone grid are removed for computational efficiency. Next, the grid is modified into an adaptive one, where the fine core region keeps track of the vortices and can be split into two regions when the vortex separation distance exceeds a specified limit length. In the final step a multi zonal feature is added to this grid by means of two embedded grids placed at the vortex centers …

Estimation And Goodness-Of-Fit In The Case Of Randomly Censored Lifetime Data, David M. Reineke

Theses and Dissertations

A new continuous distribution function estimator for randomly censored data is developed, discussed, and compared to existing estimators. Minimum distance estimation is shown to be effective in estimating Weibull location parameters when random censoring is present. A method of estimating all 3 parameters of the 3-parameter Weibull distribution using a combination of minimum distance and maximum likelihood is also given. Cramer-von Mises and Anderson-Darling goodness-of-fit test statistics are modified to measure the discrepancy between the maximum likelihood estimate and the Kaplan-Meier product-limit estimate of the distribution function of the random variable of interest. These modified test statistics are used to …

Dynamical Systems Associated With Particle Flow Models : Theory And Numerical Methods, Roman V. Samulyak

Dissertations

A new class of integro - partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of infinite-dimensional dynamical systems models) on the Newtonian equations of motion of a many-particle system incorporating widely used inelastic particle-particle force formulas. By using Taylor series expansions, these models can be approximated by a system of partial differential equations of the Navier-Stokes type. Solutions of the new models for granular flows down inclined planes and in vibrating beds are compared with known experimental and …

Tracking The Trochoid On Safari, Andrew Simoson

ACMS Conference Proceedings 1999

While on sabbatical in Dar es Salaam in 1997–98, I was tasked to be the department’s seminar director and discovered that a dearth of speakers roam about in east Africa; so I opted to set up a lecture tour for myself to include Zambia, Zimbabwe, and Botswana as well as Tanzania—and spoke about the envelope of curves generated by a series of line segments obtained when two runners attached by an ideal bungee cord (the line segments) proceed about a circular track. Herein we describe life in east Africa and show that those envelopes are trochoids.

Revolutions In Mathematics (Book Review), Kevin Vander Meulen

ACMS Conference Proceedings 1999

A review of Revolutions in Mathematics, edited by Donald Gillies, Clarendon Press, Oxford 1992.

Lewis Carroll: Author, Mathematician, And Christian, David L. Neuhouser

ACMS Conference Proceedings 1999

Although a Christian, an author, and a mathematician, Charles Letwidge Dodgson (better known as Lewis Carroll) wrote very few works in which these three aspects of his person was present. The only examples of him merging these interests are in Sylvie and Bruno and Sylvie and Bruno Concluded. This paper will explore what motivated him to make these works and whether or not they were successful.

The Deconstruction Of Mathematics, David J. Stucki

ACMS Conference Proceedings 1999

This paper is a criticism of Reuben Hersh's What is Mathematics, Really? and the humanist philosophy of mathematics.

Book Review, David J. Stucki

ACMS Conference Proceedings 1999

A book review of Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science by Alan Sokal and Jean Bricmont.

Book Review: Virtual Gods: The Seduction Of Power And Pleasure In Cyberspace, Jonathan R. Senning

ACMS Conference Proceedings 1999

This paper is a review of Virtual Gods: The Seduction of Power and Pleasure in Cyberspace, edited by Tal Brooke, Harvest House Publishers, 1997.

Teaching Linear Algebra And Abstract Algebra With Two Way Video And Audio, Edward Reinke

ACMS Conference Proceedings 1999

An outline of a presentation discussing teaching two different algebra courses long-distance as well as in a classroom.

A Mathematician At The Science And Theology Book Club, Greg Crow

ACMS Conference Proceedings 1999

This paper is a case study of the insights gained and the contributions made in a weekly Science and Theology Faculty Book Club. The contribution of other group members to the expansion of one’s general understanding of their fields is demonstrated in increased vocabulary, use of existing theoretical models, glimpses of the depth of their disciplines, and in the recognition of the need for humility. The mathematician may contribute by helping to clarify definitions, by applying basic ideas in their own and related fields, and only very rarely by bringing their own research to the table.

Book Review - The Language Of Mathematics: Making The Invisible Visible By Kieth Devlin, Charles R. Hampton

ACMS Conference Proceedings 1999

Charles R. Hampton reviews The Language of Mathematics: Making the Invisible Visible. By Kieth Devlin. W. H. Freeman and Company, 1998

Determinism, Chaos, And The Meaning Of Randomness, Or Quantum Theory And The Sovereignty Of God, John Wicks

ACMS Conference Proceedings 1999

No abstract provided.