Applied Mathematics Commons^™

An Investigation Of Plume Rise From Titan Iv Rocket Launches, Joseph D. Brands

Theses and Dissertations

Space launches at Cape Canaveral Air Station (CCAS) and Vandenberg Air Force Base (vAFB) produce exhaust ground clouds from the solid rocket boosters and liquid hypergolic fuels containing several toxic substances. In order to estimate the health effects that would be imposed upon the public by scheduled launches, range safety officials rely on the Rocket Exhaust Effluent Diffusion Model to predict ground level concentrations of these substances. A drawback to the REEDM is its underprediction of the initial ground clouds stabilization height. This underprediction causes an overprediction of the ground level toxic substance concentrations. This thesis focused on increasing the …

Averaged Motion Of Charged Particles In A Curved Strip, Avner Friedman, Chaocheng Huang

Mathematics and Statistics Faculty Publications

This paper is concerned with the motion of electrically charged particles in a "curved" infinite strip.

Optimal Pulsed Pumping For Remediation Of Aquifers When Sorption Is Rate-Limited, Lawrence J. Schmitt

Theses and Dissertations

A variational optimization technique is developed to acquire an optimal schedule of pulsed pumping operations for use at existing pump-and-treat aquifer remediation sites. The optimization problem is stated as a minimization of a generic management objective functional, constrained by the contaminant transport equations in two-dimensional or three-dimensional flow models which account for rate-limited sorption. The two-dimensional case is fully developed and a first-order rate equation is used to describe the transport of sorbing contaminant. The first variation provides necessary optimality conditions that must be met by any optimal solution, in turn leading to a pulsed pumping schedule of operation. The …

The Rational Resolution Analysis: A Generalization Of Multi-Resolution Analyses With Application To To The Specific Emitter Identification Problem, Bruce P. Anderson

Theses and Dissertations

The rational resolution analysis RRA is introduced and developed as a generalization of the integer, dilation multiresolution analyses MRA developed by Mallat and Meyer. Rational dilation factors are achieved by relaxing the condition on MRAs that successive approximation spaces be embedded. Conditions for perfect reconstruction are discussed and it is shown that perfect reconstruction is possible with specific constraints on the scaling function the scaling filter must have its roots on the unit circle. Furthermore, the required arrangement of the roots indicate the scaling function must be derived from a B-spline of some degree. It is proven the only compactly …

Corrigendum To “Post-Surgical Passive Response Of Local Environment To Primary Tumor Removal”: Mathl. Comput. Modelling, Vol. 25, No. 6, Pp. 7–17, 1997, J. A. Adam, C. Bellomo

Mathematics & Statistics Faculty Publications

The computer program that was used to generate the graphs for the concentration of inhibitor contained an error. This influenced the scaling in the original Figures 2 and 3. As an example, a sample of the corrected graphs are given below. Copies of other corrected figures can be obtained from the authors. It is important to note that the “pulse” appears for the function rC(r, t). As can be seen, it travels slowly outward with decreasing amplitude. The mathematical analysis in the paper remains unchanged.

Diffusive And Wavelike Phenomena In Thermal Processing Of Materials, John A. Pelesko

Dissertations

Contemporary materials science abounds with novel processing methods. Devices such as lasers, microwave sources, and electron beam guns, provide unprecedented control over the deposition of energy within a material. The modern materials scientist has the ability to deposit energy volumetrically, to precisely control the location of energy deposition within a material, and to deposit energy in extremely short intervals of time. While making possible numerous thermal processing methods, these devices also push the limits of our understanding of the response of materials to energy deposition. In order to optimize and control these processing methods, it becomes necessary to further our …

On The Product Of Two Generalized Derivations, Mohamed Barraa, Steen Pedersen

Mathematics and Statistics Faculty Publications

Two elements A and B in a ring R determine a generalized derivation delta_A,B on R by setting δ_A,B(X) = AX - XA for any X in R. We characterize when the product δ_C,Dδ_A,B is a generalized derivation in the cases when the ring R is the algebra of all bounded operators on a Banach space epsilon, and when R is a C*-algebra U. We use the se characterizations to compute the commutant of the range of δ_A,B.

Parameter Estimation For Real Filtered Sinusoids, Daniel R. Zahirniak

Theses and Dissertations

This research develops theoretical methods for parameter estimation of filtered, pulsed sinusoids in noise and demonstrates their effectiveness for Electronic Warfare EW applications. Within the context of stochastic modeling, a new linear model, parameterized by a set of Linear Prediction LP coefficients, is derived for estimating the frequencies of filtered sinusoids. This model is an improvement over previous modeling techniques since the effects of the filter and the coefficients upon the noise statistics are properly accounted for during model development. From this linear model, a relationship between LP coefficient estimation and Maximum Likelihood ML frequency estimation is derived and several …

Invariant Subspaces And Hyper-Reflexivity For Free Semigroup Algebras, Kenneth R. Davidson, David R. Pitts

Department of Mathematics: Faculty Publications

In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very strong, but it has been established in only a very few cases. Moreover the prototypes of this class of algebras are the natural candidate for a non-commutative analytic Toeplitz algebra on n variables. The case we make …

Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald

Mathematics and Statistics Faculty Publications

Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.

Quasi-Steady Monopole And Tripole Attractors In Relaxing Vortices, Louis F. Rossi, Joseph F. Lingevitch, Andrew J. Bernoff

All HMC Faculty Publications and Research

Using fully nonlinear simulations of the two-dimensional Navier–Stokes equations at large Reynolds number (Re), we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing.

Fast Discrete Polynomial Transforms With Applications To Data Analysis For Distance Transitive Graphs, J. R. Driscoll, D. M. Healy, D. N. Rockmore

Dartmouth Scholarship

Let $\poly = \{P_0,\dots,P_{n-1}\}$ denote a set of polynomials with complex coefficients. Let $\pts = \{z_0,\dots,z_{n-1}\}\subset \cplx$ denote any set of {\it sample points}. For any $f = (f_0,\dots,f_{n-1}) \in \cplx^n$, the {\it discrete polynomial transform} of f (with respect to $\poly$ and $\pts$) is defined as the collection of sums, $\{\fhat(P_0),\dots,\fhat(P_{n-1})\}$, where $\fhat(P_j) = \langle f,P_j \rangle = \sum_{i=0}^{n-1} f_iP_j(z_i)w(i)$ for some associated weight function w. These sorts of transforms find important applications in areas such as medical imaging and signal processing.

In this paper, we present fast algorithms for computing discrete orthogonal polynomial transforms. For a system …

Correlation Of Finite Element Prediction And Experimental Measurements Of Aircraft Panel Structural Vibration, Olaf L. Storaasli

Mechanical & Aerospace Engineering Theses & Dissertations

With the rapid development of computational capabilities and the implementation of complex tools for commercial finite element programs, predicting structural dynamics and related acoustics of complex structures is presently achievable. Structural finite element modeling is a design tool widely utilized for analysis of problems of all kinds. However, high frequency vibration of complex structures, such as the reinforced aircraft panel used for this study, currently does not correlate well with experimental measurements using conventional modeling methods. An investigation into the commonly used modeling techniques as well as the new tools of commercial finite element analysis packages for the prediction of …

A Robust Estimate For An Autoregressive Time Series, Jeffrey Terpstra

Dissertations

A weighted rank-based estimate for estimating the parameter of an auto-regressive time series is considered. When the weights are constant, the estimate is equivalent to using Jaeckel’s estimate and Wilcoxon scores. The estimate can be shown to be asymptotically normal at rate y/n. In a linear regression setting this estimate has the desired properties of a continuous totally bounded influence function and a positive breakdown point. It is shown via examples and Monte Carlo that these properties are preserved in an autoregressive time series setting.

Domination In Digraphs, Lisa Hansen

Dissertations

No abstract provided.

Solomon's Sea And The Biblical Π, Andrew Simoson

ACMS Conference Proceedings 1997

From I Kings 7:23, the apparent diameter and circumference of a circular ring are given as 10 and 30 cubits which suggests that the Biblical value of π is 3 rather a number closer to π. However we recount seven different somewhat whimsical explanations as to why this conclusion is overly-hasty.

Mathematics And Values: Can Philosophy Guide Projects?, Michael H. Veatch

ACMS Conference Proceedings 1997

The philosophy of mathematics has provided insight on questions of foundations and mathematical truth; however, it has not been very fruitful in guiding the practice of mathematics. This paper attempts to find points of contact between a Christian worldview and the choice of mathematical projects and methods. Three areas are considered: (i) dubitability in current research, (ii) the intrinsic value of contemporary mathematics to contemporary society, and (iii) the affirmation of human value in the use of mathematics. Finally, a framework for valuing mathematics is proposed as an encouragement to think more deeply about how a Christian might choose a …

An Investigation Of The Behavior Of Calculus Students Working Collaboratively In An Interactive Software Environment, Angela Hare

ACMS Conference Proceedings 1997

Recent work in the area of cognitive research in mathematics education focuses on detailed examinations of the learning process of students and how this process is affected by current innovations in the classroom, including collaborative learning and the use of computers and interactive software. Much of this work is supported by the learning framework of constructivism, a school of thought which is based on the work and writings of Jean Piaget. Piaget, a French psychologist in the mid-twentieth century, observed the learning behavior of children and concluded that individuals construct their own knowledge by creating mental structures which explain their …

Mathematics At Chartres Cathedral, Richard Stout

ACMS Conference Proceedings 1997

Having had several opportunities to travel to France, often with groups of students, our trips have usually included a visit to Chartres, especially to visit the magnificent Gothic cathedral that dominates the town. On a recent visit I was again struck by the beauty, majesty and awe that the cathedral inspires. The building not only does a remarkable job of telling Biblical stories and of enclosing a space conducive to worship, it directs one's eyes and one's spirits upward. This is achieved not only by the beautiful stained glass windows and the striking sculptures, but also by the overall design …

Digital Filtering And Smoothing: A Student Simulation Project, Eric Gossett

ACMS Conference Proceedings 1997

A bug tracking problem is used to introduce students to filtering and smoothing real-time data. A predictor-corrector filter/smoother algorithm is developed and a simulation platform is provided so that students can program and test implementations of the filter/smoother. The platform includes the ability to animate the simulation.

The tracking problem: A small computer bug is traveling around the $x-y$ plane trying to avoid detection. We can eliminate the bug if we can produce a reasonably accurate approximation to its trajectory.

We have a bug detecting device which can be pointed at the plane. It can measure the $x$ and $y$ …

The Role Of Mathematics In Culture, W. James Bradley

ACMS Conference Proceedings 1997

This paper examines theories of the role of mathematics in culture and seeks to understand how a Christian should view the role of mathematics.

The Mathematical Sciences And The Mediator Of Creation, W. David Laverell

ACMS Conference Proceedings 1997

This article stems from a conviction that while the development of a theistic view of the mathematical sciences is a laudable goal and much to be encouraged, it is incumbent upon us to explore every avenue that might lead to a distinctively Christian perspective. This leads naturally to a consideration of the unique role played by Christ in Creation, and a convenient framework is provided by seeing Christ as Mediator of Creation. We shall discuss the term itself, examine the biblical passages that seem to present the concept, consider the ways these passages have been understood by theologians, and …

Fractal Geometry And Chaos Theory: From Old Problems To New Models And Methods, Terence H. Perciante

ACMS Conference Proceedings 1997

Fractal geometry and chaos theory are deeply rooted in significant problems in the history of mathematics and science. While mathematicians have geometrical descriptions of space with its properties, scientists have attempted to characterize the physical properties of fundamental entities present in space and time. The separate investigations frequently influenced each other and led to profound theories, answers, and models. However, at the same time new problems repeatedly arose internal to mathematics and externally in the applications to which mathematics was applied. Fractal geometry issues from these antecedents in response to features and processes in nature not easily represented by historical …

Teaching Generalization And Reduction Through An Elementary Probability Problem, Erian Wheeler

ACMS Conference Proceedings 1997

No abstract provided.

On Binary Quadratic Forms, Alain Togbe

ACMS Conference Proceedings 1997

No abstract provided.

Exploring Various Methods Of Interpolation, Mark Roberts

ACMS Conference Proceedings 1997

No abstract provided.

Hypothesis, Proof, And Censorship Or How Galileo Changed The Rules Of Science, Owen Gingerich

ACMS Conference Proceedings 1997

No abstract provided.

Hyperbolic Geometry With The Geometer's Sketchpad, Robert Frank

ACMS Conference Proceedings 1997

No abstract provided.

Using Java And Html For Linear Algebra Instruction, Jonathan R. Senning

ACMS Conference Proceedings 1997

This paper addresses some of the issues involved with using the HTML, JavaScript and Java to develop and serve a sequence of laboratory modules for use in teaching linear algebra. Attention is paid to the rationale for this approach as opposed to the more traditional approach of laboratory exercises executed using MATLAB or some similar computational tool. Several methods to display mathematics with HTML are described. Some implementation detail and a brief description of the HTML and Java based Linear Algebra Visualization Assistant (LAVA) is presented.

A Tale Of Two Transitions, David Klanderman, Sharon Robbert, Robert Wheeler

ACMS Conference Proceedings 1997

In this paper, we examine transitions to proof courses at two institutions. Bob Wheeler has taught the course at Northern Illinois University. Both Sharon Robbert and Dave Klanderman have taught a related course at Trinity Christian College. We analyze various features of these courses and offer suggestions for other colleges and universities.