Physical Sciences and Mathematics Commons^™

Finite-Element Ray Tracing, Yong-Chun Liu

Theses

The interesting acoustic modeling problems often push the practical limits of full-wave models. For instance, in acoustic tomography one needs to be able to predict the propagation of an acoustic pulse for successive realizations of 31) environments. For these types of problems ray methods continue to be attractive because of their speed. Unfortunately, existing codes are prone to a number of implementation difficulties which often degrade their accuracy.

As a result most ray models are actually incapable of producing the ray theoretic result. We discuss a. new method for implementing ray theory that uses a. finite-clement formulation. This method is …

Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen

Mathematics and Statistics Faculty Publications

We describe a class of measurable subsets Ω in R^d such that L²(Ω) has an orthogonal basis of frequencies e_λ(x) = e^i2πλ.x(x ε Ω) indexed by λ ∈ Λ ⊂ R^d. We show that such spectral pairs (Ω, Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L²(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis of mu may be built instead from a natural representation of the Cuntz …

Approximation Methods For Singular Diffusions Arising In Genetics, Nacer E. Abrouk

Mathematical Sciences Technical Reports (MSTR)

Stochastic models in population genetics leading to diffusion equations are considered. When the drift and the square of the diffusion coefficients are polynomials, an infinite system of ordinary differential equations for the moments of the diffusion process can be derived using the Martingale property. An example is provided to show how the classical Fokker-Planck Equation approach may not be appropriate for this derivation. A Gauss-Galerkin method for approximating the laws of the diffusion, originally proposed by Dawson (1980), is examined. In the few special cases for which exact solutions are known, comparison shows that the method is accurate and the …

Analytical Modeling Of Aquifer Decontamination By Pulsed Pumping When Contaminant Transport Is Affected By Rate-Limited Sorption And Desorption, Thomas A. Adams, Robert C. Viramontes

Theses and Dissertations

This research explores radially convergent contaminated transport in an aquifer towards an extraction well. This thesis presents the equations governing the transport of a contaminant during aquifer remediation by pulsed pumping. Contaminant transport is assumed to be affected by radial advection, dispersion, and sorption/desorption. Sorption is assumed to be either equilibrium or rate-limited, with the rate-limitation described by either a first-order law, or by Fickian diffusion of contaminant through layered, cylindrical, or spherical immobile water regions. The equations are derived using an arbitrary initial distribution of contaminant in both the mobile and immobile regions, and they are analytically solved in …

A New Look At An Old 3:16 An Acms Devotional, Russell W. Howell

ACMS Conference Proceedings 1993

This paper examines John 3:16 in the bible by examining the language and cultural backgrounds of the verse.

Knuth's (1, 2, 1) Unstacking, Paul J. Zwier

ACMS Conference Proceedings 1993

This presentation is dedicated to Donald Knuth who has proposed many interesting and challenging problems in the Problems Section of The American Mathematical Monthly. The problem considered ist hat proposed by Barry Hayes, Knuth, and Carlos Subi (E3267 [1988,456]). The published solution, due to Albert Nijenhuis, just recently appeared in the March 1993 Monthly, pages 292-294.

The problem is as follows. Suppose that we are given n piles of blocks; the i-th pile having ai blocks, i = 1, 2, …, n. Dismantle the piles by choosing a pile having 2 or more blocks, removing …

A Conjectured Paradigm Shift In 21st Century Mathematics Pedagogy, Paul Isihara

ACMS Conference Proceedings 1993

With greater and greater capacity for automated content delivery, the role of teachers may shift increasingly to providing the human touch in pedagogy such as love for students.

Paper Abstracts, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

Introduction (1993), Russell Howell

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

Schedule (1993), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

Table Of Contents (1993), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

Time-Discretization Of Hamiltonian Dynamical Systems, Yosi Shibberu

Mathematical Sciences Technical Reports (MSTR)

Difference equations for Hamiltonian systems are derived from a discrete variational principle. The difference equations completely determine piecewise-linear, continuous trajectories which exactly conserve the Hamiltonian function at the midpoints of each linear segment. A generating function exists for transformations between the vertices of the trajectories. Existence and uniqueness results are present as well as simulation results for a simple pendulum and an inverse square law system.

Distances Associated With Subgraphs And Subdigraphs, Steven John Winters

Dissertations

The defining properties of several important subgraphs and subdigraphs rely on the concept of distance in graphs and digraphs. In this dissertation, we investigate many of these subgraphs and subdigraphs.

In Chapter I, we present some preliminary definitions and examples. In addition, many known results are recalled. We then introduce several new induced subgraphs and subdigraphs.

In Chapter n, we investigate the general structure of the center and periphery of a graph. We introduce two new induced subgraphs of the center along with a new induced subgraph of the periphery of a graph in order to study these structures.

For …

Radome Depolarization Effects On Monopulse Receiver Tracking Performance, Michael A. Temple

Theses and Dissertations

Boresight Error (BSE), defined as the angular deviation between the true position and the apparent position of a target as indicated by a radar, is an important figure of merit for a tracking radar. A significant contributor to system BSE is the protective radome. This research effort employed a GO technique to investigate the effects of a radome on BSE, expanding previous ray- trace receive techniques to include: (1) a uniquely defined/developed mathematical description for each surface within arbitrary multi-layer tapered radomes, (2) an 'ideal' taper function concept for obtaining optimum BSE prediction performance, (3) a generalized technique for calculating …

Bayesian Methods In Preoperative Risk Assessment For Cardiac Surgery, Huey-Chung Teng

Theses

Many strides have been made in the last decade to improve the accuracy of preoperative risk estimation, particular for cardiovascular surgery. It is our goal to estimate the preoperative risk associated with cardiac bypass surgery for patients in different risk categories. These risk categories are determined by the Parsonett model.

The Parsonett model assigns a risk value to a range of risk factors consisting of patient attributes and disease parameters. Logistic modeling is applied to generate a comprehensive risk function. The database being utilized contains over 3,000 patients who have had cardiovascular surgery within the last 5 years.

This thesis …

Electrostatic Positioning Of Droplets In Turbulent Flows (Lstm 375/Te/93), Nihad E. Daidzic, Adrian Melling

Aviation Department Publications

Report LSTM 375/TE/93, Lehrstuhl fuer Stroemungsmechanik Universitaet Erlangen-Nuernberg Cauerstr. 4, 8520 Erlangen Germany.

Robust Rank-Based Inference Procedures In The Heteroscedastic Linear Model, Sherry L. Dixon

Dissertations

No abstract provided.

Tracking Plasma Lactate Concentration In Vivo With A Catheter-Tip L-Lactate Sensor, Brett T. Weinzapfel, Mark D. Ball, Lee R. Waite, Nacer E. Abrouk, Shun P. Lim

Mathematical Sciences Technical Reports (MSTR)

To circumvent the problems of repeated blood sampling for in vitro analysis, a catheter-tip L-lactate sensor has been developed. The sensor was tested in anesthetized pigs (n=6). The sensor in vivo tracked the lactate concentration non-linearly, seeming to obey Michaelis-Menten kinetics. Calibration time was short, typically 1.5 min per lactate standard. Furthermore, time drift was small, typically -1.3% to -3.3% per hour of in vivo use.

Optimal Silo Attack Plan For The Red Integrated Strategic Offensive Plan (Risop), Richard C. Pace

Theses and Dissertations

The Joint Staff Directorate for Force Structure, Resources, and Assessment (J-8) sought a procedure which could be used to generate an optimal missile allocation for the silo attack portion of the Red Integrated Strategic Offensive Plan (RISOP). Their current solution procedure is a manual heuristic which is time-consuming and is not guaranteed to lead to an optimal solution. J- 8 defines an optimal solution as a feasible solution which minimizes both the flight time of the missile that impacts first and the duration of the attack. J- 8 defined several input rules which limit how missiles may be allocated. A …

An Analysis Of The Generalized Lambda Distribution, Robert J. Bergevin

Theses and Dissertations

The Generalized Lambda Distribution (GLD) is a four parameter function that is capable of mimicking the behavior of a wide range of probability density functions (pdfs). Unfortunately, the GLD presently cannot model every possible type of pdf. Since the reasons for this limitation are unknown, this thesis examines several potential problems in an attempt to expand the range of distributions the GLD can mimic. We first present a discussion of the behavior of the algorithm that is used to search for the appropriate GLD parameter values. In particular, we examine the effect of using an unconstrained search to find the …

A Fuzzy Logic Optimal Control Law Solution To The Cmmca Tracking Problem, Randy E. Nelson

Theses and Dissertations

The Air Force uses the C-18 Cruise Missile Mission Control Aircraft (CMMCA) to radar track cruise missiles (CM) during test flights. Because of the complexity of the CM flight profiles, maintaining radar coverage at all times is very difficult. This thesis attempted to apply optimal control theory to construct a simulation providing 100% radar coverage. The simulation was divided into ten second intervals, and fuzzy logic was used at the start of each interval to determine the set point, i.e., that point in space where the CMMCA should be in ten seconds. The set point calculation's fuzzy logic balanced CMMCA …

The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer

Mathematics and Statistics Faculty Publications

We study the group of all ''R-automorphisms'' of a countable equivalence relation R on a standard Borel space, special Borel automorphisms whose graphs lie in R. We show that such a group always contains periodic maps of each order sufficient to generate R. A construction based on these periodic maps leads to totally nonperiodic R-automorphisms all of whose powers have disjoint graphs. The presence of a large number of periodic maps allows us to present a version of the Rohlin Lemma for R-automorphisms. Finally we show that this group always contains copies of free …

The Flow Approach To Swept Volume, Haitao Jiang

Theses

In this thesis, a method for representing swept volume based on the sweep differential equation and sweep vector field flow is developed. This method can be used to determine the boundary representation of a swept volume generated by any polygonal object undergoing a general smooth 2-D sweep. For any given sweep and object, a. set of candidate boundary points is computed using a selection criterion based on vector field behavior. The set of candidate boundary points is then trimmed in order to obtain the true boundary of the swept volume. This trimming procedure is based on some simple topological principles …

The Proportion Of Fixed-Point-Free Elements Of A Transitive Permutation Group, Nigel Boston, Walter Dabrowski, Tuval Foguel, Paul J. Gies, Judy Leavitt Walker, David T. Ose, David A. Jackson

Department of Mathematics: Faculty Publications

In 1990 Hendrik W. Lenstra, Jr. asked the following question: if G is a transitive permutation group of degree n and A is the set of elements of G that move every letter, then can one find a lower bound (in terms of n) for f(G) = |A|/|G|? Shortly thereafter, Arjeh Cohen showed that 1/n is such a bound.

Lenstra’s problem arose from his work on the number field sieve. A simple example of how f(G) arises in number theory is the following: if h is an irreducible polynomial …

Optimal Control And Differential Games With Measures, E. N. Barron, R. Jensen, J. L. Menaldi

Mathematics Faculty Research Publications

We consider control problems with trajectories which involve ordinary measureable control functions and controls which are measures. The payoff involves a running cost in time and a running cost against the control measures. In the optimal control problem we are trying to minimize this payoff with both controls. In the differential game problem we are trying to minimize the cost with the ordinary controls assuming that the measure controls are chosen to maximize the cost. We will characterize the value functions in both cases using viscosity solution theory by deriving the Bellman and Isaacs equations.

Tables Of Coincidence Orientations For Ordered Tetragonal L Lo Alloys For A Range Of Axial Ratios, Abha Singh, Alexander H. King

Alexander H. King

In this paper we develop and apply techniques for computation of CSL, DSCL and step-vector data for grain boundaries in tetragonal materials for a range of axial ratios. This has application to L10 alloys including TiA1, which is a candidate for lightweight high-temperature structural applications. Our results are compared with others and found to be more accurate and complete. We provide data for a wider range of axial ratios than those considered by previous workers. We have also derived equivalent quaternions for tetragonal crystals in tetragonal-crystal coordinates and listed conditions for selecting a unique reduced rotation in tetragonal-crystal coordinates so …

A Geometrical Rationalization Of The Special Properties Of The 14° [001] Grain Boundary In Yba2cu3o7−Δ, Alexander H. King, Abha Singh

Alexander H. King

14° [001] tilt grain boundaries in YBa2Cu3O7−δ have been found to exhibit anomalously good superconducting critical currents, associated with magnetic flux pinning, although no special interfacial structure has heretofore been associated with this misorientation. We present an analysis of the geometry of the grain boundary in question and show that it can correspond to a special interface, within the definition of constrained lattice coincidence, which may lead to new understanding of the superconducting behavior of grain boundaries. Our analysis shows that the tetragonal‐to‐orthorhombic phase transformation may have important effects upon grain boundary structure and properties, indicating new approaches to producing …

Uniqueness Of Radial Solutions Of Semilinear Elliptic Equations, Man Kam Kwong, Yi Li

Yi Li

E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one finite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coefficients.

Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni

Yi Li

No abstract provided.

On The Positive Solutions Of The Matukuma Equation, Yi Li

Yi Li

No abstract provided.