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Articles 1 - 30 of 55
Full-Text Articles in Physical Sciences and Mathematics
Symbol Sense And Its Development In Two Computer Algebra System Environments, Brian A. Keller
Symbol Sense And Its Development In Two Computer Algebra System Environments, Brian A. Keller
Dissertations
The purposes of this study were to: (a) explicate the nature of symbol sense, (b) determine the differential effects of two computer algebra system (CAS) environments on students' development of symbol sense, (c) explore differences in symbol sense among students using a CAS and students not using a CAS, and (d) examine students' achievement in calculus with and without the use of a CAS.
Six sections of first-semester calculus at Western Michigan University during the 1992-93 academic year were used in the study. The investigator taught two CAS sections both semesters (n = 41, 34 Fall and n = 35, …
Reconstruction Of Multiple Cracks From Experimental, Electrostatic Boundary Measurements, Kurt M. Bryan, Valdis Liepa, Michael Vogelius
Reconstruction Of Multiple Cracks From Experimental, Electrostatic Boundary Measurements, Kurt M. Bryan, Valdis Liepa, Michael Vogelius
Mathematical Sciences Technical Reports (MSTR)
We demonstrate the viability of using Electrical Impedance Tomography (EIT) for the reconstruction of multiple macroscopic cracks in a conductive medium.
Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho
Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho
Mathematics and Statistics Faculty Publications
Controllability and stabilizability of a system of coupled strings with control applied at the coupled points is studied. By investigating the properties of certain exponential series, it is shown that the system is approximate controllable if and only if related systems of uncoupled strings do not share a common eigenvalue. A sufficient condition for exact controllability is also obtained in terms of the Riesz basis properties of those exponential series.
Finite-Element Ray Tracing, Yong-Chun Liu
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
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 Rd such that L2(Ω) has an orthogonal basis of frequencies eλ(x) = ei2πλ.x(x ε Ω) indexed by λ ∈ Λ ⊂ Rd. 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
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 …
A New Look At An Old 3:16 An Acms Devotional, Russell W. Howell
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
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
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
Paper Abstracts, Association Of Christians In The Mathematical Sciences
ACMS Conference Proceedings 1993
Paradigm Shifts in the Mathematical Sciences
Introduction (1993), Russell Howell
Introduction (1993), Russell Howell
ACMS Conference Proceedings 1993
Paradigm Shifts in the Mathematical Sciences
Schedule (1993), Association Of Christians 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
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
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.
Radome Depolarization Effects On Monopulse Receiver Tracking Performance, Michael A. Temple
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 …
Distances Associated With Subgraphs And Subdigraphs, Steven John Winters
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 …
Bayesian Methods In Preoperative Risk Assessment For Cardiac Surgery, Huey-Chung Teng
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
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
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
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.
The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer
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
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
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
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
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
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
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
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
Quasilinearization For Some Nonlocal Problems, Yunfeng Yin
Quasilinearization For Some Nonlocal Problems, Yunfeng Yin
Mathematics and System Engineering Faculty Publications
The method of generalized quasilinearization [4] is applied to study semilinear parabolic equation ut – Lu = f{t,x,u) with nonlocal boundary conditions u(t,x)=∫Ωϕ(x,y)u(t,y)dy in this paper. The convexity of f in u is relaxed by requiring f(t,x,u) Muz to be convex for some M > 0. The quadratic convergence of monotone sequence is obtained.