Physical Sciences and Mathematics Commons^™

Effect Of Computer Graphics Use On Student Understanding Of Calculus Concepts, Charlene E. Beckmann

Dissertations

Student understanding of selected calculus concepts as developed through use of a Cartesian coordinate graphical representation system were investigated. Subjects (N = 163) enrolled in first-semester calculus sections at Western Michigan University participated in one of four treatment conditions: Graphics (G), exposure to a computer-graphically-developed conceptual course; Graphics Plus (G+), exposure to the same course as G subjects plus provision of computer graphics software and related supplemental assignments; Standard 1 (S1), exposure to a graphically-developed, conceptual course; and Standard 2 (S2), exposure to a traditional skill-oriented course.

Two investigations were undertaken. In Investigation 1, comparisons were made between G and …

On The Numerical Approximations Of An Optimal Correction Problem, M. C. Bancora-Imbert, P. L. Chow, J. L. Menaldi

Mathematics Faculty Research Publications

The numerical solution of an optimal correction problem for a damped random linear oscillator is studied. A numerical algorithm for the discretized system of the associated dynamic programming equation is given. To initiate the computation, we adopt a numerical scheme derived from the deterministic version of the problem. Next, a correction-type algorithm based on a discrete maximum principle is introduced to ensure the convergence of the iteration procedure.

Slip, Twinning, And Fracture At A Grain Boundary In The L12 Ordered Structure—Aς = 9 Tilt Boundary, Alexander H. King, M. H. Yoo

Alexander H. King

The role of interaction between slip dislocations and a Σ = 9 tilt boundary in localized microplastic deformation, cleavage, or intergranular fracture in the Li2 ordered structure has been analyzed by using the anisotropic elasticity theory of dislocations and fracture. Screw superpartials cross slip easily at the boundary onto the (1$\overline 1$1) and the (001) planes at low and high temperatures, respectively. Transmission of primary slip dislocations onto the conjugate slip system occurs with a certain degree of difficulty, which is eased by localized disordering. When the transmission is impeded, cleavage fracture on the ($\overline 1$11) plane is predicted to …

The Centrality Of Mathematics In The History Of Western Thought, Judith V. Grabiner

Pitzer Faculty Publications and Research

This article explores the interplay of mathematics and philosophy in Western thought as well as applications to other fields.

Multiple Solutions For A Dirichlet Problem With Jumping Nonlinearities Ii, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

No abstract provided for this article.

Remarks On A Semilinear Elliptic Equation On Rn, Yi Li

Yi Li

No abstract provided.

Remarks On A Semilinear Elliptic Equation On Rn, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Spectral Measures, Orthogonal Polynomials, And Absolute Continuity, Joanne Dombrowski

Mathematics and Statistics Faculty Publications

This paper studies the spectral measure of an unbounded tridiagonal matrix operator for which the matrix entries satisfy a certain growth condition, and presents a sufficient condition for the existence of an absolutely continuous part. The results are related to a class of orthogonal polynomials with exponential weights.

Stability Of Steady Cross-Waves: Theory And Experiment, Seth Lichter, Andrew J. Bernoff

All HMC Faculty Publications and Research

A bifurcation analysis is performed in the neighborhood of neutral stability for cross waves as a function of forcing, detuning, and viscous damping. A transition is seen from a subcritical to a supercritical bifurcation at a critical value of the detuning. The predicted hysteretic behavior is observed experimentally. A similarity scaling in the inviscid limit is also predicted. The experimentally observed bifurcation curves agree with this scaling.

Higher Level Modeling In Resqme, Robert F. Gordon Ph.D., Kurtiss J. Gordon

Faculty Works: MCS (1984-2023)

RC 13554 (#60544)

The RESearch Queueing Package Modeling Environment (RESQME) is a graphical workstation environment for iteratively constructing, running and analyzing models of resource contention systems. It is built on top of the RESearch Queueing Package (RESQ) which provides the functionality to evaluate extended queueing networks. In this paper we describe the high-level building component design for RESQME. The modeler is provided with tools to create his own icons and to associate them with submodels. He then uses ilicsc building blocks to construct his model. This capability extends the funtlaiiicnlal building blocks of RESQ and allows the user to create …

On Conformal Scalar Curvature Equations In Rn, Yi Li, Wei-Ming Ni

Yi Li

No abstract provided.

On Conformal Scalar Curvature Equations In Rn, Yi Li, Wei-Ming Ni

Mathematics and Statistics Faculty Publications

No abstract provided.

Matrix Methods Of Approximating Classical Predator-Prey Problems, E. Y. Rodin, R. Greenberg, B. Nelson

Computer Science: Faculty Publications and Other Works

No abstract provided.

Nonnegative Solutions For A Class Of Nonpositone Problems, Alfonso Castro, Ratnasingham Shivaji

All HMC Faculty Publications and Research

In the recent past many results have been established on non-negative solutions to boundary value problems of the form

-u''(x) = λf(u(x)); 0 < x < 1,

u(0) = 0 = u(1)

where λ>0, f(0)>0 (positone problems). In this paper we consider the impact on the non-negative solutions when f(0)<0. We find that we need f(u) to be convex to guarantee uniqueness of positive solutions, and f(u) to be appropriately concave for multiple positive solutions. This is in contrast to the case of positone problems, where the roles of convexity and concavity were interchanged to obtain similar results. We further establish the existence of non-negative solutions with interior zeros, which did not exist in positone problems.

Reliable Computation By Formulas In The Presence Of Noise, Nicholas Pippenger

All HMC Faculty Publications and Research

It is shown that if formulas are used to compute Boolean functions in the presence of randomly occurring failures then: (1) there is a limit strictly less than 1/2 to the failure probability per gate that can be tolerated, and (2) formulas that tolerate failures must be deeper (and, therefore, compute more slowly) than those that do not. The heart of the proof is an information-theoretic argument that deals with computation and errors in very general terms. The strength of this argument is that it applies with equal ease no matter what types of gate are available. Its weaknesses is …

Uniform L1 Behavior In Classes Of Integrodifferential Equations With Convex Kernels, Richard Noren

Mathematics & Statistics Faculty Publications

No abstract provided.

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …

Periodic Solutions Of Volterra Integral Equations, Muhammad Islam

Mathematics Faculty Publications

Consider the system of equations

x(t)=f(t)+∫−∞tk(t,s)x(s)ds,           (1)

and

x(t)=f(t)+∫−∞tk(t,s)g(s,x(s))ds.        (2)

Existence of continuous periodic solutions of (1) is shown using the resolvent function of the kernel k. Some important properties of the resolvent function including its uniqueness are obtained in the process. In obtaining periodic solutions of (1) it is necessary that the resolvent of k is integrable in some sense. For a scalar convolution kernel k some explicit conditions are derived to determine whether or not the resolvent of k is integrable. Finally, the existence and uniqueness of continuous periodic solutions of (1) and (2) are obtained using the …

On A General Class Of Multivariate Linear Smoothing Operators, Tian-Xiao He

Tian-Xiao He

No abstract provided.

Asymptotic Properties Of Positive Summation-Integral Operators, Tian-Xiao He

Tian-Xiao He

No abstract provided.

On Minimal And Quasi-Minimal Supported Bivariate Splines, Tian-Xiao He

Tian-Xiao He

No abstract provided.