Digital Commons Network^™

A Multicultural Matrix For Mathematics Education: Generic Ideas, Rheta N. Rubenstein

Humanistic Mathematics Network Journal

No abstract provided.

Complete Issue 8, 1993

Humanistic Mathematics Network Journal

No abstract provided.

Boundary Value Problems In Rectilinearly Anisotropic Thermoelastic Solids, Gilbert Kerr

Mathematics & Statistics Theses & Dissertations

The boundary value problems which are considered are the type that arise due to the presence of a Griffith crack (or cracks) in an anisotropic thermoelastic solid. The thermoelastic field, in such materials, when the infinitesimal theory is employed, is governed by a set of elliptic partial differential equations. The general solution of these equations is expressed in terms of arbitrary analytic functions whose real parts, in turn, are expressed in terms of Fourier type integrals or Fourier series. Integral transform techniques are then used to determine the stress intensity factors (and other pertinent information) for various crack geometries. In …

Symmetries Of The Einstein Equations, Ian M. Anderson, C. Torre

Mathematics and Statistics Faculty Publications

We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. They consist of constant scalings of the metric, and of the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ‘‘observables’’ for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.

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.

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 …

Paper Abstracts, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

Using Maple To Teach Calculus, Ken Rietz

ACMS Conference Proceedings 1993

No abstract provided.

Georg Cantor And The Battle For Transfinite Set Theory, Joseph W. Dauben

ACMS Conference Proceedings 1993

No abstract provided.

Introduction (1993), Russell Howell

ACMS Conference Proceedings 1993

Paradigm Shifts in the Mathematical Sciences

Using Matlab And Mathematica In Numerical Analysis, John H. Matthews

ACMS Conference Proceedings 1993

No abstract provided.

Abraham Robinson (1918-1974): The Man And The Mathematics, Joseph W. Dauben

ACMS Conference Proceedings 1993

No abstract provided.

Infinity And The Absolute: Insights Into Our World, Our Faith, And Ourselves, Tim Pennings

ACMS Conference Proceedings 1993

No abstract provided.

Devotional Reflections, Jonathan Leech

ACMS Conference Proceedings 1993

No abstract provided.

Georg Cantor And The Battle For Transfinite Set Theory, Joseph Dauben

ACMS Conference Proceedings 1993

Georg Cantor is well known as the founder of transfinite set theory. Equally celebrated, however, are the obstacles he faced in trying to win acceptance for his seemingly unorthodox views, his acrimonious differences with Leopold Kronecker and his unfortunate but progressively debilitating nervous breakdowns that some authors have linked directly to his many problems with set theory. Above all, Cantor's justification of set theory was all the more urgent because of Kronecker's critical denunciation of Cantor's mathematics. In tracing the evolution of Cantorian set theory, it is necessary to examine the opposition it met, and evaluate the technical, philosophical, psychological, …

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

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

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.

Signal Processing With Neural Networks, Pero Smrzlic

Masters Theses

In this study, we introduce the Adaptive Back Propagation (ABP) learning algorithm, computationally superior to the standard Back Propagation. The ABP is based on the new activation function, with its corresponding adaptive learning parameter. By using the combination of computer simulations and analysis in the domain of activation function, the Method of One Hidden layer was developed for the effective utilization of units in one-hidden layer networks. A parallel version of the ABP was designed and implemented on a nCUBE-2 supercomputer with 128 processors.

The simulation results suggested a strong correlation between frequency of signals and the role of hidden …

Rely To "Comment On 'Nonexistence Of Certain Perfect Binary Arrays' And 'Nonexistence Of Perfect Binary Arrays'", Jonathan Jedwab, James A. Davis

Department of Math & Statistics Faculty Publications

Yang's comment [C] is based on a lemma which claims to construct an s₀ x s₁ x s₂ x ... x s, perfect binary array (PBA) from an s₀s₁ x s₂ x ... x s_r PBA.

Applications Of The Wavelet Transform To Signal Analysis, Jie Chen '93

Honors Projects

Like the Fourier Transform, the Wavelet Transform decomposes signals as a superposition of simple units from which the original signals can be reconstructed. The Fourier Transform decomposes signals into sine and cosine functions of different frequencies, while the Wavelet Transform decomposes signals into wavelets. Since the Fourier Transform is a global integration transform and there is no time factor in it, it cannot effectively analyze nonstationary signals whose statistical properties change with time. In order to analyze nonstationary signals, we need to decompose signals into units that are localized in both the time and frequency domains. Using the Wavelet Transform …

Multisurface Method Of Pattern Separation, Jennifer L. Jancik

Honors Projects

The recognition and separation of patterns is becoming increasingly important in modern applications. For example, it is currently being used at the University of Wisconsin Hospitals to aid in the diagnosis of breast cancer.

Bounds On Squares Of Two-Sets, Dan Slilaty, Jeff Vanderkam

Mathematical Sciences Technical Reports (MSTR)

For a finite group G, let p_i(G) denote the proportion of (x,y) in GxG for which the set {x²,xy,yx,y²} has cardinality i. In this paper we develop estimates on the p_i(G) for various i.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Linear Operators That Preserve Qualitative Matrix Structures, Shumin Ye

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We characterized the group of linear operators that preserve sign-nonsingular matrices over M_n(R). Then we extended these results to n show that a linear operator T that strongly preserves L-matrices over M_m,n(R) if and only if T preserves L-matrices and T is also one to one on m,n the set of cells. We also characterized the group of linear operators that strongly preserve L-matrices.

In addition, we characterized the group of linear operators that preserve super L- matrices, the subset of L-matrix. Also we investigated linear …

Symmetric Designs, Difference Sets, And A New Way To Look At Macfarland Difference Sets, John Bowen Polhill Jr.

Honors Theses

In this paper, the topics of symmetric designs and difference sets are discussed both separately and in relation to each other. Then an approach to MacFarland Difference Sets using the theory behind homomorphisms from groups into the complex numbers is introduced. This method is contrasted with the method of finding this type of difference set used by E.S. Launder in his book Symmetric Designs: An Algebraic Approach.

Topics In Cyclotomic And Quadratic Fields, Pam Mellinger

Honors Theses

This paper introduces cyclotomic and quadratic fields and explores some of their properties and applications to problems in number theory. After some preliminary definitions and theorems, the paper looks at the relationship between quadratic and cyclotomic fields, at Kummer's lemma on units in the pth cyclotomic field, and at the Quadratic Reciprocity Law and its applications to diophantine equations.

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.

On The Distribution Of Sums Of Residues, Jerrold R. Griggs

Faculty Publications

No abstract provided.