Digital Commons Network^™

Counting Nilpotent Pairs In Finite Groups: Some Conjectures, H Dubose-Schmidt, Michael D. Galloy, D,L, Wilson

Mathematical Sciences Technical Reports (MSTR)

The number of nilpotent pairs is determined for a number of small groups.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Effects Of Nonsymmetric Release Times On Rate Monotonic Scheduling, R. G. Karl, T. L. Lo, D. C. St. Clair

Computer Science Technical Reports

This paper discusses problems associated with scheduling periodic tasks in a hard, real-time processing or computing environment using a static-priority, preemptive-resume operating system . The scheduling problems associated with a task set containing a single periodic task which has two fixed release periods of unequal length are examined. Some real-world applications may require task release times which are periodic, but whose tasking periods are not symmetric. A scheduling algorithm for task sets with a single nonsymmetric task has been developed for staticpriority, preemptive-resume operating systems. The nonsymmetric scheduling algorithm is based on the rate monotonic scheduling algorithm which assigns higher …

Design Of Backpropagation Neural Network Architectures Using A Decision Tree Classifier, B. M. Van Horn, D. C. St. Clair

Computer Science Technical Reports

The backpropagation neural network algorithm is a popular machine learning methodology. One difficulty with using the algorithm is that the network architecture must be designed before learning can occur. This includes deciding the number of layers, the number of nodes in each layer, and the number of connections. Traditionally this problem is solved by heuristics gained by an expert through experience.

This paper presents an algorithm for using ID3 decision trees to design the network architecture. Previous approaches rely on binary decision trees. The proposed technique utilizes n-ary trees. These trees are easier to understand, are better suited for continuous-valued …

Optimizing Accuracy And Generalization In Numeric Classification Systems, M. D. Walters, D. C. St. Clair

Computer Science Technical Reports

Classifier systems are knowledge-based learning algorithms that take training instances as input and produce a set of rules as output. The classifier systems focused on in this paper represent the knowledge they learn in the form of decision trees, and are built upon Quinlan's [ 1986] inductive algorithm ID3.

The ID3 algorithm suffers from the inability to easily and effectively handle domains with numeric-valued attributes. Numeric attributes are those whose values are taken from a continuous domain or from a domain with a large number of discrete values. A number of approaches have been developed for extending ID3 to handle …

The Identification And Processing Of Don't-Care Attribute Values In Id3 Decision Tree Construction, P. D. Dorr, D. C. St. Clair

Computer Science Technical Reports

ID3 is most successful when used with sets of training and testing data that contain no missing attribute values. Many times, however, real-world domains have attributes with missing values. Sometimes these attribute values may not be needed to classify an instance. Such attribute values are called don't-care attribute values. In other cases, the values are needed but are unavailable. These values are called unknown attribute values. This paper describes the difference between unknown and don't-care attribute values and discusses several ways of identifying don't-care attribute values in ID3. Numerical results are described which validate the practicality of these approaches.

Network Key Management In A Large Distributed Environment, J. J. Stapleton, D. C. St. Clair

Computer Science Technical Reports

The technique of using encryption for protecting information in a network environment involves managing encryption keys within that same network. In large distributed networks the goal of achieving a secure environment requires a secure method of performing network key management. Network security, system security, and application security by means of data encryption rely on encryption keys remaining secret.

Both international and domestic standards organizations such as the International Organization for Standardization (ISO), the American National Standards Institute (ANSI), and the National Institute of Standards and Technology (NIST) address the issues of encryption through various standards. However, these standards discuss methods …

Logical "Paradox": A Response To Fallacies, Flaws, And Flimflam #36, Calvin Jongsma

Faculty Work Comprehensive List

Response to "Fallacies, Flaws, and Flimflam" by Ed Barbeau in The College Mathematics Journal, Vol. 23, No. 3 (May, 1992), pp. 203-206. Fallacies, Flaws, and Flimflam is a column in The College Mathematics Journal edited by Ed Barbeau of the Department of Mathematics at the University of Toronto.

A Maple Package For The Variational Calculus, Cinnamon Hillyard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The HELMHOLTZ package, written in Maple V, is a collection of commands to support research in the variational calculus. These commands include the standard operators on differential forms, Euler-Lagrange operators, homotopy operators, Lie bracket, Lie derivatives, and the prolongation of a vector field. We give a brief introduction to the variational calculus. We describe each of the commands in the HELMHOLTZ package completely along with numerous examples of each. Applications of the package include verification of symmetry groups for differential equations, solving the inverse problem of the calculus of variations, computing generalized symmetries, and finding variational integrating factors. A complete …

A Comparison Of Two Linear Nonparametric Regression Techniques, Sylvain Sardy

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis presented a useful tool in regression. Nonparametric linear regression techniques were described in the general context of regression. A comparison of two of these techniques, kernel regression and iterative regression, showed various aspects of nonparametric linear regressors.

Inverse Problem In Porous Medium Using Homogenization, Helen Alkes

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The problem under consideration is that of obtaining a representation of the permeability of a porous medium which is heterogeneous and anisotropic from limited information. To solve this inverse problem we propose the use of two different pieces that work together. A simulated annealing algorithm is presented and coupled with an homogenization technique; together these solve the problem which was posed. Further, numerical simulation results are presented illustrating the use of the simulated annealing algorithm as well as a coupling with the homoginization technique. This study illustrates that the performance of the annealing algorithm is enhanced with usage of homogenization.

Disconjugacy And Oscillation Theory Of Linear Differential And Difference Equations, Yuhua Xu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This dissertation is both a literature survey and a presentation of new and independent results.

The survey gives an overview of disconjugacy and oscillation theory for linear differential and difference equations with an emphasis on comparing the theory of difference equations to the theory of differential equations. Second order scalar equations, higher order scalar equations, matrix equations (systems) and Hamiltonian systems are discussed. A chapter on three-term recurrences of systems is also included. Both similarities and differences between differential and difference equations are described.

The new and independent results are for Hamiltonian systems of difference equations. Those results include the …

Hopf Bifurcation In A Parabolic Free Boundary Problem, Yoon-Mee Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We deal with a free boundary problem for a nonlinear parabolic equation, which includes a parameter in the free boundary condition. This type of system has been used in models of ecological systems, in chemical reactor theory and other kinds of propagation phenomena involving reactions and diffusion.

The main purpose of this dissertation is to show the global existence, uniqueness of solutions and that a Hopf bifurcation occurs at a critical value of the parameter r. The existence and uniqueness of the solution for this problem are shown by finding an equivalent regular free boundary problem to which existence …

Mielnik Probability Spaces And Functional Equations, J. J. Mitchell

Opportunities for Undergraduate Research Experience Program (OURE)

The invariance properties of the solutions of those functional equations naturally occurring in the construction of Mielnik probability spaces are studied, and in turn are related to one another. In particular, the possibilities for fixed points of these solutions are found, and the relationships between these results are discussed. The two functional equations studied include a representation of the generalized parallelogram law and an equation used in the modeling of polarization phenomena. The main result of the paper lies in the extention of previous research on Mielnik probability spaces to a higher dimension, as well as a discussion of their …

Shooting Method Solutions Of Eigenvalue Problems, Xi Chen

Opportunities for Undergraduate Research Experience Program (OURE)

A shooting method was developed to study eigenvalue problems derived from Schrodinger equation. The challenging problem, the two-dimensional hydrogen system with the logarithmic potential function, was successfully solved by the shooting method. But no complete proof was given for its rationale and correctness. This paper not only gives the complete proof for the shooting method, but also generalizes it to solve a large class of eigenvalue problems. In a certain sense, the shooting method proves more effective numerically and more powerful theoretically than the classical functional analysis approach.

Some Facts About Cycels And Tidy Groups, Kevin O'Bryant, D. Patrick, Lawren Smithline, Eric Wepsic

Mathematical Sciences Technical Reports (MSTR)

No abstract provided.

Letter To Professor Joanne S. Growney, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.

Poems Taken From "An Evening Of Mathematical Poetry"

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics As A Humanistic Discipline, Elena Anne Corie Marchisotto

Humanistic Mathematics Network Journal

No abstract provided.

Writing Humanistic Mathematics, Ruth Hubbard

Humanistic Mathematics Network Journal

No abstract provided.

The Profit Motive: The Bane Of Mathematics Education, Neal Koblitz

Humanistic Mathematics Network Journal

No abstract provided.

Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92

All HMC Faculty Publications and Research

No abstract provided in this article.

From The Editor, Issue 7, 1992, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Three Comments On Ethics, Saunders Maclane

Humanistic Mathematics Network Journal

No abstract provided.

Toward A Definition Of 'Humanistic Mathematics', Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical References In Literature, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.

Epistemological Pluralism: Styles And Voices Within The Computer Culture, Sherry Turkle, Seymour Papert

Humanistic Mathematics Network Journal

No abstract provided.

What Is Mathematics And Why Don't They Know That?, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics From An English Major's Point Of View, Elizabeth Miller, Kathleen M. Shannon

Humanistic Mathematics Network Journal

No abstract provided.

On Electron Attraction & Newtonian Methodology For Approximating Quantum Mechanical Phenomena, Donald Greenspan

Mathematics Technical Papers - Archive

Classical dynamical computations for ground state [see pdf for notation], and [see pdf for notation] have been shown to yield correct vibrational frequencies and molecular diameters under an assumption of electron attraction for bonding electrons. In this paper, it is shown that such a mechanism also extends to [see pdf for notation] and to the nonhomogeneous molecules [see pdf for notation] and [see pdf for notation]. The vibrational motions are, apparently, quasi-periodic rather than periodic.