Digital Commons Network^™

Supercomputer Simulation Of The Modes Of Colliding Microdrops Of Water, Larry F. Heath, Donald Greenspan

Mathematics Technical Papers - Archive

No abstract provided.

Notions Of Relative Ubiquity For Invariant Sets Of Relational Structures, Paul Bankston, Wim Ruitenburg

Mathematics, Statistics and Computer Science Faculty Research and Publications

Given a finite lexicon L of relational symbols and equality, one may view the collection of all L-structures on the set of natural numbers w as a space in several different ways. We consider it as: (i) the space of outcomes of certain infinite two-person games; (ii) a compact metric space; and (iii) a probability measure space. For each of these viewpoints, we can give a notion of relative ubiquity, or largeness, for invariant sets of structures on w. For example, in every sense of relative ubiquity considered here, the set of dense linear orderings on w is …

Mathematical Visions: The Pursuit Of Geometry In Victorian England (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Joan L. Richards. Mathematical Visions: The Pursuit of Geometry in Victorian England. xiii + 266 pp., illus., figs., bibl., index. Boston/New York: Academic Press, Harcourt Brace Jovanovich, 1988.

Rewriteable Sequencings Of Groups, Jeanne Nielsen

Mathematical Sciences Technical Reports (MSTR)

A finite group is called P_n-sequenceable if its nonidentity elements can be listed x₁ , x₂ , ..., x_k so that the product x _i x _i+i · · · x _i+n-1 can be rewritten in at least one nontrivial way for all i. It is shown that S_n , A_n , D_n are P₃-sequenceable, that every finite simple group is P₄ -sequenceable, and that every finite group is P_s-sequenceable. It is conjectured that every finite group is P₃-sequenceable.

Sums Of Semiprime, Z, And D L-Ideals In A Class Of F-Rings, Suzanne Larson

Mathematics, Statistics and Data Science Faculty Works

In this paper it is shown that there is a large class of f-rings in which the sum of any two semiprime i-ideals is semiprime. This result is used to give a class of commutative f-rings with identity element in which the sum of any two z-ideals which are i-ideals is a z-ideal and the sum of any two d-ideals is a d-ideal.

Some Np-Complete Problems In Linear Algebra, Santhosh Sastry '90

Honors Projects

This research project is aimed at studying the theory of NP-Completeness and determining the complexity of certain problems in linear algebra. The first chapter introduces the reader to Complexity theory and defines NP-Completeness. It is supported by Appendices 1 and 2. Appendix 3 lists some known NP-Complete problems.

An Artificial Neural Approach To The Decomposition Problem, Chandrashekar L. Masti

Electrical & Computer Engineering Theses & Dissertations

The goal of this thesis is to develop an artificial neural approach toward addressing the intractability involved with the decomposition problem. The search for the lattice of substitution property (s. p.) partitions essential to decompositions is cast into the framework of constraint satisfaction. An artificial neural network is developed to provide solutions by performing optimization of a mathematically derived objective function over the problem space. The issue of transitivity is verified to belong to a class of problems beyond the scope of solvability for conventional quadratic-order constraint satisfaction neural networks. A theorem is stated and proved establishing that third-order correlations …

A Mathematical Model Of The Dynamics Of An Optically Pumped Codoped Solid State Laser System, Thomas G. Wangler

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model for the dynamics of an optically pumped codoped solid state laser system. The model comprises five first order, nonlinear, coupled, ordinary differential equations which describe the temporal evolution of the dopant electron populations in the laser crystal as well as the photon density in the laser cavity. The analysis of the model is conducted in three parts.

First, a detailed explanation of the modeling process is given and the full set of rate equations is obtained. The model is then simplified and certain qualitative properties of the solution are obtained.

In the …

The Fokker-Planck And Related Equations In Theoretical Population Dynamics, George Derise

Mathematics & Statistics Theses & Dissertations

The population growth of a single species is modeled by a differential equation with initial condition(s) so that the number of organisms in the population is derived using some mechanism of growth, i.e. a growth rate function. However, such deterministic models are often highly unrealistic in population dynamics because population growth is basically a random event. There are a large number of chance factors influencing growth that might not be taken into account by deterministic models. The effect of other species (for example, in the chance meeting of a predator), population fluctuations due to weather changes that would alter food …

Oscillations In Lotka-Volterra Systems Of Chemical Reactions, Roger H. Hering

Mathematics and Statistics Faculty Research & Creative Works

For a chemical reaction system modeled by x =k₁Ax -k₂x² -k₃xy +k₄y², y =k₃xy -k₄y² -k₅y +k₆B, it is shown that for each positive choice of parameters k₁A, B there exists a unique stationary state which is globally asymptotically stable in the positive quadrant. A criterion for the non-existence of periodic solutions is given for the generalized Lotka-Volterra system:x = f(x)h(x, y), y. © 1990 J.C. Baltzer AG, Scientific Publishing Company.

Lifted P-Adic Homology With Compact Supports Of The Weierstrass Family And Its Zeta Endomorphism, Goro Kato

Mathematics

The relations among the generators for the lifted p-adic homology with compact supports of the various subfamilies of the Weierstrass family in characteristic p > 0 (p ≠ 2, 3) are explicitly given in Section 2. Then, the universal coefficient spectral sequence and the zeta endomorphism in Section 3 enable one to compute explicitly the lifted p-adic homology with compact supports of all fibres, including all the elliptic curves and all their singular degenerations in the family.

On The Error In Quasi-Quantum Mechanical Calculations, Donald Greenspan

Mathematics Technical Papers - Archive

A numerical simulation of the vibration of a ground state H2 molecule is made from a quasi-quantum mechanical point of view, that is, energy has been determined by quantum mechanics and trajectories determined by Newtonian mechanics. The numerical method used is implicit and conserves the energy exactly at each time step. A variety of CRAY X-MP/SE14 calculations are described and discussed. Comparisons are made with correct oscillation and diameter values.

A Particle Model Of Ground State H2, Donald Greenspan

Mathematics Technical Papers - Archive

A particle model is developed for the ground state H2 molecule. Interparticle forces are formulated which are noncoulombic, but nearly coulombic. The vibration is simulated by a numerical method which conserves the molecule's energy exactly. Numerical examples are described and discussed.

Taxonomies Of Model-Theoretically Defined Topological Properties, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

A topological classification scheme consists of two ingredients: (1) an abstract class K of topological spaces; and (2) a "taxonomy", i.e. a list of first order sentences, together with a way of assigning an abstract class of spaces to each sentence of the list so that logically equivalent sentences are assigned the same class.K, is then endowed with an equivalence relation, two spaces belonging to the same equivalence class if and only if they lie in the same classes prescribed by the taxonomy. A space X in K is characterized within the classification scheme if whenever Y _{E …}

Eigenvalue Problems Of Ginzburg–Landau Operator In Bounded Domains, Kening Lu, Xing-Bin Pan

Faculty Publications

In this paper we study the eigenvalue problems for the Ginzburg–Landau operator with a large parameter in bounded domains in [openface R]2 under gauge invariant boundary conditions. The estimates for the eigenvalues are obtained and the asymptotic behavior of the associated eigenfunctions is discussed. These results play a key role in estimating the critical magnetic field in the mathematical theory of superconductivity.

Some Contributions To Generalized Inverse And The Linear Complementarity Problem., N. Eagambaram Dr.

Doctoral Theses

A generalized inverse (g-inverse) of a matrix A is a solution x to the matrix equationA XA = A(1.1.1)A g-inverse of A can be defined alternatively as a matrix x such that x = Xb is a solution to the linear equation Ax -b for any b that makes - b consistent. There is a vast literature on g-inverse. For a number of results on g-inverses and their applications one may refer to the well known books in the literature by Rao and Mitra (1971); and by Ben Israel and Greville (1974).Another inverse that lies hidden in the definition of …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Editorial, Issue 5, 1990, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Advanced Displacement Exam, Robert Messer

Humanistic Mathematics Network Journal

No abstract provided.

Real Needs Of School Children, Hassler Whitney

Humanistic Mathematics Network Journal

No abstract provided.

Teaching Global Issues Through Mathematics, Richard H. Schwartz

Humanistic Mathematics Network Journal

No abstract provided.

What Has Mathematics Got To Do With Values?, Stephen Lerman

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics And Ethics, Reuben Hersh

Humanistic Mathematics Network Journal

No abstract provided.

A Social View Of Mathematics: Iimplications For Mathematics Education, Stephen Lerman

Humanistic Mathematics Network Journal

No abstract provided.

The Humanistic Aspects Of Mathematics And Their Importance, Philip J. Davis

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics — A Significant Force In Our Culture, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

Heuristic Thinking And Mathematics, J. F. Lucas

Humanistic Mathematics Network Journal

No abstract provided.

Preparing Teachers To Teach Mathematics Within A Humanistic Perspective, Beatriz S. D'Ambrosio

Humanistic Mathematics Network Journal

No abstract provided.

Discriminatory Von Neumann-Morgenstern Solutions, J. G. C. Heijmans

Mathematics Technical Papers - Archive

The von Neumann-Morgenstern solution (vN-M solution) or stable set is arguably the most dynamic and flexible solution concept for cooperative games with side-payments. Perhaps the most striking phenomenon is that vN-M solutions often suggest intricate coalition formation processes and corresponding payoffs. Why this occurs is not well understood. On the other hand, vN-M solutions are difficult to find. This paper deals with the class of discriminatory vN-M solutions and presents results that give insights in the corresponding coalition formation process. A computationally effective procedure is presented to answer the decision problem whether or not a proposed set of imputations to …

Norms Of Positive Operators On Lp-Spaces, Ralph Howard, Anton R. Schep

Faculty Publications

No abstract provided.