Digital Commons Network^™

Concerning Periodic Points In Mappings Of Continua, W. (William) T. (Thomas) Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we present some conditions which are sufficient for a mapping to have periodic points. © 1988 American Mathematical Society.

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.

Subspaces Of Lp,Q, N L. Carothers, S J. Dilworth

Faculty Publications

We examine the subspace structure of the Lorentz function space Lp,q[0, oo). Our main result is that a subspace of Lp,q[0, oo), p ^ 2, q < oo,must either strongly embed in Lp[0,1] or contain a complemented copy of lq.

Cycle Lengths In Aᵏb, Charles M. Grinstead

Mathematics & Statistics Faculty Works

Let A be a nonnegative, n n matrix, and let b be a nonnegative, nxn vector. Let S be the sequence {Akb }, k = 0, l, 2, .... Define m(A, b) to be the length of the cycle of zero-nonzero patterns into which S eventually falls. Define m(A) to be the maximum, over all nonnegative b of m(A, b). Finally, define m(n) to be the maximum, over all nonnegative, nxn matrices A of m(A). This paper shows given A and b, that m(A, b) is a divisor of a certain number, which is determined by the structure of A …

Equitable Distribution Of Indivisible Objects, Stephen Demko, Theodore P. Hill

Research Scholars in Residence

Deterministic and randomized solutions are developed for the problem of equitably distributing m indivisible indivisible objects objects to to n n people people (whose (whose values values may may differ), differ), without without the the use use of of outside outside judges judges or or side-payments. Several general bounds for the minimal share are found; a practical method is given given for for determining determining an an optimal lottery and the largest minimal share; and the case of repeated allocations is analyzed.

Computer Science—A Mathematical Science And Accreditation, Frank Garnett Walters

Mathematics and Statistics Faculty Research & Creative Works

No abstract provided.

Odd Primary Periodic Phenomena In The Classical Adams Spectral Sequence, Paul L. Shick

Mathematics and Computer Science

We study certain periodic phenomena in the cohomology of the mod ρ Steenrod algebra which are related to the polynomial generators υ_n ∈ π∗ΒΡ. A chromatic resolution of the Ε₂ term of the classical Adams spectral sequence is constructed.

The Space Of Minimal Prime Ideals Of C(X) Need Not Be Basically Disconnected, Alan Dow, Melvin Henriksen, Ralph Kopperman, J. Vermeer

All HMC Faculty Publications and Research

Problems posed twenty and twenty-five years ago by M. Henriksen and M. Jerison are solved by showing that the space of minimal prime ideals of the ring C(X) of continuous real-valued functions on a compact (Hausdorff) space need not be basically disconnected-or even an F-space.

Inequalities For Sums Of Independent Random Variables, N L. Carothers, S J. Dilworth

Faculty Publications

A moment inequality is proved for sums of independent random variables in the Lorentz spaces LPtq, thus extending an inequality of Rosenthal. The latter result is used in combination with a square function inequality to give a proof of a Banach space isomorphism theorem. Further moment inequalities are also proved.

Public Policy And The Dynamics Of Development: A Macroeconomic Theory For Developing Economics., B. K. Pradhan Dr.

Doctoral Theses

If I am given the cholce to define Development Economi ea, I would do so in such a way that the work reported here aust eni nent ly belong to the realm of that discipline. Before proceeding further one must remenber what Hirschman said nearly 28 yeara ago ...probably that econonists have not been able to construct, much less agree on, a alngle and unbroken chain of causes and effects that would neatly explain the transition from While this f ailure is of course only to the credit of economists, it cannot be denied that Underdevelopment to development. In comparison …

On Sequential Test Procedure With Application In Identification And Selection., Atasi Basu Dr.

Doctoral Theses

The area of sequential testing of statistical hypothesss is an important part of sequential analysis. The idea of a sequential test goes back to Dodge and Romig (1929) who cons tructed a double sampling procedure for sampling inspection. They wers motivated by the obser- vation that the double sampling plan requires a smaller number of observations on the average when compared uith the corresponding single sampling plan, Later schemes like multiple sampling vide Wlalter Bartky (1943) and interesting practical application of large scale experimente in successive stages vide Mahalanobis (1940) started comni ng up.The formal theory in sequential analysis began …

Some Aspects Of Majorization And Their Applications In Statistics., Subir Kumar Bhandari Dr.

Doctoral Theses

The works in this dissertation are primarily baset ur. difterent concepts of majorization and the results thereof. True first part of this dissertation is a study on dirfferent concepts of uni variate and multivariate majorization. The latter part of this dissertation includes studies on some problems in Sample Survey, and problems relating to ranking and selection with the use of some results, old and new, in majorization.The concept of univariate majorization has been consi- dered by economists in relation to Lorenz ourve, as well as by mathematicians and statisticians, especially in the field of reliability. It appears that the results …

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.

Generalized Distance In Graphs, Garry L. Johns

Dissertations

No abstract provided.

General Equilbrium Analysis Of Price And Distribution Controls For Foodgrains And Textiles In India., P. V. Srinivasan Dr.

Doctoral Theses

Unlike in many developed countries, in India, institutions for distribution of goods and services are not well developed. Hence policy makers are concerned with the development of economic institutions to promote growth, remove unemployment and eradicate poverty. In addition to the general fiscal and monetary policy instruments such as taxes, su bsidies, bank rate, open market operations etc, the government also uses several price and non-price controls. For example, it administers the prices of essential inputs such as steel, coal, power ete, and distributes certain essential commodities through ration s hops at a price lower than the market prices.One way …

Analysis Of The Convergence History Of Fluid Flow Through Nozzles With Shocks, Mohammad Saleem, A Cheer, M Hafez, T Pulliam

Faculty Publications

"Convergence of iterative methods for the solution of the steady quasi-one-dimensional nozzle problem with shocks is considered. The finite-difference algorithms obtained from implicit schemes are used to approximate both the Euler and Navier-Stokes Equations. These algorithms are investigated for stability and convergence characteristics. The numerical methods are broken down into their matrix-vector components and then analyzed by examining a subset of the eigensystem using a method based on the Arnoldi process. The eigenvalues obtained by this method are accurate to within 5 digits for the largest ones and to within 2 digits for the ones smaller in magnitude compared the …

Remarks On A Semilinear Elliptic Equation On Rn, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Locally Finite Families, Completely Separated Sets And Remote Points, Melvin Henriksen, Thomas J. Peters

All HMC Faculty Publications and Research

It is shown that if X is a nonpseudocompact space with a σ-locally finite π-base, then X has remote points. Within the class of spaces possessing a σ-locally finite π-base, this result extends the work of Chae and Smith, because their work utilized normality to achieve complete separation. It provides spaces which have remote points, where the spaces do not satisfy the conditions required in the previous works by Dow, by van Douwen, by van Mill, or by Peters.

The lemma: "Let X be a space and let {Cε: € < α} be a locally finite family of cozero sets of X. Let {Zε: € < α } be a family of zero sets of X such that for each € < α, Zε с Cε. Then ∪_ε<α Zε is completely separated from X/∪εCε", is a fundamental …

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.

Atamm Multicomputer System Design, William Robert Tymchyshyn

Electrical & Computer Engineering Theses & Dissertations

The Algorithm To Architecture Mapping Model, or ATAMM, is a graph theoretic design methodology that has been created to resolve design and performance issues involved with concurrent processing. Petri-net marked graphs are used to represent the computational environment.

This thesis describes the development of a multicomputer system which will operate within the bounds specified by the ATAMM model. The system is first designed and implemented using the framework of standard multicomputer design theory. A validation is then performed by the comparison of the system's computational performance to results predicted by ATAMM. This validation is shown to be successful for three …

The Decay And Formation Of One-Dimensional Nonconservative Shocks, Marek Elźanowski, Marcelo Epstein

Mathematics and Statistics Faculty Publications and Presentations

The method of singular surfaces is used to obtain explicit conditions under which a one-dimensional acceleration wave develops into a shock when some dissipation mechanism is present. The conditions which secure the initial growth of the strong shock wave propagating into an undeformed nonlinear and dissipative medium are also derived. The analysis is pre- sented for a single balance law, one-dimensional elasticity, and the non- linear Maxwellian continuum.

Riemann Surfaces: Distribution Of Weierstrass Points On Nodal Curves Of Genus 2, Kathryn A. Furio '88

Fenwick Scholar Program

No abstract provided.

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Common Hyperplane Medians For Random Vectors, Theodore P. Hill

Research Scholars in Residence

No abstract provided.

Maximal Rank-One Spaces Of Matrices Over Chain Semirings, Daniel Joseph Scully

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Vectors and matrices over the Boolean (0,1) semiring have been studied extensively along with their applications to graph theory. The Boolean (0,1) semiring has been generalized to a class of semirings called chain semirings. This class includes the fuzzy interval. Vectors and matrices over chain semirings are examined. Rank-1 sets of vectors are defined and characterized. These rank-1 sets of vectors are then used to construct spaces of matrices (rank-1 spaces) with the property that all nonzero matrices in the space have semiring rank equal to 1. Finally, three classes of maximal (relative to containment) rank-1 spaces are identified.

Review Of “Constructive Combinatorics” By D. Stanton And D. White, Stephen B. Maurer

Mathematics & Statistics Faculty Works

No abstract provided.

Self Consistent Model Of The Glow Discharge, Hao Chen

Electrical & Computer Engineering Theses & Dissertations

The strong spatial variation of the electric field intensity in the vicinity of the cathode of a gas discharge requires the use of microscopic methods to describe the nonequilibrium behavior of the electron dynamics in this region. A one-dimensional Monte Carlo code was developed. It allows one to obtain the distribution of the electron drift velocity and rate coefficients for a given electric field intensity in the cathode fall. The results of this calculation are used to find the density distribution of charged particles in this region and consequently, by means of Poisson's equation, a corrected electric field intensity. In …

Two Discrete Forms Of The Jordan Curve Theorem, Lawrence Stout

Scholarship

The Jordan curve theorem is one of those frustrating results in topology: it is intuitively clear but quite hard to prove. In this note we will look at two discrete analogs of the Jordan curve theorem that are easy to prove by an induction argument coupled with some geometric intuition. One of the surprises is that when we discretize the plane we get two Jordan curve theorems rather than one, a consequence of the interplay between two natural products in the category of graphs. Topology in this context has been studied by Farmer in [2]. To state the discrete versions, …

I'Ll Carry My Coals Where They're Needed, Professor Henriksen, Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

Readings In Mathematics Education, Harriet Edwards

Humanistic Mathematics Network Journal

No abstract provided.