Digital Commons Network^™

M-Isometric Transformations Of Hilbert Space, Ii, Jim Alger, Mark Stankus

Mathematics

No abstract provided.

Educating Dilbert, Michael C. Sullivan

Articles and Preprints

A commentary on calculus reform efforts.

On Stable Homotopy Equivalences, Robert R. Bruner, F. R. Cohen, C. A. Mcgibbon

Mathematics Faculty Research Publications

No abstract provided.

Supereulerian Graphs And The Petersen Graph, Ii, Zhi-Hong Chen, Hong-Jian Lai

Scholarship and Professional Work - LAS

In this note, we verify two conjectures of Catlin in [J. Graph Theory 13 (1989) 465 - 483] for graphs with at most 11 vertices. These are used to prove the following theorem which improves prior results in [10] and [13]:

Let G be a 3-edge-connected simple graph with order n. If n is large and if for every edge 11.v E E(G), d(u) + d(v) 2 % - 2, then either G has a spanning eulerian subgraph or G can be contracted to the Petersen graph.

Sensible Rules For Remembering Duals -- The S-O-B Method, Arthur T. Benjamin

All HMC Faculty Publications and Research

We present a natural motivation and simple mnemonic for creating the dual LP of any linear programing problem.

Base-Invariance Implies Benford's Law, Theodore P. Hill

Research Scholars in Residence

A derivation of Benford's Law or the First-Digit Phenomenon is given assuming only base-invariance of the underlying law. The only base-invariant distributions are shown to be convex combinations of two extremal probabilities, one corresponding to point mass and the other a log-Lebesgue measure. The main tools in the proof are identification of an appropriate mantissa σ-algebra on the positive reals, and results for invariant measures on the circle.

On Nonparametric Families Of Life Distributions: Some Issues And Applications., Murari Mitra Dr.

Doctoral Theses

In reliability theury, one in primarily concerned with the study of the lifetime of a unit. The unit may be a mechanical device or a component of such a device; it may also be a living organism. By lifetime, we usually mean the duration for which the unit under study continues to perform cartain specific functions before it passes on to what is popularly known as the 'failed state'. More generally, however, lifetime can be, and often is, interpreted as the time to occurrence of a certain event such as the elapsed time before a broken down machine starts functioning …

Some Problems In Equivariant Topology., Aniruddha C. Naolekar Dr.

Doctoral Theses

This thesis has grown out of efforts to understand in an equivariant set up two old problems which were revived and developed extensively by Quillen, and also by others. The first problem concerns a de Rham type theorem over the field of rationals Q for a G-simplicial set where G is a finite group. The second problem deals with equivariant plus construction, classification of equivariant acyclic maps, and equivariant G-homotopy type of a G-space where G is a compact Lie group. More specifically, the content of the thesis is governed by the following two theorems, and our main objective is …

Computer Squares And Principal Graphs Of Subfactors., Uma Krishnan Dr.

Doctoral Theses

This thosin in devoted to the study of aome probloms related to the inclusion of a pair of (usually hyperfinite) Ili factors R. Specifically, the following and the relation between them are studied:(a) pairs of graphs which can occur as principal grapha for NC M;(b) construction of commuting squares starting with a pair of finite graphs;(c) computation of the higher relative commutants of sublactorn con- structed from specific commuting squares.The first chapter is introductory in nature and is included for the sake of comploteness and convenience of reference. It contains a rather perfunctory description of the basic construction for a …

Polygonal Approximation And Scale-Space Analysis Of Closed Digital Curves., Bimal Kumar Roy Dr.

Doctoral Theses

This thesis presents a series of algorithms for polygonal approximation of closed digital curves followed by scale-space analysis with its application to corner detection.Approximation of a closed curve by plece straight line segments is known as polygonal approximation. Any curve can be approximated by a polygon with any desired degree of accuracy.Polygonal approximation is useful in reducing the number of points required to represent a curve and to smooth data. Such representation facilitates extraction of numerical features for description and classification of curves. Basically there are two approaches to the problem. One is to subdivide the points into groups each …

Some Contributions To Linear Complementarity Problem., G. S. R. Murthy Dr.

Doctoral Theses

This dissertation deals with a number of problems related to linear comple- mentarity problem (LCP). Given a real square matrix A of order n and a real n-vector q, the LCP is to find a nonnegative n-vector z such that Az + q 2 0 and zt(Az + 9) = 0. There is vast literature on LCP, evolved during the last four decades. LCP plays a crucial role in the study of mathematical program- ming from the view point of algorithms as well as applications. The inherent nature of the problem has led the researchers to introduce and study a …

Asymptotic Properties Of Posterior Distributions And Study Of Some Nonregular Cases., Subhashis Ghosal Dr.

Doctoral Theses

The asymptotic approach to statistical estimation is frequently adopted be cause of ita general applicability and relative simplicity. The modern study of asymptotic theory, initiated in Le Cam (1953), has undergone a vigorous devel- opment through the classic works of Le Cam, Hájek, Bahadur, Ibragimov and Has'minskii (Khas'minskii), Bickel, Pfanzagl, Millar and many other scholars; see Le Cam (1986), Le Cam and Yang (1990), Ibragimov and Has'minskii (1981) and the review article by Ghosh (1985) for an account of this development.Most of the results in asymptotic theory of estimation are obtained under the classical Cramér-Rao type regularity conditions or their …

Regge Calculus As A Fourth Order Method In Numerical Relativity, Mark A. Miller

Physics - All Scholarship

The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge equations converge to zero as the second power of the lattice spacing, but that an average over local Regge equations converges to zero as (at the very least) the third power of the lattice spacing. Numerical studies using analytic solutions to the Einstein equations show …

An Elementary Proof That Finite Groups Lack Unique Product Structures, Matthew Cushman

Mathematical Sciences Technical Reports (MSTR)

We provide an elementary proof that no nontrivial finite group has a unique m-element product structure for any m greater than or equal to 2.

Missing Dimensions Of Mathematics Instruction, Walter Meyer

Humanistic Mathematics Network Journal

No abstract provided.

Writing Assignments In An Abstract Algebra Course, Krystina K. Leganza

Humanistic Mathematics Network Journal

No abstract provided.

Poetry, Monte J. Zerger

Humanistic Mathematics Network Journal

No abstract provided.

And This Is The Tale That Xeno Told, Sanda Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

Human Values And Science, Art & Mathematics, Cindy Cichy

Humanistic Mathematics Network Journal

No abstract provided.

Reaction To Human Values, Science, And Mathematics By Lillian R. And Hugh Gray Lieber, Jeanette Nelson

Humanistic Mathematics Network Journal

No abstract provided.

Math Puzzler, Paul J. Tobias

Humanistic Mathematics Network Journal

No abstract provided.

Letters From The Editor And Production Manager, Issue 11, 1995, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

In Memory Of Stavros Busenberg, Mario Martelli, Graeme Wake, Courtney Coleman, Melissa Aczon

Humanistic Mathematics Network Journal

No abstract provided.

Poetry, Lee Goldstein

Humanistic Mathematics Network Journal

No abstract provided.

A New Start For College Mathematics; Or Mathematics' Greatest Hits, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

To Stephen W. Hawking, Lillia N. Apostolova

Humanistic Mathematics Network Journal

No abstract provided.

The Study Of Mathematics And Growth In The Spirit, Rosemary Schmalz

Humanistic Mathematics Network Journal

No abstract provided.

Some Notes On How Students Perceive Mathematics, Joan Countryman

Humanistic Mathematics Network Journal

No abstract provided.

What Is Mathematics?: An Answer To Our Liberal Arts Dilemma, Bruce Williamson

Humanistic Mathematics Network Journal

No abstract provided.

Principal Points And Self-Consistent Points Of Elliptical Distributions, Thaddeus Tarpey, Luning Li, Bernard Flury

Mathematics and Statistics Faculty Publications

In this paper we study principal points and self-consistent points of p-variate elliptical distributions. We also discuss implications of our results for the computation and estimation of principal points.