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Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Free-Boundary Problems For Potential And Stokes Flows Via Nonsmooth Analysis, Srdjan Stojanovic, Tom Svobodny

Mathematics and Statistics Faculty Publications

A new approach to some free boundary problems of the type of jets and cavities for potential flows is introduced. Both potential and Stokes flows are considered. The variable domain problems are relaxed so that they become nonsmooth optimization problems on fixed domains for somewhat singular state equations. State equations are considered, and multivalued generalized gradients of the variational functionals are studied. The method is constructive.

Parameter Estimation By Conditional Coding, Taylor Duersch

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Conditional coding is an application of Markov Chain Monte Carlo methods for sampling from conditional distributions. It is applied here to the problem of estimating the parameters of a computer-simulated pattern of fractures in an isomorphic, homotropic material under plane strain. We investigate the theory and procedures of conditional coding and show the viability of the technique by its application.

On LP Solutions Of Second Order Linear Differential Equations, James C. Smith

Doctoral Dissertations

In this dissertation we study the L_p solutions of second order linear differential equations. The question as to when the equation -(q_o(x)y'(x))' + q₁(x)y(x) = f(x), α ≤ x < ∞, admits L_p solutions y(x) for arbitrary f(x) in L_p is investigated. We show the condition Re(q₁(x)) ≥ 1 or the conditions Re(q₁(x)) ≥ 0 and Im(q₁(x)) ≥ 1 are sufficient for a L_p solution y(x) to exist.

Functions that bound a solution of the homogeneous equation …

The Significant-Digit Phenomenon, Theodore P. Hill

Research Scholars in Residence

No abstract provided.

Imsa Math Journal: A Resource Notebook For High School Mathematics, Illinois Mathematics And Science Academy

IMSA Math Journal

We have been encouraged by the support, kind words, and constructive suggestions we have received from readers of our previous issues of the IMSAMJ. We look forward to hearing from you and value your ideas, suggestions, criticisms. We would welcome your identification of issues, topics, etc. that you would like us to address in future issues and future IMSA mathematics publications. Also we request that you take time to fill out the enclosed Feedback form.

Excerpt: Letter from the Editors

The Operator (Sgn X) D²/Dx² Is Similar To A Selfadjoint Operator In L² (R), Branko Ćurgus, Branko Najman

Mathematics Faculty Publications

Krein space operator-theoretic methods are used to prove that the operator (sgn x) d²/dx² is similar to a selfadjoint operator in the Hilbert space L²(R).

Descartes And Problem-Solving, Judith V. Grabiner

Pitzer Faculty Publications and Research

What can Descartes' Geometry teach us about problem solving?

A Reverse Isoperimetric Inequality, Stability And Extremal Theorems For Plane-Curves With Bounded Curvature, Ralph Howard, Andrejs Treibergs

Faculty Publications

No abstract provided.

Elimination Of Edge Effects Using Spline Wavelets Which Maintain A Uniform Two-Scale Relation, Sang Kyu Yang

Mathematics & Statistics Theses & Dissertations

Use of the compactly supported B-spline wavelet of Chui and Wang is hindered by loss of accuracy on decomposition, through truncation of weight sequences which are countably infinite. Adaptations to finite intervals often encounter significant problems with error near boundaries, called edge effects. For multiresolution analysis on a finite interval which employ the piecewise linear B-wavelet the present research provides a frontal approach to decomposition which avoids truncation of weight sequences, experiences no error at boundaries, and which exhibits a factor of three increase in computational efficiency, over the usual approach characterized by truncation of infinite weight sequences. As a …

Thermal Ignition Analysis In The Laminar Boundary Layer Behind A Propagating Shock Front, Mushtaq Ahmed Khan

Mathematics & Statistics Theses & Dissertations

Asymptotic analysis in the limit of large activation energy is performed to investigate the ignition of a reactive gas in the laminar boundary layer behind a propagating shock front. The study is based on a one-step, irreversible Arrhenius reaction of a premixed gas; therefore, the ignition phenomenon is thermally induced. The boundary layer consists of a thin, diffusive, reaction region at the point where the temperature is maximum and diffusive-convective non-reacting regions adjacent to the reacting region. Both adiabatic and isothermal boundary conditions are examined. For the adiabatic wall, the reaction zone is near the insulated boundary. The reaction zone …

Essays In Dynamic Games., Saikat Datta Dr.

Doctoral Theses

This thesis contains four essays which broadly come under the area of Dynamic Games. All the essays involve developments or applications of non-cooperative equilibrium concepts to games played over infinite horizons. The two essays in Chapter 2 and Chapter 3 involve the concept of renegotiation proof equilibriain repeated games. The essay in Chapter 4 discusses how a social norm of slow building of trust in bilateral relationships can be understood as a social equi- librium even in the absence of asymmetric information problems. Chapter 5, which represents joint work with Prabal Raychaudhuri, applies non-cooperative bargaining theory to a context where …

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.

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.

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

Mathematics Faculty Research Publications

No abstract provided.

Lazutkin Coordinates And Invariant Curves For Outer Billiards, Edoh Y. Amiran

Mathematics Faculty Publications

The outer billiard ball map (OBM) is defined from and to the exterior of a domain, Ω, in the plane as taking a point, q, to another point, q ₁, when the line segment with endpoints q and q ₁ is tangent to the boundary, ∂Ω (with a chosen orientation), and the point of tangency with the boundary divides the segment in half. Let C be an invariant circle for the OBM on Ω, with ∂Ω smooth with positive curvature. After computing the loss of derivatives between ∂Ω and C, it is shown via KAM theory that …

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.

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.

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 …

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 …

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 …

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 …

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 …

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.

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

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.