Digital Commons Network^™

The Intermediate Value Theorem, Dale Varberg

ACMS Conference Proceedings 1995

The Intermediate Value Theorem (a continuous function on an interval assumes all values between any two of its values) is one of the big theorems of calculus. Yet the theorem is absent or briefly mentioned in most calculus textbooks. The theorem deserves better as we intend to show by listing ten picturesque consequences that we think could enliven any calculus course.

Constructivism, Mathematics Education And Christianity, Ted Watanabe

ACMS Conference Proceedings 1995

In this paper, I briefly describe what constructivism is and its implications in the field of mathematics education. I will then discuss what this epistemology may mean to Christians who are in the field of mathematics education

Statistics, Mathematics, And Teaching, David S. Moore

ACMS Conference Proceedings 1995

In discussing our teaching, we may focus on content, what we want our students to learn, or on pedagogy, what we do to help them learn. These two topics are of course related. In particular, changes in pedagogy are often driven in part by changing priorities for what kinds of things we want students to learn. It is nonetheless convenient to address content and pedagogy separately. Pedagogy, certainly the less specific of the two, is the topic of my second paper. This paper concerns content, and in particular contains one side of a conversation between a statistician and mathematicians …

The 25 Greatest Mathematicians, Robert L. Brabenec

ACMS Conference Proceedings 1995

No abstract provided.

Adjacencies In Words, Jean-Marc Fedou, Don Rawlings

Mathematics

Based on two inversion formulas for enumerating words in the free monoid by adjacencies, we present a new approach to a class of permutation problems having Eulerian-type generating functions. We also show that a specialization of one of the inversion formulas gives Diekert's lifting to the free monoid of an inversion theorem due to Cartier and Foata.

Introduction (1995), David L. Neuhouser

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Efficient Dominating Sets In Oriented Trees, Quan Yue

Dissertations

No abstract provided.

On The Equivalence Of Certain Consequences Of The Proper Forcing Axiom, Peter Nyikos, Leszek Piatkiwicz

Faculty Publications

No abstract provided.

Table Of Contents (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Schedule (1995), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 1995

Tenth ACMS Conference on Mathematics from a Christian Perspective

Transitions In Masculinity And Hemingway's Developed "Code", Daniel Polk

Honors Theses

The "Hemingway Code" is much more than two words that fit nicely together for a scholar's usage; the words signify a much deeper championing of masculinity, almost a haunting presence. For Ernest Hemingway living life every day, every moment with its fullest masculine fervor, became an obsession, a never-ending quest to be at one with the attitude of never complaining, never crying out, panicking, thinking too much, or regretting. To live a manly life in a series of tactical victories, performed with steadfast ritualistic mannerisms, is to embody masculinity, and therefore the "Hemingway Code."

Population Genetics: Estimation Of Distributions Through Systems Of Non-Linear Differential Equations, Nacer E. Abrouk, Robert J. Lopez

Mathematical Sciences Technical Reports (MSTR)

In stochastic population genetics, the fundamental quantity used for describing the genetic composition of a Mendelian population is the gene frequency. The process of change in the gene frequency is generally modeled as a stochastic process satisfying a stochastic differential equation. The drift and diffusion coefficients in this equation reflect such mechanisms as mutation, selection, and migration that affect the population. Except in very simple cases, it is difficult to determine the probability law of the stochastic process of change in gene frequency. We present a method for obtaining approximations of this process, enabling us to study models more realistic …

Σary, Moorhead State University, Mathematics Department

Math Department Newsletters

No abstract provided.

Discovery Of Integrity Relationships In Relational Databases, D. Harrier, D. C. St. Clair

Computer Science Technical Reports

The use of database management system integrity constraints has been a powerful tool in raising the quality of data within an application subject database. Unfortunately, the successful use of integrity constraints requires that the database administrator has implemented the constraint before data are inserted into the database.

The results of this research provide a methodology for discovering previously unknown integrity relationships in a relational database. The methodology uses the principles of knowledge discovery from the artificial intelligence community, and Quinlan's ID3 machine learning algorithm as the discovery tool. Experimental results are provided that demonstrate how the methodology can be applied.

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.

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

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.

The Significant-Digit Phenomenon, Theodore P. Hill

Research Scholars in Residence

No abstract provided.

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 …

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 …

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.

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 …