Digital Commons Network^™

Writing Humanistic Mathematics, Ruth Hubbard

Humanistic Mathematics Network Journal

No abstract provided.

The Profit Motive: The Bane Of Mathematics Education, Neal Koblitz

Humanistic Mathematics Network Journal

No abstract provided.

Optimization In Chemical Kinetics, Arthur T. Benjamin, Gordon J. Hogenson '92

All HMC Faculty Publications and Research

No abstract provided in this article.

From The Editor, Issue 7, 1992, Alvin White

Humanistic Mathematics Network Journal

No abstract provided.

Three Comments On Ethics, Saunders Maclane

Humanistic Mathematics Network Journal

No abstract provided.

Toward A Definition Of 'Humanistic Mathematics', Sherman K. Stein

Humanistic Mathematics Network Journal

No abstract provided.

Mathematical References In Literature, John S. Lew

Humanistic Mathematics Network Journal

No abstract provided.

Epistemological Pluralism: Styles And Voices Within The Computer Culture, Sherry Turkle, Seymour Papert

Humanistic Mathematics Network Journal

No abstract provided.

What Is Mathematics And Why Don't They Know That?, Harald M. Ness

Humanistic Mathematics Network Journal

No abstract provided.

Mathematics From An English Major's Point Of View, Elizabeth Miller, Kathleen M. Shannon

Humanistic Mathematics Network Journal

No abstract provided.

On Electron Attraction & Newtonian Methodology For Approximating Quantum Mechanical Phenomena, Donald Greenspan

Mathematics Technical Papers - Archive

Classical dynamical computations for ground state [see pdf for notation], and [see pdf for notation] have been shown to yield correct vibrational frequencies and molecular diameters under an assumption of electron attraction for bonding electrons. In this paper, it is shown that such a mechanism also extends to [see pdf for notation] and to the nonhomogeneous molecules [see pdf for notation] and [see pdf for notation]. The vibrational motions are, apparently, quasi-periodic rather than periodic.

Triangle Trek, Thomas E. Moore

Bridgewater Review

No abstract provided.

Some Solutions To A Lens Model With Applications To Warm-Core Eddies, Juping Liu

OES Theses and Dissertations

A model of lens-shaped anticyclonic eddies based on nonlinear shallow water equations is developed. The model is a three-layer fluid and allows for one asymmetric mode as well as specified environmental flows. The solution scheme is a polynomial expansion of the field variables. When inserted into the hydrographic equations, the expansion yields eight first-order differential equations for the time dependent amplitudes. This system of ordinary differential equations is numerically tractable. As long as the initial values meet the requirement of elliptical structure and the prescribed external force is tolerable for the initial values, the numerical solutions are stable. Numerical solutions …

Graph Theory Based Routing Algorithms, Bo Wu

Masters Theses

In this thesis, we study two VLSI layout problems.

We investigate the Minimum-Bend Single Row Routing Problem in which the objective function is to minimize the number of doglegs (or blends) per net. Our approach uses a graph theoretic representation in which an instance of the Single Row Routing Problem is represented by three graphs, an overlap graph, a containment graph and an interval graph. Using this graph representation, we develop three algorithms for minimum-bend single row routing problem.

We present a three-layer over-the-cell router (ICR-3) for the standard cell design style based on a new cell model which assumes …

A4 Rewriteability, Eric Wepsic, Kevin O'Bryant, Lawren Smithline

Mathematical Sciences Technical Reports (MSTR)

The concept of 4-rewriteability with permutation coming form the alternating group A₄ is explored.

Pointwise Kernels Of Schwartz Distributions, Todor D. Todorov

Mathematics

We show that Schwartz distributions have kernels in the class of the pointwise nonstandard functions.

Some Lesson About The Law From Self-Referential Problems In Mathematics, John M. Rogers, Robert E. Molzon

Michigan Law Review

We first describe briefly mathematician Kurt Gödel's brilliant Incompleteness Theorem of 1931, and explore some of its general implications. We then attempt to draw a parallel between axiomatic systems of number theory (or of logic in general) and systems of law, and defend the analogy against anticipated objections. Finally, we reach two types of conclusions. First, failure to distinguish between language and metalanguage in mathematical self-referential problems leads to fallacies that are highly analogous to certain legal fallacies. Second, and perhaps more significantly, Gödel's theorem strongly suggests that it is impossible to create a legal system that is "complete" in …

Multiweighted Shapley Values And Random Order Values, Irinel C. Dragan

Mathematics Technical Papers - Archive

Recently, R. J. Weber introduced axiomatically in [14] the concept of random order value, an operator from [see pdf for notation], the space of TU games, to [see pdf for notation], satisfying linearity, dummy, efficiency and monotonicity axioms. In the present paper, we consider the concept of multiweighted Shapley value (MWSV), an operator from [see pdf for notation], satisfying linearity and carrier axioms. In the first section, we show that a MWSV is defined by its matrix representation relative to the unanimity basis for [see pdf for notation] and the standard basis for [see pdf for notation], if and only …

A Generalization Of Kraemer's Result On Difference Sets, James A. Davis

Department of Math & Statistics Faculty Publications

Kraemer has shown that every abelian group of order 2^{2d+ 2} with exponent less than 2^{2d+ 3} has a difference set. Generalizing this result, we show that any nonabelian group with a central subgroup of size 2^{d+ 1} together with an exponent-like condition will have a difference set.

Some Aspects Of Multi Source Satellite Image Processing., L. Lalitha Dr.

Doctoral Theses

The observation of a target by a device plaoed at some distance from it is cal.led remote sensing as ngainst in situ sensing where the sensor is kept in contact with the target. Usually physical emanations such as the electr omagnetic radiation from the target s observed by the sensing device. Sensors mounted on aircraft or satallite platforms measure the amount of energy reflected from or emitted by the earth's surface. Sensors scan the ground below a nd to either side of the satellite platform and as the platform noves forward, an image of the earths surface is formed.A satellite …

Diagnostic Regional Analysis On The Shortfalls In Development And Utilization Of Human Resource In India: A Statistical Study On The Spatial Variations By Districts Of India., Prasanta Pathak Dr.

Doctoral Theses

The main objective of this study has been estimation of model formulations, empirical evaluations and statistical analyses for identifying the existing regional patterns and structures of human resource development in the formative phase of human life-span through education, and the utilisation, or other- wise non-utilisation, during the activity phase of life-span in existing productive and related activities of our labour-abundant developing economy of India. Despite some awareness to the problems of development and balanced-utilisations of human resources into activities and also despite the various follow- up planning efforts undertaken, or stated to be undertaken, as reported in different Five-Year Plan …

Equivariant Cohomology With Local Coefficients., Goutam Mukherjee Dr.

Doctoral Theses

In this thesis we shall present an equivariant analogue of the steenrod cohomology with local coefficients, and use this to develop an obstruction therory for equivariant fibrations. The work is inspired by a remark of tom dieck [2] which says that a sensible translation of the classical obstruction theory to equivariant fibrations uses (meaning 'should use') equivariant cohomology with local coefficients.The equivariant singular cohomology of illman (9] is unsuitable for obstruction theory for equivariant sections of an equivariant fibration. The difficulty lies in connecting the obstruction cochains which arise from different fixed point sets, and the situation becomes no better …

Contributions To The Neyman-Scott And Mixture Problem., Joydeep Bhanja Dr.

Doctoral Theses

Neyman and Scott (1948) were the first to point out that the method of maximum likelihood fails to provide elfficient estimates when the number of parameters grows with the sample size n. Consider the following examples introduced by them:Ezample 1.1 Let { Xi } be a sequence of independent random vectors in I", components Xij of Xi being independent normal with mean u, and variance o2 Ilere o2 is the parameter of interest. It is casy to sce that the maxinum likelihood estimate for o2 is not even consistent. It is also known (see Lindsay (1980), Pfanzagl (1982), van der …

The Mazur Intersection Property In Banach Spaces And Related Topics., Pradipta Bandyopadhyaya Dr.

Doctoral Theses

In the first part of this chapter we explain in general terms the main theme of this thesis and provide a chapter wise summary of its principal results. The second part recapitulates some of the known notions and results used in the subsequent chapters. The numbers given in parentheses correspond to those in the list of references on page 70.S. Mazur (40] was the first to consider the following smoothness property in normed linear spaces, called the Mazur Intersection Property (MIP), or, more briefly, the Property (1):Every closed bounded convex set is the intersection of closed balls containing it.He showed …

Rewriteability, Commutators, And Fundamental N-Rewritings, Lawren Smithline

Mathematical Sciences Technical Reports (MSTR)

We consider the relationship between commutators and rewriteability.

Boundedness And Periodic Solutions In Infinite Delay Systems, Roger H. Hering

Mathematics and Statistics Faculty Research & Creative Works

Liapunov methods are used to give conditions ensuring that solutions of infinite delay equations are uniformly bounded and uniformly ultimately bounded with respect to unbounded (Cg) initial function spaces; and the connection to proving existence of periodic solutions is examined. Several examples illustrate the application of these results, especially to integrodifferential equations. © 1992.

Fixed Point Theorems For D-Complete Topological Spaces I, Troy L. Hicks

Mathematics and Statistics Faculty Research & Creative Works

Generalizations of Banach's fixed point theorem are proved for a large class of non-metric spaces. These include d-complete symmetric (semi-metric) spaces and complete quasi-metric spaces. The distance function used need not be symmetric and need not satisfy the triangular inequality. © 1992, Hindawi Publishing Corporation. All rights reserved.

Prediction Intervals, Based On Ranges And Waiting Times, For An Exponential Distribution, Laura Colangelo, Jagdish K. Patel

Mathematics and Statistics Faculty Research & Creative Works

This article contains two prediction intervals applicable to a 2-parameter as well as a 1-parameter exponential distribution. One can be used to predict a future sample range on the basis of an observed sample range. Appropriate prediction factors are tabulated. The other can be used to predict a waiting time between two future successive failures on the basis of an observed waiting time between two previous successive failures. © 1992 IEEE

Calculator Use And Incorporation In The Mathematics Classroom, Celia D. Denton

Capstone Research Projects

No abstract provided.

An Investigation Of Iterated Function Systems And Fractals, David Wuolu

Honors Theses, 1963-2015

This paper explores some of the fascinating ideas involved in the generation of fractals. A linear algebra and strong calculus background is sufficient to understand the main ideas, however many of the proofs require analysis. I examined metric spaces, and in particular, the metric space H(X), which consists of the compact subsets of the space X. The completeness of this space is proven, enabling the construction of fractals as fixed points of contractive transformations on H(X). I use the classical Cantor set and the Sierpinski triangle to illustrate the construction of fractals using iterated function systems (IFS's) which consist of …