Digital Commons Network^™

Mathematics And Poetry : Isolated Or Integrated?, Joanne S. Growney

Humanistic Mathematics Network Journal

No abstract provided.

On Teaching In The Mathematical Sciences, James M. Cargal

Humanistic Mathematics Network Journal

No abstract provided.

Linear Operators Strongly Preserving Polynomial Equations Over Antinegative Semirings, Sang-Gu Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = X^r₁ + X^r₂ + ... + X^r_t and r₁>r₂>...>r_t≥2.

In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We …

On A Class Of Bargaining Schemes For Points In The Core Of A Cooperative N-Person Game, Yair Censor, Dan Butnariu

Mathematics Technical Papers - Archive

Projection methods of solving convex feasibility problems lead naturally to a class of bargaining scheme's for points in the core of cooperative n-person games. Each such bargaining scheme is by itself a mathematical model of "rational behavior" describing a specific way of achieving "equilibrated" payoff vectors. We show that many of these bargaining schemes are "stable"' and have meaningful heuristic interpretations.

Incremental Learning Of Numeric Clusters In Classifier Systems, K. R. Hacke, D. C. St. Clair

Computer Science Technical Reports

Classifier systems are knowledge-based learning algorithms which take training instances as input and produce a set of rules as output Many classifier systems represent the knowledge they learn in the form of one or more decision trees. Accurate knowledgebase systems for a variety of domains have been constructed by generating decision trees using J. R. Quinlan's (1986) inductive algorithm ID3 and P. E. Utgoffs (1988) IDS. IDS is an incremental version of ID3.

Unfortunately, all these algorithms suffer from the inability to easily and effectively handle domains with numeric-valued attributes. Numeric attributes are those whose values are taken from a …

Modeling The Software Design Project, C. C. Dziedzic, D. C. St. Clair

Computer Science Technical Reports

The information content of the software design product as needed by various user communities is identified. Definitions of design in classical engineering disciplines are investigated and then applied specifically to the area of software design. The Entity-Relationship model is used to describe the information content of the software design product. All the relationship types and entity types that compose the design product are described in detail. The Military Standard: Defense System Software Development, DOD-STD-2167A, is analyzed to determine how it meets the relationship type requirements.

Incremental Learning Of Numeric Clusters In Classifier Systems, K. R. Hacke, D. C. St. Clair

Computer Science Technical Reports

Classifier systems are knowledge-based learning algorithms which take training instances as input and produce a set of rules as output Many classifier systems represent the knowledge they learn in the form of one or more decision trees. Accurate knowledgebase systems for a variety of domains have been constructed by generating decision trees using J. R. Quinlan's (1986) inductive algorithm ID3 and P. E. Utgoffs (1988) IDS. IDS is an incremental version of ID3.

Unfortunately, all these algorithms suffer from the inability to easily and effectively handle domains with numeric-valued attributes. Numeric attributes are those whose values are taken from a …

Modeling The Software Design Project, C. C. Dziedzic, D. C. St. Clair

Computer Science Technical Reports

The information content of the software design product as needed by various user communities is identified. Definitions of design in classical engineering disciplines are investigated and then applied specifically to the area of software design. The Entity-Relationship model is used to describe the information content of the software design product. All the relationship types and entity types that compose the design product are described in detail. The Military Standard: Defense System Software Development, DOD-STD-2167A, is analyzed to determine how it meets the relationship type requirements.

Indifference Graphs And The Single Row Routing Problem, Peter J. Looges

Computer Science Theses & Dissertations

This thesis investigates the subclass of interval graphs known as indifference graphs. New optimal algorithms for recognition, center, diameter, maximum matching, Hamiltonian path and domination in indifference graphs are presented. The recognition algorithm produces a linear order with properties which allow the solution of the other problems in linear time. Indifference graphs are further applied to the single row routing problem which results in both sequential,. and parallel routing algorithms.

Numerical Simulation Of Saturated Flow With Fractal Analysis Of The Hydraulic Conductivity Distribution, Joan Leilani Oana

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this report is to investigate the behavior of a nonreactive contaminant in a perfectly stratified aquifer under uniform, steady-state flow. The design and the implementation of a solute transport model which characterizes the heterogeneities of the aquifer properties in a stochastic framework is reviewed. The model closely examines the advection and dispersion of the plume. The advection is the process by which the plume is transported in the aquifer by the bulk average motion of the groundwater whereas the dispersion refers to the spreading of the plume about its mean displacement position. The relationship between the fractally …

Mathematical Programming Applications In Agroforestry Planning, Laurence H. Reeves

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Agroforestry as a sustainable production system has been recognized as a land use system with the potential to slow encroachment of agriculture onto forested lands in developing countries. However, the acceptance of nontraditional agroforestry systems has been hampered in some areas due to the risk-averse nature of rural agriculturalists. By explicitly recognizing risk in agroforestry planning, a wider acceptance of agroforestry is possible. This thesis consists of a collection of three papers that explore the potential of modern stock portfolio theory to reduce financial risk in agroforestry planning.

The first paper presents a theoretical framework that incorporates modern stock portfolio …

Mathematica Demonstrations For Calculus, Bryan Krueger

Opportunities for Undergraduate Research Experience Program (OURE)

The objective of this research was to generate useful classroom demonstrations of fundamental Calculus concepts. Herein are the code listings of two Mathematica "programs." The first displays individual plots of two dimensional Taylor Series approximations. The second set of code creates a TNB frame on a three dimensional space curve. Folowing this introduction is a complete listing of each "program" along with an example of its function.

Mathematica Calculus Illustrations, Jeremy Squires

Opportunities for Undergraduate Research Experience Program (OURE)

The purpose of this project was to create a collection of computer illustrations that would represent certain concepts of calculus. These illustrations were to be performed on a calculus based program called Mathematica. Another of the underlying objectives of this project was the potential of using these illustrations as classroom demonstrations. These demonstrations might convey an idea that is not easily understood on just verbal communication alone.

A Simple Proof Of Zorn's Lemma, Jonathan W. Lewin

Faculty Articles

No abstract provided.

Finite Abelian Groups In Which The Probability Of An Automorphism Fixing An Element Is Large, Gary J. Sherman

Mathematical Sciences Technical Reports (MSTR)

Let G be a finite group and let A be its automorphism group. We obtain various results on the probability that a random element of A fixes a random element of G.

Advice For Undergraduates On Special Aspects Of Writing Mathematics, Stephen B. Maurer

Mathematics & Statistics Faculty Works

There are several guides to good mathematical writing for professionals, but few for undergraduates. Yet undergraduates who write mathematics papers need special guidance. For instance, professionals may need help writing clear definitions, but at least they know why explicit definitions are needed and know the basic format. In general, mathematics has many special formats that are not mere technical conventions but instead serve important purposes. Often students are not conscious of these conventions, and they rarely know their purposes. This paper contains a guide for students written in light of these observations.

Some Non-Existence Results On Divisible Difference Sets, K. T. Arasu, James A. Davis, Dieter Jungnickel, Alexander Pott

Department of Math & Statistics Faculty Publications

In this paper, we shall prove several non-existence results for divisible difference sets, using three approaches:

(i) character sum arguments similar to the work of Turyn [25] for ordinary difference sets,

(ii) involution arguments, and

(iii) multipliers in conjunction with results on ordinary difference sets.

Among other results, we show that an abelian affine difference set of odd order s (s not a perfect square) in G can exist only if the Sylow 2-subgroup of G is cyclic. We also obtain a non-existence result for non-cyclic (n, n, n, 1) relative difference sets of odd …

The Analysis Of A Model For Wave Motion In A Liquid Semiconductor: Boundary Interaction And Variable Conductivity, William V. Smith

Faculty Publications

The theory of conducting fluids in relative motion with small conductivity is studied with a model including the Maxwell displacement current. The model is linearized, and the interaction of waves with a plane boundary in three space is studied for two orientations of the external magnetic field. It is found that two families of boundary conditions preserve energy in one orientation (external field orthogonal to the boundary), while in the other (external field parallel to the boundary) only one condition exists which preserves energy. It is shown that generalized Fourier transforms exist, generated from the generalized eigenfunction expansions. Further, it …

Planning And Resource Mobilization In A Developing Economy., Dilip Ratha Dr.

Doctoral Theses

In developing economies, the per capita availability of essential goods and services is quite low. Hence a large section of the society cannot afford even the mininum necessities of 1ite. While human and natural resources are plenty, produced means of produetion like plant and equipment and construction materiais are soaroe. Hence the human resources are not fully utilized. Since the distribution of income and assets is highly skewed, even the snall quantity of essential goods and services is not equitably distributed. When resources 11ke land and capital are privately owned and goods and services are distributed through the narket mechanism, …

Component Importance In A Consecutive K-Out Of N:F System., Arvind Seth Dr.

Doctoral Theses

Reliability theory has nequired a special significance during the last few decades. It is mainly because of rapid advancement in technology which has given rise to complex and sophisticated systems. These systema suf- fer from derign flawe and wenknesses and their failures not only result in monetary lom but also pose a serious threat to human life and national se curity. Hence product reliability and safety is of paramount importance to us. Since system effectiveness can be optimised during design and develop- ment phases, it therefore calls for a detailed reliability engineering program during initial stanges. Often we find that …

On Image Information Measures And Object Extraction., Nikhil Ranjan Pal Dr.

Doctoral Theses

The field of image processing deals with the manipulation of data which are inherently two-dimensional in nature. techniques of image processing sten from two principal application The areas, namely, Improvement of pictorial information for human interpretation and processing of scene data for automatic machine perception. These areas together have experienced a vigorous growth in recent years because they have offered a number of important applications in solving scientific and engineering problems. In biological and medical sciences, we are interested in automatie analysis and interpretation of radiographs, cell images micrographs. In netallurgical, geological and and tissue environmental sciences, we are concerned …

Moore Cohomology, Principal Bundles, And Actions Of Groups On C*-Algebras, Ian Raeburn, Dana P. Williams

Dartmouth Scholarship

In recent years both topological and algebraic invariants have been associated to group actions on C*-algebras. Principal bundles have been used to describe the topological structure of the spectrum of crossed products [18, 19], and as a result we now know that crossed products of even the very nicest non-commutative algebras can be substantially more complicated than those of commutative algebras [19, 5]. The algebraic approach involves group cohomological invariants, and exploits the associated machinery to classify group actions on C*-algebras; this originated in [2], and has been particularly successful for actions of R and tori ([19; Section 4], [21]). …

An Operator Formalism For Unitary Matrix Models, Konstantinos N. Anagnostopoulos, Mark Bowick, N. Ishibashi

Physics - All Scholarship

We analyze the double scaling limit of unitary matrix models in terms of trigonometric orthogonal polynomials on the circle. In particular we find a compact formulation of the string equation at the k th multicritical point in terms of pseudo-differential operators and a corresponding action principle. We also relate this approach to the mKdV hierarchy which appears in the analysis in terms of conventional orthogonal polynomials on the circle.

Normal Semigroups Of One-To-One Transformations., Inessa Levi

Faculty Bibliography

No abstract provided.

Type 3 Diminimal Maps On The Torus, Adrian Riskin

Mathematics

A polyhedral map on the torus is diminimal if either shrinking or removing an edge yields a nonpolyhedral map. We show that all such maps on the torus fall into one of two classes, type 2 and type 3, and show that there are exactly two type 3 ones, which are given explicitly.

On A Lower Bound For The Redundancy Of Reliable Networks With Noisy Gates, Nicholas Pippenger

All HMC Faculty Publications and Research

A proof is provided that a logarithmic redundancy factor is necessary for the reliable computation of the parity function by means of a network with noisy gates. This result was first stated by R.L. Dobrushin and S.I. Ortyukov (1977). However, the authors believe that the analysis given by Dobrushin and Ortyukov is not entirely correct. The authors establish the result by following the same steps and by replacing the questionable part of their analysis with entirely new arguments.

A Double Chain Of Coupled Circuits In Analogy With Mechanical Lattices, J. N. Boyd, P. N. Raychowdhury

Mathematics and Applied Mathematics Publications

A unitary transformation obtained from group theoretical considerations is applied to the problem of finding the resonant frequencies of a system of coupled LC-circuits. This transformation was previously derived to separate the equations of motion for one dimensional mechanical lattices. Computations are performed in matrix notation. The electrical system is an analog of a pair of coupled linear lattices. After the resonant frequencies have been found, comparisons between the electrical and mechanical systems are noted.

Selection Networks, Nicholas Pippenger

All HMC Faculty Publications and Research

An upper bound asymptotic to $2n\log _e n$ is established for the number of comparators required in a network that classifies $n$ values into two classes, each containing $n / 2$ values, with each value in one class less than or equal to each value in the other. (The best lower bound known for this problem is asymptotic to $(n / 2)\log _2 n$.)

Stochastic Orderings Induced By Star-Shaped Functions, Henry A. Krieger

All HMC Faculty Publications and Research

The non-decreasing functions whicl are star-shaped and supported above at each point of a non-empty closed proper subset of the real line induce an ordering, on the class of distribution functions with finite first moments, that is strictly weaker than first degree stochastic dominance and strictly stronger than second degree stochastic dominance. Several characterizations of this ordering are developed, both joint distribution criteria and those involving only marginals. The latter are deduced from a decomposition theorem, which reduces the problem to consideration of certain functions which are star-shaped on the complement of an open interval.

Uniform Convergence Of Polynomials Associated With Varying Jacobi Weights, Matthew He, X. Li

Mathematics Faculty Articles

No abstract provided.