Mathematics Commons^™

Knots And Links In Three-Dimensional Flows, Robert W. Ghrist, Philip J. Holmes, Michael C. Sullivan

Books, Monographs, Book Chapters and Lecture Notes

No abstract provided.

Orbit Structure Of Finite And Reductive Monoids, Zhuo Li

Digitized Theses

A reductive monoid is an algebraic monoid with a reductive unit group. We introduce a new class of reductive monoids, $({\cal T}, \sigma)$-irreducible monoids. Generally, we have the question of finding the orbits of the unit group of a reductive monoid acting on both sides of the monoid. Putcha and Renner give a recipe to determine the orbits for ${\cal T}$-irreducible monoids. Motivated by their construction of finite reductive monoids, the concept of (${\cal T}, \sigma)$-irreducible monoid arises naturally.

We obtain that the ${\cal T}$-irreducible monoids turn out to be a special class of the $({\cal T}, \sigma)$-irreducible monoids. We …

Mathematics At Chartres Cathedral, Richard Stout

ACMS Journal 2004

Chartres Cathedral is highly regarded as a magnificent Gothic structure including beautiful stained glass windows and striking sculptures. Mathematics, especially geometry, played a central role in the design of this cathedral. This paper explores that mathematics and how it contributes to the overall effectiveness of the design.

Mathematics And Values: Can Philosophy Guide Projects?, Michael H. Veatch

ACMS Journal 2004

The philosophy of mathematics has provided insight on questions of foundations and mathematical truth; however, it has not been very fruitful in guiding the practice of mathematics. This paper attempts to find points of contact between a Christian worldview and the choice of mathematical projects and methods. Three areas are considered: (i) dubitability in current research, (ii) the intrinsic value of contemporary mathematics to contemporary society, and (iii) the affirmation of human value in the use of mathematics. Finally, a framework for valuing mathematics is proposed as an encouragement to think more deeply about how a Christian might choose a …

Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.

Genetic Algorithms: A Visual Search, Paul W. Jones

Honors Theses, 1963-2015

Genetic algorithms apply the biological principles of selection, mutation, and crossover to a population set containing individuals representing target solutions to a given problem. Using these principles genetic algorithms attempt to create a migration of the individuals in subsequent generations toward the optimal solution.

This project is an attempt to visually represent the progress of a genetic algorithm. The coordinate fitness program attempts to find the maximum or minimum value of a given function. It visually represents the progress of the algorithm by providing a plot of each individual in each generation in time. It is then possible to view …

The Nordstrom–Robinson Code Is Algebraic-Geometric, Judy L. Walker

Department of Mathematics: Faculty Publications

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite field since the early 1980’s. Recently, there has been an increased interest in the study of linear codes over finite rings. In a previous paper [10], we combined these two approaches to coding theory by introducing and studying algebraic-geometric codes over rings. In this correspondence, we show that the Nordstrom–Robinson code is the image under the Gray mapping of an algebraic geometric code over Z = 4Z.

Some Recursive Definitions Of The Shapley Value And Other Linear Values Of Cooperative Tu Games, Irinel C. Dragan

Mathematics Technical Papers - Archive

Let N be a finite set of players, |N| = n; a cooperative TU game in coalitional form is a function v : P(N) -> R, with v(ø) = 0. It is well known that the set of all games with the set of players N, denoted below G(N), is a space of dimension 2n - 1. Let S be any coalition in v E G(N) and denote by G(S) the space of games with the set of players S. If v E G(N), then the restriction of v to S is a game in G(S). To avoid a notation …

The Generation Of Turbulence In A Compressed Gas, Donald Greenspan

Mathematics Technical Papers - Archive

A molecular mechanics type formulation is applied to generate turbulence in a compressed gas. Turbulence is defined in terms of the rapid appearance and disappearance of many small vortices. The generating mechanism lies in the large repulsive forces between particles.

A Dual Approach To Constrained Interpolation From A Convex Subset Of Hilbert Space, Frank Deutsch, Wu Li, Joseph D. Ward

Mathematics & Statistics Faculty Publications

Many interesting and important problems of best approximationare included in (or can be reduced to) one of the followingtype: in a Hilbert spaceX, find the best approximationPK(x) to anyx∈Xfrom the setK≔C∩A−1(b),whereCis a closed convex subset ofX,Ais a bounded linearoperator fromXinto a finite-dimensional Hilbert spaceY, andb∈Y. The main point of this paper is to show thatPK(x)isidenticaltoPC(x+A*y …

The Dynamics Of Phase Farming: A Mathematical Model Of Economic Aspects Of Switching Between Cropping And Land Rehabilitation, Tuyet Tran

Theses : Honours

In this thesis we consider the following problem: Suppose that a farmer wishes to determine the best course of action to maximise returns from his I her land which has undergone some form of degradation. In order to rehabilitate the land, the farmer may have to change to a different farming practice for some time until the previous practice becomes profitable again. Switching from cropping to rehabilitation Of from rehabilitation to cropping incurs costs. From an economical point of view, the question then arises: When is the optimal time to switch from cropping· to rehabilitation and when is it optimal …

Positive Solution Curves Of Semipositone Problems With Concave Nonlinearities, Alfonso Castro, Sudhasree Gadam, Ratnasingham Shivaji

All HMC Faculty Publications and Research

We consider the positive solutions to the semilinear equation:

-Δu(x) = λf(u(x)) for x ∈ Ω

u(x) = 0 for x ∈ ∂Ω

where Ω denotes a smooth bounded region in R^N (N > 1) and λ > 0. Here f :[0, ∞)→R is assumed to be monotonically increasing, concave and such that f(0) < 0 (semipositone). Assuming that f'(∞) ≡ lim t→∞ f'(t) > 0, we establish the stability and uniqueness of large positive solutions in terms of (f(t)/t)'. When Ω is a ball, we determine the exact number of positive solutions for each λ > 0. We also obtain the geometry of the branches of positive solutions completely and establish how …

The Interaction Of A Point Vortex With A Wall-Bounded Vortex Layer, Oliver V. Atassi, Andrew J. Bernoff, Seth Lichter

All HMC Faculty Publications and Research

The interaction of a point vortex with a layer of constant vorticity, bounded below by a wall and above by an irrotational flow, is investigated as a model of vortex–boundary layer interaction. This model calculates both the evolution of the interface which separates the vortex layer from the irrotational flow and the trajectory of the vortex. In order to determine the conditions which lead to sustained unsteady interaction, three cases are investigated where the mutual interaction between the vortex and interface is initially assumed to be weak. (i) When a weak point vortex lies outside the layer, the vortex moves …

Conservative Motion Of A Discrete, Nonsymmetric, Hexahedral Gyroscope, Donald Greenspan

Mathematics Technical Papers - Archive

Gyroscopic motion is simulated by applying a molecular dynamics formulation to a rigid hexahedron. The conservative dynamical differential equations are solved numerically in such a fashion that all the system invariants are preserved. The difficult problem of nonsymmetry is emphasized. Examples of the complex motions which result are described and discussed.

A Molecular Mechanics Type Approach To Turbulence, Donald Greenspan

Mathematics Technical Papers - Archive

A molecular mechanics type formulation is applied to the cavity problem to generate primary vortices, secondary vortices, and turbulent flow. The fluid considered is water. Turbulence is defined in terms of the absence of a primary vortex and the rapid appearance and disappearance of many small vortices. The mechanism for generating turbulent flow lies in the generation of large repulsive forces between the particles of the model. This results from the increase in particle speeds due to the increase in wall speed.

Controlling Curvature In The Minkowski Plane, Mostafa Ghandehari

Mathematics Technical Papers - Archive

Pontryagin's maximum principle is used to find the curve of shortest length with bounded Minkowskian curvature passing through two points with given initial and terminal tangents.

Ray Optics On Surfaces, Mostafa Ghandehari

Mathematics Technical Papers - Archive

Variational techniques are used to find path of light rays on surfaces. Using Fermat's principle of least time the problem is treated as a constraint optimization to obtain a system of partial differential equations.

Estimating Transition Probabilities From Aggregate Samples Augmented By Haphazard Recaptures Ii. The Case Of Covariates., Chien-Pai Han, D. L. Hawkins

Mathematics Technical Papers - Archive

The paper extends the authors' earlier methods for estimating transition probabilities, by combining aggregate and haphazard recapture data, to the case of categorical covariates. Both fixed and time-dependent covariates are considered. A two-stage estimation procedure is proposed. The first stage uses a Markov model to estimate multivariate transition probabilities for the response and all covariates. The second stage uses the Stage 1 estimates to model covariate effects. The required number of sampling waves depends only on the number of response levels and time-dependent covariate levels — and not on the number of fixed covariate levels. Recommendations are given for the …

Snell's Law In Normed Linear Planes, Mostafa Ghandehari

Mathematics Technical Papers - Archive

The method of Lagrange multipliers is used to find a reflection principle in a real normed linear plane with smooth unit circle. A generalization of Snell's law of refraction with two different norms is given. The case where the unit circles of the two norms are Euclidean circles with different radii leads to Snell's law.

A Value For Digraph-Restricted Games, Oltion Voshtina

Mathematics Technical Papers - Archive

Digraph-restricted games model situations where some of the players, due to the lack of communication among them, are unable to cooperate. A digraph-restricted game v is defined as a function from the set of feasible coalitions to the reals. By strengthening the symmetry axiom we obtain an extension of the Shapley value for this class of games. Key words. Shapley value, cooperative game, directed graph.

A Quadratic Volterra Integral Equation And Its Solution For Various Kernels, Merlynd K. Nestell, Mostafa Ghandehari

Mathematics Technical Papers - Archive

Consider the Volterra integral equation [see pdf for notation], ^ is a parameter Solutions of this equation are discussed for separable and difference kernels using Laplace transform and differential equation techniques. Existence and uniqueness questions are explored for various assumptions on the kernel.

On The Level Crossing Of Multi-Dimensional Delayed Renewal Processes, Jewgeni H. Dshalalow

Mathematics and System Engineering Faculty Publications

The paper studies the behavior of an (l+3)th-dimensional, delayed renewal process with dependent components, the first three (called active) of which are to cross one of their respective thresholds. More specifically, the crossing takes place when at least one of the active components reaches or exceeds its assigned level. The values of the other two active components, as well as the rest of the components (passive), are to be registered. The analysis yields the joint functional of the crossing level and other characteristics (some of which can be interpreted as the first passage time) in a closed form, refining earlier …

Fuzzy Logic: An Analysis Of Logical Connectives And Their Characterizations, John F. Hamman

Dissertations and Theses @ UNI

The focus of this thesis is to determine exactly which functions serve as appropriate fuzzy negation, conjunction and disjunction functions. To this end, the first chapter serves as motivation for why fuzzy logic is needed, and includes an original demonstration of the inadequacy of many valued logics to resolve the sorites paradox. Chapter 2 serves as an introduction to fuzzy sets and logic. The canonical fuzzy set of tall men is examined as a motivating example, and the chapter concludes with a discussion of membership functions.

Four desirable conditions of the negation function are given in Chapter 3, but it …

Cyclic Permutations In Doubly-Transitive Groups, John P. Mcsorley

Articles and Preprints

Let Ω be a finite set of size n. A cyclic permutation on Ω is a permutation whose cycle decomposition is one cycle of length n. This paper classifies all finite doubly-transitive permutation groups which contain a cyclic permutation. The classification appears in Table 1.

We use (G, Ω) for a finite doubly-transitive permutation group G acting on a finite set Ω. For other notation and definitions see the self-contained article Cameron [1].