Mathematics Commons^™

Optimal Control Of Neutral Functional-Differential Inclusions, Boris S. Mordukhovich, Lianwen Wang

Mathematics Research Reports

This paper deals with optimal control problems for dynamical systems governed by constrained functional-differential inclusions of neutral type. Such control systems contain time-delays not only in state variables but also in velocity variables, which make them essentially more complicated than delay-differential (or differential-difference) inclusions. Our main goal is to derive necessary optimality conditions for general optimal control problems governed by neutral functional-differential inclusions with endpoint constraints. While some results are available for smooth control systems governed by neutral functional-differential equations, we are not familiar with any results for neutral functional-differential inclusions, even with smooth cost functionals in the absence of …

Direct Paths Of Wavelets, Eugen J. Ionascu

Faculty Bibliography

We associate a von Neumann algebra with each pair of complete wandering vectors for a unitary system. When this algebra is nonatomic, there is a norm–continuous path of a simple nature connecting the original pair of wandering vectors. We apply this technique to wavelet theory and compute the above von Neumann algebra in some special cases. Results from selection theory and ergodic theory lead to nontrivial examples where both atomic and nonatomic von Neumann algebras occur.

A First Course In Computer Science: Languages And Goals, Dennis C. Smolarski

Mathematics and Computer Science

The College Board Advanced Placement exam in computer science will use the language Java starting in fall 2003. The language chosen for this exam is based on the language commonly taught in introductory computer science courses at the university level. This article reviews the purpose of an introductory course and the various suggestions for the curriculum of introductory courses published by the Association for Computing Machinery. It then proposes that such a course stress foundational concepts over specific language syntax, and then provides a list of such foundational concepts and related topics. Based on this fundamental curriculum, the article recommends …

Septic Fields With Discriminant ±2A3B, John W. Jones, David P. Roberts

Mathematics Publications

We classify septic number fields which are unramified outside of {∞,2,3} by a targeted Hunter search; there are exactly 10 such fields, all with Galois group S₇. We also describe separate computations which strongly suggest that none of these fields come from specializing septic genus zero three-point covers.

Curvature (Abstract), Chikako Mese

Undergraduate Mathematics Day: Programs, Lectures, Promotional Materials

We may have an intuitive idea of what it means for surfaces to be curved, but what does it mean for higher dimensional spaces to be curved?

Mimeomatroids, Vadim Ponomarenko

Mathematics Faculty Research

A mimeomatroid is a matroid union of a matroid with itself. We develop several properties of mimeomatroids, including a generalization of Rado's theorem, and prove a weakened version of a matroid conjecture by Rota[2].

Hyperbolic Transformations On Cubics In H², Frank S. Marfai

Theses Digitization Project

The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).

Ideals, Varieties, And Groebner Bases, Joyce Christine Ahlgren

Theses Digitization Project

The topics explored in this project present and interesting picture of close connections between algebra and geometry. Given a specific system of polynomial equations we show how to construct a Groebner basis using Buchbergers Algorithm. Gröbner bases have very nice properties, e.g. they do give a unique remainder in the division algorithm. We use these bases to solve systems of polynomial quations in several variables and to determine whether a function lies in the ideal.

The Derangement Problem Relative To The Mahonian Process, Jessica Delfert, Hillary Einziger, Don Rawlings

Mathematics

We survey n! plus q-derangement problems. Solutions to four Mahonian statistics arising in connection with cycle placement rules are presented. A few conjectures are also made.

The Embedding Of Complete Bipartite Graphs Onto Grids With A Minimum Grid Cutwidth, Mário Rocha

Theses Digitization Project

Algorithms will be domonstrated for how to embed complete bipartite graphs onto 2xn type grids, where the imimum grid cutwidth is attained.

Feedback Classification Of Nonlinear Single-Input Control Systems With Controllable Linearization: Normal Forms, Canonical Forms, And Invariants, Issa Amadou Tall, Witold Respondek

Articles and Preprints

We study the feedback group action on single-input nonlinear control systems. We follow an approach of Kang and Krener based on analyzing, step by step, the action of homogeneous transformations on the homogeneous part of the same degree of the system. We construct a dual normal form and dual invariants with respect to those obtained by Kang. We also propose a canonical form and a dual canonical form and show that two systems are equivalent via a formal feedback if and only if their canonical forms (resp., their dual canonical forms) coincide. We give an explicit construction of transformations bringing …

A Characterization Of Primitive Polynomials Over Finite Fields, Robert W. Fitzgerald

Articles and Preprints

No abstract provided.

Determination Of The Topological Structure Of An Orbifold By Its Group Of Orbifold Diffeomerphisms, Joseph E. Borzellino, Victor Brunsden

Mathematics

We show that the topological structure of a compact, locally smooth orbifold is determined by its orbifold diffeomorphism group. Let Diff^r_Orb (O) denote the C^r orbifold diffeomorphisms of an orbifold O. Suppose that Φ: Diff^r_Orb(O₁) → Diff^r_Orb (O₂) is a group isomorphism between the the orbifold diffeomorphism groups of two orbifolds O₁ and O₂. We show that Φ is induced by a homeomorphism h: X_O1 → X_O2 , where X_O denotes the underlying topological …

Software Requirements Specification Of A University Class Scheduler, Sergiu M. Dascalu, Fredrick C. Harris Jr., Deanna Needell, Jeff A. Stuart, Tamara C. Thiel

CMC Faculty Publications and Research

The University Class Scheduler (UCS) presented in this paper is a novel scheduling tool intended to be used by universities to schedule classes into classrooms. In essence, UCS allows university administrators to enter relevant college and building information, schedule the input classes (courses) into input classrooms, and create web pages that provide detailed schedule information on a semester-by-semester basis. The UCS, which performs the scheduling of classes according to a number of user-selected parameters, can be easily adapted for applications outside the academic realm. This paper presents the main aspects of the University Class Scheduler’s UML-based specification, gives details of …

A Mathematical Model Of Immune Response To Tumor Invasion, Lisette De Pillis, Ami Radunskaya

All HMC Faculty Publications and Research

Recent experimental studies by Diefenbach et al. [1] have brought to light new information about how the immune system of the mouse responds to the presence of a tumor. In the Diefenbach studies, tumor cells are modified to express higher levels of immune stimulating NKG2D ligands. Experimental results show that sufficiently high levels of ligand expression create a significant barrier to tumor establishment in the mouse. Additionally, ligand transduced tumor cells stimulate protective immunity to tumor rechallenge. Based on the results of the Diefenbach experiments, we have developed a mathematical model of tumor growth to address some of the questions …

Vertex-Magic Labeling Of Trees And Forests, I. D. Gray, J. Macdougall, John P. Mcsorley, Walter D. Wallis

Articles and Preprints

A vertex-magic total labeling of a graph G(V,E) is a one-to-one map λ from E ∪ V onto the integers {1, 2, . . . , |E| + |V|} such that

λ(x) + Σ λ(xy) where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite different from the conjectured behavior of edge-magic total labelings …

Resources Related To Mathematics, Art And Nature, Vicki Beitler

Sabbaticals

The purpose of my sabbatical work was to learn about resources related to mathematics and art, nature, music and architecture. These subjects appeal to a wide audience, yet their mathematical connections are often on the periphery of a mathematics student's studies. In this way I planned to increase my knowledge of mathematics but at the same time broaden my understanding of cross-disciplinary subjects.

A Christian Perspective On Mathematics – History Of Mathematics And Study Guides, Johan Deklerk

ACMS Journal 2004

This paper addresses two questions: (1) Will a study of the history of the subject serve any purpose in promoting a Christian perspective on mathematics? (2) Can the "science in context" approach be of further help in promoting such a perspective? The author answers both positively and provides specific examples of how he has done this in his own classes.

Creationism – A Viable Philosophy Of Mathematics, Jonathan Zderad

ACMS Journal 2004

In this paper, the author addresses two classical questions of the philosophy of mathematics: What, if any, of mathematics exists in the objective sense? How do humans know that our knowledge of mathematics is correct? He argues that the Christian doctrine of God as creator provides a basis for answering these questions. He also provides a critique of eight widely discussed philosophies of mathematics.

On Abel-Gontscharoff-Gould's Polynomials, Tian-Xiao He, Leetsch Hsu, Peter Shiue

Scholarship

In this paper a connective study of Gould’s annihilation coefficients and Abel-Gontscharoff polynomials is presented. It is shown that Gould’s annihilation coefficients and Abel-Gontscharoff polynomials are actually equivalent to each other under certain linear substitutions for the variables. Moreover, a pair of related expansion formulas involving Gontscharoff’s remainder and a new form of it are demonstrated, and also illustrated with several examples.

Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang

Mathematics and Statistics Faculty Publications

We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.

Mathematics And The Love Of God: An Introduction To The Thought Of Simone Weil, Scott Taylor

ACMS Journal 2004

Simone Weil was the sister of Andre Weil, one of the twentieth century's foremost mathematicians. She is a widely read and creative writer on spiritual themes. She addressed mathematics extensively in her writings. This paper discusses her views of mathematics and beauty, her critiques of modern science, her views on truth, and her concept that mathematical ideas can serve as symbols of spiritual ideas.

Homogeneous Weights And Exponential Sums, José Felipe Voloch, Judy L. Walker

Department of Mathematics: Faculty Publications

In this paper, we give a formula as an exponential sum for a homogeneous weight defined by Constantinescu and Heise [3] in the case of Galois rings (or equivalently, rings of Witt vectors) and use this formula to estimate the weight of codes obtained from algebraic geometric codes over rings.

The Connective K-Theory Of Finite Groups, Robert R. Bruner, John Greenlees

Mathematics Faculty Research Publications

This paper is devoted to the connective K homology and cohomology of finite groups G. We attempt to give a systematic account from several points of view. In Chapter 1, following Quillen [50, 51], we use the methods of algebraic geometry to study the ring ku^*(BG) where ku denotes connective complex K-theory. We describe the variety in terms of the category of abelian p-subgroups of G for primes p dividing the group order. As may be expected, the variety is obtained by splicing that of periodic complex K-theory and that of integral ordinary homology, however the way these parts fit …

Unification Scale, Proton Decay, And Manifolds Of G2 Holonomy, Tamar Friedmann, Edward Witten

Mathematics Sciences: Faculty Publications

Models of particle physics based on manifolds of G2 holonomy are in most respects much more complicated than other string-derived models, but as we show here they do have one simplification: threshold corrections to grand unification are particularly simple. We compute these corrections, getting completely explicit results in some simple cases. We estimate the relation between Newton’s constant, the GUT scale, and the value of αGUT , and explore the implications for proton decay. In the case of proton decay, there is an interesting mechanism which (relative to four-dimensional SUSY GUT’s) enhances the gauge boson contribution to p → π …

Spaces X In Which All Prime Z-Ideals Of C(X) Are Minimal Or Maximal, Melvin Henriksen, Jorge Martinez, R. G. Woods

All HMC Faculty Publications and Research

Quasi P-spaces are defined to be those Tychonoff spaces X such that each prime z-ideal of C(X) is either minimal or maximal. This article is devoted to a systematic study of these spaces, which are an obvious generalization of P-spaces. The compact quasi P-spaces are characterized as the compact spaces which are scattered and of Cantor-Bendixson index no greater than 2. A thorough account of locally compact quasi P-spaces is given. If X is a cozero-complemented space and every nowhere dense zeroset is a z-embedded P-space, then X is a quasi P-space. Conversely, if X is a quasi P-space and …

The Effect Of The Domain Topology On The Number Of Minimal Nodal Solutions Of An Elliptic Equation At Critical Growth In A Symmetric Domain, Alfonso Castro, Mónica Clapp

All HMC Faculty Publications and Research

We consider the Dirichlet problem Δu + λu + |u|^2*−2u = 0 in Ω, u = 0 on ∂Ω where Ω is a bounded smooth domain in R^N, N≥4, and 2* = 2N/(N−2) is the critical Sobolev exponent. We show that if Ω is invariant under an orthogonal involution then, for λ>0 sufficiently small, there is an effect of the equivariant topology of Ω on the number of solutions which change sign exactly once.

Am I Too Fat? Bulimia As An Epidemic, Christopher Kribs, Beverly Gonzalez, Emilia Huerta-Sanchez, Angela Ortiz-Nieves, Terannie Vazquez-Alvarez

Mathematics Faculty Publications - Archive

For at least the past ten years, eating disorders have had a major impact in the physical and mental health of women, particularly young women. Anorexia and bulimia nervosa are closely linked eating disorders. Anorexia often precedes bulimia. However, there are about 2 million women in college that have been exclusively bulimic. In this article, we focus on the role of college-peer pressure on the dynamics of anorexia-free bulimia. The model looks at bulimia as a progressive disease and explores the impact of intervention (treatment) at two stages of disease progression. The impact of relapse (a common occurrence among bulimics) …

An Algebraic Characterization Of Projective-Planar Graphs, Lowell Abrams, Dan Slilaty

Mathematics and Statistics Faculty Publications

We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G∗ on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homology groups.

Recent Applications Of Fractional Calculus To Science And Engineering, Lokenath Debnath

School of Mathematical & Statistical Sciences Faculty Publications

This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. Special attention is given to numerical computation of fractional derivatives and integrals.