Physical Sciences and Mathematics Commons^™

Infinitely Many Hyperbolic 3-Manifolds Which Contain No Reebless Foliation, R. Roberts, J. Shareshian, Melanie Stein

Faculty Scholarship

We investigate group actions on simply-connected (second countable but not necessarily Hausdorff) 1-manifolds and describe an infinite family of closed hyperbolic 3-manifolds whose fundamental groups do not act nontrivially on such 1-manifolds. As a corollary we conclude that these 3-manifolds contain no Reebless foliation. In fact, these arguments extend to actions on oriented -order trees and hence these 3-manifolds contain no transversely oriented essential lamination; in particular, they are non-Haken.

Benefits Of A Comprehensive Undergraduate Teaching Assistant Program, Christopher Goff, Brigitte Lahme

Christopher Goff

Essays In Financial Intermediation., Bappaditya Mukhopadhyay Dr.

Doctoral Theses

No abstract provided.

Certain Pattern Recognition Tasks For Data Mining Problems., Pabitra Mitra Dr.

Doctoral Theses

Pattern recognition (PR) is an activity that we humans normally excel in. We do it almost all the time, and without conscious effort. We receive information via our various sensory organs, which is processed instantaneously by our brain so that, almost immediately, we are able to identify the source of the information, without having made any perceptible effort. What is even more impressive is the accuracy with which we can perform recognition tasks even under non-ideal conditions, for instance, when the information that needs to be processed is vague, imprecise or even incomplete. In fact, most of our day-to-day activities …

On The Approximability Of Linear Ordering And Related Np-Optimization Problems., Sounaka Mishra Dr.

Doctoral Theses

We investigate approximability of both maximum and minimum linear ordering problems (MAX-LOP and MIN-LOP) and several related problems such as the well known feedback set problems, acyclie subdigraph problem and several others and their variants.We show that both MAX-LOP and MIN-LOP are strongly NP-complete, and MIN- LOP, MIN-QAP(S) (a special case of minimum quadratic assignment problem) and MIN-W-FAS are equivalent with respect to strict-reduction. The strict-equivalence is also established among these problems as well as MIN-W-FVS, with weights on arcs/vertices bounded by a polynomial, and the unweighted versions of the feedback set. problems. We also show that MAX-LOP is strict-equivalent …

Deformation Theory Of Dialgebras., Anita Majumdar Dr.

Doctoral Theses

The main objective of this thesis is to develop an algebraic deformation theury for associative dialgebras, which are binary quadratic algebras discovered by J.-L. Loday in (16). (17), and subisequently, to derive a G-algebra siructure ou the dialgebra colhomology with cocfticients in itself.Deformation theory dates back at Ieast to Riemann's 1837 memoir on alelian fianetions in which he studied IHanifolds of complex dimension one and calculated the mumber of parameters (called moduli) upon which a deformation depends. The modern theory of deformations of structures on manifolds was developed extensively ly Frolicher-Kodaira-Nijenhnis-Nirenberg-Spencer (13], [14], [15). [25|, [26).The study of deformations of …

Spectral Triples And Metric Aspects Of Geometry On Some Noncommutative Spaces., Partha Sarathi Chakraborty Dr.

Doctoral Theses

Quantization of mathematical theories is now more than half a century old idea in mathe- matics. It goes back to Gelfand-Naimarks seminal paper [37] in 1943. As the name suggests noncommutative geometry is the quantization" of differential geometry. It is the study of noncommutative algebras as if they were algebras of functions on spaces like the commuta- tive algebras associated to affine algebraic varieties, smooth manifolds, topological spaces. One can trace its roots in the Gelfand-Naimark theorems (1943, 37]). In modern terminol- ogy their theorem says there is an antiequivalence between the category of (locally) compact Hausdorff spaces and (proper, …

Bounding The Number Of Graphs Containing Very Long Induced Paths, Steven Kay Butler

Theses and Dissertations

Induced graphs are used to describe the structure of a graph, one such type of induced graph that has been studied are long paths.

In this thesis we show a way to represent such graphs in terms of an array with two colors and a labeled graph. Using this representation and the techniques of Polya counting we will then be able to get upper and lower bounds for graphs containing a long path as an induced subgraph.

In particular, if we let P(n,k) be the number of graphs on n+k vertices which contains P_n, a path on n vertices, as …

The Cohomology Of The Steendrod Algebra And Representations Of The General Linear Groups, Nguyen H. V. Hu'ng

Mathematics Research Reports

Let Tr_k be the algebraic transfer that maps from the coinvariants of certain GL_k-representation to the cohomology of the Steenrod algebra. This transfer was defined by W. Singer as an algebraic version of the geometrical transfer tr_k : pi_*^S((B[doublestrike V]_k)_+) --> pi_*^S(S^0). It has been shown that the algebraic transfer is highly nontrivial, more precisely, that Tr_k is an isomorphism for k = 1, 2, 3 and that T_r = ⊕_k(Tr_k) is a homomorphism of algebras.

In this paper, we first recognize the phenomenon that if we start from any degree d, and apply Sq^0 repeatedly at most (k- 2) …

Designing Radiotherapy Plans With Elastic Constraints And Interior Point Methods, Allen G. Holder

Mathematics Faculty Research

A new linear programming model used to aid in the design of radiotherapy plans is introduced. This model incorporates elastic constraints, and when solved with a path following interior point method, produces favorable plans. A sound mathematical analysis shows how to interpret the solution, and hence, the treatment planner receives meaningful knowledge about the radiotherapy plan being developed. Preliminary experiments are conducted.

A Sign-Changing Solution For A Superlinear Dirichlet Problem, Ii, Alfonso Castro, Pavel Drabek, John M. Neuberger

All HMC Faculty Publications and Research

In previous work by Castro, Cossio, and Neuberger [2], it was shown that a superlinear Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of -Δ with zero Dirichlet boundry condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the k-th and k+1-st eigenvalues there still exists a solution which changes sign at most k times. In particular, when k=1 the sign-changing exactly-once solution persists although one-sign solutions no …

Consensus-Halving Via Theorems Of Borsuk-Ulam And Tucker, Forrest W. Simmons, Francis E. Su

All HMC Faculty Publications and Research

In this paper we show how theorems of Borsuk-Ulam and Tucker can be used to construct a consensus-halving: a division of an object into two portions so that each of n people believes the portions are equal. Moreover, the division takes at most n cuts, which is best possible. This extends prior work using methods from combinatorial topology to solve fair division problems. Several applications of consensus-halving are discussed.

Noise-Induced Unstable Dimension Variability And Transition To Chaos In Random Dynamical Systems, Ying-Cheng Lai, Zonghua Liu, Lora Billings, Ira B. Schwartz

Department of Mathematics Facuty Scholarship and Creative Works

Results are reported concerning the transition to chaos in random dynamical systems. In particular, situations are considered where a periodic attractor coexists with a nonattracting chaotic saddle, which can be expected in any periodic window of a nonlinear dynamical system. Under noise, the asymptotic attractor of the system can become chaotic, as characterized by the appearance of a positive Lyapunov exponent. Generic features of the transition include the following: (1) the noisy chaotic attractor is necessarily nonhyperbolic as there are periodic orbits embedded in it with distinct numbers of unstable directions (unstable dimension variability), and this nonhyperbolicity develops as soon …

Stage Based Interventions For Low Fat Diet With Middle School Students, Marilyn Frenn, Shelly Malin, Naveen K. Bansal

College of Nursing Faculty Research and Publications

Preventing obesity and cardiovascular disease at early ages is important; however, few effective interventions for early adolescents have been reported. In this study, low-income, culturally diverse students from an urban middle school (n = 60) received four classroom interventions with the use of a combined Health Promotion/Transtheoretical Model to control fat in diet and increase physical activity. A control group (n = 57) received the usual classroom education. Pretest percentage fat in diet was regressed on demographics, access to low-fat foods, perceived self-efficacy, benefits/barriers, and stage of change with results as proposed by the model [F(9,64) …

Closed-Loop Control Of Vortex Shedding By Means Of Lorentz Force, Xiaoyun Sun

Dissertations

When an incompressible fluid flows past a circular cylinder, vortex shedding occurs as soon as the Reynolds number exceeds about 40. Vortex shedding is usually undesirable, as it generates a significant increase in drag, as well an oscillating lift force on the cylinder leading to cross-stream structural vibrations. Flow control to either delay the appearance of vortex shedding or fully suppress it has attracted much attention during the last decade. The focus of this dissertation is to control vortex shedding from a circular cylinder by applying an external electromagnetic field. As in previous works, the latter is generated by electrodes …

Every Three-Point Set Is Zero Dimensional, David L. Fearnley, J. W. Lamoreaux, David L. Fearnley

Faculty Publications

This paper answers a question of Jan J. Dijkstra by giving a proof that all three-point sets are zero dimensional. It is known that all two-point sets are zero dimensional, and it is known that for all n > 3, there are n-point sets which are not zero dimensional, so this paper answers the question for the last remaining case.

Khovanov Homology And Conway Mutation, Stephan Wehrli

Mathematics - All Scholarship

We present an easy example of mutant links with different Khovanov homology. The existence of such an example is important because it shows that Khovanov homology cannot be defined with a skein rule similar to the skein relation for the Jones polynomial.

Plane-Wave Impulse Approximation Extraction Of The Neutron Magnetic Form Factor From Quasielastic 3He → (E,E') At Q2=0.3 To 0.6(Gev/C)2, W. Xu, B. Anderson, L. Auberbach, T. Averett, W. Bertozzi, T. Black, J. Calarco, L. Cardman, G. D. Cates, Z. W. Chai, J. P. Chen, S. Choi, E. Chudakov, S. Churchwell, G. S. Corrado, C. Crawford, D. Dale, A. Deur, P. Djawotho, T. W. Donnelly, D. Dutta, J. M. Finn, H. Gao, R. Gilman, A. V. Glamazdin, C. Glashausser, W. Glockle, J. Golak, J. Gomez, V. G. Gorbenko, J. O. Hansen, F. W. Hersman, D. W. Higinbotham, R. Holmes, C. R. Howell, E. Hughes, B. Humensky, S. Incerti, C. W. De Jager, J. S. Jensen, X. Jiang, C. E. Jones, M. Jones, R. Kahl, H. Kamada, A. Kievsky, I. Kominis, W. Korsch, K. Kramer, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, M. Liang, N. Liyanage, J. Lerose, S. Malov, D. J. Margaziotis, J. W. Martin, K. Mccormick, R. D. Mckeown, K. Mcilhany, Z. E. Meziani, R. Michaels, G. W. Miller, J. Mitchell, S. Nanda, E. Pace, T. Pavlin, G. G. Petratos, R. I. Pomatsalyuk, D. Pripstein, D. Prout, R. D. Ransome, Y. Roblin, M. Rvachev, A. Saha, G. Salme, M. Schnee, T. Shin, K. Slifer, P. A. Souder, S. Strauch, R Suleiman, M. Sutter, B. Tipton, L. Todor, M. Viviani, B. Vlahovic, J. Watson, C. F. Williamson, H. Witala, B. Wojtsekhowski, F. Xiong, J. Yeh, P. Zolnierczuk

Enkeleida K. Lakuriqi

A high precision measurement of the transverse spin-dependent asymmetry AT' in 3He→(e,e') quasielastic scattering was performed in Hall A at Jefferson Lab at values of the squared four-momentum transfer, Q2, between 0.1 and 0.6 (GeV/c)2.AT' is sensitive to the neutron magnetic form factor, GnM. Values of GnM at Q2=0.1 and 0.2(GeV/c)2, extracted using Faddeev calculations, were reported previously. Here, we report the extraction of GnM for the remaining Q2 values in the range from 0.3 to 0.6(GeV/c)2 using a …

Odd Perfect Numbers Have A Prime Factor Exceeding 10^7, Paul M. Jenkins

Faculty Publications

It is proved that every odd perfect number is divisible by a prime greater than 10^7.

Two-Point Boundary Value Problems For Higher-Order Linear Differential Equations With Strong Singularities, Ravi P. Agarwal, Ivan T. Kiguradze

Mathematics and System Engineering Faculty Publications

For strongly singular higher-order linear differential equations together with two-point conjugate and right-focal boundary conditions, we provide easily verifiable best possible conditions which guarantee the existence of a unique solution. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

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.

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 …

Irreducible Polynomials Over Gf(2) With Three Prescribed Coefficients, Robert W. Fitzgerald, Joseph L. Yucas

Articles and Preprints

For an odd positive integer n, we determine formulas for the number of irreducible polynomials of degree n over GF(2) in which the coefficients of x^n-1, x^n-2 and x^n-3 are specified in advance. Formulas for the number of elements in GF(2ⁿ) with the first three traces specified are also given.

Deductive Mathematics: An Introduction To Proof And Discovery For Mathematics Education, Andrew Wohlgemuth

Mathematics and Statistics Faculty Scholarship

Mathematics has two fundamental aspects: (1) discovery/logical deduction and (2) description/ computation. Discovery/deductive mathematics asks the questions:

1. What is true about this thing being studied?

2. How do we know it is true?

On the other hand, descriptive/computational mathematics asks questions of the type:

3. What is the particular number, function, and so on, that satisfies ... ?

4. How can we find the number, function, and so on?

In descriptive/computational mathematics, some pictorial, physical, or business situation is described mathematically, and then computational techniques are applied to the mathematical description, in order to find values of interest. The …

Integral Transforms Of Functionals In L2(C0[0, T]), Byoung Soo Kim, David Skough

Department of Mathematics: Faculty Publications

In this paper we give a necessary and sufficient condition that a functional F(x) in L₂(C₀[0, T]) has an integral transform F_α,βF(x) which also belongs to L₂(C₀[0, T]).

Fixed Points Of Holomorphic Mappings For Domains In Banach Spaces, Lawrence A. Harris

Mathematics Faculty Publications

We discuss the Earle-Hamilton fixed-point theorem and show how it can be applied when restrictions are known on the numerical range of a holomorphic function. In particular, we extend the Earle-Hamilton theorem to holomorphic functions with numerical range having real part strictly less than 1. We also extend the Lumer-Phillips theorem estimating resolvents to dissipative holomorphic functions.

Approximation By Piecewise Constant Functions In A Bv Metric, Pavel Bělík, Mitchell Luskin

Faculty Authored Articles

Westudytheapproximationpropertiesofpiecewiseconstantfunc- tions with respect to triangular and rectangular finite elements in a metric defined on functions of bounded variation. We apply our results to a thin film model for martensitic crystals and to the approximation of deformations with microstructure.

Finite Element Solutions Of Heat Transfer In Molten Polymer Flow In Tubes With Viscous Dissipation, Dongming Wei, Haibiao Luo

Mathematics Faculty Publications

This paper presents the results of finite element analysis of a heat transfer problem of flowing polymer melts in a tube with constant ambient temperature. The rheological behavior of the melt is described by a temperature dependent power-law model. Aviscous dissipation term is included in the energy equation. Temperature profiles are obtained for different tube lengths and different entrance temperatures. The results are compared with some similar results in the literature.

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.

On The Nonembeddability And Crossing Numbers Of Some Kleinical Polyhedral Maps On The Torus, Adrian Riskin, Judy L. Klein

Mathematics

We designed and constructed a sundial for the purpose of observing the declination of the sun and thus marking solar seasonal variation. The 122 × 122 cm vertical sundial on the south-facing wall of our library has two unusual features: a nodus on the gnomon that casts a shadow of a point for marking the height of the sun and a large blank working space for students to mark the shadow of the nodus at different hours of the day and to connect the marks of 1 day in a line of declination. We discuss the design of a dial …