Physical Sciences and Mathematics Commons^™

Topological Conjugacy And Rigidity Of Affine Actions., Siddhartha Bhattacharya Dr.

Doctoral Theses

The main theme of this thesis is topological classiication of aline Hows on homogeneous spaces and rigidity of equivariant continuous maps between such dows. Both these aspects have been extensively studied in the literature for subgroup actions (cf. [Be), [B-Dj and [Wi) and for automorphism flows of the cyclic group (cf. [Ar]. [K-R] and [C-S). We will consider similar questions in more general situations. A detailed outline is given below. For a topological group T, by a r-flow we mean pair (X,p), where X is a opological space and p is a continuous action of I on X. For any …

Routing Algorithms For Channels, Switchboxes And Mcm's In Vlsi Layout Design., Sandip Das Dr.

Doctoral Theses

The term Very Large Scale Integration (VLSI) reflects the capability of semi- conductor industry to fabricate a complex electronic circuit consisting of millions of components on a single silicon substrate. The growth of semiconductor technol- ogy in recent years has been described by "Moore's law", enunciated in the late 1960s, which projected quadrupling of components in a chip in every three to four years. Several factors contributed to this tremendous growth : (i) reduction of line width of the basic device and interconnection wires due to the development of high- resolution lithographic techniques and improved processing capabilities, (ii) increase in …

An Ellam Scheme For Multidimensional Advection-Reaction Equations And Its Optimal-Order Error Estimate, Hong Wang, Xiquan Shi, Richard E. Ewing

Faculty Publications

We present an Eulerian-Lagrangian localized adjoint method (ELLAM) scheme for initial-boundary value problems for advection-reaction partial differential equations in multiple space dimensions. The derived numerical scheme is not subject to the Courant-Friedrichs-Lewy condition and generates accurate numerical solutions even if large time steps are used. Moreover, the scheme naturally incorporates boundary conditions into its formulation without any artificial outflow boundary conditions needed, and it conserves mass. An optimal-order error estimate is proved for the scheme. Numerical experiments are performed to verify the theoretical estimate.

A Sequential Search Distribution: Proofreading, Russian Roulette, And The Incomplete Q-Eulerian Polynomials, Travis Herbranson, Don Rawlings

Mathematics

The distribution for the number of searches needed to find k of n lost objects is expressed in terms of a refinement of the q-Eulerian polynomials, for which formulae are developed involving homogeneous symmetric polynomials. In the case when k = n and the find probability remains constant, relatively simple and efficient formulas are obtained. From our main theorem, we further (1) deduce the inverse absorption distribution and (2) determine the expected number of times the survivor pulls the trigger in an n-player game of Russian roulette.

Back To Classics: Teaching Limits Through Infinitesimals, Todor D. Todorov

Mathematics

The usual ϵ, δ-definition of the limit of a function (whether presented at a rigorous or an intuitive level) requires a “candidate L” for the limit value. Thus, we have to start our first calculus course with “guessing” instead of “calculating”. In this paper we criticize the method of using calculators for the purpose of selecting candidates for L. We suggest an alternative: a working formula for calculating the limit value L of a real function in terms of infinitesimals. Our formula, if considered as a definition of limit, is equivalent to the usual ϵ, δ-definition but does not involve …

Extreme-Value Moment Goodness-Of-Fit Tests, Theodore P. Hill, Victor Perez-Abreu

Research Scholars in Residence

A general goodness-of-fit test for scale-parameter families of distributions is introduced, which is based on quotients of expected sample minima. The test is independent of the mean of the distribution, and, in applications to testing for exponentiality of data, compares favorably to other goodness-of-fit tests for exponentiality based on the empirical distribution function, regression methods and correlation statistics. The new minimal-moment method uses ratios of easily-calculated, unbiased, strongly consistent U-statistics, and the general technique can be used to test many standard composite null hypotheses such as exponentiality, normality or uniformity (as well as simple null hypotheses).

Efficient Traitor Tracing Algorithms Using List Decoding, Alice Silverberg, Jessica Staddon, Judy L. Walker

Department of Mathematics: Faculty Publications

We use powerful new techniques for list decoding error-correcting codes to efficiently trace traitors. Although much work has focused on constructing traceability schemes, the complexity of the tracing algorithm has received little attention. Because the TA tracing algorithm has a runtime of O(N) in general, where N is the number of users, it is inefficient for large populations.We produce schemes for which the TA algorithm is very fast. The IPP tracing algorithm, though less efficient, can list all coalitions capable of constructing a given pirate. We give evidence that when using an algebraic structure, the ability to …

Group Closures Of One-To-One Transformations, Inessa Levi

Faculty Bibliography

For a semigroup 5 of transformations of an infinite set X let Gs be the group of all the permutations of X that preserve 5 under conjugation. Fix a permutation group H on X and a transformation / of X, and let (/ : H) = ({hfh~l : h 6 H}) be the //-closure of /. We find necessary and sufficient conditions on a one-to-one transformation / and a normal subgroup H of the symmetric group on X to satisfy G(f-.H) = H. We also show that if S is a semigroup of one-to-one transformations of X and Gs contains …

Rank-One Perturbations Of Diagonal Operators., Eugen J. Ionascu

Faculty Bibliography

We study rank-one perturbations of diagonal Hilbert space operators mainly from the standpoint of invariant subspace problem. In addition to proving some general properties of these operators, we identify the normal operators and contractions in this class. We show that two well known results about the eigenvalues of rank-one perturbations and one-codimension compressions of self-adjoint compact operators are equivalent. Sufficient conditions are given for existence of nontrivial invariant subspaces for this class of operators.

No-Nonsense Guide To Csab/Csac Accreditation, Pete Sanderson

Mathematics Faculty Scholarship

CSAB/CSAC provides professional accreditation of computer science bachelor's degree programs in the United States. As of October 2000, 159 institutions held this accreditation. By our count, over 80% of the accredited programs were offered by departments which also offer graduate programs in computer science. This means that few small colleges are represented. Our intent in this work is to give the small college audience an up-to-date guide to the recently-revised CSAB/CSAC accreditation standards. The guide is not comprehensive; we emphasize those issues we believe to be of greatest interest to small colleges and address them from the perspective we have …

A Penalty Method For Approximations Of The Stationary Power-Law Stokes Problem, Lew Lefton, Dongming Wei

Mathematics Faculty Publications

We study approximations of the steady state Stokes problem governed by the power-law model for viscous incompressible non-Newtonian flow using the penalty formulation. We establish convergence and find error estimates

Decay Estimates Of Heat Transfer To Melton Polymer Flow In Pipes With Viscous Dissipation, Dongming Wei, Zhenbu Zhang

Mathematics Faculty Publications

In this work, we compare a parabolic equation with an elliptic equation both of which are used in modeling temperature profile of a power-law polymer flow in a semi-infinite straight pipe with circular cross section. We show that both models are well-posed and we derive exponential rates of convergence of the two solutions to the same steady state solution away from the entrance. We also show estimates for difference between the two solutions in terms of physical data.

The Breakdown Of Synchronization In Systems Of Non-Identical Chaotic Oscillators: Theory And Experiment, Jennifer Chubb, Ernest Barreto, Paul So, Bruce J. Gluckman

Mathematics

The synchronization of chaotic systems has received a great deal of attention. However, most of the literature has focused on systems that possess invariant manifolds that persist as the coupling is varied. In this paper, we describe the process whereby synchronization is lost in systems of nonidentical coupled chaotic oscillators without special symmetries. We qualitatively and quantitatively analyze such systems in terms of the evolution of the unstable periodic orbit structure. Our results are illustrated with data from physical experiments.

Modular Miracles, John Stillwell

Mathematics

Over the last 20 years, the modular function has become widely known through its miraculous intervention in two great mathematical achievements: the proof of Fermat's last theorem and the "moonshine" of the monster simple group. In both cases, the modular function appears where no one expected it, and it bridges a chasm between seemingly unrelated fields. It is probably fair to say that, in these two cases, we do not yet fully understand how the modular magic works.

However, it can at least be said that these are not the first modular miracles. Ever since its discovery, in the early …

On The Nonembeddability And Crossing Numbers Of Some Toroidal Graphs On The Klein Bottle, Adrian Riskin

Mathematics

We show that toroidal polyhedral maps with four or more disjoint homotopic noncontractiblecircuits are not embeddable on the projective plane and that toroidal polyhedral maps with -veor more disjoint homotopic noncontractible circuits are not embeddable on the Klein bottle. Wealso show that the Klein bottle crossing numbers ofCm×Cn(m6n) form=3;4;5;6 are 1,2,4,and 6, respectively, and give upper bounds for all other values ofn. These crossing numbersdispla yat ypical behavior in that the value depends onl yonminstead of on bothmandnas isthe case for the plane and projective plane.

Constructing Regular Ramanujan Graphs Via Graph Extension, Sage Michelle Accardo

Honors Theses

No abstract provided.

A Degree Of Nonlocal Connectedness, J. J. Charatonik, W. J. Charatonik

Mathematics and Statistics Faculty Research & Creative Works

To any continuum X weassign an ordinal number (or the symbol ∞) s(X), called the degree of nonlocal connectedness of X. We show that (1) the degree cannot be increased under continuous surjections; (2) for hereditarily unicoherent continua X, the degree of a subcontinuum of X is less than or equal to s(X); (3) s(C(X)) ≤ s(X), where C(X) denotes the hyperspace of subcontinua of a continuum X. We also investigate the degrees of Cartesian products and inverse limits. As an application weconstruct an uncountable family of metric continua X homeomorphic to C(X).

Extended Powers Of Manifolds And The Adams Spectral Sequence, Robert R. Bruner

Mathematics Faculty Research Publications

The extended power construction can be used to create new framed manifolds out of old. We show here how to compute the effect of such operations in the Adams spectral sequence, extending partial results of Milgram and the author. This gives the simplest method of proving that Jones’ 30-manifold has Kervaire invariant one, and allows the construction of manifolds representing Mahowald’s classes η4 and η5, among others.

Properties Of Some Generalizations Of Kac-Murdock-Szeg"O Matrices, William Trench

William F. Trench

No abstract provided.

The Relative Performance Of Full Information Maximum Likelihood Estimation For Missing Data In Structural Equation Models, C. K. Enders, Deborah L. Bandalos

Deborah L Bandalos

No abstract provided.

Joachim Castella: Studien Zur Thematik "Kalkül Und Kreativität", Rudolf Kaehr

Rudolf Kaehr

Utopie der Zeichen – Zeichen der Utopie Vilém Flusser und Gotthard Günther als Komplement einer neuen Medienphilosophie Medientheorie als Theoriemedium Prolegomena einer allgemeinenMedientheorie Philosophie des LMR Joachim Castella 2000/2001

On The Uniform Convergence Of Walsh-Fourier Series, Ushangi Goginava

Ushangi Goginava

No abstract provided.

Mathematical Aspects Of Oriental Carpets, Carol Bier

Carol Bier

The mathematical principles of pattern making according to symmetrical repetition are well-known today, but the mathematical aspects of pattern formation have been glossed over in the study of Oriental carpets, or neglected in favor of either an appreciation of color and form or a discussion of social and ethnic origins. This article seeks to address several mathematical aspects of Oriental carpets, which are both integral to their form and manifest in their visual make-up.

On Toric Varieties And Modular Forms, Paul Gunnells

Paul Gunnells

No abstract provided.

A Brunn-Minkowski Inequality For The Integer Lattice, Richard J. Gardner, Paolo Gronchi

Mathematics Faculty Publications

A close discrete analog of the classical Brunn-Minkowksi inequality that holds for finite subsets of the integer lattice is obtained. This is applied to obtain strong new lower bounds for the cardinality of the sum of two finite sets, one of which has full dimension, and, in fact, a method for computing the exact lower bound in this situation, given the dimension of the lattice and the cardinalities of the two sets. These bounds in turn imply corresponding new bounds for the lattice point enumerator of the Minkowski sum of two convex lattice polytopes. A Rogers-Shephard type inequality for the …

Existence Criteria For Singular Initial Value Problems With Sign Changing Nonlinearities, Ravi P. Agarwal, Donal O'Regan, V. Lakshmikantham

Mathematics and System Engineering Faculty Publications

A general existence theory is presented for initial value problems where our nonlinearity may be singular in its dependent variable and may also change sign.

Rush Hour® And Dijkstra’S Algorithm, Mark Stamp, Brad Engel, Mcintosh Ewell, Victor Morrow

Faculty Publications, Computer Science

The game of Rush Hour® includes a 6 × 6 grid and game pieces representing cars and trucks. The object of the puzzle is to move a special car out of a gridlocked “traffic jam.” In this note we apply Dijkstra’s algorithm and a breadth-first search to solve any Rush Hour configuration.

Biharmonic Maps On V-Manifolds, Yuan-Jen Chiang, Hongan Sun

Mathematics

We generalize biharmonic maps between Riemannian manifolds into the case of the domain being V-manifolds. We obtain the first and second variations of biharmonic maps on V-manifolds. Since a biharmonic map from a compact V-manifold into a Riemannian manifold of nonpositive curvature is harmonic, we construct a biharmonic non-harmonic map into a sphere. We also show that under certain condition the biharmonic property of f implies the harmonic property of f. We finally discuss the composition of biharmonic maps on V-manifolds.

Open To Reason, David L. Neuhouser

Books by Taylor faculty, staff, and administrators

Open to Reason is a comparison of the roles of reason, experience, imagination, intuition, faith, love, humility, and obedience in mathematics and religion.

Boundary Layers In Channel Flow With Injection And Suction, R. Temam, X. Wang

Mathematics and Statistics Faculty Research & Creative Works

We present a rigorous result regarding the boundary layer associated with the incompressible Newtonian channel flow with injection and suction. © 2000 Elsevier Science Ltd. All rights reserved.