Physical Sciences and Mathematics Commons^™

Rhombic Penrose Tilings Can Be 3-Colored, Thomas Q. Sibley, Stan Wagon

Mathematics Faculty Publications

No abstract provided.

Isometric Extensions Of Zero Entropy Zᵈ Loosely Bernoulli Transformations, Aimee S.A. Johnson, A. A. Şahin

Mathematics & Statistics Faculty Works

In this paper we discuss loosely Bernoulli for Z(d) actions. In particular, we prove that extensions of zero entropy, ergodic, loosely Bernoulli Z(d) actions are also loosely Bernoulli.

A Rational Solution To Cootie, Arthur T. Benjamin, Matthew T. Fluet '99

All HMC Faculty Publications and Research

No abstract provided in this article.

A Group Theoretic Tabu Search Approach To The Traveling Salesman Problem, Shane N. Hall

Theses and Dissertations

The traveling salesman problem (TSP) is a combinatorial optimization problem that is mathematically modeled as a binary integer program. The TSP is a very important problem for the operations research academician and practitioner. This research demonstrates a Group Theoretic Tabu Search (GTTS) Java algorithm for the TSP. The tabu search metaheuristic continuously finds near-optimal solutions to the TSP under various different implementations. Algebraic group theory offers a more formal mathematical setting to study the TSP providing a theoretical foundation for describing tabu search. Specifically, this thesis uses the Symmetric Group on n letters, S(n), which is the set of all …

Similarity Based Approximate Reasoning., Swapan Raha Dr.

Doctoral Theses

Many years of research in Artificial Intelligence, Cognitive Science and allied area reveal that the cognitive process of human reasoning deals with imprecise premises. As cognitive process of human reasoning is mainly concerned with the individual's perception, it is liable to be imprecise in nature. Precise traditional two-valued logic and/or multi-valued logics are not effective in handling such reasoning processes. This motivated Zadeh (109) to investigate how these impreciseness in human rea- soning could be modeled through some computable entities. In this regard, Zadeh has shown how such imprecise linguistic terms could be expressed through fuzzy sets over universes of …

Quantum Stochastic Dilation Of Completely Positive Semigroups And Flows., Debashish Goswami Dr.

Doctoral Theses

The central theme of the present thesia is quantum stochastic dilation af semigroupe of completely panitive mapa on operator algebran. It is the sim of all mathemati- cal, or even all scientific theorics, to understand a given class of objects through a tanonical and simpler subclass of it. For example, abstract C"-algebras are studied through their conerete realisation as elgebra of operators, contractions on a Hilbert space by unitaries. Hilbert modules by the factorissble ones, to mention anly a few. In most af these caes, a general object of the relavant class is sociated with a canonical candidate of the …

Studies On Finite Linear Cellular Automata., Palash Sarkar Dr.

Doctoral Theses

Cellular Automata were originally proposed by John von Neumann as formal models of self reproducing organisms. The structure studied was mostly an ane and two dimensional infinite grida, though higher dimensions were also considered. Computation universality and other computation theoretic questions were considered important. See Burks [24] for a collection of essays on important problems on cellular automata during this period. Later physicists and biologists began to study cellular automsta for the purpose of modelling in their respective domains. In the present era, cellalar automata is being atudied from many widely different angles, and the relationship of these structurea to …

Some Contribution To Reliability Analysis Of A Consecutive-K-Out-Of N: F System., Mohammad Khanjari Sadegh Dr.

Doctoral Theses

Present day technology has been characterized by development of complex systems or equipments containing a large number of subaystems and com- ponents. Reliability, as a buman attribute, has been praised for a very long time. For technical systems, however, the reliability concept has not been applied for more than about 50 years. Reliability is the concern of all scien- tists and engineers engaged in developing a system, from design, through the manufacturing, to its ultimate use. Reliability technology has a potentially wide range of application areas like safety or risk analysis, environmental protection, quality, optimization, maintenance, engineering design, etc.For a …

Uncertainity Principles On Some Lie Groups., Swagato Kumar Ray Dr.

Doctoral Theses

The uncertainty principles of Harmonic Analysis say that: a nonzero func- tion and its Fourier transform cannot both be sharply concen- trated. After the initial work on this phenomenon in 1920s, the last two decades witnessed a spurt of activity in this direction (we refer the reader to a very readable survey [FS]). One may notice two broad phases in this activity, the first concentrating on R where the notion of concentration is given different formulations to see whether the phenomenon still holds. In the later phase R is replaced by other commutative or noncommutative groups, or more generally by …

On Fractal Based Representation Of Image With Application To Image Processing., Suman Kumar Mitra Dr.

Doctoral Theses

The language of an image is universal. Images were the means of communicating infor- mation in ancient days. Even today, although people from different parts of the world speak in different languages, an image conveys almost the same universal meaning to all. With the rapid development of modern computer technologies and with the increasing attempt in getting information at ones finger tips, the importance of communication of information using images can not be ignored.Images are stored in computers in the form of a collection of bits representing pixels (picture elements). Pictures are to be digitized to store them in computers. …

Generalised Bootstrap Techniques., Singdhansu Bhusan Chatterjee Dr.

Doctoral Theses

A typical problem in statistics is as follows: there is some observable data Xn = (X1,..., Xn), and a parameter of interest θ which is related in such a way to the distribution of Xn that meaningful conclusions about θ can be drawn based on Xn. Sometimes data Xn is observed keeping the objective parameter θ in mind, at other times the parameter appears while trying to model the observed data.Once the data is observed and the parameter fixed, the questions that have to be addressed are as follows:(I) How to estimate θ from the data Xn?(II) Given an estimator …

On Quantitative Evaluation Of 3-D Histo-Pathological Images From Confocal Laser Scanning Microscope., P. S. Umesh Adiga Dr.

Doctoral Theses

Automation of image analysis in the bio-medical ficld is one of the important achievements of applied image processing research. The rapid development in the electronic instrumentation during 1960s and 70s made it possible to automate the routine process of diagnosis and prognosis of many discases. Development of high resolution imaging instruments such as X-ray CT, MRI, etc., for macro imaging and electron microscope, confocal microscope, etc., for micro imaging has given a tremendous boost to the advancement of medical field. Advancement in the field of computing has made it possible to reconstruct the pictures of internal organs of the body …

G EP / G MP Ratio By Polarization Transfer In Ep→Ep, M. K. Jones, K. A. Aniol, F. T. Baker, J. Berthot, P. Y. Bertin, W. Bertozzi, A. Besson, L. Bimbot, W. U. Boeglin, E. J. Brash, D. Brown, J. R. Calarco, L. S. Cardman, C. C. Chang, J. P. Chen, E. Chudakov, S. Churchwell, E. Cisbani, D. S. Dale, R. De Leo, A. Deur, B. Diederich, J. J. Domingo, M. B. Epstein, L. A. Ewell, K. G. Fissum, A. Fleck, H. Fonvieille, S. Frullani, J. Gao, F. Garibaldi, A. Gasparian, G. Gerstner, S. Gilad, R. Gilman, A. Glamazdin, C. Glashausser, J. Gomez, V. Gorbenko, A. Green, J. O. Hansen, C. R. Howell, G. G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, G. Lavessiere, J. J. Lerose, M. Liang, R. A. Lindgren, N. Liyanage, G. J. Lolos, R. Macri, R. Madey, S. Malov, D. J. Margaziotis, P. Markowitz, K. Mccormick, J. I. Mcintyre, R. L. J. Van Der Meer, R. Michaels, B. D. Milbrath, J. Y. Mougey, S. K. Nanda, E. A. J. M. Offermann, Z. Papandreou, C. F. Perdrisat, G. G. Petratos, N. M. Piskunov, R. I. Pomatsalyuk, D. L. Prout, V. Punjabi, G. Quemener, R. D. Ransome, B. A. Raue, Y. Roblin, R. Roche, G. Rutledge, P. M. Rutt, A. Saha, T. Saito, A. J. Sarty, T. P. Smith, P. Sorokin, S. Strauch, R. Suleiman, K. Takahashi, J. A. Templon, L. Todor, P. E. Ulmer, G. M. Urciuoli, P. Vernin, B. Vlahovic, H. Voskanyan, K. Wijesooriya, B. B. Wojtsekhowski, R. J. Woo, F. Xiong, G. D. Zainea, Z. L. Zhou

Enkeleida K. Lakuriqi

The ratio of the proton's elastic electromagnetic form factors, G Ep / G Mp, was obtained by measuring Pt and Pl, the transverse and the longitudinal recoil proton polarization, respectively. For elastic ep→ep, G Ep / G Mp is proportional to Pt / Pl. Simultaneous measurement of Pt and Pl in a polarimeter provides good control of the systematic uncertainty. The results for the ratio G Ep / G Mp show a systematic decrease as Q2 increases from 0.5 to 3.5GeV2, indicating for the first time a definite difference in the spatial distribution of charge …

Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski

Mathematics and Statistics Faculty Research & Creative Works

It is shown that a metric continuum X is a dendrite if and only if for every compact space Y and for every light open mapping f : Y ->f(Y ) such that X c f(Y ) there is a copy X1 of X in Y for which the restriction fjX1 : X1 ->X is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.

Computational Geometry Column 37, Erik D. Demaine, Joseph O'Rourke

Computer Science: Faculty Publications

Open problems from the 15th Annual ACM Symposium on Computational Geometry.

Numerical Aspects Of Discrete And Continuum Hybrid Models In Cell Biology, J. C. Dallon

Faculty Publications

In this paper we introduce a method of modeling which mixes continuum and discrete variables, and explain two models in cell biology that use this method. The first application deals with wound healing, more specifically the collagen alignment in scar tissue formation and the second models early aggregation in the cellular slime mold Dictyostelium discoideum. We solve these models using numerical techniques similar to the particle-in-cell method which requires that the discrete and continuum variables are interpolated one to the other. The implementational and numerical details are discussed in an informal and practical manner with particular attention given to the …

The Phillips Properties, Walden Freedman, Ali Ülger

Walden Freedman

A Banach space  has the Phillips property if the canonical projection  is sequentially weak-norm continuous, and has the weak Phillips property if  is sequentially weak-weak continuous. We study both properties in connection with other geometric properties, such as the Dunford-Pettis property, Pelczynski's properties  and (V), and the Schur property.

A Mathematical Model Of Wheelchair Racing, Susan J. Schenk

Dissertations

Wheelchair racing strokes are very complicated movements, which involve a coupling between the athlete and his or her racing chair. Each body segment, as well as the wheel, follows a distinct trajectory as the motion is performed. Understanding the kinematics and kinetics of various stroke techniques would provide the athletes and their coaches with information, which could help guide the racers toward improved performances.

In this thesis, a mathematical model is developed, which is capable of providing such valuable kinematic and kinetic information. This two-dimensional model represents the body segments as a coupled pendulum system of point masses and the …

Perturbed Laplacian Matrix And The Structure Of A Graph., Sukanta Pati Dr.

Doctoral Theses

Laplacian matrices Let G be a connected simple graph with vertex set V = {1,2,.,n), edge set E and let each edge be associated with a positive number, the weight of the edge. The above graph is called a weighted graph. An unweighted graph is just a weighted graph with each of the edges bearing weight 1. All the graphs considered are weighted and simple, unless specified otherwise; all the matrices considered are real. The adjacency matrix A(G) related to this graph is defined as A(G) = (aij), whereaij, if (i, j] € E and the weight of the edge …

Pushpush Is Np-Hard In 2d, Erik D. Demaine, Martin L. Demaine, Joseph O'Rourke

Computer Science: Faculty Publications

We prove that a particular pushing-blocks puzzle is intractable in 2D, improving an earlier result that established intractability in 3D [OS99]. The puzzle, inspired by the game *PushPush*, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 2D by reduction from SAT.

Dynamics Of Stochastic Systems With Memory (Mathematics And Statistics Colloquium, Wright State University), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

We describe an approach to the dynamics of stochastic systems with finite memory using multiplicative cocycles in Hilbert space. We introduce the notion of hyperbolicity for stationary solutions of the stochastic differential system. We then establish the existence of smooth stable and unstable manifolds in a neighborhood of a hyperbolic stationary solution. The stable and unstable manifolds are stationary and asymptotically invariant under the stochastic semiflow. The proof uses ideas from infinite-dimensional multiplicative ergodic theory and interpolation arguments.

Singular Solutions To A Nonlinear Elliptic Boundary Value Problem Originating From Corrosion Modeling, Kurt M. Bryan, Michael Vogelius

Mathematical Sciences Technical Reports (MSTR)

We consider a nonlinear elliptic boundary value problem on a planar domain. The exponential type nonlinearity in the boundary condition is one that frequently appears in the modeling of electrochemical systems. For the case of a disk we construct a family of exact solutions that exhibit limiting logarithmic singularities at certain points on the boundary. Based on these solutions we develop two criteria that we believe predict the possible locations of the boundary singularities on quite general domains.

Inverse Limits On [0,1] Using Piecewise Linear Unimodal Bonding Maps, William Thomas Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we investigate inverse limits on [0,1] using a single bonding map chosen from a two-parameter family of piecewise linear unimodal bonding maps. This investigation focuses on the parameter values at the boundary between a hereditarily decomposable inverse limit and an inverse limit containing an indecomposable continuum. © 1999 American Mathematical Society.

Tight Bounds On The Algebraic Connectivity Of A Balanced Binary Tree, Jason J. Molitierno, Michael Neumann, Bryan L. Shader

Mathematics Faculty Publications

In this paper, quite tight lower and upper bounds are obtained on the algebraic connectivity, namely, the second-smallest eigenvalue of the Laplacian matrix, of an unweighted balanced binary tree with k levels and hence n = 2^k - 1 vertices. This is accomplished by considering the inverse of a matrix of order k - 1 readily obtained from the Laplacian matrix. It is shown that the algebraic connectivity is 1/(2^k - 2k + 3) + 0(1/2^2k).

On The Baroclinic Instability Of Axisymmetric Rotating Gravity Currents With Bottom Slope, Paul F. Choboter, Gordone E. Swaters

Mathematics

The baroclinic stability characteristics of axisymmetric gravity currents in a rotating system with a sloping bottom are determined. Laboratory studies have shown that a relatively dense fluid released under an ambient fluid in a rotating system will quickly respond to Coriolis effects and settle to a state of geostrophic balance. Here we employ a subinertial two-layer model derived from the shallow-water equations to study the stability characteristics of such a current after the stage at which geostrophy is attained. In the model, the dynamics of the lower layer are geostrophic to leading order, but not quasi-geostrophic, since the height deflections …

Nonstandard Analysis In Topology: Nonstandard And Standard Compactifications, S. Salbany, Todor D. Todorov

Mathematics

Let (X, T) be a topological space, and ^∗X a non–standard extension of X. There is a natural “standard” topology ^ST on ^∗X generated by ^∗G,where G ∈ T . The topological space (^∗X,^ST) will be used to study, in a systematic way, compactifications of (X, T).

Codes And Curves, Judy L. Walker

Department of Mathematics: Faculty Publications

When information is transmitted, errors are likely to occur. Coding theory examines effi cient ways of packaging data so that these errors can be detected, or even corrected. The traditional tools of coding theory have come from combinatorics and group theory. Lately, however, coding theorists have added techniques from algebraic geometry to their toolboxes. In particular, by re-interpreting the Reed- Solomon codes, one can see how to defi ne new codes based on divisors on algebraic curves. For instance, using modular curves over fi nite fi elds, Tsfasman, Vladut, and Zink showed that one can defi ne a sequence of …

Design Early Considered Harmful: Graduated Exposure To Complexity And Structure Based On Levels Of Cognitive Development, Duane Buck, David J. Stucki

Mathematics Faculty Scholarship

We have recognized that the natural tendency to teach according to the structure of one’s own understanding runs contrary to established models of cognitive development. Bloom’s Taxonomy has provided a basis for establishing a more efficacious pedagogy. Emphasizing a hierarchical progression of skill sets and gradual learning through example, our approach advocates teaching software development from the inside/out rather than beginning with either console apps or monolithic designs.

Three-Dimensional Computer Simulation Of Liquid Drop Evaporation, Mark Korlie

Department of Mathematics Facuty Scholarship and Creative Works

We use molecular dynamics simulation to describe a method that can be used to model liquid drop evaporation. For application, the liquid is taken to be water. Using the properties of the liquid and a Lennard-Jones potential, we derive dynamical equations, which are used to describe the gross dynamical behavior of the liquid-vapor molecular system. The resulting dynamical equations are solved numerically by a time stepping, numerical method. The evaporation of the liquid to the vapor phase is described.

Cwatset Isomorphism And Its Consequences, Carolyn M. Girod, Matthew Lipinski, Joseph R. Mileti, Jennifer R. Paulhus

Mathematical Sciences Technical Reports (MSTR)

We explore the consequences of cwatset isomorphism (there are a finite number of non-isomorphic cwatsets of each order) and consider parallels between the theory of groups and the theory of cwatsets (cwatsets of prime order are cyclic but direct sums of isomorphic cwatsets aren't necessarily isomorphic).