Mathematics Commons^™

Submanifolds Of Riemannian Product Manifolds, Mehmet Atçeken

Turkish Journal of Mathematics

In this paper, we study the geometry of the semi-invariant submanifolds of a Riemannian product manifold. Fundamental properties of these type submanifolds such as the integrability of the distributions D, D^{\bot} and mixed-geodesic property are studied. Finally, necessary and sufficient conditions are given on a semi-invariant submanifold of Riemannian product manifold to be D-geodesic and D^{\bot}-geodesic.

Phase Synchronization In Three-Dimensional Lattices And Globally Coupled Populations Of Nonidentical Rossler Oscillators, Limin Qi

Electronic Theses and Dissertations

A study on phase synchronization in large populations of nonlinear dynamical systems is presented in this thesis. Using the well-known Rossler system as a prototypical model, phase synchronization in one oscillator with periodic external forcing and in two-coupled nonidentical oscillators was explored at first. The study was further extended to consider three-dimensional lattices and globally coupled populations of nonidentical oscillators, in which the mathematical formulation that represents phase synchronization in the generalized N-coupled Rossler system was derived and several computer programs that perform numerical simulations were developed. The results show the effects of coupling dimension, coupling strength, population size, and …

Monotone Periodic Orbits For Torus Homeomorphisms, Kamlesh Parwani

Faculty Research and Creative Activity

Let f be a homeomorphism of the torus isotopic to the identity and suppose that there exists a periodic orbit with a non-zero rotation vector (p/q,r/q), then f has a topologically monotone periodic orbit with the same rotation vector.

A *-Closed Subalgebra Of The Smirnov Class, Stephan Ramon Garcia

Pomona Faculty Publications and Research

We study real Smirnov functions and investigate a certain *-closed subalgebra of the Smirnov class N^+ containing them. Motivated by a result of Aleksandrov, we provide an explicit representation for the space H^p ∩ H^p [overscore over the second H^p]. This leads to a natural analog of the Riesz projection on a certain quotient space of L^p for p ϵ (0, 1). We also study a Herglotz-like integral transform for singular measures on the unit circle ∂D.

C(X) Can Sometimes Determine X Without X Being Realcompact, Melvin Henriksen, Biswajit Mitra

All HMC Faculty Publications and Research

As usual C(X) will denote the ring of real-valued continuous functions on a Tychonoff space X. It is well-known that if X and Y are realcompact spaces such that C(X) and C(Y ) are isomorphic, then X and Y are homeomorphic; that is C(X) determines X. The restriction to realcompact spaces stems from the fact that C(X) and C(uX) are isomorphic, where uX is the (Hewitt) realcompactifcation of X. In this note, a class of locally compact spaces X that includes properly the class of locally compact realcompact spaces is exhibited such that C(X) determines X. The problem of getting …

Problems From The Cottonwood Room, Matthias Beck, Beifang Chen, Lenny Fukshansky, Christian Haase, Allen Knutson, Bruce Reznick, Sinai Robins, Achill Schürmann

CMC Faculty Publications and Research

This collection was compiled by Christian Haase and Bruce Reznick from problems presented at the problem sessions, and submissions solicited from the participants of the AMS/IMS/SIAM summer Research Conference on Integer points in polyhedra. Lattice points in homogeneously expanding compact domains. Presented by Lenny Fukshansky (Texas A&M University).

On Generalization Of The Quasi Homogeneous Riesz Potential, Hüseyi̇n Yildirim

Turkish Journal of Mathematics

In this paper, a generalization of the quasi homogeneous Riesz Potential has been defined using non-isotropic quasi-distance and its L_p (p \geq 1) continuity study.

A Tutorial On Radiation Oncology And Optimization, Allen G. Holder, Bill Salter

Mathematics Faculty Research

Designing radiotherapy treatments is a complicated and important task that affects patient care, and modern delivery systems enable a physician more flexibility than can be considered. Consequently, treatment design is increasingly automated by techniques of optimization, and many of the advances in the design process are accomplished by a collaboration among medical physicists, radiation oncologists, and experts in optimization. This tutorial is meant to aid those with a background in optimization in learning about treatment design. Besides discussing several optimization models, we include a clinical perspective so that readers understand the clinical issues that are often ignored in the optimization …

Global Stability Of Periodic Orbits Of Non-Autonomous Difference Equations And Population Biology, Saber Elaydi, Robert J. Sacker

Mathematics Faculty Research

Elaydi and Yakubu showed that a globally asymptotically stable(GAS) periodic orbit in an autonomous difference equation must in fact be a fixed point whenever the phase space is connected. In this paper we extend this result to periodic nonautonomous difference equations via the concept of skew-product dynamical systems. We show that for a k-periodic difference equation, if a periodic orbit of period r is GAS, then r must be a divisor of k. In particular sub-harmonic, or long periodic, oscillations cannot occur. Moreover, if r divides k we construct a non-autonomous dynamical system having minimum period k and …

Semantic Notation And Retrieval In Art And Architecture Image Collections, Boyan N. Dimitrov

Mathematics Publications

In this paper we analyze various methods used for semantic annotation and search in a collection of art and architecture images. We discuss the Art and Architecture Thesaurus, WordNet, ULAN and Iconclass ontology. Systems for searching and retrieval art and architecture image collections are presented. We explore if the MPEG 7 descriptors are useful for art and architecture image annotations. For illustrations we use images from Antoni Gaudi architecture and Claude Monet paintings.

Symmetric Generation Of Finite Homomorphic Images?, Lee Farber

Theses Digitization Project

The purpose of this thesis was to present the technique of double coset enumeration and apply it to construct finite homomorphic images of infinite semidirect products. Several important homomorphic images include the classical groups, the Projective Special Linear group and the Derived Chevalley group were constructed.

Symmetrically Generated Groups, Benny Nguyen

Theses Digitization Project

This thesis constructs several groups entirely by hand via their symmetric presentations. In particular, the technique of double coset enumeration is used to manually construct J₃ : 2, the automorphism group of the Janko group J₃, and represent every element of the group as a permutation of PSL₂ (16) : 4, on 120 letters, followed by a word of length at most 3.

Math, Music, And Membranes: A Historical Survey Of The Question "Can One Hear The Shape Of A Drum"?, Tricia Dawn Mccorkle

Theses Digitization Project

In 1966 Mark Kac posed an interesting question regarding vibrating membranes and the sounds they make. His article entitled "Can One Hear the Shape of a Drum?", which appeared in The American Mathematical Monthly, generated much interest and scholarly debate. The evolution of Kac's intriguing question will be the subject of this project.

A Topological Approach To Nonlinear Analysis, Wendy Ann Peske

Theses Digitization Project

A topological approach to nonlinear analysis allows for strikingly beautiful proofs and simplified calculations. This topological approach employs many of the ideas of continuous topology, including convergence, compactness, metrization, complete metric spaces, uniform spaces and function spaces. This thesis illustrates using the topological approach in proving the Cauchy-Peano Existence theorem. The topological proof utilizes the ideas of complete metric spaces, Ascoli-Arzela theorem, topological properties in Euclidean n-space and normed linear spaces, and the extension of Brouwer's fixed point theorem to Schauder's fixed point theorem, and Picard's theorem.

Survival Analysis, Mohammad Alif Wardak

Theses Digitization Project

Survival analysis pertains to a statistical approach designed to take into account the amount of time an experimental unit contributes to a study. A Mayo Clinic study of 418 Primary Biliary Cirrhosis patients during a ten year period was used. The Kaplan-Meier Estimator, a non-parametric statistic, and the Cox Proportional Hazard methods were the tools applied. Kaplan-Meier results include total values/censored values.

Symmetric Generation Of Finite Groups, MaríA De La Luz Torres Bisquertt

Theses Digitization Project

Advantages of the double coset enumeration technique include its use to represent group elements in a convenient shorter form than their usual permutation representations and to find nice permutation representations for groups. In this thesis we construct, by hand, several groups, including U₃(3) : 2, L₂(13), PGL₂(11), and PGL₂(7), represent their elements in the short form (symmetric representation) and produce their permutation representations.

The Expected Variation Of Random Bounded Integer Sequences Of Finite Length, Rudolfo Angeles, Don Rawlings, Lawrence Sze, Mark Tiefenbruck

Mathematics

From the enumerative generating function of an abstract adjacency statistic, we deduce the mean and variance of the variation on random permutations, rearrangements, compositions, and bounded integer sequences of finite length.

The Solvability Of Polynomials By Radicals: A Search For Unsolvable And Solvable Quintic Examples, Robert Lewis Beyronneau

Theses Digitization Project

This project centers around finding specific examples of quintic polynomials that were and were not solvable. This helped to devise a method for finding examples of solvable and unsolvable quintics.

Symmetric Representation Of Elements Of Sporadic Groups, Elena Yavorska Harris

Theses Digitization Project

Uses the techniques of symmetric presentations to manipulate elements of large sporadic groups and to represent elements of these groups in much shorter forms than their corresponding permutation or matrix representation. Undertakes to develop a nested algorithm and a computer program to manipulate elements of large sporadic groups.

Root Subgroups Of The Rank Two Unitary Groups, Matthew Thomas Henes

Theses Digitization Project

Discusses certain one-parameter subgroups of the low-rank unitary groups called root subgroups. Unitary groups also have representations of Lie type which means they consist of transformations that act as automorphisms of an underlying Lie algebra, in this case the special linear algebra. Exploring this definition of the unitary groups, we find a correlation, via exponentiation, to the basis elements of Lie algebra.

Convergence Analysis Of Mcmc Method In The Study Of Genetic Linkage With Missing Data, Diana Fisher

Theses, Dissertations and Capstones

Computational infeasibility of exact methods for solving genetic linkage analysis problems has led to the development of a new collection of stochastic methods, all of which require the use of Markov chains. The purpose of this work is to investigate the complexities of missing data in pedigree analysis using the Monte Carlo Markov Chain (MCMC) method as compared to the exact results. Also, we attempt to determine an association between missing data in a familial pedigree and the convergence to stationarity of a descent graph Markov chain implemented in the stochastic method for parametric linkage analysis.

In particular, we will …

Forward-Backward Diffusion With Continuous Spectrum, Jorge Aarao

Turkish Journal of Mathematics

We prove existence and uniqueness of solutions for a class of forward-backward diffusion equations via a representative example, where the second-order part has continuous spectrum, and the initial and boundary data are suitably chosen.

Corrigendum Uniqueness Of Primary Decompositions [Turkish J. Math. 27 (2003), 425--434], Patrick F. Smith

Turkish Journal of Mathematics

No abstract provided.

Beamer By Example, Andrew Mertz, William Slough

Faculty Research and Creative Activity

There are a variety of LaTeX classes which can be used to produce "overhead slides" for presentations. One of these, beamer, provides flexible and powerful environments which can be used to create slides and PDF-based documents suitable for presentations. Although the class is extensively documented, first-time users may prefer learning about this class using a collection of graduated examples. The examples presented here cover a wide spectrum of use, from the simplest static slides to those with dynamic effects.

Monotone Periodic Orbits For Torus Homeomorphisms, Kamlesh Parwani

Faculty Research and Creative Activity

Let f be a homeomorphism of the torus isotopic to the identity and suppose that there exists a periodic orbit with a non-zero rotation vector (p/q,r/q), then f has a topologically monotone periodic orbit with the same rotation vector.

Equivariant Flow Equivalence Of Shifts Of Finite Type By Matrix Equivalence Over Group Rings, Mike Boyle, Michael C. Sullivan

Articles and Preprints

Let G be a finite group. We classify G-equivariant flow equivalence of non-trivial irreducible shifts of finite type in terms of

(i) elementary equivalence of matrices over ZG and

(ii) the conjugacy class in ZG of the group of G-weights of cycles based at a fixed vertex.

In the case G = Z/2, we have the classification for twistwise flow equivalence. We include some algebraic results and examples related to the determination of E(ZG) equivalence, which involves K₁(ZG).

Assimilation Of Simulated Float Data In Lagrangian Coordinates, J. L. Mead

Mathematics Faculty Publications and Presentations

We implement an approach for the accurate assimilation of Lagrangian data into regional general ocean circulation models. The forward model is expressed in Lagrangian coordinates and simulated float data are incorporated into the model via four dimensional variational data assimilation. We show that forward solutions computed in Lagrangian coordinates are reliable for time periods of up to 100 days with phase speeds of 1 m/s and deformation radius of 35 km. The position and depth of simulated floats are assimilated into the viscous, Lagrangian shallow water equations. The weights for the errors in the model and data are varied and …

Symbolic Dynamics And Its Applications, Michael C. Sullivan

Articles and Preprints

Book review of Symbolic Dynamics and its Applications, edited by Susan Williams, AMS.

Microarray Data From A Statistician’S Point Of View, Johanna S. Hardin

Pomona Faculty Publications and Research

No abstract provided.

Properties Of One-Point Completions Of A Noncompact Metrizable Space, Melvin Henriksen, Ludvík Janoš, R. G. Woods

All HMC Faculty Publications and Research

If a metrizable space X is dense in a metrizable space Y, then Y is called a metric extension of X. If T₁ and T₂ are metric extensions of X and there is a continuous map of T₂ into T₁ keeping X pointwise fixed, we write T₁ ≤ T₂. If X is noncompact and metrizable, then (M(X),≤) denotes the set of metric extensions of X, where T₁ and T₂ are identified if T₁ ≤ T₂ and T₂ ≤ T₁, i.e., if there is a homeomorphism of …