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2006

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Articles 151 - 180 of 414

Full-Text Articles in Mathematics

Homogeneous Products Of Conjugacy Classes, Edith Adan-Bante Apr 2006

Homogeneous Products Of Conjugacy Classes, Edith Adan-Bante

Faculty Publications

Let G be a finite group and a ∈G. Let a G ={g −1 a g | g ∈ G} be the conjugacy class of a in G. Assume that a G and b G are conjugacy classes of G with the property that C G (a)=C G (b). Then a G b G is a conjugacy class if and only if [a,G]=[b,G]=[ab,G] and [ab,G] is a normal subgroup of G.

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A Numerical Method For Obtaining An Optimal Temperature Distribution In A Three-Dimensional Triple-Layered Skin Structure Embedded With Multi-Level Blood Vessels, Xingui Tang Apr 2006

A Numerical Method For Obtaining An Optimal Temperature Distribution In A Three-Dimensional Triple-Layered Skin Structure Embedded With Multi-Level Blood Vessels, Xingui Tang

Doctoral Dissertations

The research related to hyperthermia has stimulated a lot of interest in recent years because of its application in cancer treatment. When heating the tumor tissue, the crucial problem is keeping the temperature of the surrounding normal tissue below a certain threshold in order to avoid the damage to the normal tissue. Hence, it is important to obtain the temperature field of the entire region during the treatment. The objective of this dissertation is to develop a numerical method for obtaining an optimal temperature distribution in a 3D triple-layered skin structure embedded with multi-level blood vessels where the surface of …

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An Implicit Level Set Model For Firespread, Pallop Huabsomboon Apr 2006

An Implicit Level Set Model For Firespread, Pallop Huabsomboon

Mathematics & Statistics Theses & Dissertations

The level set method is a mathematical and computational, technique for tracking a moving interface over time. It can naturally handle topological changes such as merging or breaking interfaces. Intrinsic geometric properties of the interface, such as curvature and normal direction, are easily determined from the level set function &phis;. There are many applications of the level set method, including kinetic crystal growth, epitaxial growth of thin films, image restoration, vortex dominated flows, and so forth. Most applications described in the growing literature on the applications of level sets advance the level set equation with explicit time integration. Hence, small …

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Correction To "Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering", Baha-Eldin Khaledi, Subhash C. Kochar Apr 2006

Correction To "Dependence, Dispersiveness, And Multivariate Hazard Rate Ordering", Baha-Eldin Khaledi, Subhash C. Kochar

Mathematics and Statistics Faculty Publications and Presentations

In the article published last year, three inequalities should be in the opposite direction.

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Forecasting Police Calls During Peak Times For The City Of Cleveland, John P. Holcomb, Norean Radke Sharpe Apr 2006

Forecasting Police Calls During Peak Times For The City Of Cleveland, John P. Holcomb, Norean Radke Sharpe

Mathematics and Statistics Faculty Publications

For a period of time, professors from the Cleveland State University worked closely with the City of Cleveland Police Department. This partnership resulted in access to police records cataloging all emergency 911 calls for the city since 1995. Here, we describe forecasting approaches that can be used by the Police Department based on hourly 911 calls in the years 2001 to 2003 throughout the city during peak call time: the third shift during summer months. This case study is appropriate for class discussions in advanced courses in statistics to explore the application of time series analysis techniques.

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Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods For Elliptic Inverse Problems, Widodo Samyono Apr 2006

Hessian Matrix-Free Lagrange-Newton-Krylov-Schur-Schwarz Methods For Elliptic Inverse Problems, Widodo Samyono

Mathematics & Statistics Theses & Dissertations

This study focuses on the solution of inverse problems for elliptic systems. The inverse problem is constructed as a PDE-constrained optimization, where the cost function is the L2 norm of the difference between the measured data and the predicted state variable, and the constraint is an elliptic PDE. Particular examples of the system considered in this stud, are groundwater flow and radiation transport. The inverse problems are typically ill-posed due to error in measurements of the data. Regularization methods are employed to partially alleviate this problem. The PDE-constrained optimization is formulated as the minimization of a Lagrangian functional, formed …

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A Beautiful Mind, Christopher D. Goff Apr 2006

A Beautiful Mind, Christopher D. Goff

College of the Pacific Faculty Presentations

No abstract provided.

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Nilpotent Orbits On Infinitesimal Symmetric Spaces, Joseph A. Fox Apr 2006

Nilpotent Orbits On Infinitesimal Symmetric Spaces, Joseph A. Fox

Dissertations

Let G be a reductive linear algebraic group defined over an algebraically closed field k whose characteristic is good for G. Let [straight theta] be an involution defined on G, and let K be the subgroup of G consisting of elements fixed by [straight theta]. The differential of [straight theta], also denoted [straight theta], is an involution of the Lie algebra [Special characters omitted.] = Lie (G ), and it decomposes [Special characters omitted.] into +1- and -1-eigenspaces, [Special characters omitted.] and [Special characters omitted.] , respectively. The space [Special characters omitted.] identifies with the tangent space at the …

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Testing Procedures For Group Sequential Clinical Trials With Multiple Survival Endpoints, Rebecca C. Scherzer Apr 2006

Testing Procedures For Group Sequential Clinical Trials With Multiple Survival Endpoints, Rebecca C. Scherzer

Dissertations

This research gives methods for sequential monitoring of survival data in clinical trials with multiple endpoints. We illustrate the use of marginal proportional hazards models and other survival models with various group sequential methods to test multiple survival endpoints at K interim analyses. To adjust for multiplicity at each interim analysis, we consider and extend methods developed by Tang and Geller (1999), Follmann, et al. (1994), and others. These methods are motivated, compared, and evaluated using survival data from a clinical study and using simulation studies.

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Secondary Terms In The Number Of Vanishings Of Quadratic Twists Of Elliptic Curve L-Functions, J. Brian Conrey, Atul Pocharel, Michael O. Rubinstein, Mark Watkins Mar 2006

Secondary Terms In The Number Of Vanishings Of Quadratic Twists Of Elliptic Curve L-Functions, J. Brian Conrey, Atul Pocharel, Michael O. Rubinstein, Mark Watkins

Mathematics - All Scholarship

We examine the number of vanishings of quadratic twists of the L-function associated to an elliptic curve. Applying a conjecture for the full asymptotics of the moments of critical L-values we obtain a conjecture for the first two terms in the ratio of the number of vanishings of twists sorted according to arithmetic progressions.

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Asymptotic Stability Of A Fluid-Structure Semigroup, George Avalos Mar 2006

Asymptotic Stability Of A Fluid-Structure Semigroup, George Avalos

Department of Mathematics: Faculty Publications

The strong stability problem for a fluid-structure interactive partial differential equation (PDE) is considered. The PDE comprises a coupling of the linearized Stokes equations to the classical system of elasticity, with the coupling occurring on the boundary interface between the fluid and solid media. It is now known that this PDE may be modeled by a $C_{0}$-semigroup of contractions on an appropriate Hilbert space. However, because of the nature of the unbounded coupling between fluid and structure, the resolvent of the semigroup generator will \emph{not} be a compact operator. In consequence, the classical solution to the stability problem, by means …

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Matrices And The Game Of Chutes And Ladders, Katherine Jedlicka Mar 2006

Matrices And The Game Of Chutes And Ladders, Katherine Jedlicka

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

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Influence Of Surface Tension On The Conical Miniscus Of A Magnetic Fluid In The Field Of A Current-Carrying Wire, Thomas John, Dirk Rannacher, Adreas Engel Mar 2006

Influence Of Surface Tension On The Conical Miniscus Of A Magnetic Fluid In The Field Of A Current-Carrying Wire, Thomas John, Dirk Rannacher, Adreas Engel

Mathematics - All Scholarship

We study the influence of surface tension on the shape of the conical miniscus built up by a magnetic fluid surrounding a current-carrying wire. Minimization of the total energy of the system leads to a singular second order boundary value problem for the function zeta(r) describing the axially symmetric shape of the free surface. An appropriate transformation regularizes the problem and allows a straightforward numerical solution. We also study the effects a superimposed second liquid, a nonlinear magnetization law of the magnetic fluid, and the influence of the diameter of the wire on the free surface profile.

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The Local Gromov–Witten Invariants Of Configurations Of Rational Curves, Dagan Karp, Chiu-Chu Melissa Liu, Marcos Mariño Mar 2006

The Local Gromov–Witten Invariants Of Configurations Of Rational Curves, Dagan Karp, Chiu-Chu Melissa Liu, Marcos Mariño

All HMC Faculty Publications and Research

We compute the local Gromov–Witten invariants of certain configurations of rational curves in a Calabi–Yau threefold. These configurations are connected subcurves of the “minimal trivalent configuration”, which is a particular tree of ℙ1’s with specified formal neighborhood. We show that these local invariants are equal to certain global or ordinary Gromov–Witten invariants of a blowup of ℙ3 at points, and we compute these ordinary invariants using the geometry of the Cremona transform. We also realize the configurations in question as formal toric schemes and compute their formal Gromov–Witten invariants using the mathematical and physical theories of the …

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Reflection Of A Wave Off A Surface, Brendan Guilfoyle, Wilhelm Klingenberg Mar 2006

Reflection Of A Wave Off A Surface, Brendan Guilfoyle, Wilhelm Klingenberg

Preprints

Recent advances in twistor theory are applied to geometric optics in R 3 . The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the reflecting surface is a plane, when the incoming wave is a plane and when the incoming wave is spherical. In each case particular examples are computed exactly and the results plotted to illustrate the outgoing wavefront.

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Optimization And Equilibrium Problems With Equilibrium Constraints In Infinite-Dimensional Spaces, Boris S. Mordukhovich Mar 2006

Optimization And Equilibrium Problems With Equilibrium Constraints In Infinite-Dimensional Spaces, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern variational f).nalysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as MPECs (mathematical programs with equilibrium constraints) and EPECs (equilibrium problems with equilibrium constraints) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The …

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What Happened When A Mathematician Found Himself Funded By The National Endowment For The Humanities, Joel K. Haack Mar 2006

What Happened When A Mathematician Found Himself Funded By The National Endowment For The Humanities, Joel K. Haack

UNIversitas: Journal of Research, Scholarship, and Creative Activity

Exploring the relationships between mathematics and the humanities can be stimulating for both faculty and students. That there are connections should surprise no one in interdisciplinary studies, but finding them might prove to be more difficult; humanists and mathematicians have not been involved in extensive dialogue in recent years. This study provides a field guide to the kinds of connections that one might find with examples of each.

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Asynchronous Random Boolean Network Model With Variable Number Of Parents Based On Elementary Cellular Automata Rule 126, Mihaela Teodora Matache Mar 2006

Asynchronous Random Boolean Network Model With Variable Number Of Parents Based On Elementary Cellular Automata Rule 126, Mihaela Teodora Matache

Mathematics Faculty Publications

A Boolean network with N nodes, each node’s state at time t being determined by a certain number of parent nodes, which can vary from one node to another is considered. This is a generalization of previous results obtained for a constant number of parent nodes, by Matache and Heidel in Asynchronous random Boolean network model based on elementary cellular automata rule 126, Phys. Rev. E 71, 026232, 2005. The nodes, with randomly assigned neighborhoods, are updated based on various asynchronous schemes. The Boolean rule is a generalization of rule 126 of elementary cellular automata, and is assumed to be …

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A General Theory Of Almost Convex Functions, S J. Dilworth, Ralph Howard, James W. Roberts Mar 2006

A General Theory Of Almost Convex Functions, S J. Dilworth, Ralph Howard, James W. Roberts

Faculty Publications

No abstract provided.

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Application Of Fuzzy State Aggregation And Policy Hill Climbing To Multi-Agent Systems In Stochastic Environments, Dean C. Wardell Mar 2006

Application Of Fuzzy State Aggregation And Policy Hill Climbing To Multi-Agent Systems In Stochastic Environments, Dean C. Wardell

Theses and Dissertations

Reinforcement learning is one of the more attractive machine learning technologies, due to its unsupervised learning structure and ability to continually even as the operating environment changes. Applying this learning to multiple cooperative software agents (a multi-agent system) not only allows each individual agent to learn from its own experience, but also opens up the opportunity for the individual agents to learn from the other agents in the system, thus accelerating the rate of learning. This research presents the novel use of fuzzy state aggregation, as the means of function approximation, combined with the policy hill climbing methods of Win …

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Some New Methodologies For Pattern Recognition Aided By Self-Organizing Maps., Arijit Laha Dr. Feb 2006

Some New Methodologies For Pattern Recognition Aided By Self-Organizing Maps., Arijit Laha Dr.

Doctoral Theses

In this thesis we develop several techniques for performing different pattern recognition tasks. In particular, the pattern recognition tasks considered here are classification and vector quantization. We propose several methods for designing classifiers and address various issues involved in the task. For vector quantization, we develop a method for image compression with superior psychovisual reproduction quality. We also propose a method for fast codebook search in a vector quantizer. We exploit different properties of Self-organizing Map (SOM) network for developing these methods. Along with SOM, we also use fuzzy sets theory and Dempster-Shafer theory of evidence to design classi- fiers …

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Studies On Pairing-Based And Constant Round Dynamic Group Key Agreement., Ratna Dutta Dr. Feb 2006

Studies On Pairing-Based And Constant Round Dynamic Group Key Agreement., Ratna Dutta Dr.

Doctoral Theses

This thesis describes research that I conducted during the course of my Ph.D. study at Indian Statistical Institute (ISI), Kolkata. I hope that this work is of use and will be carried on.I would like to begin by thanking my supervisor, Prof. Rana Barua for his support and endless patience. He has provided me background in Cryptography, Combinatorics and Theory of Automata during the period 2000-2002 of my course work of M.Tech in Computer Science at Indian Statistical Institute. I really appreciate his extraordinary patience in reading my numerous inferior drafts, for listening and analyzing all my ideas, forcing me …

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Quantum Stochastic Dilation Of A Class Of Quantum Dynamical Semigroups And Quantum Random Walks., Lingaraj Sahu Dr. Feb 2006

Quantum Stochastic Dilation Of A Class Of Quantum Dynamical Semigroups And Quantum Random Walks., Lingaraj Sahu Dr.

Doctoral Theses

No abstract provided.

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Duan's Fixed Point Theorem: Proof And Generalization, Martin Arkowitz Feb 2006

Duan's Fixed Point Theorem: Proof And Generalization, Martin Arkowitz

Dartmouth Scholarship

Let X be an H-space of the homotopy type of a connected, finite CW-complex, f : X→X any map and pk : X→X the kth power map. Duan proved that pkf : X → X has a fixed point if k ≥ 2. We give a new, short and elementary proof of this. We then use rational homotopy to generalize to spaces X whose rational cohomology is the tensor product of an exterior algebra on odd dimensional generators with the tensor product of truncated polynomial algebras on even dimensional generators. The role of the power map …

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The Linear Complexity Of A Graph, David L. Neel, Michael E. Orrison Jr. Feb 2006

The Linear Complexity Of A Graph, David L. Neel, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

The linear complexity of a matrix is a measure of the number of additions, subtractions, and scalar multiplications required to multiply that matrix and an arbitrary vector. In this paper, we define the linear complexity of a graph to be the linear complexity of any one of its associated adjacency matrices. We then compute or give upper bounds for the linear complexity of several classes of graphs.

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On Hamilton’S Characteristic Functions For Reflection, Brendan Guilfoyle, Wilhelm Klingenberg Feb 2006

On Hamilton’S Characteristic Functions For Reflection, Brendan Guilfoyle, Wilhelm Klingenberg

Publications

We review the complex differential geometry of the space of oriented affine lines in R3 and give a description of Hamilton’s characteristic functions for reflection in an oriented C1 surface in terms of this geometry.

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Building Blocks Problem Related To Harmonic Series, Yutaka Nishiyama Feb 2006

Building Blocks Problem Related To Harmonic Series, Yutaka Nishiyama

The Mathematics Enthusiast

In this discussion I give an explanation of the divergence and convergence of infinite series through the building blocks problem and at the same time I touch on the fact that mathematics is not just about manipulating complicated numerical formulas but also a field in which logical ways of thought are learnt. I emphasize that in order to overcome the aversion of university students to mathematics, teachers must pour their energies into developing study materials taken from topics relevant to the students.

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Automated Geometric Theorem Proving: Wu's Method, Joran Elias Feb 2006

Automated Geometric Theorem Proving: Wu's Method, Joran Elias

The Mathematics Enthusiast

Wu’s Method for proving geometric theorems is well known. We investigate the underlying algorithms involved, including the concepts of pseudodivision, Ritt’s Principle and Ritt’s Decomposition algorithm. A simple implementation for these algorithms in Maple is presented, which we then use to prove a few simple geometric theorems to illustrate the method.

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Problems To Discover And To Boost Mathematical Talent In Early Grades: A Challenging Situations Approach, Viktor Freiman Feb 2006

Problems To Discover And To Boost Mathematical Talent In Early Grades: A Challenging Situations Approach, Viktor Freiman

The Mathematics Enthusiast

Several studies of mathematical giftedness conducted in the past two decades reveal the importance of creation of learning and teaching environment favourable to the identification and nurturing mathematically talented students. Based on psychological, methodological and didactical models created by Krutetskii (1976), Shchedrovtiskii (1968), Brousseau (1997) and Sierpinska (1994), we have developed our challenging situation approach. During 7 years of field study in the elementary K-6 classroom, we collected sufficient amount of data that demonstrate how these challenging situations help to discover and to boost mathematical talent in very young children keeping and increasing their interest towards more advanced mathematics curriculum. …

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Mathematically Promising Students From The Space Age To The Information Age, Linda Jensen Sheffield Feb 2006

Mathematically Promising Students From The Space Age To The Information Age, Linda Jensen Sheffield

The Mathematics Enthusiast

On October 4, 1957, with the launch of Sputnik 1 by the Soviet Union, the world entered the Space Age and the United States became quite concerned that the Soviet Union had a head start in the space race. A year later, realizing that the support of gifted and talented mathematics and science students was critical to national security, the United States federal government passed the National Defense Education Act (NDEA), providing aid to education in the United States at all levels, primarily to stimulate the advancement of education in science, mathematics, and modern foreign languages. Also, during this time, …

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