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2006

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Articles 151 - 180 of 413

Full-Text Articles in Mathematics

New Developments Of The Deformation Method, Jie Liu Apr 2006

New Developments Of The Deformation Method, Jie Liu

Mathematics Dissertations - Archive

New developments of deformation method for grid generation are presented in this work. Theorems for three different cases and different methods for implementing deformation method are presented. One of the new developments is a 3D multi-block moving grid method. In this version, a Poisson equation is solved by finite difference method to get the vector field for moving grid. Special treatment applies to the common boundary of different blocks. Another new development is a numerical method for reconstructing a given differentiable transformations by solving a system of div-curl equation directly formed from each point of the graph. The determinacy and …

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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Not Out Of The Blue: Historical Roots Of Mathematics Education In Italy, Fulvia Furinghetti Feb 2006

Not Out Of The Blue: Historical Roots Of Mathematics Education In Italy, Fulvia Furinghetti

The Mathematics Enthusiast

In this note I outline some elements of the history of mathematics education in Italy. Initially the chief characters were mathematicians who played a role in designing curricula and in editing textbooks. The development of the Italian community of mathematics educators towards the present day trend in research was fostered by participation in international activities after the Second World War. I also identify some elements of continuity with the past to stress the influence of some mathematicians in the development of present research.

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Tme Volume 3, Number 1 Feb 2006

Tme Volume 3, Number 1

The Mathematics Enthusiast

No abstract provided.

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Periodic Prime Knots And Toplogically Transitive Flows On 3-Manifolds, William Basener, Michael C. Sullivan Feb 2006

Periodic Prime Knots And Toplogically Transitive Flows On 3-Manifolds, William Basener, Michael C. Sullivan

Articles and Preprints

Suppose that φ is a nonsingular (fixed point free) C1 flow on a smooth closed 3-dimensional manifold M with H2(M)=0. Suppose that φ has a dense orbit. We show that there exists an open dense set N ⊆ M such that any knotted periodic orbit which intersects N is a nontrivial prime knot.

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A C-Symplectic Free S1-Manifold With Contractible Orbits And Cat = 1/2 Dim, Christopher Allday, John Oprea Feb 2006

A C-Symplectic Free S1-Manifold With Contractible Orbits And Cat = 1/2 Dim, Christopher Allday, John Oprea

Mathematics and Statistics Faculty Publications

An interesting question in symplectic geometry concerns whether or not a closed symplectic manifold can have a free symplectic circle action with orbits contractible in the manifold. Here we present a c-symplectic example, thus showing that the problem is truly geometric as opposed to topological. Furthermore, we see that our example is the only known example of a c-symplectic manifold having non-trivial fundamental group and Lusternik-Schnirelmann category precisely half its dimension.

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