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Articles 6301 - 6330 of 7948

Full-Text Articles in Applied Mathematics

Automorphic Decompositions Of Graphs, Robert Beeler Aug 2007

Automorphic Decompositions Of Graphs, Robert Beeler

All Dissertations

Let G and H be graphs. A G-decomposition D of a graph H is a partition of the edge set of H such that the subgraph induced by the edges in each part of the partition is isomorphic to G. It is well known that a graceful labelling (or more generally a rho-valuation) of a graph G induces a cyclic G-decomposition of a complete graph. We will extend these notions to that of a general valuation in a cyclic group. Such valuations yield decompositions of circulant graphs. We will show that every graph has a valuation and hence is a …

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The Barycenter Of The Numerical Range Of A Matrix, Sean A. Broughton, Roger G. Lautzenheiser, Thomas Werne Aug 2007

The Barycenter Of The Numerical Range Of A Matrix, Sean A. Broughton, Roger G. Lautzenheiser, Thomas Werne

Mathematical Sciences Technical Reports (MSTR)

The numerical range W(A) of an nxn matrix A is the totality of the scalar products <Ax,x> as x varies over all unit vectors in Cn The barycenter (center of mass) of the numerical range is defined geometrically as the center of mass of W(A) considered as a planar lamina with variable density and also as a limit of sample averages (<Ax1,x1>+...+<AxN,xN>)/N. Under a wide range the sampling schemes it is shown that the barycenter is the average of the spectrum …

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Estimates Related To The Arithmetic Of Elliptic Curves, Bryan Faulkner Aug 2007

Estimates Related To The Arithmetic Of Elliptic Curves, Bryan Faulkner

All Dissertations

This dissertation presents results related to two problems in the arithmetic of elliptic curves.
Feng and Xiong equate the nontriviality of the Selmer groups associated with congruent number curves to the presence of certain types of partitions of graphs associated with the prime factorization of n. The triviality of the Selmer groups associated to the congruent number curve implies that the curve has rank zero which in turn implies n is noncongruent. We extend the ideas of Feng and Xiong in order to compute the Selmer groups of congruent number curves.
We prove an average version of a generalization of …

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Permutation Decoding Of Codes From Graphs And Designs, Padmapani Seneviratne Aug 2007

Permutation Decoding Of Codes From Graphs And Designs, Padmapani Seneviratne

All Dissertations

Permutation decoding is a technique, developed by Jessie McWilliams in 1960's. It involves finding a set of automorphisms of the code, called a PD-set. If such a set exists and if the generator matrix of the code is in standard form then a simple algorithm using this set can be followed to correct the maximum number of errors of which the code is capable. Primarily this method was used originally on cyclic codes and Golay codes.
In this dissertation we study binary codes formed from an adjacency matrix of some classes of graphs and apply the permutation decoding method to …

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Planning, Scheduling, And Timetabling In A University Setting, Christine Kraft Aug 2007

Planning, Scheduling, And Timetabling In A University Setting, Christine Kraft

All Dissertations

Methods and procedures for modeling university student populations, predicting course enrollment, allocating course seats, and timetabling final examinations are studied and proposed. The university enrollment model presented uses a multi-dimensional state space based on student demographics and the Markov property, rather than longitudinal data to model student movement. The procedure for creating adaptive course prediction models uses student characteristics to identify groups of undergraduates whose specific course enrollment rates are significantly different than the rest of the university population. Historical enrollment rates and current semester information complete the model for predicting enrollment for the coming semester. The course prediction model …

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Numerical Approximation Of Shear-Thinning And Johnson-Segalman Viscoelastic Fluid Flows, Jason Howell Aug 2007

Numerical Approximation Of Shear-Thinning And Johnson-Segalman Viscoelastic Fluid Flows, Jason Howell

All Dissertations

In this work computational approaches to the numerical simulation of steady-state viscoelastic fluid flow are investigated. In particular, two aspects of computing viscoelastic flows are of interest: 1) the stable computation of high Weissenberg number Johnson-Segalman fluids and 2) low-order approaches to simulating the flow of fluids obeying a power law constitutive model.
The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge. For the nonlinear Johnson-Segalman constitutive model, defect-correction and continuation methods are examined …

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Optimization And Feedback Design Of State-Constrained Parabolic Systems, Boris S. Mordukhovich Aug 2007

Optimization And Feedback Design Of State-Constrained Parabolic Systems, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to optimal control and feedback design of stateconstrained parabolic systems in uncertainty conditions. Problems of this type are among the most challenging and difficult in dynamic optimization for any kind of dynamical systems. We pay the main attention to considering linear multidimensional parabolic'systems with Dirichlet boundary controls and pointwise state constraints, while the methods developed in this study are applicable to other kinds of boundary controls and dynamical systems of the parabolic type. The feedback design problem is formulated in the minimax sense to ensure stabilization of transients within the prescribed diapason and robust stability of …

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On Backward Stochastic Evolution Equations In Hilbert Space And Optimal Control, Nazim I. Mahmudov, Mark A. Mckibben Aug 2007

On Backward Stochastic Evolution Equations In Hilbert Space And Optimal Control, Nazim I. Mahmudov, Mark A. Mckibben

Mathematics Faculty Publications

In this paper a new result on the existence and uniqueness of the adapted solution to a backward stochastic evolution equation in Hilbert spaces under non Lipschitz condition is established. The applicability of this result is then illustrated in a discussion of some concrete backward stochastic partial differential equation. Furthermore, stochastic maximum principle for optimal control problems of stochastic systems governed by backward stochastic evolution equations in Hilbert spaces is obtained.

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Decompositions Of Signed-Graphic Matroids, Dan Slilaty, Hongxun Qin Aug 2007

Decompositions Of Signed-Graphic Matroids, Dan Slilaty, Hongxun Qin

Mathematics and Statistics Faculty Publications

We give a decomposition theorem for signed graphs whose frame matroids are binary and a decomposition theorem for signed graphs whose frame matroids are quaternary.

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Greedy Signal Recovery And Uncertainty Principles, Deanna Needell, Roman Vershynin Jul 2007

Greedy Signal Recovery And Uncertainty Principles, Deanna Needell, Roman Vershynin

CMC Faculty Publications and Research

This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of the Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of the L1-minimization. Our algorithm ROMP reconstructs a sparse signal in a number of iterations linear in the sparsity, and the reconstruction is exact provided the linear measurements satisfy the Uniform Uncertainty Principle. In the case of inaccurate measurements and approximately sparse …

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Transmission Dynamics Of Avian Influenza Among Poultry With And Without Vaccination, Qiao Liang Jul 2007

Transmission Dynamics Of Avian Influenza Among Poultry With And Without Vaccination, Qiao Liang

Mathematics & Statistics ETDs

The continuing avian influenza (AI) out break that began in late 2003 and early 2004 has been disastrous for the poultry industry worldwide. It has resulted in severe socio-economic damage, and it has raised serious concerns for general public health. In this research, we use mathematics to analyze transmission dynamics of AI among poultry. We use a status-based approach to construct systems of differential equations to describe virus transmission dynamics. We develop theoretical means to eradicate the spread of the disease, and we calculate the size of healthy and infected populations during an AI outbreak, and the final population size …

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Survival Analysis With Large Dimensional Covariates: An Application In Microarray Studies, David A. Engler, Yi Li Jul 2007

Survival Analysis With Large Dimensional Covariates: An Application In Microarray Studies, David A. Engler, Yi Li

Harvard University Biostatistics Working Paper Series

Use of microarray technology often leads to high-dimensional and low- sample size data settings. Over the past several years, a variety of novel approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptation of the elastic net approach is presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time …

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As Flat As Possible, Jon T. Jacobsen Jul 2007

As Flat As Possible, Jon T. Jacobsen

All HMC Faculty Publications and Research

How does one determine a surface which is as flat as possible, such as those created by soap film surfaces? What does it mean to be as flat as possible? In this paper we address this question from two distinct points of view, one local and one global in nature. Continuing with this theme, we put a temporal twist on the question and ask how to evolve a surface so as to flatten it as efficiently as possible. This elementary discussion provides a platform to introduce a wide range of advanced topics in partial differential equations and helps students …

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Suboptimality Conditions For Mathematical Programs With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich Jul 2007

Suboptimality Conditions For Mathematical Programs With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study mathematical programs with equilibrium constraints (MPECs) described by generalized equations in the extended form 0 is an element of the set G(x,y) + Q(x,y), where both mappings G and Q are set-valued. Such models arise, in particular, from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish new weak and strong suboptimality conditions for the general MPEC problems under consideration in finite-dimensional and infinite-dimensional spaces that do not assume the existence of optimal solutions. This issue is particularly important for infinite-dimensional optimization problems, where the existence of optimal …

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Preliminary Estimates Of Building Cost And The Lowest Evaluated Tender, Harriet Eliufoo Jun 2007

Preliminary Estimates Of Building Cost And The Lowest Evaluated Tender, Harriet Eliufoo

Tanzania Journal of Engineering and Technology (TJET)

The paper has investigated and established to what extent are preliminary estimates of building costs close to the lowest evaluated tender and how geographical proximity influences the variance between preliminary estimate and the lowest evaluated tender. A multiple case study constituting 43 building projects in Tanzania were statistically analysed covering a period from 1995- 1999. Findings reveal a significant variance exists between the quantity surveyor’s preliminary estimate figure and the lowest evaluated tender; and that the variance between the quantity surveyor’s figure and the bidder is small when the proposed building project is geographically closer to the quantity surveyor’s base. …

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Simultaneous Confidence Intervals Based On The Percentile Bootstrap Approach, Micha Mandel, Rebecca A. Betensky Jun 2007

Simultaneous Confidence Intervals Based On The Percentile Bootstrap Approach, Micha Mandel, Rebecca A. Betensky

Harvard University Biostatistics Working Paper Series

No abstract provided.

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Distributed Reproducible Research Using Cached Computations, Roger Peng, Sandrah P. Eckel Jun 2007

Distributed Reproducible Research Using Cached Computations, Roger Peng, Sandrah P. Eckel

Johns Hopkins University, Dept. of Biostatistics Working Papers

The ability to make scientific findings reproducible is increasingly important in areas where substantive results are the product of complex statistical computations. Reproducibility can allow others to verify the published findings and conduct alternate analyses of the same data. A question that arises naturally is how can one conduct and distribute reproducible research? This question is relevant from the point of view of both the authors who want to make their research reproducible and readers who want to reproduce relevant findings reported in the scientific literature. We present a framework in which reproducible research can be conducted and distributed via …

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Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg Jun 2007

Nonlinear Dynamics In Combinatorial Games: Renormalizing Chomp, Eric J. Friedman, Adam S. Landsberg

WM Keck Science Faculty Papers

We develop a new approach to combinatorial games that reveals connections between such games and some of the central ideas of nonlinear dynamics: scaling behaviors, complex dynamics and chaos, universality, and aggregation processes. We take as our model system the combinatorial game Chomp, which is one of the simplest in a class of "unsolved" combinatorial games that includes Chess, Checkers, and Go. We discover that the game possesses an underlying geometric structure that "grows" (reminiscent of crystal growth), and show how this growth can be analyzed using a renormalization procedure adapted from physics. In effect, this methodology allows one to …

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Numerical Simulation Of Waves And Fronts In Inhomogeneous Solids, A. Berezovski, M. Berezovski, J. Engelbrecht, G. A. Maugin Jun 2007

Numerical Simulation Of Waves And Fronts In Inhomogeneous Solids, A. Berezovski, M. Berezovski, J. Engelbrecht, G. A. Maugin

Publications

Dynamic response of inhomogeneous materials exhibits new effects, which often do not exist in homogeneous media. It is quite natural that most of studies of wave and front propagation in inhomogeneous materials are associated with numerical simulations. To develop a numerical algorithm and to perform the numerical simulations of moving fronts we need to formulate a kinetic law of progress relating the driving force and the velocity of the discontinuity. The velocity of discontinuity is determined by means of the non-equilibrium jump relations at the front. The obtained numerical method generalizes the wave-propagation algorithm to the case of moving discontinuities …

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Teach A Course In The Math Of Voting And Choice, Karl-Dieter Crisman Jun 2007

Teach A Course In The Math Of Voting And Choice, Karl-Dieter Crisman

ACMS Conference Proceedings 2007

Many mathematics instructors at the college level are looking for a curricular option that has the potential to serve a number of different constituencies. It could be to encourage more students to take math courses, or to give worthwhile options to students who need to take math but who are not ready for calculus (or its sequence). On the other hand, one may wish to add a new course for majors outside of the typical offerings, or even to prepare students for undergraduate research. The mathematics of voting and choice is ideally suited to meet all these needs in the …

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Bach (To The Calculus Of) Variations, Charles R. Hampton Jun 2007

Bach (To The Calculus Of) Variations, Charles R. Hampton

ACMS Conference Proceedings 2007

While it is quite common for professionals (doctors, lawyers, academics, etc) to be talented in many ways, including musical talent, there is a special connection between music and mathematics. Musicians collectively are not more talented in mathematics than other professionals and other academics. This paper examines the connections between math and music, particularly calculus and the music of Johann Sebastian Bach.

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Chaos Theory And Metaphysical (In) Determinism, Tim Rogalsky Jun 2007

Chaos Theory And Metaphysical (In) Determinism, Tim Rogalsky

ACMS Conference Proceedings 2007

This paper will begin by introducing the issues that arise from chaos theory for the Christian mathematician and scientist: What is at stake in this debate? It will then briefly review chaos theory, by means of two examples. It will then introduce the metaphysical interpretations given to chaos theory by three different scientist-theologians. The paper will conclude with a brief introduction to open theists, and analyze their use of chaos theory to supper their theological claims.

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Trigonometry Without Sines And Geometry Without Angles, Phillip Lestmann Jun 2007

Trigonometry Without Sines And Geometry Without Angles, Phillip Lestmann

ACMS Conference Proceedings 2007

In his book, Divine Proportions, N. J. Wildberger advocates for a "rational" trigonometry by substituting the squares of the common trigonometric ratios for those ratios themselves. This presentation examines and critiques the claims of the book by evaluating its presented methods.

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Portrayls Of Mathematics In Culture, Jeremy Case Jun 2007

Portrayls Of Mathematics In Culture, Jeremy Case

ACMS Conference Proceedings 2007

This paper looks at various portrays of mathematicians in culture, and how that can influence perceptions of mathematics.

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Integrating Moral And Spiritual Themes In Middle School And High School Mathematics Teaching Units, Dave Klanderman, Sean Bird Jun 2007

Integrating Moral And Spiritual Themes In Middle School And High School Mathematics Teaching Units, Dave Klanderman, Sean Bird

ACMS Conference Proceedings 2007

In 2006, the Kuyers Institute published a total of nine math lessons for the middle school and high school which incorporate a Christian perspective. This paper examines the impact of teaching all of these lessons at a the high school level as well as selected lessons at the college level with preservice elementary and secondary mathematics teachers.

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An Augustinian Perspective On The Philosophy Of Mathematics, James Bradley Jun 2007

An Augustinian Perspective On The Philosophy Of Mathematics, James Bradley

ACMS Conference Proceedings 2007

Enlightenment thinkers saw the universe as mechanistic and mathematics as the language in which the universe is written. They viewed mathematics as eternal, as transcending human minds, and as comprehensible by human beings. Thus mathematics, from their perspective, is our best tool for understanding the secrets of nature. This outlook was nicely summarized by Morris Kline: (Kline, 1953) In brief the whole world is the totality of mathematically expressible motions of objects in space and time, and the entire universe is a great, harmonious, and mathematically designed machine. From a Christian perspective, however, the Enlightenment outlook is flawed. It privileges …

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Rules And Insights: Connecting The Mathematical And Linguistic Abilities Of C.S. Lewis, Kim Jongerius Jun 2007

Rules And Insights: Connecting The Mathematical And Linguistic Abilities Of C.S. Lewis, Kim Jongerius

ACMS Conference Proceedings 2007

While most biographical works on C.S. Lewis give passing reference to Lewis' problems with elementary mathematics, few have made an attempt at diagnosing the difficulty or exploring its impact on his writing. A careful study of family correspondence, however, makes it clear that his learning difficulties were not with mathematics alone and suggests connections between attitudes toward and abilities in both mathematics and language. This paper will make these connections clear and will illustrate their ties to Lewis' effective mathematical references.

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Global Stability Results Of An Sis Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma Jun 2007

Global Stability Results Of An Sis Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SIS age-structured epidemic model for a vertically as well as horizontally transmitted disease is investigated when the fertility, mortality and cure rates depend on age and the force of infection of proportionate mixing assumption type. We determine the steady states and prove the global stability for the endemic equilibriums.

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Counting Tulips: Three Combinatorial Proofs, Eric Gossett Jun 2007

Counting Tulips: Three Combinatorial Proofs, Eric Gossett

ACMS Conference Proceedings 2007

A gardener has r ≥ 1 red tulips and b ≥ 1 blue tulips, each in its own pot. She plans to plant them in a line along the edge of her driveway. In how many visually distinguishable ways can she arrange them?

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Tanzania, Mathematics, And Me: Reflections From My Work With Tanzanian Teachers, Mandi Maxwell Jun 2007

Tanzania, Mathematics, And Me: Reflections From My Work With Tanzanian Teachers, Mandi Maxwell

ACMS Conference Proceedings 2007

In June 2006 I had the privilege of participating in a four-day teacher training workshop in Mumba, Tanzania. In this paper I will discuss the challenges and triumphs of working with Tanzanian Secondary Mathematics teachers. We will discuss the educational environment, teaching strategies, and curricular issues that affect mathematics teachers in rural areas of Tanzania and contrast that with the American educational experience. We will also discuss some of the goals of the Teacher Training workshop that my colleagues and I led and look at some of the specific mathematical ideas and applications that I shared with the Mathematics teachers …

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