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2007

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Articles 31 - 60 of 591

Full-Text Articles in Mathematics

Schrödinger Type Equation Associated With The Lévy And Volterra Laplacians, Kazuyoshi Sakabe Dec 2007

Schrödinger Type Equation Associated With The Lévy And Volterra Laplacians, Kazuyoshi Sakabe

Communications on Stochastic Analysis

No abstract provided.

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Coplanar Constant Mean Curvature Surfaces, Karsten Grosse-Brauckmann, Robert Kusner, John M. Sullivan Dec 2007

Coplanar Constant Mean Curvature Surfaces, Karsten Grosse-Brauckmann, Robert Kusner, John M. Sullivan

Robert Kusner

We consider constant mean curvature surfaces with finite topology, properly embedded in three-space in the sense of Alexandrov. Such surfaces with three ends and genus zero were constructed and completely classified by the authors. Here we extend the arguments to the case of an arbitrary number of ends, under the assumption that the asymptotic axes of the ends lie in a common plane: we construct and classify the entire family of these genus-zero, coplanar constant mean curvature surfaces.

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On The Asymptotic Stability Of Linear Volterra Difference Equations Of Convolution Type, Saber Elaydi, E Messina, A Vecchio Dec 2007

On The Asymptotic Stability Of Linear Volterra Difference Equations Of Convolution Type, Saber Elaydi, E Messina, A Vecchio

Mathematics Faculty Research

We show that the condition |a| + |∑+∞l=0bl| < 1 is not necessary, though sufficient, for the asymptotic stability of xn+1 = axn + ∑+∞l=0bn-lxl. We prove the existence of a class of Volterra difference equations (VDEs) that violate this condition but whose zero solutions are asymptotically stable.

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The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang Dec 2007

The Substitution Theorem For Semilinear Stochastic Partial Differential Equations, Salah-Eldin A. Mohammed, Tusheng Zhang

Articles and Preprints

In this article we establish a substitution theorem for semilinear stochastic evolution equations (see's) depending on the initial condition as an infinite-dimensional parameter. Due to the infinitedimensionality of the initial conditions and of the stochastic dynamics, existing finite-dimensional results do not apply. The substitution theorem is proved using Malliavin calculus techniques together with new estimates on the underlying stochastic semiflow. Applications of the theorem include dynamic characterizations of solutions of stochastic partial differential equations (spde's) with anticipating initial conditions and non-ergodic stationary solutions. In particular, our result gives a new existence theorem for solutions of semilinear Stratonovich spde's with anticipating …

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A New Family Of Pr Two Channel Filter Banks, Jian-Ao Lian Dec 2007

A New Family Of Pr Two Channel Filter Banks, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

A new family of multidimensional dimensional (MD) perfect reconstruction (PR) two channel filter banks with finite impulse response (FIR) filters induced from systems of biorthogonal MD scaling functions and wavelets are introduced. One of the advantages of this construction is that the biorthogonal scaling functions and wavelets are easy to establish due to the interpolatory property of the scaling functions to start with. The other advantage is that all filters can be centrosymmetric or bi-linear phase. Examples of two dimensional (2D) bi-linear phase PR twochannel FIR filter banks will be demonstrated.

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Teaching Time Savers: The Exam Practically Wrote Itself!, Michael E. Orrison Jr. Dec 2007

Teaching Time Savers: The Exam Practically Wrote Itself!, Michael E. Orrison Jr.

All HMC Faculty Publications and Research

When I first started teaching, creating an exam for my upper division courses was a genuinely exciting process. The material felt fresh and relatively unexplored (at least by me), and I remember often feeling pleasantly overwhelmed with what seemed like a vast supply of intriguing and engrossing exam-ready problems. Crafting the perfect exam, one that was noticeably inviting, exceedingly fair, and unavoidably illuminating, was a real joy.

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Recounting Determinants For A Class Of Hessenberg Matrices, Arthur T. Benjamin, Mark A. Shattuck Dec 2007

Recounting Determinants For A Class Of Hessenberg Matrices, Arthur T. Benjamin, Mark A. Shattuck

All HMC Faculty Publications and Research

We provide combinatorial interpretations for determinants which are Fibonacci numbers of several recently introduced Hessenberg matrices. Our arguments make use of the basic definition of the determinant as a signed sum over the symmetric group.

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Effective Structure Theorems For Quadratic Spaces Via Height, Lenny Fukshansky Dec 2007

Effective Structure Theorems For Quadratic Spaces Via Height, Lenny Fukshansky

CMC Faculty Publications and Research

Lecture given at the Second International Conference on The Algebraic and Arithmetic Theory of Quadratic Forms, December 2007.

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Bidimensional Pr Qmf With Fir Filters, Jian-Ao Lian Dec 2007

Bidimensional Pr Qmf With Fir Filters, Jian-Ao Lian

Applications and Applied Mathematics: An International Journal (AAM)

Multidimensional perfect reconstruction (PR) quadrature mirror filter (QMF) banks with finite impulse response (FIR) filters induced from systems of biorthogonal multivariate scaling functions and wavelets are investigated. In particular, bivariate scaling functions and wavelets with dilation as an expansive integer matrix whose determinant is two in absolute value are considered. Demonstrative quincunxial examples are explicitly given and new FIR filters are constructed.

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What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz Dec 2007

What Allows Teachers To Extend Student Thinking During Whole-Group Discussions, Nesrin Cengiz

Dissertations

Research indicates that extending students' mathematical thinking during whole-group discussions is challenging, even for the most experienced teachers. That is, it is challenging for teachers to help students move beyond their initial mathematical observations and solutions during whole-group discussions. To better understand this phenomena, the teaching of six experienced elementary school teachers, who had been teaching aStandards-based curriculum for several years and had participated in a multi-year professional development project focused on that curriculum, is explored in this study. In particular, two issues are addressed: what it looks like to extend student thinking during whole-group discussions and how …

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On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi Dec 2007

On Mathematical Modeling, Nonlinear Properties And Stability Of Secondary Flow In A Dendrite Layer, Daniel N. Riahi

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper studies instabilities in the flow of melt within a horizontal dendrite layer with deformed upper boundary and in the presence or absence of rotation during the solidification of a binary alloy. In the presence of rotation, it is assumed that the layer is rotating about a vertical axis at a constant angular velocity. Linear and weakly nonlinear stability analyses provide results about various flow features such as the critical mode of convection, neutral stability curve, preferred flow pattern and the solid fraction distribution within the dendrite layer. The preferred shape of the deformed upper boundary of the layer, …

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Templated Fabrication Of Large Area Subwavelength Antireflection Gratings On Silicon, Chih-Hung Sun, Wei-Lun Min, Nicholas C. Linn, Peng Jiang, Bin Jiang Dec 2007

Templated Fabrication Of Large Area Subwavelength Antireflection Gratings On Silicon, Chih-Hung Sun, Wei-Lun Min, Nicholas C. Linn, Peng Jiang, Bin Jiang

Mathematics and Statistics Faculty Publications and Presentations

We report a cheap and scalable bottom-up technique for fabricating wafer-scale, subwavelength-structured antireflection coatings on single-crystalline silicon substrates. Spin-coated monolayer colloidal crystals are utilized as shadow masks to generate metallic nanohole arrays. Inverted pyramid arrays in silicon can then be templated against nanoholes by anisotropic wet etching. The resulting subwavelength gratings greatly suppress specular reflection at normal incidence. The reflection spectra for flat silicon and the templated gratings at long wavelengths agree well with the simulated results using a rigorous coupled wave analysis model. These subwavelength gratings are of great technological importance in crystalline silicon solar cells.

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Trends In Uspto Office Actions, Ron D. Katznelson Nov 2007

Trends In Uspto Office Actions, Ron D. Katznelson

Ron D. Katznelson

No abstract provided.

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Evaluating Variance Of The Model Credibility Index, Yan Xiao Nov 2007

Evaluating Variance Of The Model Credibility Index, Yan Xiao

Mathematics Theses

Model credibility index is defined to be a sample size under which the power of rejection equals 0.5. It applies goodness-of-fit testing thinking and uses a one-number summary statistic as an assessment tool in a false model world. The estimation of the model credibility index involves a bootstrap resampling technique. To assess the consistency of the estimator of model credibility index, we instead study the variance of the power achieved at a fixed sample size. An improved subsampling method is proposed to obtain an unbiased estimator of the variance of power. We present two examples to interpret the mechanics of …

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Analysis And Implementation Of High-Order Compact Finite Difference Schemes, Jonathan G. Tyler Nov 2007

Analysis And Implementation Of High-Order Compact Finite Difference Schemes, Jonathan G. Tyler

Theses and Dissertations

The derivation of centered compact schemes at interior and boundary grid points is performed and an analysis of stability and computational efficiency is given. Compact schemes are high order implicit methods for numerical solutions of initial and/or boundary value problems modeled by differential equations. These schemes generally require smaller stencils than the traditional explicit finite difference counterparts. To avoid numerical instabilities at and near boundaries and in regions of mesh non-uniformity, a numerical filtering technique is employed. Experiments for non-stationary linear problems (convection, heat conduction) and also for nonlinear problems (Burgers' and KdV equations) were performed. The compact solvers were …

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Selecting The Working Correlation Structure By A New Generalized Aic Index For Longitudinal Data, Wei-Lun Lin Nov 2007

Selecting The Working Correlation Structure By A New Generalized Aic Index For Longitudinal Data, Wei-Lun Lin

Mathematics Theses

The analysis of longitudinal data has been a popular subject for the recent years. The growth of the Generalized Estimating Equation (GEE) Liang & Zeger, 1986) is one of the most influential recent developments in statistical practice for this practice. GEE methods are attractive both from a theoretical and a practical standpoint. In this paper, we are interested in the influence of different "working" correlation structures for modeling the longitudinal data. Furthermore, we propose a new AIC-like method for the model assessment which generalized AIC from the point of view of the data generating. By comparing the difference of the …

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The Exponential Function Of Matrices, Nathalie Nicholle Smalls Nov 2007

The Exponential Function Of Matrices, Nathalie Nicholle Smalls

Mathematics Theses

The matrix exponential is a very important subclass of functions of matrices that has been studied extensively in the last 50 years. In this thesis, we discuss some of the more common matrix functions and their general properties, and we specifically explore the matrix exponential. In principle, the matrix exponential could be computed in many ways. In practice, some of the methods are preferable to others, but none are completely satisfactory. Computations of the matrix exponential using Taylor Series, Scaling and Squaring, Eigenvectors, and the Schur Decomposition methods are provided.

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Empirical Likelihood Based Confidence Intervals For The Difference Between Two Sensitivities Of Continuous-Scale Diagnostic Tests At A Fixed Level Of Specificity, Suqin Yao Nov 2007

Empirical Likelihood Based Confidence Intervals For The Difference Between Two Sensitivities Of Continuous-Scale Diagnostic Tests At A Fixed Level Of Specificity, Suqin Yao

Mathematics Theses

Diagnostic testing is essential to distinguish non-diseased individuals from diseased individuals. The sensitivity and specificity are two important indices for the diagnostic accuracy of continuous-scale diagnostic tests. If we want to compare the effectiveness of two tests, it is of interest to construct a confidence interval for the difference of the two sensitivities at a fixed level of specificity. In this thesis, we propose two empirical likelihood based confidence intervals (HBELI and HBELII) for the difference of two sensitivities at a predetermined specificity level. Simulation studies show that when correlation between the two test results exists, HBELI and HBELII intervals …

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Empirical Likelihood Confidence Intervals For Generalized Lorenz Curve, Nelly E. Belinga-Hill Nov 2007

Empirical Likelihood Confidence Intervals For Generalized Lorenz Curve, Nelly E. Belinga-Hill

Mathematics Theses

Lorenz curves are extensively used in economics to analyze income inequality metrics. In this thesis, we discuss confidence interval estimation methods for generalized Lorenz curve. We first obtain normal approximation (NA) and empirical likelihood (EL) based confidence intervals for generalized Lorenz curves. Then we perform simulation studies to compare coverage probabilities and lengths of the proposed EL-based confidence interval with the NA-based confidence interval for generalized Lorenz curve. Simulation results show that the EL-based confidence intervals have better coverage probabilities and shorter lengths than the NA-based intervals at 100p-th percentiles when p is greater than 0.50. Finally, two real examples …

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Inference For Cox's Regression Model Via A New Version Of Empirical Likelihood, Ali Jinnah Nov 2007

Inference For Cox's Regression Model Via A New Version Of Empirical Likelihood, Ali Jinnah

Mathematics Theses

Cox Proportional Hazard Model is one of the most popular tools used in the study of Survival Analysis. Empirical Likelihood (EL) method has been used to study the Cox Proportional Hazard Model. In recent work by Qin and Jing (2001), empirical likelihood based confidence region is constructed with the assumption that the baseline hazard function is known. However, in Cox’s regression model the baseline hazard function is unspecified. In this thesis, we re-formulate empirical likelihood for the vector of regression parameters by estimating the baseline hazard function. The EL confidence regions are obtained accordingly. In addition, Adjusted Empirical Likelihood (AEL) …

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Individual Growth Models Of Change In Peabody Picture Vocabulary Scores Of Children Treated For Brain Tumors, Ying Shen Nov 2007

Individual Growth Models Of Change In Peabody Picture Vocabulary Scores Of Children Treated For Brain Tumors, Ying Shen

Mathematics Theses

The individual growth model is a relatively new statistical technique. It is now widely used to examine the trajectories of individuals and groups in repeated measures data. This study examines the association of the receptive vocabulary over time and characteristics of children who were treated for brain tumors. The children undertook different types of treatment from one to any combinations of surgery, radiation and chemotherapy. The individual growth model is used to analyze the longitudinal data and to address the issues behind the data. Results of this study present several factors' influences to the rate of change of PPVT scores. …

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A Delayed Option Pricing Formula (Mittag-Leffler Institute Workshop), Salah-Eldin A. Mohammed Nov 2007

A Delayed Option Pricing Formula (Mittag-Leffler Institute Workshop), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

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A Delayed Option Pricing Formula (University Of Manchester Probability Seminar), Salah-Eldin A. Mohammed Nov 2007

A Delayed Option Pricing Formula (University Of Manchester Probability Seminar), Salah-Eldin A. Mohammed

Miscellaneous (presentations, translations, interviews, etc)

No abstract provided.

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Deformable Image Registration With Inclusion Of Auto-Detected Homologous Tissue Features, Y. Xie, Lei Xing, Dana C. Paquin, Doron Levy, T. Yang Nov 2007

Deformable Image Registration With Inclusion Of Auto-Detected Homologous Tissue Features, Y. Xie, Lei Xing, Dana C. Paquin, Doron Levy, T. Yang

Mathematics

No abstract provided.

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Relative Pareto Minimizers To Multiobjective Problems: Existence And Optimality Conditions, Truong Q. Bao, Boris S. Mordukhovich Nov 2007

Relative Pareto Minimizers To Multiobjective Problems: Existence And Optimality Conditions, Truong Q. Bao, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we introduce and study enhanced notions of relative Pareto minimizers to constrained multiobjective problems that are defined via several kinds of relative interiors of ordering cones and occupy intermediate positions between the classical notions of Pareto and weak Pareto efficiency/minimality. Using advanced tools of variational analysis and generalized differentiation, we establish the existence of relative Pareto minimizers to general multiobjective problems under a refined version of the subdifferential Palais-Smale condition for set-valued mappings with values in partially ordered spaces and then derive necessary optimality conditions for these minimizers (as well as for conventional efficient and weak efficient …

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On Enumeration Of Conjugacy Classes Of Coxeter Elements, Matthew Macauley, Henning S. Mortveit Nov 2007

On Enumeration Of Conjugacy Classes Of Coxeter Elements, Matthew Macauley, Henning S. Mortveit

Publications

In this paper we study the equivalence relation on the set of acyclic orientations of a graph Y that arises through source-to-sink conversions. This source-to-sink conversion encodes, e.g. conjugation of Coxeter elements of a Coxeter group. We give a direct proof of a recursion for the number of equivalence classes of this relation for an arbitrary graph Y using edge deletion and edge contraction of non-bridge edges. We conclude by showing how this result may also be obtained through an evaluation of the Tutte polynomial as T (Y, 1, 0), and we provide bijections to two other classes of acyclic …

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The Correlation Coefficients, Rudy Gideon Nov 2007

The Correlation Coefficients, Rudy Gideon

Mathematical Sciences Faculty Publications

A generalized method of defining and interpreting correlation coefficients is given. Seven correlation coefficients are defined — three for continuous data and four on the ranks of the data. A quick calculation of the rank based correlation coefficients using a 0-1 graph-matrix is shown. Examples and comparisons are given.

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Problem Solving And Proving Via Generalisation, Michael De Villiers, Mary Garner Nov 2007

Problem Solving And Proving Via Generalisation, Michael De Villiers, Mary Garner

Faculty and Research Publications

No abstract provided.

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Sphere Packing, Lattices, And Epstein Zeta Function, Lenny Fukshansky Nov 2007

Sphere Packing, Lattices, And Epstein Zeta Function, Lenny Fukshansky

CMC Faculty Publications and Research

The sphere packing problem in dimension N asks for an arrangement of non-overlapping spheres of equal radius which occupies the largest possible proportion of the corresponding Euclidean space. This problem has a long and fascinating history. In 1611 Johannes Kepler conjectured that the best possible packing in dimension 3 is obtained by a face centered cubic and hexagonal arrangements of spheres. A proof of this legendary conjecture has finally been published in 2005 by Thomas Hales. The analogous problem in dimension 2 has been solved by Laszlo Fejes Toth in 1940, and this really is the extent of our current …

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Household Food Insecurity Is Inversely Associated With Social Capital And Health In Females From Special Supplemental Nutrition Program For Women, Infants, And Children Households In Appalachian Ohio, Jennifer L. Walker, David H. Holben, Mary L. Kropf, John P. Holcomb Jr., Heidi Anderson Nov 2007

Household Food Insecurity Is Inversely Associated With Social Capital And Health In Females From Special Supplemental Nutrition Program For Women, Infants, And Children Households In Appalachian Ohio, Jennifer L. Walker, David H. Holben, Mary L. Kropf, John P. Holcomb Jr., Heidi Anderson

Mathematics and Statistics Faculty Publications

Food insecurity has been negatively associated with social capital (a measure of perceived social trust and community reciprocity) and health status. Yet, these factors have not been studied extensively among women from households participating in the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) or the WIC Farmers’ Market Nutrition Program. A cross-sectional, self-administered, mailed survey was conducted in Athens County, Ohio, to examine the household food security status, social capital, and self-rated health status of women from households receiving WIC benefits alone (n=170) and those from households receiving both WIC and Farmers’ Market Nutrition Program benefits (n=65), …

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