Mathematics Commons^™

Breaking Spaces And Forms For The Dpg Method And Applications Including Maxwell Equations, Carsten Carstensen, Leszek Demkowicz, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

Discontinuous Petrov Galerkin (DPG) methods are made easily implementable using `broken' test spaces, i.e., spaces of functions with no continuity constraints across mesh element interfaces. Broken spaces derivable from a standard exact sequence of first order (unbroken) Sobolev spaces are of particular interest. A characterization of interface spaces that connect the broken spaces to their unbroken counterparts is provided. Stability of certain formulations using the broken spaces can be derived from the stability of analogues that use unbroken spaces. This technique is used to provide a complete error analysis of DPG methods for Maxwell equations with perfect electric boundary conditions. …

Realizing Spaces As Classifying Spaces, Gregory Lupton, Samuel Bruce Smith

Mathematics and Statistics Faculty Publications

Which spaces occur as a classifying space for fibrations with a given fibre? We address this question in the context of rational homotopy theory. We construct an infinite family of finite complexes realized (up to rational homotopy) as classifying spaces. We also give several non-realization results, including the following: the rational homotopy types of and are not realized as the classifying space of any simply connected, rational space with finite-dimensional homotopy groups.

Aesthetics In School Mathematics: A Potential Model And A Possible Lesson, Hartono Tjoe

The Mathematics Enthusiast

Earlier studies on improving classroom practice in mathematics have suggested a closer attention to nurturing an aesthetic appreciation for mathematics in students’ learning experiences. Recent evidence nonetheless reveals little indication of its presence. This article offers a potential model of the case for aesthetics in school mathematics. Central to this model is the harmonious hierarchy of necessity, existence, and uniqueness without any of which the case for aesthetics in student learning might be suboptimal, if not untenable. This article offers an example of the proposed model using a possible lesson designed to engage students aesthetically in the learning of mathematics. …

Meet The Authors

The Mathematics Enthusiast

No abstract provided.

Hybrid Chebyshev Polynomial Scheme For The Numerical Solution Of Partial Differential Equations, Balaram Khatri Ghimire

Dissertations

In the numerical solution of partial differential equations (PDEs), it is common to find situations where the best choice is to use more than one method to arrive at an accurate solution. In this dissertation, hybrid Chebyshev polynomial scheme (HCPS) is proposed which is applied in two-step approach and one-step approach. In the two-step approach, first, Chebyshev polynomials are used to approximate a particular solution of a PDE. Chebyshev nodes which are the roots of Chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence. Then, the resulting homogeneous equation is solved by boundary type methods including …

Optimal Recovery Of Integral Operators And Its Applications, Vladyslav Babenko, Yuliya Babenko, Nataliya Parfinovych, Dmytro Skorokhodov

Faculty Articles

In this paper we present the solution to a problem of recovering a rather arbitrary integral operator based on incomplete information with error. We apply the main result to obtain optimal methods of recovery and compute the optimal error for the solutions to certain integral equations as well as boundary and initial value problems for various PDE’s.

Homological Characterizations Of Quasi-Complete Intersections, Jason M. Lutz

Department of Mathematics: Dissertations, Theses, and Student Research

Let R be a commutative ring, (f) an ideal of R, and E = K(f; R) the Koszul complex. We investigate the structure of the Tate construction T associated with E. In particular, we study the relationship between the homology of T, the quasi-complete intersection property of ideals, and the complete intersection property of (local) rings.

Advisers: Luchezar L. Avramov and Srikanth B. Iyengar

Bridge Spectra Of Cables Of 2-Bridge Knots, Nicholas John Owad

Department of Mathematics: Dissertations, Theses, and Student Research

We compute the bridge spectra of cables of 2-bridge knots. We also give some results about bridge spectra and distance of Montesinos knots.

Advisors: Mark Brittenham and Susan Hermiller

The Density Topology On The Reals With Analogues On Other Spaces, Stuart Nygard

Boise State University Theses and Dissertations

A point x is a density point of a set A if all of the points except a measure zero set near to x are contained in A. In the usual topology on ℝ, a set is open if shrinking intervals around each point are eventually contained in the set. The density topology relaxes this requirement. A set is open in the density topology if for each point, the limit of the measure of A contained in shirking intervals to the measure of the shrinking intervals themselves is one. That is, for any point x and a small enough …

Biomarkers For Radiation Pneumonitis Using Noninvasive Molecular Imaging, Meetha Medhora, Steven Haworth, Yu Liu, Jayashree Narayanan, Feng Gao, Ming Zhao, Said H. Audi, Elizabeth R. Jacobs, Brian L. Fish, Anne V. Clough

Mathematics, Statistics and Computer Science Faculty Research and Publications

Our goal is to develop minimally invasive biomarkers for predicting radiation-induced lung injury before symptoms develop. Currently, there are no biomarkers that can predict radiation pneumonitis. Radiation damage to the whole lung is a serious risk in nuclear accidents or in radiologic terrorism. Our previous studies have shown that a single dose of 15 Gy of x-rays to the thorax causes severe pneumonitis in rats by 6–8 wk. We have also developed a mitigator for radiation pneumonitis and fibrosis that can be started as late as 5 wk after radiation. Methods: We used 2 functional SPECT probes in vivo in …

Characterizations Of Pareto, Weibull And Power Function Distributions Based On Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterization of Pareto and Weibull distributions based on the conditional expectation of generalized order statistics extending the characterization results reported by Jin and Lee (2014). We also present a characterization of the power function distribution based on the conditional expectation of lower generalized order statistics.

Lie Symmetry To Second-Order Nonlinear Differential Equations And Its First Integrals, Pengfei Gu

Theses and Dissertations

There are many well-known techniques for obtaining exact solutions of differential equations, but most of them are merely special cases of a few powerful symmetry methods. In this paper, we focus our attention on a second-order nonlinear ordinary differential equation of special forms with arbitrary parameters, which is a combination of Liénard-type equation and equation with quadratic friction. With the help of Lie Symmetry methods, we identify several integrable cases of this equation. And for each case, we use the Lie Symmetry method to derive the associated determining system, and apply it further to find infinitesimal generators under …

A Comparative Study And Data Analysis For The Ultimate Fighting Championship, Victor Villalpando

Theses and Dissertations

Mixed Martial Arts is the fastest growing sport with many organizations worldwide. The biggest stage or biggest organization for Mixed Martial Arts is the Ultimate Fighting Championship (UFC). There are eight weight classes for men. The website: http://www.foxsports.com/ufc/stats provides data on fighters in all these categories. This data measures Striking Accuracy, Take downs, Reversals, Knockdowns, etc. in each category. It is interesting to understand and interpret all these numbers and study their relationships. Statistical tools like both parametric and nonparametric inference may give rise to such interpretations and provide explanations how the weight classes differ from one another. In this …

Note On Vertex And Total Proper Connection Numbers, Emily C. Chizmar, Colton Magnant, Pouria Salehi Nowbandegani

Mathematical Sciences: Faculty Publications

This note introduces the vertex proper connection number of a graph and provides a relationship to the chromatic number of minimally connected subgraphs. Also a notion of total proper connection is introduced and a question is asked about a possible relationship between the total proper connection number and the vertex and edge proper connection numbers.

Multilevel Models For Longitudinal Data, Aastha Khatiwada

Electronic Theses and Dissertations

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each …

Active Calculus 1.0, Matthew Boelkins, David Austin, Steven Schlicker

Open Textbooks

Active Calculus is different from most existing calculus texts in at least the following ways: the text is free for download by students and instructors in .pdf format; in the electronic format, graphics are in full color and there are live html links to java applets; the text is open source, and interested instructors can gain access to the original source files upon request; the style of the text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving …

Accuracy And Precision Of Occlusal Contacts Of Stereolithographic Casts Mounted By Digital Interocclusal Registrations, Jason T. Krahenbuhl, Seok-Hwan Cho, Jon Patrick Irelan, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statement of problem

Little peer-reviewed information is available regarding the accuracy and precision of the occlusal contact reproduction of digitally mounted stereolithographic casts.

Purpose

The purpose of this in vitro study was to evaluate the accuracy and precision of occlusal contacts among stereolithographic casts mounted by digital occlusal registrations.

Material and methods

Four complete anatomic dentoforms were arbitrarily mounted on a semi-adjustable articulator in maximal intercuspal position and served as the 4 different simulated patients (SP). A total of 60 digital impressions and digital interocclusal registrations were made with a digital intraoral scanner to fabricate 15 sets of mounted stereolithographic …

Newsvendor Models With Monte Carlo Sampling, Ijeoma W. Ekwegh

Electronic Theses and Dissertations

Newsvendor Models with Monte Carlo Sampling by Ijeoma Winifred Ekwegh The newsvendor model is used in solving inventory problems in which demand is random. In this thesis, we will focus on a method of using Monte Carlo sampling to estimate the order quantity that will either maximizes revenue or minimizes cost given that demand is uncertain. Given data, the Monte Carlo approach will be used in sampling data over scenarios and also estimating the probability density function. A bootstrapping process yields an empirical distribution for the order quantity that will maximize the expected profit. Finally, this method will be used …

An Algorithm For The Machine Calculation Of Minimal Paths, Robert Whitinger

Electronic Theses and Dissertations

Problems involving the minimization of functionals date back to antiquity. The mathematics of the calculus of variations has provided a framework for the analytical solution of a limited class of such problems. This paper describes a numerical approximation technique for obtaining machine solutions to minimal path problems. It is shown that this technique is applicable not only to the common case of finding geodesics on parameterized surfaces in R³, but also to the general case of finding minimal functionals on hypersurfaces in Rⁿ associated with an arbitrary metric.

Numerical Study For Non-Newtonian Fluid-Structure Interaction Problems, Shuhan Xu

All Dissertations

In this work, we consider non-Newtonian fluid structure problems, which have significant applications in biology and industry. Numerical approximation schemes are developed based on the Arbitrary Lagrangian-Eulerian (ALE) formulation of the flow equations. A spatial discretization is accomplished by the finite element method, and the time discretization is carried out by the implicit Euler method. We first consider a fluid-structure interaction problem that consists of a two-dimensional viscoelastic flow and a one-dimensional structure equation. We show how the system can be decoupled and how each subproblem can be solved using interface conditions. Numerical results of different algorithms are presented, showing …