Mathematics Commons^™

Bytes Of Π, Fall 2013, Department Of Mathematics, Bridgewater State University

Department of Mathematics Newsletter

No abstract provided.

From Urysohn's Universal Metric Space To A Universal Space-Time, A. G. Aksoy, Z. Glassman, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A known Urysohn's result shows that there exists a universal} metric space, i.e., a metric space into every other (separable) metric space can be isomorphically embedded. Moreover, this universal metric space can be selected to be ultra-homogeneous -- every isomorphism of its two finite subsets can be extended to the isomorphism of the whole space.

Starting with Einstein's theories of Special and General relativity, space-times are described by a different type of structure -- a set (of events) equipped with the proper time t(a,b) between points a and b; such spaces are known as space-times with kinematic metric, or k-space-times. …

A Primer For Mathematical Modeling, Marla A. Sole

Publications and Research

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school with the mathematics they will use outside of school. Instructors have found mathematical modeling difficult to teach. To successfully incorporate modeling activities I believe that curricular changes should be accompanied by professional development for curriculum developers, classroom teachers, and higher education professionals. This article serves as an introduction to modeling by …

Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey

Doctoral Dissertations

Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …

Inclusion: Problems And Potential Solutions In Mathematics Instruction, Lynnea Marie Salscheider

Mathematics Graduate Theses

The purpose of this study was (1) to identify and describe the attitudes and beliefs of general and special education teachers about inclusion and (2) to identify significant recommendations based on teacher attitudes for improving the teaching of mathematics to special needs students using inclusion.

Differentiated Instruction In The High School Mathematics Classroom, Sherri Kruger

Mathematics Graduate Theses

The purpose of this research paper is to address the challenges of instruction within a classroom whose census is a diverse mixture of student mathematical abilities. The diverse ability of low and high achieving students all required to master the different strands of mathematics creates problems for instructors and students to stay engaged and actively moving forward deepening and widening their knowledge base. This paper will focus on differentiated lessons, assessments, and projects of a mathematics classroom in a public high school.

The Stratified Structure Of Spaces Of Smooth Orbifold Mappings, Joseph E. Borzellino, Victor Brunsden

Mathematics

We consider four notions of maps between smooth C^∞ orbifolds , with compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between and with the C^r topology carries the structure of a smooth C^∞ Banach (r finite)/Fréchet (r = ∞) manifold. For the notion of complete reduced orbifold map, the corresponding set of C^r maps between and with the C^r topology carries the …

Exploring The Effects Of Conversational Repair As A Scaffolding Strategy To Promote Mathematics Explanations Of Students With Learning Disabilities, Jia Liu

Open Access Dissertations

Conversational repair often occurs in conversations when people attempt to address communicative breakdowns or inaccuracy by way of repeating what have been said or putting them in another way. The review of literature on conversational repair revealed that as an important concept in pragmatic aspect of language, it is an effective strategy to improve communication of different populations with disabilities. However, it is rarely studied in the domain of mathematics and with the population with learning disabilities/difficulties (LD). In current reform-based, discourse-oriented mathematics classrooms, students with LD encounter difficulties articulating or explaining well their reasoning processes due to the mathematical …

A Jackknife Empirical Likelihood Approach To Goodness Of Fit U-Statistic Testing With Side Information, Qun Lin

Open Access Dissertations

Motivated by applications to goodness of fit U-statistics testing, the jackknife empirical likelihood of Jing, et al. (2009) is justified with an alternative approach, and the Wilks theorem for vector U-statistics is proved. This generalizes Owen's empirical likelihood theorem for a vector mean to a vector U-statistics-based mean and includes the jackknife empirical likelihood of U-statistics with side information as a special case. The results are generalized to allow for the constraints to use estimated criteria functions and for the number of constraints to grow with the sample size. The latter is needed to handle naturally occurring nuisance parameters in …

Methods For Increasing Domains Of Convergence In Iterative Linear System Solvers, David Michael Imberti

Open Access Dissertations

In this thesis, we introduce and improve various methods for increasing the domains of convergence for iterative linear system solvers. We rely on the following three approaches: making the iteration adaptive, or nesting an inner iteration inside of a previously determined outer iteration; using deflation and projections to manipulate the spectra inherent to the iteration; and/or focusing on reordering schemes. We will analyze a specific combination of these three strategies. In particular, we propose to examine the influence of nesting a Flexible Generalized Minimum Residual algorithm together with an inner Recursive Projection Method using a banded preconditioner resulting from the …

An Epidemic Model Structured By The Time Since Last Infection, Jorge Alturo Alfaro Murillo

Open Access Dissertations

Epidemiological models structured by time since infection have their origin in the seminal work of 1927 by Kermack and McKendrick. Compared to ordinary differential equations (ODE) models, they are able to capture differences in infectivity of the individuals in a more suitable manner. Their use declined in the second half of the 20th century, probably because the theory for ODE models is more robust, complete and has proved successful in providing insights and predictions for many epidemiological problems. Nevertheless, it is important to understand in what occasions the inclusion of time since infection may alter the outcomes in a significant …

Characterizations Of Distribution Of Ratio Of Rayleigh Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of the distribution of the ratio of two independent Rayleigh random variables are presented. These characterizations are based, on a truncated moment; on hazard function; and on certain functions of order statistics.

A Primal Dpg Method Without A First-Order Reformulation, L. Demkowicz, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

We show that it is possible to apply the DPG methodology without reformulating a second-order boundary value problem into a first-order system, by considering the simple example of the Poisson equation. The result is a new weak formulation and a new DPG method for the Poisson equation, which has no numerical trace variable, but has a numerical flux approximation on the element interfaces, in addition to the primal interior variable.

2013 (Fall), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2013 Fall Colloquium.

Multigrid For An Hdg Method, Bernardo Cockburn, O. Bubois, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

We analyze the convergence of a multigrid algorithm for the Hybridizable Discontinuous Galerkin (HDG) method for diffusion problems. We prove that a non-nested multigrid V-cycle, with a single smoothing step per level, converges at a mesh independent rate. Along the way, we study conditioning of the HDG method, prove new error estimates for it, and identify an abstract class of problems for which a nonnested two-level multigrid cycle with one smoothing step converges even when the prolongation norm is greater than one. Numerical experiments verifying our theoretical results are presented.

Mexican-American Children's Perspectives: Neighborhood Characteristics And Physical Activity In Texas-Mexico Border Colonias, Nelda Mier, Chanam Lee, Matthew Lee Smith, Xiaohui Wang, Elias H. Avila-Rodriguez, Laura Trevino, Marcia G. Ory

School of Mathematical & Statistical Sciences Faculty Publications

The qualitative study described in this article investigated perceptions about environmental factors influencing physical activity (PA) among children from underserved neighborhoods known as colonias in the U.S.-Mexico border. Ten focus groups were conducted with 67 Mexican-American colonia children ages 8 to 13 living in one of the poorest border counties in the U.S. Analyses indicated that PA among children was influenced by neighborhood characteristics, including litter, speeding cars, unleashed dogs, and dark streets. The children also underlined intrapersonal and social environmental factors. Findings may inform policy makers and public health professionals about ways to promote PA among underserved children through …

Mexican-American Children’S Perspectives: Neighborhood Characteristics And Physical Activity In Texas-Mexico Border Colonias, Nelda Mier, Chanam Lee, Matthew Lee Smith, Xiaohui Wang, David Irizarry, Elias H. Avila-Rodriguez, Laura Trevino, Marcia G. Ory

School of Mathematical & Statistical Sciences Faculty Publications

The qualitative study described in this article investigated perceptions about environmental factors infl uencing physical activity (PA) among children from underserved neighborhoods known as colonias in the U.S.-Mexico border. Ten focus groups were conducted with 67 Mexican-American colonia children ages 8 to 13 living in one of the poorest border counties in the U.S. Analyses indicated that PA among children was influenced by neighborhood characteristics, including litter, speeding cars, unleashed dogs, and dark streets. The children also underlined intrapersonal and social environmental factors. Findings may inform policy makers and public health professionals about ways to promote PA among underserved children …

Using A Pedagogical Content Knowledge Assessment To Inform A Middle Grades Mathematics Teacher Preparation Program, Woong Lim, Paula Guerra

Georgia Educational Researcher

This study provided a springboard for teacher preparation evaluation studies by examining what content and pedagogical content knowledge mathematics pre-service teachers demonstrated in the 4 – 8 mathematics teacher preparation program at an urban research university. Twenty nine pre-service students participated in an assessment called Diagnostic Mathematics Assessments for Middle School Teachers. The study found that pre-service teachers displayed the highest scores for Memorized/Factual Knowledge, followed by Conceptual Understanding, Reasoning/Problem Solving, and Pedagogical Content Knowledge. Pre-service teachers had higher Memorized/Factual Knowledge than Pedagogical Content Knowledge. The pre-service teachers’ overall content knowledge was not strong, and the two lowest-performing content knowledge …

Identifiability Of Additive, Time-Varying Actuator And Sensor Faults By State Augmentation, Jason M. Upchurch

Electrical & Computer Engineering Theses & Dissertations

Faults in dynamical systems can have serious safety and reliability implications. For example, actuator and sensor faults have been factors in past incidents and mishaps in many aerospace systems. A large body of research is devoted to developing methods to detect and identify actuator and sensor faults in such systems.

One fault detection and identification menthol employs state augmentation, whereby a set of time-varying faults of interest are modeled as outputs of exogenous linear, time-invariant systems and augmented to the state of the nominal system model. The resulting model represents the system dynamics due to a particular actuator-sensor fault configuration. …

Efektivitas Sekolah Menengah Kejuruan Berstandar Iso 9001:2008 Terhadap Pencapaian Standar Isi, Standar Proses, Dan Standar Kompetensi Lulusan, Yeni Ratih Pratiwi

Jurnal Pendidikan Sains

Penelitian ini bertujuan untuk mengetahui perbedaan efektivitas pencapaian standar isi, standar proses, dan standar kompetensi lulusan pada Sekolah Menengah Kejuruan (SMK) yang telah menerapkan standar mutu ISO 9001:2008 dan SMK yang belum menerapkannya, baik pada sekolah negeri maupun swasta. Pengumpulan data dilakukan menggunakan kuesioner tertutup dengan skala Likert. Analisis data menggunakan uji ANOVA satu arah dengan bantuan program SPSS. Hasil penelitian menunjukkan bahwa terdapat perbedaan efektivitas antara SMK negeri berstandar ISO dan SMK swasta berstandar ISO (p = 0,001), antara SMK negeri berstandar ISO dan SMK negeri belum berstandar ISO (p = 0,000), serta antara SMK negeri berstandar ISO dan …