K-S-Rings,
2012
Brigham Young University - Provo
K-S-Rings, Emma Louise Turner
Theses and Dissertations
For a finite group G we study certain rings called k-S-rings, one for each non-negative integer k, where the 1-S-ring is the centralizer ring of G. These rings have the property that the (k+1)-S-ring determines the k-S-ring. We show that the 4-S-ring determines G when G is any group with finite classes. We show that the 3-S-ring determines G for any finite group G, thus giving an answer to a question of Brauer. We show the 2-characters defined by Frobenius and the extended 2-characters of Ken Johnson are characters of representations of the 2-S-ring of G. We find the character …
Unknotting Tunnels Of Hyperbolic Tunnel Number N Manifolds,
2012
Brigham Young University - Provo
Unknotting Tunnels Of Hyperbolic Tunnel Number N Manifolds, Stephan Daniel Burton
Theses and Dissertations
Adams conjectured that unknotting tunnels of tunnel number 1 manifolds are always isotopic to a geodesic. We generalize this question to tunnel number n manifolds. We find that there exist complete hyperbolic structures and a choice of spine of a compression body with genus 1 negative boundary and genus n ≥ 3 outer boundary for which (n−2) edges of the spine self-intersect. We use this to show that there exist finite volume one-cusped hyperbolic manifolds with a system of n tunnels for which (n−1) of the tunnels are homotopic to geodesics arbitrarily close to self-intersecting. This gives evidence that the …
Some Unified Results On Comparing Linear Combinations Of Independent Gamma Random Variables,
2012
Portland State University
Some Unified Results On Comparing Linear Combinations Of Independent Gamma Random Variables, Subhash C. Kochar, Maochao Xu
Mathematics and Statistics Faculty Publications and Presentations
In this paper, a new sufficient condition for comparing linear combinations of independent gamma random variables according to star ordering is given. This unifies some of the newly proved results on this problem. Equivalent characterizations between various stochastic orders are established by utilizing the new condition. The main results in this paper generalize and unify several results in the literature including those of Amiri, Khaledi, and Samaniego [2], Zhao [18], and Kochar and Xu [9].
Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative,
2012
Marquette University
Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen K. Bansal, Gholamhossein Hamedani, Ru Sheng
Mathematics, Statistics and Computer Science Faculty Research and Publications
We consider a hypothesis problem with directional alternatives. We approach the problem from a Bayesian decision theoretic point of view and consider a situation when one side of the alternatives is more important or more probable than the other. We develop a general Bayesian framework by specifying a mixture prior structure and a loss function related to the Kullback–Leibler divergence. This Bayesian decision method is applied to Normal and Poisson populations. Simulations are performed to compare the performance of the proposed method with that of a method based on a classical z-test and a Bayesian method based on the …
Dark Lattice Solitons In One-Dimensional Waveguide Arrays With Defocusing Saturable Nonlinearities And Alternating Couplings,
2012
UMass, Amherst
Dark Lattice Solitons In One-Dimensional Waveguide Arrays With Defocusing Saturable Nonlinearities And Alternating Couplings, Andrey Kanshu, Christian E. Rüter, Detlef Kip, Jesús Cuevas, Panos Kevrekidis
Panos Kevrekidis
In the present work, we examine "binary" waveguide arrays, where the coupling between adjacent sites alternates between two distinct values $C_1$ and $C_2$ and a saturable nonlinearity is present on each site. Motivated by experimental investigations of this type of system in fabricated LiNbO$_3$ arrays, we proceed to analyze the nonlinear wave excitations arising in the self-defocusing nonlinear regime, examining, in particular, dark solitons and bubbles. We find that such solutions may, in fact, possess a reasonably wide, experimentally relevant parametric interval of stability, while they may also feature both prototypical types of instabilities, namely exponential and oscillatory ones, for …
Decision Making Under Interval And Fuzzy Uncertainty: Towards An Operational Approach,
2012
Azerbaijan State Oil Academy
Decision Making Under Interval And Fuzzy Uncertainty: Towards An Operational Approach, Rafik Aliev, Oleg H. Huseynov, Vladik Kreinovich
Departmental Technical Reports (CS)
Traditional decision theory is based on a simplifying assumption that for each two alternatives, a user can always meaningfully decide which of them is preferable. In reality, often, when the alternatives are close, the user is either completely unable to select one of these alternatives, or selects one of the alternatives only "to some extent". How can we extend the traditional decision theory to such realistic interval and fuzzy cases? In their previous papers, the first two authors proposed a natural generalization of the usual decision theory axioms to interval and fuzzy cases, and described decision coming from this generalization. …
Membership Functions Or Alpha-Cuts? Algorithmic (Constructivist) Analysis Justifies An Interval Approach,
2012
The University of Texas at El Paso
Membership Functions Or Alpha-Cuts? Algorithmic (Constructivist) Analysis Justifies An Interval Approach, Vladik Kreinovich
Departmental Technical Reports (CS)
In his pioneering papers, Igor Zaslavsky started an algorithmic (constructivist) analysis of fuzzy logic. In this paper, we extend this analysis to fuzzy mathematics and fuzzy data processing. Specifically, we show that the two mathematically equivalent representations of a fuzzy number -- by a membership function and by alpha-cuts -- are not algorithmically equivalent, and only the alpha-cut representation enables us to efficiently process fuzzy data.
General Allee Effect In Two-Species Population Biology,
2012
Trinity University
General Allee Effect In Two-Species Population Biology, G Livadiotis, Saber Elaydi
Mathematics Faculty Research
The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator–prey models. The study is restricted to the strong Allee effect caused by an inter-specific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a ‘phase space core’ of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar …
2012 (Summer),
2012
University of Dayton
2012 (Summer), University Of Dayton. Department Of Mathematics
Colloquia
Abstracts of the talks given at the 2012 Summer Colloquium.
On The Brilliance Of Black Children: A Response To A Clarion Call,
2012
Georgia State University
On The Brilliance Of Black Children: A Response To A Clarion Call, Erika Bullock, Maisie Gholson, Nathan Alexander
Middle-Secondary Education and Instructional Technology Faculty Publications
In this editorial, three dotoral students in Mathematics Education reflect on their experiences as conference organizers and co-editors of the Proceedings of the 2010 Philadelphia and 2011 Atlanta Bejamin Banneker Associaton Conferences.
Beyond The Numbers: A Benjamin Banneker Association Conference Series,
2012
Arcadia University
Beyond The Numbers: A Benjamin Banneker Association Conference Series, Jacqueline Leonard, Erica R. Davila, David W. Stinson
Middle-Secondary Education and Instructional Technology Faculty Publications
The authors discuss how the "white male math myth" can be effectively debunked by conferences such as the Benjamin Banneker Association Beyond the Numbers conference series, which focus on urban mathematical education and highlight the achievements of black children.
Inquiry- Without Posing Questions?,
2012
University of Montana
Inquiry- Without Posing Questions?, Helle Alrø, Marit Johnsen-Høines
The Mathematics Enthusiast
This article discusses what inquiry conversations could mean when learning mathematics.3 Referring to Gadamar’s distinction of true and apparent questions it is discussed what it takes to be inquiring and if this attitude necessarily includes posing questions. Which qualities are expressed in inquiring questions, and what other ways of communicating may have an inquiring function in learning conversations? The intention is to develop and frame the concept of ’inquiry’ in learning conversations, and this is the focus of analysis of an authentic classroom situation, where teacher and pupils are exploring the concept of ’volume’. Further, this analysis informs a …
Beyond Post-Modernity In Mathematics Education,
2012
University of Montana
Beyond Post-Modernity In Mathematics Education, Ole Skovsmose
The Mathematics Enthusiast
A radical form of postmodernity is presented with reference to Nietzsche’s ideas with respect to truth, knowledge, sciences, progress, democracy, and ethical values in general. Thereafter is presented Foucault’s archaeology of knowledge. This brings us forward to the notion of genealogy, which is a defining idea for the postmodern conception of critique. However, it is emphasised that a critique can address the generativity of mathematical rationality by considering mathematics-based fabrications. Finally, imagination is presented as yet another feature of a critical enterprise. It is illustrated how such a three dimensional critical enterprise is relevant for both mathematics and mathematics education. …
Demographics Of Self-Selected Participants In Mathematical Tracks In Swedish Upper Secondary School,
2012
University of Montana
Demographics Of Self-Selected Participants In Mathematical Tracks In Swedish Upper Secondary School, Linda Mattsson
The Mathematics Enthusiast
This study investigates the three demographic factors gender, geographical origin and parents educational level among self-selected students in mathematical tracks in Swedish Upper Secondary School (n=147). Comparisons are made, through statistical tests of significance, with corresponding student distributions on the closely related Natural Science program (n = 1528). Data is obtained from Statistics Sweden. Results confirm that females are under-represented in mathematical tracks (p<0,01) and that parents of students in mathematical tracks have higher educational level than parents of students in the comparison group (p<0,05). Results do not show that students with foreign background are underrepresented in mathematical tracks, but raise questions about under-representation of Swedish students. Possible implications of these findings for these and similar programs are discussed.
Investigating Engineers’ Needs As A Part Of Designing A Professional Development Program For Engineers Who Are To Become Mathematics Teachers,
2012
University of Montana
Investigating Engineers’ Needs As A Part Of Designing A Professional Development Program For Engineers Who Are To Become Mathematics Teachers, Ragnhild Johanne Rensaa
The Mathematics Enthusiast
The average age for teachers in mathematics and physics in Norway is about 60 (Sørensen, 2003) and few students taking a masters degree in a science subject choose a career as a teacher (KD, 2006). This implies that there may be a critical lack of science teachers in schools in the near future (Næss, 2002). At the same time, rather many graduated engineers – who have worked as engineers sometimes several years – want to contribute to the educational setting by taking part time jobs as teachers; lector-II (Vassnes, 2008). To combine this supply and demand for qualified teachers in …
From Designing To Implementing Mathematical Tasks: Investigating The Changes In The Nature Of The T-Shirt Task,
2012
University of Montana
From Designing To Implementing Mathematical Tasks: Investigating The Changes In The Nature Of The T-Shirt Task, Claire Vaugelade Berg
The Mathematics Enthusiast
From looking at research literature it is possible to see that research on design, implementation and analysis of mathematical tasks is an actual theme: there is a special issue of the Journal of Mathematics Teacher Education (2007) with Anne Watson, John Mason and Orit Zaslavsky as editors (Watson and Mason, 2007), a book published by Clarke, Grevholm and Millman (2009) concerning “Tasks in primary mathematics teacher education” and under ICME 11 in Mexico (2008) the title of one of the Topic Study Groups was “Research and development in task design and analysis”. In addition several substantial research projects conducted in …
Loss Of Dimension In The History Of Calculus And In Student Reasoning,
2012
University of Montana
Loss Of Dimension In The History Of Calculus And In Student Reasoning, Robert Ely
The Mathematics Enthusiast
Research indicates that calculus students often imagine objects losing a dimension entirely when a limit is taken, and that this image serves as an obstacle to their understanding of the fundamental theorem of calculus. Similar imagery, in the form of “indivisibles”, was similarly unsupportive of the development of the fundamental theorem in the mid-1600s, unlike the more powerful subsequent imagery of infinitesimals. This parallel between student issues and historical issues suggests several implications for how to provide students with imagery that is more productive for understanding the fundamental theorem, such as the imagery of infinitesimals or the more modern quantitative …
Foundations For Success In Mathematical Competitions: A Study Of Best Praxis In Lower Secondary Schools In Norway,
2012
University of Montana
Foundations For Success In Mathematical Competitions: A Study Of Best Praxis In Lower Secondary Schools In Norway, Steinar Thorvaldsen, Lars Vavik
The Mathematics Enthusiast
The purpose of this study is to investigate the following questions: What factors leads to success in mathematics, and how can these success factors and qualities be described? Will the teacher’s education and pedagogical praxis have an impact on good learning results? We report results from a case-control association study on among high achievement classes in mathematics in Norway. The data were collected from matched pairs of schools, paired on the basis of location and socioeconomic status. The questionnaire was first distributed to teachers in 38 Norwegian secondary schools at grade 9, which have had repeated success in the annual …
University Mathematics Teachers' Views On The Required Reasoning In Calculus Exams,
2012
University of Montana
University Mathematics Teachers' Views On The Required Reasoning In Calculus Exams, Ewa Bergqvist
The Mathematics Enthusiast
Students often use imitative reasoning, i.e. copy algorithms or recall facts, when solving mathematical tasks. Research shows that this type of imitative reasoning might weaken the students' understanding of the underlying mathematical concepts. In a previous study, the author classified tasks from 16 final exams from introductory calculus courses at Swedish universities. The results showed that it was possible to pass 15 of the exams, and solve most of the tasks, using imitative reasoning. This study examines the teachers' views on the reasoning that students are expected to perform during their own and others mathematics exams. The results indicate that …
Values In Effective Mathematics Lessons In Sweden: What Do They Tell Us?,
2012
University of Montana
Values In Effective Mathematics Lessons In Sweden: What Do They Tell Us?, Aihui Peng, Mikaela Nyroos
The Mathematics Enthusiast
This study aims to examine values in effective mathematics lessons in Sweden from the perspectives of students in different groups and their teachers. By using methods with lesson observations, student focus group interviews and teacher interviews, it shows that instructional explanation and classroom atmosphere with quietness are shared-values of students and their teachers. The findings propose some crucial issues which related to how mathematics teaching could be adjusted to different students’ learning conditions and whether it needs more instructional explanation in mathematics teaching in Sweden.
