Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Abstract Algebra -- Study and teaching (1)
- Approximation theory (1)
- Chemotaxis (1)
- Crystals -- Defects -- Mathematical models (1)
- Crystals -- Mechanical properties (1)
-
- Culturally relevant pedagogy -- Study and teaching (Elementary) (1)
- Discontinuous functions (1)
- Elastic waves (1)
- Elementary school teachers -- In-service training (1)
- Entropy (1)
- Experiential learning (1)
- Finite element method (1)
- Galerkin methods (1)
- Homogeneous spaces (1)
- Laws of thermodynamics (1)
- Marine animals -- Effect of noise on -- Columbia River (1)
- Mathematical analysis (1)
- Mathematics -- Formulae (1)
- Mathematics -- Study and teaching (1)
- Mathematics -- Study and teaching (Elementary) (1)
- Mathematics -- Study and teaching (Primary) (1)
- Mathematics teachers -- Training of (1)
- Mathematics teaching and learning (1)
- Multicultural education -- Study and teaching (Elementary) (1)
- Multigrid methods (Numerical analysis) (1)
- Numerical analysis (1)
- Piling (Civil engineering) -- Environmental aspects -- Columbia River (1)
- Poisson’s equation (1)
- Random variables -- Statistical methods (1)
- Reformulation (Mathematical programming) (1)
- Publication
- Publication Type
Articles 1 - 10 of 10
Full-Text Articles in Physical Sciences and Mathematics
Supplementary Balance Laws For Cattaneo Heat Propagation, Serge Preston
Supplementary Balance Laws For Cattaneo Heat Propagation, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (conservation laws ) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature (λ0(ϑ),KA (ϑ), A = 1, 2, 3). The requirements of the II law of thermodynamics leads to the exclusion of three functional degrees (KA= 0, A …
A Primal Dpg Method Without A First-Order Reformulation, L. Demkowicz, Jay Gopalakrishnan
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.
Multigrid For An Hdg Method, Bernardo Cockburn, O. Bubois, Jay Gopalakrishnan
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.
Building A Knowledge Base: Understanding Prospective Elementary Teachers’ Mathematical Content Knowledge, Eva Thanheiser, Christine Browning, Alden Edson, Signe Kastberg, Jane-Jane Lo
Building A Knowledge Base: Understanding Prospective Elementary Teachers’ Mathematical Content Knowledge, Eva Thanheiser, Christine Browning, Alden Edson, Signe Kastberg, Jane-Jane Lo
Mathematics and Statistics Faculty Publications and Presentations
This survey of the literature summarizes and reflects on research findings regarding elementary preservice teachers’ (PSTs’) mathematics conceptions and the development thereof. Despite the current focus on teacher education, peer-reviewed journals offer a surprisingly sparse insight in these areas. The limited research that exists chiefly presents views of PSTs’ reasoning at singular points during a term, thus focusing on conceptions almost to the exclusion of the their development. We summarize the current findings, which are a beginning of a collective understanding of PSTs’ mathematical content knowledge. We believe much more work is needed to understand how PSTs can best develop …
Elementary Teacher Candidates' Images Of Mathematics, Diverse Students, And Teaching: An Exploratory Study With Implications For Culturally Responsive Mathematics Education, Bernd Richard Ferner
Elementary Teacher Candidates' Images Of Mathematics, Diverse Students, And Teaching: An Exploratory Study With Implications For Culturally Responsive Mathematics Education, Bernd Richard Ferner
Dissertations and Theses
Children from many culturally diverse backgrounds do not achieve in mathematics at the same rates as their counterparts from the dominant White, European-American culture (Gay, 2010). This so-called achievement gap is an artifact of an educational system that continues to fail to provide equal learning opportunities to culturally diverse children (Ladson-Billings, 2006; Nieto & Bode, 2011). Teachers who employ culturally responsive teaching (Gay, 2010) may help to close this opportunity gap and hence, the achievement gap. This study investigated, "How do elementary teacher candidates perceive teaching mathematics in a multicultural environment"; Using a critical constructivism research paradigm, this qualitative instrumental …
A Parabolic Equation Analysis Of The Underwater Noise Radiated By Impact Pile Driving, Nathan Laws
A Parabolic Equation Analysis Of The Underwater Noise Radiated By Impact Pile Driving, Nathan Laws
Dissertations and Theses
Impact pile driving can produce extremely high underwater sound levels, which are of increasing environmental concern due to their deleterious effects on marine wildlife. Prediction of underwater sound levels is important to the assessment and mitigation of the environmental impacts caused by pile driving. Current prediction methods are limited and do not account for the dynamic pile driving source, inhomogeneities in bathymetry and sediment, or physics-based sound wave propagation.
In this thesis, a computational model is presented that analyzes and predicts the underwater noise radiated by pile driving and is suitable for shallow, inhomogeneous environments and long propagation ranges. The …
Establishing Foundations For Investigating Inquiry-Oriented Teaching, Estrella Maria Salas Johnson
Establishing Foundations For Investigating Inquiry-Oriented Teaching, Estrella Maria Salas Johnson
Dissertations and Theses
The Teaching Abstract Algebra for Understanding (TAAFU) project was centered on an innovative abstract algebra curriculum and was designed to accomplish three main objectives: to produce a set of multi-media support materials for instructors, to understand the challenges faced by mathematicians as they implemented this curriculum, and to study how this curriculum supports student learning of abstract algebra. Throughout the course of the project I took the lead investigating the teaching and learning in classrooms using the TAAFU curriculum. My dissertation is composed of three components of this research. First, I will report on a study that aimed to describe …
Some New Applications Of P-P Plots, Isha Dewan, Subhash C. Kochar
Some New Applications Of P-P Plots, Isha Dewan, Subhash C. Kochar
Mathematics and Statistics Faculty Publications and Presentations
The P-P plot is a powerful graphical tool to compare stochastically the magnitudes of two random variables. In this note, we introduce a new partial order, called P?P order based on P-P plots. For a pair of random variables (X 1, Y1) and (X 2, Y 2) one can see the relative precedence of Y 2 over X 2 versus that of Y 1 over X 1 using P-P order. We show that several seemingly very technical and difficult concepts like convex transform order and super-additive ordering can be easily explained with the …
On Continuously Defective Elastic Crystals, Marek Elźanowski, Serge Preston
On Continuously Defective Elastic Crystals, Marek Elźanowski, Serge Preston
Mathematics and Statistics Faculty Publications and Presentations
We analyze mathematical underpinnings of Davini's theory of defective crystals when the defectiveness of a kinematic state may be material point dependent. We show how the underlying space can be identified with a suitably chosen homogeneous space and how the uniformly defective structure is just a special case.
Nonnegativity Of Exact And Numerical Solutions Of Some Chemotactic Models, Patrick De Leenheer, Jay Gopalakrishnan, Erica Zuhr
Nonnegativity Of Exact And Numerical Solutions Of Some Chemotactic Models, Patrick De Leenheer, Jay Gopalakrishnan, Erica Zuhr
Mathematics and Statistics Faculty Publications and Presentations
We investigate nonnegativity of exact and numerical solutions to a generalized Keller–Segel model. This model includes the so-called “minimal” Keller–Segel model, but can cover more general chemistry. We use maximum principles and invariant sets to prove that all components of the solution of the generalized model are nonnegative. We then derive numerical methods, using finite element techniques, for the generalized Keller–Segel model. Adapting the ideas in our proof of nonnegativity of exact solutions to the discrete setting, we are able to show nonnegativity of discrete solutions from the numerical methods under certain standard assumptions. One of the numerical methods is …