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Articles 1 - 14 of 14
Full-Text Articles in Physical Sciences and Mathematics
The Conjugacy Problem For Automorphism Groups Of Countable Homogeneous Structures, Samuel Coskey, Paul Ellis
The Conjugacy Problem For Automorphism Groups Of Countable Homogeneous Structures, Samuel Coskey, Paul Ellis
Mathematics Faculty Publications and Presentations
We consider the conjugacy problem for the automorphism groups of a number of countable homogeneous structures. In each case we find the precise complexity of the conjugacy relation in the sense of Borel reducibility.
Clawpack: Building An Open Source Ecosystem For Solving Hyperbolic Pdes, Donna Calhoun
Clawpack: Building An Open Source Ecosystem For Solving Hyperbolic Pdes, Donna Calhoun
Mathematics Faculty Publications and Presentations
Clawpack is a software package designed to solve nonlinear hyperbolic partial differential equations using high-resolution finite volume methods based on Riemann solvers and limiters. The package includes a number of variants aimed at different applications and user communities. Clawpack has been actively developed as an open source project for over 20 years. The latest major release, Clawpack 5, introduces a number of new features and changes to the code base and a new development model based on GitHub and Git submodules. This article provides a summary of the most significant changes, the rationale behind some of these changes, and a …
Longitudinal Success Of Calculus I Reform, Doug Bullock, Kathrine E. Johnson, Janet Callahan
Longitudinal Success Of Calculus I Reform, Doug Bullock, Kathrine E. Johnson, Janet Callahan
Mathematics Faculty Publications and Presentations
This paper describes the second year of an ongoing project to transform calculus instruction at Boise State University. Over the past several years, Calculus I has undergone a complete overhaul that has involved a movement from a collection of independent, uncoordinated, personalized, lecture-based sections, into a single coherent multi-section course with an activelearning pedagogical approach. The overhaul also significantly impacted the course content and learning objectives. The project is now in its fifth semester and has reached a steady state where the reformed practices are normative within the subset of instructors who might be called upon to teach Calculus I. …
Maximum Waring Ranks Of Monomials And Sums Of Coprime Monomials, Erik Holmes, Paul Plummer, Jeremy Siegert, Zach Teitler
Maximum Waring Ranks Of Monomials And Sums Of Coprime Monomials, Erik Holmes, Paul Plummer, Jeremy Siegert, Zach Teitler
Mathematics Faculty Publications and Presentations
We show that monomials and sums of pairwise coprime monomials in four or more variables have Waring rank less than the generic rank, with a short list of exceptions. We asymptotically compare their ranks with the generic rank.
A High-Order Radial Basis Function (Rbf) Leray Projection Method For The Solution Of The Incompressible Unsteady Stokes Equations, Edward J. Fuselier, Varun Shankar, Grady B. Wright
A High-Order Radial Basis Function (Rbf) Leray Projection Method For The Solution Of The Incompressible Unsteady Stokes Equations, Edward J. Fuselier, Varun Shankar, Grady B. Wright
Mathematics Faculty Publications and Presentations
A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for computing the Leray-Helmholtz projection of a vector field using generalized interpolation with divergence-free and curl-free RBFs. Unlike traditional projection methods, this new method enables matching both tangential and normal components of divergence-free vector fields on the domain boundary. This allows incompressibility of the velocity field to be enforced without any time-splitting or pressure boundary conditions. Spatial derivatives are approximated using collocation with global RBFs …
Decompositions Of Ideals Of Minors Meeting A Submatrix, Kent M. Neuerburg, Zach Teitler
Decompositions Of Ideals Of Minors Meeting A Submatrix, Kent M. Neuerburg, Zach Teitler
Mathematics Faculty Publications and Presentations
We compute the primary decomposition of certain ideals generated by subsets of minors in a generic matrix or in a generic symmetric matrix, or subsets of Pfaffians in a generic skew-symmetric matrix. Specifically, the ideals we consider are generated by minors that have at least some given number of rows and columns in certain submatrices.
On Phase Ii Monitoring Of The Probability Distributions Of Univariate Continuous Processes, Partha Sarathi Mukherjee
On Phase Ii Monitoring Of The Probability Distributions Of Univariate Continuous Processes, Partha Sarathi Mukherjee
Mathematics Faculty Publications and Presentations
Statistical process control (SPC) charts are widely used in industry for monitoring the stability of certain sequential processes like manufacturing, health care systems etc. Most SPC charts assume that the parametric form of the “in-control” process distribution F1 is available. However, it has been demonstrated in the literature that their performances are unreliable when the pre-specified process distribution is incorrect. Moreover, most SPC charts are designed to detect any shift in mean and/or variance. In real world problems, shifts in higher moments can happen without much change in mean or variance. If we fail to detect those and let …
Prefrontal White Matter Pathology In Air Pollution Exposed Mexico City Young Urbanites And Their Potential Impact On Neurovascular Unit Dysfunction And The Development Of Alzheimer’S Disease, Partha S. Mukherjee
Mathematics Faculty Publications and Presentations
Millions of urban children are chronically exposed to high concentrations of air pollutants, i.e., fine particulate matter (PM2.5) and ozone, associated with increased risk for Alzheimer’s disease. Compared with children living with clear air those in Mexico City (MC) exhibit systemic, brain and intrathecal inflammation, low CSF Aβ 42, breakdown of the BBB, attention and short-term memory deficits, prefrontal white matter hyperintensities, damage to epithelial and endothelial barriers, tight junction and neural autoantibodies, and Alzheimer and Parkinson's hallmarks. The prefrontal white matter is a target of air pollution. We examined by light and electron microscopy the prefrontal …
Evaluation Of Nasa's Merra Precipitation Product In Reproducing The Observed Trend And Distribution Of Extreme Precipitation Events In The United States, Hamed Ashouri, Soroosh Sorooshian, Kuo-Lin Hsu, Michael G. Bosilovich, Jaechoul Lee, Michael F. Wehner, Allison Collow
Evaluation Of Nasa's Merra Precipitation Product In Reproducing The Observed Trend And Distribution Of Extreme Precipitation Events In The United States, Hamed Ashouri, Soroosh Sorooshian, Kuo-Lin Hsu, Michael G. Bosilovich, Jaechoul Lee, Michael F. Wehner, Allison Collow
Mathematics Faculty Publications and Presentations
This study evaluates the performance of NASA’s Modern-Era Retrospective Analysis for Research and Applications (MERRA) precipitation product in reproducing the trend and distribution of extreme precipitation events. Utilizing the extreme value theory, time-invariant and time-variant extreme value distributions are developed to model the trends and changes in the patterns of extreme precipitation events over the contiguous United States during 1979–2010. The Climate Prediction Center (CPC) U.S. Unified gridded observation data are used as the observational dataset. The CPC analysis shows that the eastern and western parts of the United States are experiencing positive and negative trends in annual maxima, respectively. …
Computing With Functions In Spherical And Polar Geometries I. The Sphere, Alex Townsend, Heather Wilber, Grady B. Wright
Computing With Functions In Spherical And Polar Geometries I. The Sphere, Alex Townsend, Heather Wilber, Grady B. Wright
Mathematics Faculty Publications and Presentations
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian elimination together with the double Fourier sphere method. We show that this procedure allows for stable differentiation, reduces the oversampling of functions near the poles, and converges for certain analytic functions. Operations such as function evaluation, differentiation, and integration are particularly efficient and can be computed by essentially one-dimensional algorithms. A highlight is an optimal complexity direct solver for Poisson's equation on the sphere using a spectral method. …
Calculus Students’ Ideas About Functions: Identifying Opportunities To Support Teacher Learning, Laurie Overman Cavey, Patrick R. Lowenthal
Calculus Students’ Ideas About Functions: Identifying Opportunities To Support Teacher Learning, Laurie Overman Cavey, Patrick R. Lowenthal
Mathematics Faculty Publications and Presentations
We describe the first phase of a study aimed at developing video-based instructional modules for secondary mathematics teachers. We began by consulting the literature on figural pattern tasks (c.f. Rivera, 2010) and teachers’ ability to interpret student work (c.f. El Mouhayar & Jurdak, 2012). Interpreting student work on figural pattern tasks requires awareness of different problem solving strategies, such as recursive and constructive, and how students might use them with tasks that require different levels of generalization (El Mouhayar & Jurdak, 2012).
Arithmagons And Geometrically Invariant Multiplicative Integer Partitions, J. A. Franco, J. Champion, J. W. Lyons
Arithmagons And Geometrically Invariant Multiplicative Integer Partitions, J. A. Franco, J. Champion, J. W. Lyons
Mathematics Faculty Publications and Presentations
In this article, we introduce a formal definition for integral arithmagons. Informally, an arithmagon is a polygonal figure with integer labeled vertices and edges in which, under a binary operation, adjacent vertices equal the included edge. By considering the group of automorphisms for the associated graph, we count the number of integral arithmagons whose exterior sum or product equals a fixed number.
Improving Middle Grades Stem Teacher Content Knowledge And Pedagogical Practices Through A School-University Partnership, Cherie Mccollough, Tonya Jeffery, Kim Moore, Joe Champion
Improving Middle Grades Stem Teacher Content Knowledge And Pedagogical Practices Through A School-University Partnership, Cherie Mccollough, Tonya Jeffery, Kim Moore, Joe Champion
Mathematics Faculty Publications and Presentations
This paper outlines a University-School District partnership with the intent to increase the number of middle grades mathematics and science teachers. This externally funded initiative includes onsite, authentically situated professional development for pre- and in-service teachers at three different urban, low-socioeconomic schools with a majority Hispanic population of students. Program objectives include increasing mathematics and science content knowledge, increasing self-efficacy in teaching math and science, building and incorporating a success-driven school culture and infrastructure to increase student performance in a well-articulated, scalable and transformable model. Program components include site based common planning times, STEM Thursdays where science and mathematics lessons …
Using Ciliate Operations To Construct Chromosome Phylogenies, Jacob L. Herlin, Anna Nelson, Marion Scheepers
Using Ciliate Operations To Construct Chromosome Phylogenies, Jacob L. Herlin, Anna Nelson, Marion Scheepers
Mathematics Faculty Publications and Presentations
Whole genome sequencing has revealed several examples where genomes of different species are related by permutation. The number of certain types of rearrangements needed to transform one permuted list into another can measure the distance between such lists. Using an algorithm based on three basic DNA editing operations suggested by a model for ciliate micronuclear decryption, this study defines the distance between two permutations to be the number of ciliate operations the algorithm performs during such a transformation. Combining well-known clustering methods with this distance function enables one to construct corresponding phylogenies. These ideas are illustrated by exploring the phylogenetic …