Editorial: (Why) Yet Another Issue On Problem Solving?,
2013
University of Montana
Editorial: (Why) Yet Another Issue On Problem Solving?, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Cognition And Affect In Mathematics Problem Solving With Prospective Teachers,
2013
University of Montana
Cognition And Affect In Mathematics Problem Solving With Prospective Teachers, Lorenzo J. Blanco, Eloisa Guerrero Barona, Ann Caballero Carrasco
The Mathematics Enthusiast
Recent studies relating the affective domain with the teaching and learning of mathematics, and more specifically with mathematics problem solving, have focused on teacher education. The authors of these studies have been ever more insistently pointing to the need to design educational programs that take an integrated cognitive and affective approach to mathematics education. Given this context, we have designed and implemented a program of intervention on mathematics problem solving for prospective primary teachers. We here describe some results of that program.
The Beverton–Holt Q-Difference Equation,
2013
Missouri University of Science and Technology
The Beverton–Holt Q-Difference Equation, Martin Bohner, Rotchana Chieochan
Mathematics and Statistics Faculty Research & Creative Works
The Beverton–Holt model is a classical population model which has been considered in the literature for the discrete-time case. Its continuous-time analogue is the well-known logistic model. In this paper, we consider a quantum calculus analogue of the Beverton–Holt equation. We use a recently introduced concept of periodic functions in quantum calculus in order to study the existence of periodic solutions of the Beverton–Holt q-difference equation. Moreover, we present proofs of quantum calculus versions of two so-called Cushing–Henson conjectures. © 2013 The Author(s). Published by Taylor & Francis.
Supercharacters, Exponential Sums, And The Uncertainty Principle,
2013
Pomona College
Supercharacters, Exponential Sums, And The Uncertainty Principle, J.L. Brumbaugh '13, Madeleine Bulkow '14, Patrick S. Fleming, Luis Alberto Garcia '14, Stephan Ramon Garcia, Gizem Karaali, Matt Michal '15, Andrew P. Turner '14
Pomona Faculty Publications and Research
The theory of supercharacters, which generalizes classical character theory, was recently introduced by P. Diaconis and I.M. Isaacs, building upon earlier work of C. Andre. We study supercharacter theories on $(Z/nZ)^d$ induced by the actions of certain matrix groups, demonstrating that a variety of exponential sums of interest in number theory (e.g., Gauss, Ramanujan, and Kloosterman sums) arise in this manner. We develop a generalization of the discrete Fourier transform, in which supercharacters play the role of the Fourier exponential basis. We provide a corresponding uncertainty principle and compute the associated constants in several cases.
Fourteenth Kenneth C. Schraut Memorial Lecture (Poster),
2013
University of Dayton
Fourteenth Kenneth C. Schraut Memorial Lecture (Poster), University Of Dayton. Department Of Mathematics
Kenneth C. Schraut Memorial Lectures
No abstract provided.
Generalized Gauss Maps And Integrals For Three-Component Links: Toward Higher Helicities For Magnetic Fields And Fluid Flows,
2013
Bryn Mawr College
Generalized Gauss Maps And Integrals For Three-Component Links: Toward Higher Helicities For Magnetic Fields And Fluid Flows, Dennis Deturck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Clayton Shonkwiler, David Shea Vela-Vick
Mathematics Faculty Research and Scholarship
To each three-component link in the 3-sphere we associate a generalized Gauss map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin invariants that classify its generalized Gauss map up to homotopy. We view this as a natural extension of the familiar situation for two-component links in 3-space, where the linking number is the degree of the classical Gauss map from the 2-torus to the 2-sphere. The generalized Gauss map, like its prototype, is geometrically natural in the sense …
Extender Sets And Multidimensional Subshifts,
2013
Department of Mathematics, University of Denver
Extender Sets And Multidimensional Subshifts, Nic Ormes, Ronnie Pavlov
Mathematics Preprint Series
In this paper, we consider a Z d extension of the well-known fact that subshifts with only finitely many follower sets are sofic. As in [4], we adopt a natural Z d analogue of a follower set called an extender set. The extender set of a finite word w in a Z d subshift X is the set of all configurations of symbols on the rest of Z d which form a point of X when concatenated with w. As our main result, we show that for any d ≥ 1 and any Z d subshift X, if there exists …
Symmetric Random Walks On Homeo+(R),
2013
Eastern Illinois University
Symmetric Random Walks On Homeo+(R), B. Deroin, V. Klepstyn, A. Navas, Kamlesh Parwani
Faculty Research and Creative Activity
We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence. Except for a few special cases, which can be treated separately, we prove a property of "global stability at a finite distance": roughly speaking, there exists a compact interval such that any two trajectories get closer and closer whenever one of them returns to the compact interval. The probabilistic techniques employed here lead to interesting results for the study of group actions on the …
Functions Defined By Improper Integrals,
2013
Trinity University
Functions Defined By Improper Integrals, William Trench
Mathematics Faculty Research
This is a supplement to the author's Introduction to Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Textbook Initiative. It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons license Attribution-NonCommercial-ShareAlike 3.0 Unported License. A complete instructor's solution manual is available by email to [email protected] subject to verification of the requestor's faculty status.
The Method Of Lagrange Multipliers,
2013
Trinity University
The Method Of Lagrange Multipliers, William Trench
Mathematics Faculty Research
This is a supplement to the author's "Introduction to Real Analysis." It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Open Textbook Initiative. It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. A complete instructor's solution manual is available by email to [email protected], subject to verification of the requestor's faculty status.
Bayesian Approach For Inconsistent Information,
2013
National University of Singapore
Bayesian Approach For Inconsistent Information, M. Stein, Michael Beer, Vladik Kreinovich
Departmental Technical Reports (CS)
In engineering situations, we usually have a large amount of prior knowledge that needs to be taken into account when processing data. Traditionally, the Bayesian approach is used to process data in the presence of prior knowledge. Sometimes, when we apply the traditional Bayesian techniques to engineering data, we get inconsistencies between the data and prior knowledge. These inconsistencies are usually caused by the fact that in the traditional approach, we assume that we know the {\it exact} sample values, that the prior distribution is {\it exactly} known, etc. In reality, the data is imprecise due to measurement errors, the …
Topological Symmetry Groups Of Graphs In 3-Manifolds,
2013
Pomona College
Topological Symmetry Groups Of Graphs In 3-Manifolds, Erica Flapan, Harry Tamvakis
Pomona Faculty Publications and Research
We prove that for every closed, connected, orientable, irreducible 3-manifold there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group G there is an embedding T of some graph in a hyperbolic rational homology 3-sphere such that the topological symmetry group of T is isomorphic to G.
The Complexity Of Linear Algebra,
2013
California State University, San Bernardino
The Complexity Of Linear Algebra, Leann Kay Christensen
Theses Digitization Project
This study examines the complexity of linear algebra. Complexity means how much work, or the number of calculations or time it takes to perform a task. As linear algebra is used more and more in different fields, it becomes useful to study ways of reducing the amount of work required to complete basic procedures.
A Study Of Finite Symmetrical Groups,
2013
California State University, San Bernardino
A Study Of Finite Symmetrical Groups, May Majid
Theses Digitization Project
This study investigated finite homomorphic images of several progenitors, including 2*⁵ : S₅, 2*⁶ : A₆, and 3*⁵ : C₅ The technique of manual of double coset enumeration is used to construct several groups by hand and computer-based proofs are given for the isomorphism types of the groups that are not constructed.
Enumeration And Symmetric Presentations Of Groups, With Music Theory Applications,
2013
California State University, San Bernardino
Enumeration And Symmetric Presentations Of Groups, With Music Theory Applications, Jesse Graham Train
Theses Digitization Project
The purpose of this project is to construct groups as finite homomorphic images of infinite semi-direct products. In particular, we will construct certain classical groups and subgroups of sporadic groups, as well groups with applications to the field of music theory.
Plasma Confinement: Mathematical Modeling Of A Fusion Reactor,
2013
California State University, San Bernardino
Plasma Confinement: Mathematical Modeling Of A Fusion Reactor, James Scott Jones
Theses Digitization Project
This study will discuss currently used power sources and their drawbacks, leading to covering fusion as an energy source and its potential. Fusion has three significant important advantages: Fuel reserves, safety, and environment. A significant amount of fuel reserves comes from the natural occurrence in ocean water of deuterium at a 1 to 6700 ratio, accounting for the energy supply being on the order of 2 billion years. Fusion does not produce any greenhouse gases and its only 'exhaust' is that of harmless inert helium.
Hyperbolicity Equations For Knot Complements,
2013
California State University, San Bernardino
Hyperbolicity Equations For Knot Complements, Christopher Martin Jacinto
Theses Digitization Project
This study analyzes Carlo Petronio's paper, An Algorithm Producing Hyperbolicity Equations for a Link Complement in S³. Using the figure eight knot as an example, we will explain how Petronio's algorithm was able to decompose the knot complement of an alternating knot into tetrahedra. Then, using the vertex invariants of these tetrahedra, we will explain how Petronio was able to create hyperbolicity equations.
A Study Of Different Modeling Choices For Simulating Platelets Within The Immersed Boundary Method,
2013
University of Utah
A Study Of Different Modeling Choices For Simulating Platelets Within The Immersed Boundary Method, Varun Shankar, Grady B. Wright, Aaron L. Fogelson, Robert M. Kirby
Mathematics Faculty Publications and Presentations
The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid–structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations – radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical …
Generalized Least-Squares Regressions Ii: Theory And Classification,
2013
CUNY Kingsborough Community College
Generalized Least-Squares Regressions Ii: Theory And Classification, Nataniel Greene
Publications and Research
In the first paper of this series, a variety of known and new symmetric and weighted least-squares regression methods were presented with efficient derivations. This paper continues and generalizes the previous work with a theory for deriving, analyzing, and classifying all symmetric and weighted least-squares regression methods.
Bekenstein Bound Of Information Number N And Its Relation To Cosmological Parameters In A Universe With And Without Cosmological Constant,
2013
Wilfrid Laurier University
Bekenstein Bound Of Information Number N And Its Relation To Cosmological Parameters In A Universe With And Without Cosmological Constant, Ioannis Haranas, Ioannis Gkigkitzis
Physics and Computer Science Faculty Publications
Bekenstein has obtained is an upper limit on the entropy S, and from that, an information number bound N is deduced. In other words, this is the information contained within a given finite region of space that includes a finite amount of energy. Similarly, this can be thought as the maximum amount of information required to perfectly describe a given physical system down to its quantum level. If the energy and the region of space are finite then the number of information N required in describing the physical system is also finite. In this short letter two information number …
