Mathematics Commons^™

Microscopic-Macroscopic Simulations Of Rigid-Rod Polymer Hydrodynamics: Heterogeneity And Rheochaos, M. Gregory Forest, Ruhai Zhou, Qi Wang

Mathematics & Statistics Faculty Publications

Rheochaos is a remarkable phenomenon of nematic (rigid-rod) polymers in steady shear, with sustained chaotic fluctuations of the orientational distribution of the rod ensemble. For monodomain dynamics, imposing spatial homogeneity and linear shear, rheochaos is a hallmark prediction of the Doi-Hess theory [M. Doi, J. Polym. Sci. Polym. Phys. Ed., 19 (1981), pp. 229-243; M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, London, New York, 1986; S. Hess, Z. Naturforsch., 31 (1976), pp. 1034-1037. The model behavior is robust, captured by second-moment tensor approximations G. Rienäcker, M. Kröger, and S. Hess, Phys. Rev. …

Lipschitz Continuity And Gateaux Differentiability Of The Best Approximation Operator In Vector-Valued Chebyshev Approximation, Martin Bartelt, John Swetits

Mathematics & Statistics Faculty Publications

When G is a finite-dimensional Haar subspace of C ( X, R^k), the vector-valued functions (including complex-valued functions when k is 2) frorn a finite set X to Euclidean k-dimensional space, it is well-known that at any function f in C ( X, R^k) the best approximation operator satisfies the Strong Unicity condition of order 2 and a Lipschitz (Holder) condition of order 1/2. This note shows that in fact the best approximation operator satisfies the usual Lipschitz condition of order 1 and has a Gateaux derivative on a dense set of functions in C …

Clarifications Of Rule 2 In Teaching Geometric Dimensioning And Tolerancing, Cheng Lin, Alok Verma

Engineering Technology Faculty Publications

Geometric dimensioning and tolerancing is a symbolic language used on engineering drawings and computer generated three-dimensional solid models for explicitly describing nominal geometry and its allowable variation. Application cases using the concept of Rule 2 in the Geometric Dimensioning and Tolerancing (GD&T) are presented. The rule affects all fourteen geometric characteristics. Depending on the nature and location where each feature control frame is specified, interpretation on the applicability of Rule 2 is quite inconsistent. This paper focuses on identifying the characteristics of a feature control frame to remove this inconsistency. A table is created to clarify the confusions for students …

Pi-Calculus In Logical Form, Marcello M. Bonsangue, Alexander Kurz

Engineering Faculty Articles and Research

Abramsky’s logical formulation of domain theory is extended to encompass the domain theoretic model for picalculus processes of Stark and of Fiore, Moggi and Sangiorgi. This is done by defining a logical counterpart of categorical constructions including dynamic name allocation and name exponentiation, and showing that they are dual to standard constructs in functor categories. We show that initial algebras of functors defined in terms of these constructs give rise to a logic that is sound, complete, and characterises bisimilarity. The approach is modular, and we apply it to derive a logical formulation of pi-calculus. The resulting logic is a …

The Mathematical Preparation Of Secondary School Teachers, Kelly W. Edenfield

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

In the summer of 2007, a group of doctoral students at the University of Georgia gathered to discuss the mathematical preparation of secondary teachers. The group used Mathematics for High School Teachers: An Advanced Perspective by Usiskin, Peressini, Marchisotto, and Stanley (2003) as the catalyst for the discussion. Participants agreed that future teachers need opportunities to examine high school and college mathematics differently from the way they had as students, with specific emphasis on connections, representations, and history. Features of this text that were highlighted in the discussions were the attention topics with commonly held misconceptions, the historical rationales and …

Graded Sparse Graphs And Matroids, Audrey Lee, Ileana Streinu, Louis Theran

Computer Science: Faculty Publications

Sparse graphs and their associated matroids play an important role in rigidity theory, where they capture the combinatorics of some families of generic minimally rigid structures. We define a new family called graded sparse graphs, arising from generically pinned bar-and-joint frameworks, and prove that they also form matroids. We also address several algorithmic problems on graded sparse graphs: Decision, Spanning, Extraction, Components, Optimization, and Extension. We sketch variations on pebble game algorithms to solve them.

Using Technology To Design Teaching Modules In Mathematics And Science, Ollie I. Manley

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Technology is changing the way in which mathematics and science are taught, and this radical transformation in teaching is causing teachers to take a closer look at how lessons are designed. In an effort to demonstrate how to design instructional modules using technology, this paper will include the following: 1)A review of the National Educational Technology Standards for teachers to establish a framework for the development of the teaching modules; 2)instructional designs and techniques with special emphasis on multiple intelligence and critical thinking skills; 3) strategies and techniques for infusing technology into a standard based curriculum; and 4) an analysis …

The Kennesaw State University Mathematics Methods Model, Angela L. Teachey

Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators

Kennesaw State University’s comprehensive, nine-credit-hour, methods course integrates general and mathematics-specific pedagogical training with a structured four-week field experience prior to student teaching. This course blends essential units on conceptual understanding of mathematics, lesson planning, assessment, classroom management, and diversity with mathematics-specific methods. All topics are aligned with National Council of Teachers of Mathematics standards and Georgia Performance Standards. Throughout the course, students complete a variety of assignments that require them to practice the skills highlighted in class readings and discussions, and they adapt and generalize those skills during their field experiences. Students have numerous opportunities in class and in …

Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang

Mathematics and Statistics Faculty Publications and Presentations

The standard continuous Galerkin (CG) finite element method for second order elliptic problems suffers from its inability to provide conservative flux approximations, a much needed quantity in many applications. We show how to overcome this shortcoming by using a two step postprocessing. The first step is the computation of a numerical flux trace defined on element inter- faces and is motivated by the structure of the numerical traces of discontinuous Galerkin methods. This computation is non-local in that it requires the solution of a symmetric positive definite system, but the system is well conditioned independently of mesh size, so it …

Carathéodory Functions In The Banach Space Setting, Daniel Alpay, Olga Timoshenko, Dan Volok

Mathematics, Physics, and Computer Science Faculty Articles and Research

We prove representation theorems for Carathéodory functions in the setting of Banach spaces.

A Functional Calculus In A Non Commutative Setting, Fabrizio Colombo, Graziano Gentili, Irene Sabadini, Daniele C. Struppa

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we announce the development of a functional calculus for operators defined on quaternionic Banach spaces. The definition is based on a new notion of slice regularity, see [6], and the key tools are a new resolvent operator and a new eigenvalue problem. This approach allows us to deal both with bounded and unbounded operators.

The Wright Message, 2007, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- Dear Department Alumni and Friends
-- 2007 - 2008 Tenure or Tenure-Track Faculty
-- New Faces in the Mathematics Department
-- Faculty Notes
-- Alumni Survey Conducted
-- Actuarial Program Thrives
-- Board of Regents Collaborative Mathematics and Science Initiative
-- TEAM News
-- DoDEA/UNI Project
-- Online Course Development
-- Math Day at UNI
-- First Millar Scholarship Awarded
-- In Memory of Paul Trafton
-- Major Gifts to the Department

Digit Reversal Without Apology, Lara Pudwell

Lara K. Pudwell

No abstract provided.

Graphing Transformations: Does Order Make A Difference?, John Hawkins

John B. Hawkins

No abstract provided.

Open Source Surveys With Asset, Bert Wachsmuth

Bert Wachsmuth

No abstract provided.

Symbolization Of Generating Functions; An Application Of The Mullin–Rota Theory Of Binomial Enumeration, Tian-Xiao He, Peter J.S. S, Leetsch C. Hsu

Tian-Xiao He

We have found that there are more than a dozen classical generating functions that could be suitably symbolized to yield various symbolic sum formulas by employing the Mullin–Rota theory of binomial enumeration. Various special formulas and identities involving well-known number sequences or polynomial sequences are presented as illustrative examples. The convergence of the symbolic summations is discussed.

Fourier Transform Of Bernstein–Bézier Polynomials, Tian-Xiao He, Charles K. Chui, Qingtang Jiang

Tian-Xiao He

Explicit formulae, in terms of Bernstein–Bézier coefficients, of the Fourier transform of bivariate polynomials on a triangle and univariate polynomials on an interval are derived in this paper. Examples are given and discussed to illustrate the general theory. Finally, this consideration is related to the study of refinement masks of spline function vectors.

Two Number-Theoretic Problems That Illustrate The Power And Limitations Of Randomness, Andrew Shallue

Andrew Shallue

This thesis contains work on two problems in algorithmic number theory. The first problem is to give an algorithm that constructs a rational point on an elliptic curve over a finite field. A fast and easy randomized algorithm has existed for some time. We prove that in the case where the finite field has characteristic 2, there is a deterministic algorithm with the same asymptotic running time as the existing randomized algorithm.

Construction Of Biorthogonal B-Spline Type Wavelet Sequences With Certain Regularities, Tian-Xiao He

Tian-Xiao He

No abstract provided.

The Abacus Of Universal Logics, Rudolf Kaehr

Rudolf Kaehr

No abstract provided.

The Sheffer Group And The Riordan Group, Tian-Xiao He, Peter J.S. Shiue, Leetsch C. Hsu

Tian-Xiao He

We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs.