Physical Sciences and Mathematics Commons^™

Local Rings Of Embedding Codepth At Most 3 Have Only Trivial Semidualizing Complexes, Saeed Nasseh, Sean Sather-Wagstaff

Department of Mathematical Sciences Faculty Publications

We prove that a local ring R of embedding codepth at most 3 has at most two semidualizing complexes up to shift-isomorphism, namely, R itself and a dualizing R-complex if one exists.

Exponentiated Kumaraswamy-Dagum Distribution With Applications To Income And Lifetime Data, Shujiao Huang, Broderick O. Oluyede

Department of Mathematical Sciences Faculty Publications

A new family of distributions called exponentiated Kumaraswamy-Dagum (EKD) distribution is proposed and studied. This family includes several well known sub-models, such as Dagum (D), Burr III (BIII), Fisk or Log-logistic (F or LLog), and new sub-models, namely, Kumaraswamy-Dagum (KD), Kumaraswamy-Burr III (KBIII), Kumaraswamy-Fisk or Kumaraswamy-Log-logistic (KF or KLLog), exponentiated Kumaraswamy-Burr III (EKBIII), and exponentiated Kumaraswamy-Fisk or exponentiated Kumaraswamy-Log-logistic (EKF or EKLLog) distributions. Statistical properties including series representation of the probability density function, hazard and reverse hazard functions, moments, mean and median deviations, reliability, Bonferroni and Lorenz curves, as well as entropy measures for this class of distributions and the …

The Apostles And Brothers Of Jesus, Andrew Sills

Department of Mathematical Sciences Faculty Publications

Excerpt: The Talpiot tomb, a tomb excavated outside Jerusalem in 1980 and brought to worldwide public attention in 2007, contained ten ossuaries, six of which were inscribed with names. The English equivalents of the names are Jesus son of Joseph, two Marys, a rare diminutive form of Joseph, a diminutive of Matthew, and a Judah son of Jesus. Because of the similarities between this collection of names and certain names appearing in the Christian New Testament, some are curious as to whether the Talpiot tomb may have once interred the remains of Jesus of Nazareth and some of his relatives. …

Mathematical Model Of Dynamic Protein Interactions Regulating P53 Protein Stability For Tumor Suppression, Hua Wang, Guang Peng

Department of Mathematical Sciences Faculty Publications

In the field of cancer biology, numerous genes or proteins form extremely complex regulatory network, which determines cancer cell fate and cancer cell survival. p53 is a major tumor suppressor that is lost in more than 50% of human cancers. It has been well known that a variety of proteins regulate its protein stability, which is essential for its tumor suppressive function. It remains elusive how we could understand and target p53 stabilization process through network analysis. In this paper we discuss the use of random walk and stationary distribution to measure the compound effect of a network of genes …

Multiple Solutions Of A P(X)-Laplacian Equation Involving Critical Nonlinearities, Yuan Liang, Xianbin Wu, Qihu Zhang, Chunshan Zhao

Department of Mathematical Sciences Faculty Publications

In this paper, we consider the existence of multiple solutions for the following p(x)-Laplacian equations with critical Sobolev growth conditions

−div(|∇u| p(x)−2 ∇u) + |u| ^p(x)−2 u = f(x, u) in Ω,

u = 0 on ∂Ω.

We show the existence of infinitely many pairs of solutions by applying the Fountain Theorem and the Dual Fountain Theorem respectively. We also present a variant of the concentration-compactness principle, which is of independent interest.

Using A Pedagogical Content Knowledge Assessment To Inform A Middle Grades Mathematics Teacher Preparation Program, Woong Lim, Paula Guerra

Georgia Educational Researcher

This study provided a springboard for teacher preparation evaluation studies by examining what content and pedagogical content knowledge mathematics pre-service teachers demonstrated in the 4 – 8 mathematics teacher preparation program at an urban research university. Twenty nine pre-service students participated in an assessment called Diagnostic Mathematics Assessments for Middle School Teachers. The study found that pre-service teachers displayed the highest scores for Memorized/Factual Knowledge, followed by Conceptual Understanding, Reasoning/Problem Solving, and Pedagogical Content Knowledge. Pre-service teachers had higher Memorized/Factual Knowledge than Pedagogical Content Knowledge. The pre-service teachers’ overall content knowledge was not strong, and the two lowest-performing content knowledge …

Discrete Fourier Restriction Associated With Kdv Equations, Yi Hu, Xiaochun Li

Department of Mathematical Sciences Faculty Publications

In this paper, we consider a discrete restriction associated with KdV equations. Some new Strichartz estimates are obtained. We also establish the local well-posedness for the periodic generalized Korteweg-de Vries equation with nonlinear term $F(u)\p_x u$ provided F∈C5 and the initial data ϕ∈Hs with s>1/2.

Comparing The Effects Of Interactive And Noninteractive Complementary Nutrients On Growth In A Chemostat, James P. Braselton, Martha L. Abell, Lorraine Braselton

Department of Mathematical Sciences Faculty Publications

We compare the effects of interactive and noninteractive complementary nutrients on the growth of an organism in the chemostat. We also compare these two situations to the case when the nutrients are substitutable. In previous studies, complementary nutrients have been assumed to be noninteractive. However, more recent research indicates that some complementary nutrient relationships are interactive. We show that interactive complementary and substitutable nutrients can lead to higher population densities than do noninteractive complementary nutrients. We numerically illustrate that if the washout rate is high, an organism can persist at higher densities when the complementary nutrients are interactive than when …

Rock-Paper-Scissors In The Chemostat, James P. Braselton, Martha L. Abell, Lorraine Braselton

Department of Mathematical Sciences Faculty Publications

Rock-Paper-Scissors is a game played by two players to determine a single winner. Biological relationships of Rock-Paper-Scissors are documented. In this paper, we form a continuous model of Rock-Papers-Scissors in the chemostat that coincides with the biology of such relationships. The basic models that we develop coincide with the observed phenomena. Because the model involves a system of seven nonlinear differential equations, global results are difficult to obtain. We present several numerical studies that are the result of a substantial number of numerical trials to illustrate the various possibilities that might occur in the context of the problem discussed here.

Developing A Stem Teacher Recruitment Pipeline, Kimberly Shaw, Cindy Ticknor, Tim Howard

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

The Columbus Region Academy of Future Teachers of STEM (CRAFT-STEM), a Phase I Robert Noyce Teacher Scholarship Program, combines internships and scholarships, an exciting summer STEM Honors Camp, a new Teaching Connections Seminar, and an impressive array of existing resources to recruit, prepare, and graduate an increasing number of STEM teachers committed to serving high need high schools.

Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

The aim of this session is to demonstrate the tools used to help reinforce and recreate students’ conceptual knowledge of fractions, specifically targeting the unit of reference. These manipulatives will provide teachers with instructional support for Common Core Standards, which emphasize critical thinking skills and various representations of knowledge, specifically with fractions. Participants will become actively engaged in learning about these tools, including jumping on a number line floor mat, working with circular fraction pieces and placing fractions on a number line rope. By representing knowledge through circular and linear methods, students will use critical thinking skills and support will …

Joining & Using Google Plus Communities: Georgia Stem Teaching & Learning Conference Community, Daniel Rivera

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

The 2nd Annual Georgia STEM Teaching & Learning Conference has chosen Google Plus Communities as the designated tool for encouraging communication among university faculty, K-12 teachers & administrators, research institutions, and businesses. The purpose of this session is to show participants how to get connected and then how to use Google Plus Communities for collaboration.

Creating A Faculty Learning Community To Support Scholarship Of Teaching And Learning Among Stem University Faculty, Cher C. Hendricks, Myrna Gantner

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

In this session, we describe the creation of a Faculty Learning Community for university faculty in science, mathematics, and computer science. These faculty, recipients of mini-grants funded by the USG STEM Initiative, are studying ways to improve their instruction and increase student learning in STEM courses. Through the FLC, they are able to collaborate and support each others’ work.

Research Participants Discuss Stem Conference Participation And Impacton Thinking And Practice, Colleen Beyer, Thomas Koballa, Delena Bell Gatch, Leslie S. Jones, Sharmistha Basu-Dutt, Farooq Khan

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

Last spring, Georgia Southern University hosted its first Scholarship of STEM Teaching and Learning conference. Conference participants were asked to respond to a survey and a subset of participants was selected for an in-depth study. In this session, an overview of the research project will be presented and current research participants will discuss the impact of conference participation on their thinking and practice.

Trig-Star, James M. Anderson

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

A TRIG-STAR is a mathematics student who has demonstrated in competition that he or she is the most skilled among classmates in the practical application of trigonometry. The competition for the honor is a timed exercise which is the solving of a trigonometry problem that incorporates the use of right triangle formulas, circle formulas, the law of sines, and the law of cosines. The contest helps to promote careers in surveying and mapping to students at the High Schools across the country. The award is sponsored by the National Society of Professional Surveyors and cosponsored locally. State winners also have …

Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

Many students are overwhelmed by mathematics because the language is too difficult, the teaching strategies are insufficient or they have lost motivation. With a recent emphasis on meeting the Common Core expectations, using manipulatives to eliminate misconceptions in the mathematical classroom has become even more prevalent. I explored the misconceptions that many students struggle with and provided possible methods of eliminating them at all levels for learning. During this investigation, I studied the effect of manipulatives on students’ understanding of fraction concepts and the students’ conceptions of the unit of reference when working with fraction word problems. I learned that …

I2StemE - What, Who, Where?, Kania Greer, Bob Mayes

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

I²STEM^e is a new Institute on the campus of GSU whose focus is to increase opportunities for K-20 students, teachers, and businesses to partner together to improve STEM Education in Georgia around the tenets of place-based learning, problem based learning and teaching for understanding.

Building, Refining & Defining Stem Learning Outcomes: K-16 Implications, Richard A. Duschl

Interdisciplinary STEM Teaching & Learning Conference (2012-2019)

The July 2012 release of the National Research Council Framework for K-12 Science Education: Practices, Crosscutting Concepts and Core Ideas heralds ‘a new vision of science in education.’ The Framework sets out a comprehensive agenda for the reform of science and engineering education coordinated around 3 Dimensions: Science & Engineering Practices, Crosscutting Concepts, and Core Ideas. While the Framework’s central mission is to impact K-12 education through implementation of the Next Generation Science Standards, there are important but less understood implications for higher education, informal science education and publics’ understandings of science communication efforts. In this talk, I will provide …

Sum Formula Of Multiple Hurwitz-Zeta Values, Jianqiang Zhao

Department of Mathematical Sciences Faculty Publications

Let s1,⋯,sd be d positive integers and define the multiple t-values of depth d byt(s1,⋯,sd)=∑n1>⋯>nd≥11(2n1−1)s1⋯(2nd−1)sd,which is equal to the multiple Hurwitz-zeta value 2−wζ(s1,⋯,sd;−12,⋯,−12) where w=s1+⋯+sd is called the weight. For d≤n, let T(2n,d) be the sum of all multiple t-values with even arguments whose weight is 2n and whose depth is d. In 2011, Shen and Cai gave formulas for T(2n,d) for d≤5 in terms of t(2n), t(2)t(2n−2) and t(4)t(2n−4). In this short note we generalize their results to arbitrary depth by using the theory of symmetric functions established by Hoffman (2012).

Proceedings Of The Seventh Annual Meeting Of The Georgia Association Of Mathematics Teacher Educators Introductory Texts

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

Contents of 7th Annual GAMTE Proceedings Front Matter:

• Proceedings Committee
• Officers of GAMTE
• Purposes and Goals of GAMTE
• Table of Contents
• Letter from President

Exponential Kleisli Monoids As Eilenberg-Moore Algebras, Dirk Hofmann, Frédéric Mynard, Gavin J. Seal

Department of Mathematical Sciences Faculty Publications

Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes the classical identification of exponentiable topological spaces as those whose lattice of open subsets forms a continuous lattice.

The Mc-Dagum Distribution And Its Statistical Properties With Applications, Broderick O. Oluyede, Sasith Rajasooriya

Department of Mathematical Sciences Faculty Publications

In this paper, a new class of distributions called Mc-Dagum distribution is proposed. This class of distributions contains several distributions such as beta-Dagum, beta-Burr III, beta-Fisk, Dagum, Burr III and Fisk distributions as special cases. The hazard function, reverse hazard function, moments, mean residual life function, Renyi entropy and Fisher information are obtained. Lorenz, Bonferroni and Zenga curves are derived. Maximum likelihood estimates of the model parameters and numerical examples are given to illustrate the usefulness of the proposed class of distributions.

Numerical Studies Of The Generalized L₁ Greedy Algorithm For Sparse Signals, Fangjun Arroyo, Edward Arroyo, Xiezhang Li, Jiehua Zhu

Department of Mathematical Sciences Faculty Publications

The generalized l₁ greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l₁-minimization and l₁ greedy algorithms in reconstructing these medical images. In this paper the effectiveness of the generalized l₁ greedy algorithm in finding random sparse signals from underdetermined linear systems is investigated. A series of numerical experiments demonstrate that the generalized l₁ greedy algorithm is superior to the reweighted l₁-minimization and l₁ greedy algorithms …

Rademacher's Infinite Partial Fractions Conjecture Is (Almost Certainly) False, Andrew Sills, Doron Zeilberger

Department of Mathematical Sciences Faculty Publications

In his book Topics in Analytic Number Theory, Hans Rademacher conjectured that the limits of certain sequences of coefficients that arise in the ordinary partial fraction decomposition of the generating function for partitions of integers into at most N parts exist and equal particular values that he specified. Despite being open for nearly four decades, little progress has been made towards proving or disproving the conjecture, perhaps in part due to the difficulty in actually computing the coefficients in question. In this paper, we present a recurrence (alias difference equation) which provides a fast algorithm for calculating the Rademacher …

Distance-Based Graph Invariants Of Trees And The Harary Index, Stephan G. Wagner, Hua Wang, Xiao-Dong Zhang

Department of Mathematical Sciences Faculty Publications

Introduced in 1947, the Wiener index W(T) = ∑{u,v}⊆V(T) d(u, v) is one of the most thoroughly studied chemical indices. The extremal structures (in particular, trees with various constraints) that maximize or minimize the Wiener index have been extensively investigated. The Harary index H(T) = ∑{u,v}⊆V(T) , introduced in 1993, can be considered as the 'reciprocal analogue' of the Wiener index. From recent studies, it is known that the extremal structures of the Harary index and the Wiener index coincide in many instances, i.e., the graphs that maximize the Wiener index minimize the Harary index and vice versa. In this …

Greedy Trees, Subtrees And Antichains, Eric Ould Dadah Andriantiana, Stephan G. Wagner, Hua Wang

Department of Mathematical Sciences Faculty Publications

Greedy trees are constructed from a given degree sequence by a simple greedy algorithm that assigns the highest degree to the root, the second-, third-, ... highest degrees to the root's neighbors, and so on.

They have been shown to maximize or minimize a number of different graph invariants among trees with a given degree sequence. In particular, the total number of subtrees of a tree is maximized by the greedy tree. In this work, we show that in fact a much stronger statement holds true: greedy trees maximize the number of subtrees of any given order. This parallels recent …

Extremal Values Of Ratios: Distance Problems Vs. Subtree Problems In Trees, László A. Székely, Hua Wang

Department of Mathematical Sciences Faculty Publications

The authors discovered a dual behaviour of two tree indices, the Wiener index and the number of subtrees, for a number of extremal problems [Discrete Appl. Math. 155 (3) 2006, 374-385; Adv. Appl. Math. 34 (2005), 138-155]. Barefoot, Entringer and Székely [Discrete Appl. Math. 80 (1997), 37-56] determined extremal values of σT(w)/σT(u), σT(w)/σT(v), σ(T)/σT(v), and σ(T)/σT(w), where T is a tree on n vertices, v is in the centroid of …

On Q-Analogs Of Wostenholme Type Congruences For Multiple Harmonic Sums, Jianqiang Zhao

Department of Mathematical Sciences Faculty Publications

Multiple harmonic sums are iterated generalizations of harmonic sums. Recently Dilcher has considered congruences involving q-analogs of these sums in depth one. In this paper we shall study the homogeneous case for arbitrary depth by using generating functions and shuffle relations of the q-analog of multiple harmonic sums. At the end, we also consider some non-homogeneous cases.

The Mathematics Teacher Educator’S Reflection On Edtpa: The Basics And The Complexity Of Georgia’S Implementation, Lynn Stallings, Woong Lim

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

Beginning in fall 2015, Georgia will require that all teacher candidates pass the edTPA, a performance-based assessment, as a requirement for initial certification. With the potential to impact teacher preparation programs in a profound way, the questions and issues related to the implementation of edTPA merit some critical reflection. In this article, we introduce the brief history of the instrument and review the basics of edTPA with a particular interest in middle grades mathematics. Furthermore, drawing upon our experience with edTPA during a pilot program and the extensive knowledge base of edTPA rubrics and scoring process, we present issues related …

How Differing Interpretations Of Making Mathematics Fun Influence Teaching Practice, Amanda Sawyer

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

I investigated an experienced teacher and a beginning teacher who held similar beliefs about making mathematics learning fun yet held different interpretations of implementation. I found when a teacher equated fun with problem solving, her classroom practice included activities with higher-level thinking skills. In contrast, a teacher who defined fun as students’ enjoyment layered manipulatives and group work on top of procedures. Therefore, teachers need opportunities to reflect on the nature of student understanding as a precursor to shaping their views of fun.

Negative phrases and attitudes toward mathematics have become commonplace in popular culture. Perhaps in response to this …