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Articles 1 - 30 of 33
Full-Text Articles in Education
Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang
Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang
Department of Mathematical Sciences Faculty Publications
In this note we consider a discrete symmetric function f(x, y) where f(x; a) + f(y, b) ≥ f(y, a) + f(x, b) for any x ≥ y and a ≥ b, associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as Σ uv∈E(T) f(deg(u), deg(v)), are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randić index follow as corollaries. The extremal structures for …
Symplectic Mackey Theory, Francois Ziegler
Symplectic Mackey Theory, Francois Ziegler
Department of Mathematical Sciences Faculty Publications
Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup. In this paper, we develop the attendant imprimitivity theorem and Mackey analysis in the full generality needed to deal with arbitrary closed normal subgroups.
Information Security Newsletter
Information Security Newsletter
A Case Study Of How Ninth Grade Mathematics Students Construct Knowledge During A Productive Failure Model, Amy F. Westbrook Dr.
A Case Study Of How Ninth Grade Mathematics Students Construct Knowledge During A Productive Failure Model, Amy F. Westbrook Dr.
Georgia Educational Research Association Conference
The purpose of this qualitative study was to explain how ninth grade mathematics students at a rural high school in Georgia constructed knowledge through student talk when problem solving using Kapur’s (2012) productive failure design. An embedded case study design was used to understand how a group of students constructed knowledge through their use of talk, persistence during the task, and use of prior knowledge while working on a productive failure modeled task. Triangulation resulted from the collected data from multiple sources, which included videotaping, interviewing, and analyzing student artifacts. Utilization of the constructivist perspectives of Vygotsky (1934/1962), Piaget (1971), …
Information Security Newsletter
Information Security Newsletter
Synthetic Lethality As A Promising Approach For Targeted Cancer Prevention, Wei Tu, Hua Wang, Guang Peng
Synthetic Lethality As A Promising Approach For Targeted Cancer Prevention, Wei Tu, Hua Wang, Guang Peng
Department of Mathematical Sciences Faculty Publications
Carcinogenesis is recognized as a multistep process. It occurs over a relative long span of time, which offers intervention opportunities for cancer prevention [1] . Using drugs to prevent cancer rather than treat cancer is the major research goal in the field of ‘chemoprevention’. Tremendous research efforts have been devoted toward using natural, synthetic or biological agents to prevent, suppress or delay the initiation and or the progression of premalignant cells to cancer [1] . However a big challenge for effective cancer prevention is to identify chemoprevention agents with demonstrable efficacy and safety for healthy general …
Fast Inverse Distance Weighting-Based Spatiotemporal Interpolation: A Web-Based Application Of Interpolating Daily Fine Particulate Matter Pm2.5 In The Contiguous U.S. Using Parallel Programming And K-D Tree, Lixin Li, Travis Losser, Charles Yorke, Reinhard E. Piltner
Fast Inverse Distance Weighting-Based Spatiotemporal Interpolation: A Web-Based Application Of Interpolating Daily Fine Particulate Matter Pm2.5 In The Contiguous U.S. Using Parallel Programming And K-D Tree, Lixin Li, Travis Losser, Charles Yorke, Reinhard E. Piltner
Department of Mathematical Sciences Faculty Publications
Epidemiological studies have identified associations between mortality and changes in concentration of particulate matter. These studies have highlighted the public concerns about health effects of particulate air pollution. Modeling fine particulate matter PM2.5exposure risk and monitoring day-to-day changes in PM2.5 concentration is a critical step for understanding the pollution problem and embarking on the necessary remedy. This research designs, implements and compares two inverse distance weighting (IDW)-based spatiotemporal interpolation methods, in order to assess the trend of daily PM2.5 concentration for the contiguous United States over the year of 2009, at both the census block group level and county level. …
Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva, James P. Braselton
Epistasis In Predator-Prey Relationships, Iuliia Inozemtseva, James P. Braselton
Department of Mathematical Sciences Faculty Publications
Epistasis is the interaction between two or more genes to control a single phenotype. We model epistasis of the prey in a two-locus two-allele problem in a basic predator-prey relationship. The resulting model allows us to examine both population sizes as well as genotypic and phenotypic frequencies. In the context of several numerical examples, we show that if epistasis results in an undesirable or desirable phenotype in the prey by making the particular genotype more or less susceptible to the predator or dangerous to the predator, elimination of undesirable phenotypes and then genotypes occurs.
Fejér And Suffridge Polynomials In The Delayed Feedback Control Theory, Dmitriy Dmitrishin, Anna Khamitova, Anatolii Korenovskyi, Alexander M. Stokolos
Fejér And Suffridge Polynomials In The Delayed Feedback Control Theory, Dmitriy Dmitrishin, Anna Khamitova, Anatolii Korenovskyi, Alexander M. Stokolos
Department of Mathematical Sciences Faculty Publications
A remarkable connection between optimal delayed feedback control (DFC) and complex polynomial mappings of the unit disc is established. The explicit form of extremal polynomials turns out to be related with the Fejer polynomials. The constructed DFC can be used to stabilize cycles of one-dimensional non-linear discrete systems.
Existence Of Positive Solutions For P(X)-Laplacian Equations With A Singular Nonlinear Term, Jingjing Liu, Qihu Zhang, Chunshan Zhao
Existence Of Positive Solutions For P(X)-Laplacian Equations With A Singular Nonlinear Term, Jingjing Liu, Qihu Zhang, Chunshan Zhao
Department of Mathematical Sciences Faculty Publications
In this article, we study the existence of positive solutions for the p(x)-Laplacian Dirichlet problem −∆p(x)u = λf(x, u) in a bounded domain Ω ⊂ RN. The singular nonlinearity term f is allowed to be either f(x, s) → +∞, or f(x, s) → +∞ as s → 0+ for each x ∈ Ω. Our main results generalize the results in [15] from constant exponents to variable exponents. In particular, we give the asymptotic behavior of solutions of a simpler equation which is useful for finding supersolutions of differential equations with variable exponents, which is of independent …
Generalizations Of The Inverse Weibull And Related Distributions With Applications, Broderick O. Oluyede, Tao Yang
Generalizations Of The Inverse Weibull And Related Distributions With Applications, Broderick O. Oluyede, Tao Yang
Department of Mathematical Sciences Faculty Publications
In this paper, the generalized inverse Weibull distribution including the exponentiated or proportional reverse hazard and Kumaraswamy generalized inverse Weibull distributionsare presented. Properties of these distributions including the behavior of the hazard and reverse hazard functions, moments, coefficients of variation, skewness, andkurtosis, entropy, Fisher information matrix are studied. Estimates of the model parameters via method of maximum likelihood (ML), and method of moments (MOM) are presented for complete and censored data. Numerical examples are also presented.
Localized Quantum States, Francois Ziegler
Localized Quantum States, Francois Ziegler
Department of Mathematical Sciences Faculty Publications
Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any "large enough" subgroup G of Aut(L). This definition has two major drawbacks: when G=Aut(L) there are no known examples; and when G is a Lie subgroup the notion is, as we shall see, far from selective enough. In this paper we introduce the concept of a quantum state *localized at Y*, where Y is a coadjoint orbit of a …
On The Boundary Blow-Up Solutions Of P(X)-Laplacian Equations With Gradient Terms, Yuan Liang, Qihu Zhang, Chunshan Zhao
On The Boundary Blow-Up Solutions Of P(X)-Laplacian Equations With Gradient Terms, Yuan Liang, Qihu Zhang, Chunshan Zhao
Department of Mathematical Sciences Faculty Publications
In this paper we investigate boundary blow-up solutions of the problem
⎧⎩⎨⎪⎪−△p(x)u+f(x,u)=ρ(x,u)+K(|x|)|∇u|δ(|x|) in Ω, u(x)→+∞ as d(x, ∂Ω)→0,
where −△p(x)u=−div(|∇u|p(x)−2∇u) is called p(x)-Laplacian. The existence of boundary blow-up solutions is proved and the singularity of boundary blow-up solution is also given for several cases including the case of ρ(x,u) being a large perturbation (namely, ρ(x,u(x))f(x,u(x))→1 as x→∂Ω). In particular, we do not have the comparison principle.
Google Chrome: More Than A Browser, Daniel E. Rivera
Google Chrome: More Than A Browser, Daniel E. Rivera
Interdisciplinary STEM Teaching & Learning Conference (2012-2019)
Chrome is more than a browser. It’s an operating system in itself, and it’s transforming the educational computing experience. Come learn about Chrome’s features such as data syncing across computers (bookmarks, passwords, settings, etc), and most importantly, Chrome-specific apps. Learn about Chromebooks as well - those powerful, fast, and cheap laptops that are spreading like wildfire.
Hitting Pause On Organic Chemistry, Jenny B. Vu
Hitting Pause On Organic Chemistry, Jenny B. Vu
Interdisciplinary STEM Teaching & Learning Conference (2012-2019)
Written procedures for performing organic chemistry experiments are replaced by visual demonstrations that allow students to watch these videos at home and/ or in the laboratory. These previously recorded demonstrations allow students to watch, pause, and rewind the video to better understand laboratory techniques.
Odd Fibbinary Numbers And The Golden Ratio, Linus Lindroos, Andrew Sills, Hua Wang
Odd Fibbinary Numbers And The Golden Ratio, Linus Lindroos, Andrew Sills, Hua Wang
Department of Mathematical Sciences Faculty Publications
The fibbinary numbers are positive integers whose binary representation contains no consecutive ones. We prove the following result: If the jth odd fibbinary is the nth odd fibbinary number, then j={nɸ2]-1.
Weighted Inverse Weibull Distribution: Statistical Properties And Applications, Valeriia Sherina, Broderick O. Oluyede
Weighted Inverse Weibull Distribution: Statistical Properties And Applications, Valeriia Sherina, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
In this paper, the weighted inverse Weibull (WIW) class of distributions is proposed and studied. This class of distributions contains several models such as: length-biased, hazard and reverse hazard proportional inverse Weibull, proportional inverse Weibull, inverse Weibull, inverse exponential, inverse Rayleigh, and Fr´echet distributions as special cases. Properties of these distributions including the behavior of the hazard function, moments, coefficients of variation, skewness, and kurtosis, R´enyi entropy and Fisher information are presented. Estimates of the model parameters via method of maximum likelihood (ML) are presented. Extensive simulation study is conducted and numerical examples are given.
Multiscale Geometric Modeling Of Macromolecules I: Cartesian Representation, Kelin Xia, Xin Feng, Zhan Chen, Yiying Tong, Guo-Wei Wei
Multiscale Geometric Modeling Of Macromolecules I: Cartesian Representation, Kelin Xia, Xin Feng, Zhan Chen, Yiying Tong, Guo-Wei Wei
Department of Mathematical Sciences Faculty Publications
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace–Beltrami flows for biomolecular surface evolution and formation. The …
A Decomposition Of Gallai Multigraphs, Alexander Halperin, Colton Magnant, Kyle Pula
A Decomposition Of Gallai Multigraphs, Alexander Halperin, Colton Magnant, Kyle Pula
Department of Mathematical Sciences Faculty Publications
An edge-colored cycle is rainbow if its edges are colored with distinct colors. A Gallai (multi)graph is a simple, complete, edge-colored (multi)graph lacking rainbow triangles. As has been previously shown for Gallai graphs, we show that Gallai multigraphs admit a simple iterative construction. We then use this structure to prove Ramsey-type results within Gallai colorings. Moreover, we show that Gallai multigraphs give rise to a surprising and highly structured decomposition into directed trees.
Theoretical Properties Of The Weighted Feller-Pareto Distributions, Oluseyi Odubote, Broderick O. Oluyede
Theoretical Properties Of The Weighted Feller-Pareto Distributions, Oluseyi Odubote, Broderick O. Oluyede
Department of Mathematical Sciences Faculty Publications
In this paper, for the first time, a new six-parameter class of distributions called weighted Feller-Pareto (WFP) and related family of distributions is proposed. This new class of distributions contains several other Pareto-type distributions such as length-biased (LB) Pareto, weighted Pareto (WP I, II, III, and IV), and Pareto (P I, II, III, and IV) distributions as special cases. The pdf, cdf, hazard and reverse hazard functions, monotonicity properties, moments, entropy measures including Renyi, Shannon and s-entropies are derived.
A New Class Of Generalized Dagum Distribution With Applications To Income And Lifetime Data, Broderick O. Oluyede, Shujiao Huang, Mavis Pararai
A New Class Of Generalized Dagum Distribution With Applications To Income And Lifetime Data, Broderick O. Oluyede, Shujiao Huang, Mavis Pararai
Department of Mathematical Sciences Faculty Publications
The generalized beta distribution of the second kind (GB2), McDonald [11], McDonald and Xu [12] is an important distribution with applications in finance and actuarial sciences, as well as economics, where Dagum distribution which is a sub-model of GB2 distribution plays an important role in size distribution of personal income. In this note, a new class of generalized Dagum distribution called gamma-Dagum distribution is presented. The gamma-Dagum (GD) distribution which includes the gamma-Burr III (GB III), gamma-Fisk or gamma-log logistic (GF of GLLog), Zografos and Balakrishnan-Dagum (ZB-D), ZB-Burr III (ZB-B III), ZB-Fisk of ZB-Log logistic (ZB-F or ZB-LLog), Burr III …
Discrete Fourier Restriction Associated With Schrödinger Equations, Yi Hu, Xiaochun Li
Discrete Fourier Restriction Associated With Schrödinger Equations, Yi Hu, Xiaochun Li
Department of Mathematical Sciences Faculty Publications
In this paper, we present a different proof on the discrete Fourier restriction. The proof recovers Bourgain’s level set result on Strichartz estimates associated with Schrödinger equations on torus. Some sharp estimates on L 2(d+2) d norm of certain exponential sums in higher dimensional cases are established. As an application, we show that some discrete multilinear maximal functions are bounded on L 2 (Z).
Determinants Of Incidence And Hessian Matrices Arising From The Vector Space Lattice, Saeed Nasseh, Alexandra Seceleanu, Junzo Watanabe
Determinants Of Incidence And Hessian Matrices Arising From The Vector Space Lattice, Saeed Nasseh, Alexandra Seceleanu, Junzo Watanabe
Department of Mathematical Sciences Faculty Publications
We give explicit formulas for the determinants of the incidence and Hessian matrices arising from the interaction between the rank 1 and rank n−1 level sets of the subspace lattice of an n-dimensional finite vector space. Our exploration is motivated by the fact that both of these matrices arise naturally in the study of the combinatorial and algebraic Lefschetz properties for the vector space lattice and the graded Artinian Gorenstein algebra associated to it, respectively.
Proceedings Of The Eighth 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
- GAMTE 2014 Officers
- GAMTE 2014 Conference Committee
- GAMTE 2014 Proceedings Committee
- Purposes and Goals of GAMTE
- Letter from the President
Differences In Beliefs Across A Series Of Four Mathematics Content Courses, Susanna Molitoris Miller, Caitlin Walkey
Differences In Beliefs Across A Series Of Four Mathematics Content Courses, Susanna Molitoris Miller, Caitlin Walkey
Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators
College students often ask questions such as, “Why do I have to take this class? Is there a point to it?” For Early Childhood Education (ECE) majors these questions may often take on a slightly different form, wondering, “How can I incorporate this information into my classroom?” or “Do I understand this well enough to teach this to my students?” It is especially important for pre- service teachers to feel confident working with the mathematical content that they are learning and for them to believe that they can successfully teach that same information to a group of students. Swackhamer, Koellner, …
A Proposed Pedagogical Approach For Preparing Teacher Candidates To Incorporate (Academic) Language, Woong Lim, Lynn Stallings
A Proposed Pedagogical Approach For Preparing Teacher Candidates To Incorporate (Academic) Language, Woong Lim, Lynn Stallings
Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators
The edTPA is a performance-based assessment that aims to measure teacher candidates’ readiness for teaching. Beginning in the fall of 2015, this assessment will be a mandatory requirement for those seeking certification in Georgia. General agreement exists in the field of education about the basic knowledge and skills essential for beginning teachers to demonstrate in classroom teaching. Does edTPA measure the knowledge and skills essential for beginning mathematics teachers in particular? Assuming that edTPA can successfully measure that knowledge and skills for beginning teachers, the use of the assessment could be valuable.
One of the critical components of edTPA is …
Building A Better Bijection Between Classes Of Compositions, James D. Diffenderfer
Building A Better Bijection Between Classes Of Compositions, James D. Diffenderfer
Department of Mathematical Sciences Faculty Publications
A bijective proof is given for the following theorem: The number of compositions of n into parts congruent to a (mod b) equals the number of compositions of n + b - a into parts congruent to b (mod a) that are greater than or equal to b. The bijection is then shown to preserve palindromicity.
A Mathematics Teacher’S Journey Of Identity Construction And Change, Anthony B. Stinson
A Mathematics Teacher’S Journey Of Identity Construction And Change, Anthony B. Stinson
Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators
Despite some gains, improving mathematics instruction remains an area of concern in the United States. The implementation of the Common Core Standards and the challenge of teaching the 21st Century student require mathematics teachers to examine their pedagogy to determine if they need to change or improve their practices. This paper provides a personal account of my journey when determining my identity as a mathematics teacher and how constructing my identity helped in changing and improving my practices as a mathematics teacher. The study was done using autoethnography, a burgeoning research method, and identity theory. This study has the goals …