Mathematics Commons^™

Synthetic Lethality As A Promising Approach For Targeted Cancer Prevention, Wei Tu, Hua Wang, Guang Peng

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

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

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

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

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 ⊂ R^N. 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 …

Eigenvalue Estimates Of Laplacians Defined By Fractal Measures, Sze-Man Ngai

Mathematical Sciences: Faculty Presentations (1991-2022)

We study various lower and upper estimates for the first eigenvalue of Dirichlet Laplacians defined by positive Borel measures on bounded open subsets of Euclidean spaces. These Laplacians and the corresponding eigenvalue estimates differ from classical ones in that the defining measures can be singular. By using properties of self-similar measures, such as Strichartz's second-order self-similar identities, we improve some of the eigenvalue estimates.

Generalizations Of The Inverse Weibull And Related Distributions With Applications, Broderick O. Oluyede, Tao Yang

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

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 …

Analysis Of Resource Allocation Through Game Theory, Brittney L. Benzio

Honors College Theses

Game theory presents a set of decision-makers in a model in order to simulate how they will interact according to a set of rules. The game is set up with a set of players, actions, and preferences. The model allows each player to, in some way, be affected by the actions of all players. Nash equilibrium illustrates that the best action for any given player depends on the other players’ actions, and so, each player must make some assumption about what the competition will do. The goal of this project is to model situations of different car companies to improve …

On The Boundary Blow-Up Solutions Of P(X)-Laplacian Equations With Gradient Terms, Yuan Liang, Qihu Zhang, Chunshan Zhao

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.

Odd Fibbinary Numbers And The Golden Ratio, Linus Lindroos, Andrew Sills, Hua Wang

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

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

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 …

Note On Rainbow Connection In Oriented Graphs With Diameter 2, Rebecca Holliday, Colton Magnant, Pouria Salehi Nowbandegani

Theory & Applications of Graphs

In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter 2. For a tournament Τ of diameter 2, we show 2 ≤ → rc (Τ) ≤ 3. Furthermore, we provide a general upper bound on the rainbow κ-connection number of tournaments as a simple example of the probabilistic method. Finally, we show that an edge-colored tournament of κ^thdiameter 2 has rainbow κ-connection number at most approximately κ².

Rainbow Generalizations Of Ramsey Theory - A Dynamic Survey, Shinya Fujita, Colton Magnant, Yaping Mao, Kenta Ozeki

Theory & Applications of Graphs

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.

Hamiltonicity And Sigma-Hypergraphs, Christina Zarb

Theory & Applications of Graphs

We define and study a special type of hypergraph. A σ-hypergraph Η= Η(n,r,q |σ), where σ is a partition of r, is an r-uniform hypergraph having nq vertices partitioned into n classes of q vertices each. If the classes are denoted by V1, V2,...,Vn, then a subset Κ of V(Η) of size r is an edge if the partition of r formed by the non-zero cardinalities |Κ ∩ Vi |, 1 ≤ i ≤ n, is σ. The non-empty intersections Κ ∩ Vi are called the parts of Κ, and s(σ) …

Theoretical Properties Of The Weighted Feller-Pareto Distributions, Oluseyi Odubote, Broderick O. Oluyede

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.

Note On Rainbow Connection In Oriented Graphs With Diameter 2, Rebecca Holliday, Colton Magnant, Pouria Salehi Nowbandegani

Mathematical Sciences: Faculty Publications

In this note, we provide a sharp upper bound on the rainbow connection number of tournaments of diameter $2$. For a tournament $T$ of diameter $2$, we show $2 \leq \overrightarrow{rc}(T) \leq 3$. Furthermore, we provide a general upper bound on the rainbow $k$-connection number of tournaments as a simple example of the probabilistic method. Finally, we show that an edge-colored tournament of $k^{th}$ diameter $2$ has rainbow $k$-connection number at most approximately $k^{2}$.

Rainbow Generalizations Of Ramsey Theory - A Dynamic Survey, Shinya Fujita, Colton Magnant, Kenta Ozeki

Mathematical Sciences: Faculty Publications

In this work, we collect Ramsey-type results concerning rainbow edge colorings of graphs.

Building A Better Bijection Between Classes Of Compositions, James D. Diffenderfer

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 Decomposition Of Gallai Multigraphs, Alexander Halperin, Colton Magnant, Kyle Pula

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.

A New Class Of Generalized Dagum Distribution With Applications To Income And Lifetime Data, Broderick O. Oluyede, Shujiao Huang, Mavis Pararai

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

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

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

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 …

Design Considerations For Visually-Aided Discussion Prompts: Emphasizing Mathematical Reasoning In Teacher Education, Anne Marie S. Marshall, Kadian M. Callahan

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

The availability and familiarity of online discussion tools create new instructional options that teacher educators can use to foster prospective teachers’ understanding of mathematics. In particular, online discussion blogs provide an avenue through which teacher educators can press prospective teachers to explore mathematical concepts and share their mathematical reasoning with peers. Furthermore, by incorporating visual stimulations as a design component of these discussion blogs, prospective teachers can make sense of and respond to others’ ideas about mathematical concepts with greater clarity. This paper shares preliminary findings of a research study that examined the extent to which the design of a …

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, …

Do You See What I See? Deepening Teachers’ Understanding Of Linear Equations Through Student Interviews, Tamara Pearson, Kelli L. Nipper, Catherine Matos

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

Many teachers have trouble transitioning their students between natural recursive thinking about the data and algebraic notation for representing linear functions (Zazkis & Liljedahl, 2002).

In this study, we interviewed eighteen middle school students to see how they used prior instruction to think about a geometric pattern and construct its corresponding linear equation. All students

were given the same task to complete and were questioned about their thinking during the interview.

We found that the recording of pattern recognition plays a substantial part in helping students recognize and write explicit patterns. By having students decompose the total perimeter into how …

Caep, Nctm, And Secondary Mathematics Program Revisions, Dianna J. Spence

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

Eight assessments were developed for CAEP (formerly NCATE) and NCTM recognition of our secondary mathematics program. These assessments include internship work samples, field evaluations, and candidate portfolios addressing content knowledge, pedagogical methods, and mathematics technology. Based on data collected from these assessments, alongside ongoing evaluation of the program, several curriculum and program revisions were implemented, including: 1) development of mathematics content-specific courses in classroom management, assessment, and secondary curriculum; 2) restructuring of a senior seminar course in mathematics education; and 3) an increased content focus in probability and statistics. The adoption of new NCTM standards in the CAEP review process …