Mathematics Commons^™

Some Contemporary Issues In Software Reliability., Vignesh Subrahmaniam Dr.

Doctoral Theses

No abstract provided.

Using Survival Analysis To Identify Risk Factors For Treatment Interruption Among New And Retreatment Tuberculosis Patients In Kenya, Enos O. Masini, Omar Mansour, Clare E. Speer, Vittorio Addona, Christy L. Hanson, Joseph K. Sitienei, Hillary K. Kipruto, Martin Muhingo Githiomi, Brenda Nyambura Mungai

Faculty Publications

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Despite high tuberculosis (TB) treatment success rate, treatment adherence is one of the major obstacles to tuberculosis control in Kenya. Our objective was to identify patient-related factors that were associated with time to TB treatment interruption and the geographic distribution of the risk of treatment interruption by county. Data of new and retreatment patients registered in TIBU, a Kenyan national case-based electronic data recording system, between 2013 and 2014 was obtained. Kaplan-Meier curves and log rank tests were used to assess the adherence patterns. Mixed-effects Cox proportional hazards modeling was used for multivariate analysis. Records from 90,170 patients were …

Rank Of Submatrices Of The Pascal Matrix, Scott N. Kersey

Mathematical Sciences: Faculty Publications

In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem. In this paper, we extend this result by deriving a formula for the rank of submatrices of the Pascal matrix. Our formula works for both square and non-square submatrices. We also provide bases for the row and column spaces of these submatrices. Further, we apply our result to one-point lacunary polynomial approximation.

On Generalized Hoops, Homomorphic Images Of Residuated Lattices, And (G)Bl-Algebras, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Articles and Research

Right-residuated binars and right-divisible residuated binars are defined as precursors of generalized hoops, followed by some results and open problems about these partially ordered algebras. Next we show that all complete homomorphic images of a complete residuated lattice A can be constructed easily on certain definable subsets of A. Applying these observations to the algebras of Hajek’s basic logic (BL-algebras), we give an effective description of the HS-poset of finite subdirectly irreducible BL-algebras. The lattice of finitely generated BL-varieties can be obtained from this HS-poset by constructing the lattice of downward closed sets. These results are extended to bounded …

Exploring Mathematical Strategies For Finding Hidden Features In Multi-Dimensional Big Datasets, Tri Duong, Fang Ren, Apurva Mehta

STAR Program Research Presentations

With advances in technology in brighter sources and larger and faster detectors, the amount of data generated at national user facilities such as SLAC is increasing exponentially. Humans have a superb ability to recognize patterns in complex and noisy data and therefore, data is still curated and analyzed by humans. However, a human brain is unable to keep up with the accelerated pace of data generation, and as a consequence, the rate of new discoveries hasn't kept pace with the rate of data creation. Therefore, new procedures to quickly assess and analyze the data are needed. Machine learning approaches are …

Qualitative Theory Of Differential Equations, Difference Equations, And Dynamic Equations On Time Scales, Tongxing Li, Martin Bohner, Tuncay Candan, Yuriy V. Rogovchenko, Qi-Ru Wang

Mathematics and Statistics Faculty Research & Creative Works

This issue on qualitative analysis on differential, fractional differential, and dynamic equations and related topics aims at an all-around research and the state-of-the-art theoretical, numerical, and practical achievements that contribute to this field.

Biquasiles And Dual Graph Diagrams, Deanna Needell, Sam Nelson

CMC Faculty Publications and Research

We introduce dual graph diagrams representing oriented knots and links. We use these combinatorial structures to define corresponding algebraic structures we call biquasiles whose axioms are motivated by dual graph Reidemeister moves, generalizing the Dehn presentation of the knot group analogously to the way quandles and biquandles generalize the Wirtinger presentation. We use these structures to define invariants of oriented knots and links. In particular, we identify an example of a finite biquasile whose counting invariant distinguishes the chiral knot 9-32 from its mirror image, demonstrating that biquasile counting invariants are distinct from biquandle counting invariants.

Counting Subgraphs In F-Free Graphs, Cory T. Palmer

University Grant Program Reports

During the funded period I continued what had been a preliminary investigation into a generalization of the central theory of extremal graph theory. With the help of funding from the UGP grant I was able to cover the travel expenses for several very productive visits.

Embedding Oriented Graphs In Books, Stacey R. Mcadams

Doctoral Dissertations

A book consists of a line L in [special characters omitted]3, called the spine, and a collection of half planes, called pages, whose common boundary is L. A k-book is book with k pages. A k-page book embedding is a continuous one-to-one mapping of a graph G into a book such that the vertices are mapped into L and the edges are each mapped to either the spine or a particular page, such that no two edges cross in any page. Each page contains a planar subgraph of G. The book thickness, denoted bt( …

Algebra Tutorial For Prospective Calculus Students, Matthew Mckain

All Capstone Projects

Many undergraduate degrees require students to take one or more courses in calculus. Majors in mathematics, science, and engineering are expected to enroll in several rigorous calculus courses, but those majoring in social and behavioral sciences and business must also have some basic understanding of calculus. The goal of this project is to create a web-based tutorial that can be used by the GSU Mathematics faculty to reinforce the algebra skills needed for introductory or Applied Calculus. The tutorial covers the concepts of the slopes of lines, polynomial arithmetic, factoring polynomials, rational expressions, solving quadratic equations, linear and polynomial inequalities, …

Simulation And Optimization Of Ant Colony Optimization Algorithm For The Stochiastic Uncapacitated Location-Allocation Problem, Jean-Paul Arnaout, Georges Arnaout, John El Khoury

Engineering Management & Systems Engineering Faculty Publications

This study proposes a novel methodology towards using ant colony optimization (ACO) with stochastic demand. In particular, an optimizationsimulation-optimization approach is used to solve the Stochastic uncapacitated location-allocation problem with an unknown number of facilities, and an objective of minimizing the fixed and transportation costs. ACO is modeled using discrete event simulation to capture the randomness of customers’ demand, and its objective is to optimize the costs. On the other hand, the simulated ACO’s parameters are also optimized to guarantee superior solutions. This approach’s performance is evaluated by comparing its solutions to the ones obtained using deterministic data. The results …

A Dual-Porosity-Stokes Model And Finite Element Method For Coupling Dual-Porosity Flow And Free Flow, Jiangyong Hou, Meilan Qiu, Xiaoming He, Chaohua Guo, Mingzhen Wei, Baojun Bai

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we propose and numerically solve a new model considering confined flow in dual-porosity media coupled with free flow in embedded macrofractures and conduits. Such situation arises, for example, for fluid flows in hydraulic fractured tight/shale oil/gas reservoirs. The flow in dual-porosity media, which consists of both matrix and microfractures, is described by a dual-porosity model. And the flow in the macrofractures and conduits is governed by the Stokes equation. Then the two models are coupled through four physically valid interface conditions on the interface between dual-porosity media and macrofractures/conduits, which play a key role in a physically …

Standards-Based Assessment In A Developmental Math Course, Valorie L. Zonnefeld, Michal Huizenga, Aaron Van Beek, Kate Van Weelden

Faculty Work Comprehensive List

Learn why we decided to try standards-based instruction in an undergraduate, developmental algebra course and what we learned in the process.

Musical Sound: A Mathematical Approach To Timbre, Timothy Weiss (Class Of 2016)

Writing Across the Curriculum

What is the mathematical reasoning behind the ear’s ability to distinguish two completely different musical sounds? In answering this question, one must call to mind a fundamental term with regards to music: timbre.

Smoothness Of Subriemannian Isometries, Luca Capogna, Enrico Le Donne

Mathematics Sciences: Faculty Publications

We show that the group of isometries (i.e., distance-preserving homeomorphisms) of an equiregular subRiemannian manifold is a finite-dimensional Lie group of smooth transformations. The proof is based on a new PDE argument, in the spirit of harmonic coordinates, establishing that in an arbitrary subRiemannian manifold there exists an open dense subset where all isometries are smooth.

99mtc-Hexamethylpropyleneamine Oxime Imaging For Early Detection Of Acute Lung Injury In Rats Exposed To Hyperoxia Or Lipopolysaccharide Treatment, Said H. Audi, Anne V. Clough, Steven T. Haworth, Meetha Medhora, Mahsa Ranji, John C. Densmore, Elizabeth R. Jacobs

Biomedical Engineering Faculty Research and Publications

^99mTc-Hexamethylpropyleneamine oxime (HMPAO) is a clinical single-photon emission computed tomography biomarker of tissue oxidoreductive state. Our objective was to investigate whether HMPAO lung uptake can serve as a preclinical marker of lung injury in two well-established rat models of human acute lung injury (ALI).

Rats were exposed to >95% O₂ (hyperoxia) or treated with intratracheal lipopolysaccharide (LPS), with first endpoints obtained 24 h later. HMPAO was administered intravenously before and after treatment with the glutathione-depleting agent diethyl maleate (DEM), scintigraphy images were acquired, and HMPAO lung uptake was quantified from the images. We also measured breathing rates, heart …

Calculus Ii (University Of North Georgia), Minsu Kim, Hashim Saber, Bikash Das, Thomas Hartfield

Mathematics Grants Collections

This Grants Collection for Calculus II was created under a Round Four ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report

Genome Resources For Climate-Resilient Cowpea, An Essential Crop For Food Security, María Muñoz-Amatriaín, Hamid Mirebrahim, Pei Xu, Steve Wanamaker, Mingcheng Luo, Hind Alhakami, Matthew Alpert, Ibrahim Atokple, Benoit J. Batieno, Ousmane Boukar, Serdar Bozdag, Ndiaga Cisse, Issa Drabo, Jeffrey D. Ehlers, Andrew Farmer, Christian Fatokun, Yong Q. Gu, Yi-Ning Guo, Bao-Lam Huynh, Scott A. Jackson, Francis Kusi, Cynthia T. Lawley, Mitchell R. Lucas, Yaqin Ma, Michael P. Timko, Jiajie Wu, Frank You, Noelle A. Barkley, Philip A. Roberts, Stefano Lonardi, Timothy J. Close

Mathematics, Statistics and Computer Science Faculty Research and Publications

Cowpea (Vigna unguiculata L. Walp.) is a legume crop that is resilient to hot and drought-prone climates, and a primary source of protein in sub-Saharan Africa and other parts of the developing world. However, genome resources for cowpea have lagged behind most other major crops. Here we describe foundational genome resources and their application to the analysis of germplasm currently in use in West African breeding programs. Resources developed from the African cultivar IT97K-499-35 include a whole-genome shotgun (WGS) assembly, a bacterial artificial chromosome (BAC) physical map, and assembled sequences from 4355 BACs. These resources and WGS sequences of …

A Generalized Class Of Exponentiated Modified Weibull Distribution With Applications, Shusen Pu, Broderick O. Oluyede, Yuqi Qui, Daniel F. Linder

Mathematical Sciences: Faculty Publications

In this paper, a new class of five parameter gamma-exponentiated or generalized modified Weibull (GEMW) distribution which includes exponential, Rayleigh, Weibull, modified Weibull, exponentiated Weibull, exponentiated exponential, exponentiated modified Weibull, exponentiated modified exponential, gamma-exponentiated exponential, gamma-exponentiated Rayleigh, gamma-modified Weibull, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh and gamma-exponential distributions as special cases is proposed and studied. Mathematical properties of this new class of distributions including moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real data sets presented in order to illustrate …

Precalculus (University Of North Georgia), Minsu Kim, Hashim Saber, Bikash Das, Thomas Hartfield

Mathematics Grants Collections

This Grants Collection for Introduction to Sociology was created under a Round Four ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report