Mathematics Commons^™

Using Restrictions To Accept Or Reject Solutions Of Radical Equations, Eleftherios Gkioulekas

School of Mathematical & Statistical Sciences Faculty Publications

The standard technique for solving equations with radicals is to square both sides of the equation as many times as necessary to eliminate all radicals. Because the procedure violates logical equivalence, it results in extraneous solutions that do not satisfy the original equation, making it necessary to check all solutions against the original equation. We propose alternative solution procedures that are rigorous and simple to execute where the extraneous solutions can be identified without verification against the original equation. In this article, we review previous literature, establish and illustrate rigorous solution procedures for radical equations of depth 1 (i.e. equations …

Genetic Variation Determines Which Feedbacks Drive And Alter Predator–Prey Eco-Evolutionary Cycles, Michael H. Cortez

Mathematics and Statistics Faculty Publications

Evolution can alter the ecological dynamics of communities, but the effects depend on the magnitudes of standing genetic variation in the evolving species. Using an eco‐coevolutionary predator–prey model, I identify how the magnitudes of prey and predator standing genetic variation determine when ecological, evolutionary, and eco‐evolutionary feedbacks influence system stability and the phase lags in predator–prey cycles. Here, feedbacks are defined by subsystems, i.e., the dynamics of a subset of the components of the whole system when the other components are held fixed; ecological (evolutionary) feedbacks involve the direct and indirect effects between population densities (species traits) and eco‐evolutionary feedbacks …

Graph Pebbling: Doppelgangers And Lemke Graphs, Mark Powers

17th Annual Celebration of Undergraduate Research and Creative Performance (2018)

Graph pebbling is a mathematical game played on a connected graph. A configuration places a nonnegative number of pebbles on each vertex. A move between a pair of adjacent vertices removes two pebbles from one vertex and places one pebble on the other. A configuration is solvable if a sequence of pebbling moves can be made to place a pebble on any given vertex. The pebbling number of a graph is the minimum number of pebbles so that any configuration is solvable. A graph satisfies the two-pebbling property if any configuration of more than twice the pebbling number minus the …

Elementary/Middle School Pre-Service Teachers’ Understanding Of Variability And The Use Of Dynamical Statistical Software, Yaomingxin Lu

Research and Creative Activities Poster Day

A primary purpose of the study was to examine the effects of using dynamical statistical software (DSS) on prospective teachers’ (PSTs) understanding of statistical concepts, especially variability. Data were collected from PSTs enrolled in a probability and statistics course designed for prospective K-8 teachers. After initial analysis of the data using coding and classification schemes, we found the need to develop a more targeted framework to analyze students’ different levels of understanding. The variability framework (Garfield & Ben-Zvi, 2005) and the Structure of Observed Learning Outcomes (SOLO) taxonomy were then used in combination to develop a revised framework in order …

On Central Branch/Reinsurance Risk Networks: Exact Results And Heuristics, Florin Avram, Sooie-Hoe Loke

Mathematics Faculty Scholarship

Modeling the interactions between a reinsurer and several insurers, or between a central management branch (CB) and several subsidiary business branches, or between a coalition and its members, are fascinating problems, which suggest many interesting questions. Beyond two dimensions, one cannot expect exact answers. Occasionally, reductions to one dimension or heuristic simplifications yield explicit approximations, which may be useful for getting qualitative insights. In this paper, we study two such problems: the ruin problem for a two-dimensional CB network under a new mathematical model, and the problem of valuation of two-dimensional CB networks by optimal dividends. A common thread between …

Project-Based And Problem-Based Instruction: A Literature Review, Sarah Angelle

Mahurin Honors College Capstone Experience/Thesis Projects

Science, technology, engineering, and mathematics (STEM) education has undergone great transformative reform during the last two decades with revised education standards calling for increased rigor to promote conceptual understanding of ideas and transferable 21st Century practices. Student-centered inquiry-based pedagogies like problem- and project-based instruction (PBI and PjBI) have begun to take root in K-12 STEM classrooms as an answer to the reform call. However, there is some disagreement of the specific characteristics of each pedagogy. There is also limited information regarding prevalence of these pedagogies in practice, their contextual patterns, degree to which they benefit all children, and the benefits/challenges …

Quantum Attacks On Modern Cryptography And Post-Quantum Cryptosystems, Zachary Marron

Senior Honors Theses

Cryptography is a critical technology in the modern computing industry, but the security of many cryptosystems relies on the difficulty of mathematical problems such as integer factorization and discrete logarithms. Large quantum computers can solve these problems efficiently, enabling the effective cryptanalysis of many common cryptosystems using such algorithms as Shor’s and Grover’s. If data integrity and security are to be preserved in the future, the algorithms that are vulnerable to quantum cryptanalytic techniques must be phased out in favor of quantum-proof cryptosystems. While quantum computer technology is still developing and is not yet capable of breaking commercial encryption, these …

Mathieu-Zhao Subspaces Of Vertex Algebras, Matthew Speck

Theses and Dissertations

A Mathieu-Zhao subspace is a generalization of an ideal of an associative ring-algebra, A, first formalized in 2010. A vertex algebra is an algebraic structure first developed in conjunction with string theory in the 1960s and later axiomatized by mathematicians in the 1990s. We formally introduce the definition of a Mathieu-Zhao subspace, M, of a vertex algebra, V. Building on natural connections to associative algebras, we classify an infinite set of non-trivial, non-ideal Mathieu-Zhao subspaces for simple and general vertex algebras by group action eigenspace decomposition. Finally, we state the locally nilpotent epsilon-derivation (LNED) conjecture for vertex algebras.

Clustering Biological Data With Self-Adjusting High-Dimensional Sieve, Josselyn Gonzalez

Theses and Dissertations

Data classification as a preprocessing technique is a crucial step in the analysis and understanding of numerical data. Cluster analysis, in particular, provides insight into the inherent patterns found in data which makes the interpretation of any follow-up analyses more meaningful. A clustering algorithm groups together data points according to a predefined similarity criterion. This allows the data set to be broken up into segments which, in turn, gives way for a more targeted statistical analysis. Cluster analysis has applications in numerous fields of study and, as a result, countless algorithms have been developed. However, the quantity of options makes …

On Structures Of Large Rooted Graphs, Shilin Wang

LSU Doctoral Dissertations

A rooted graph is a pair (G,R), where G is a graph and R⊆V(G). There are two research topics in this thesis. One is about unavoidable substructures in sufficiently large rooted graphs. The other is about characterizations of rooted graphs excluding specific large graphs.

The first topic of this thesis is motivated by Ramsey Theorem, which states that K_n and ¯(K_n ) are unavoidable induced subgraphs in every sufficiently large graph. It is also motivated by a classical result of Oporowski, Oxley, and Thomas, which determines unavoidable large 3-connected minors. We first determine unavoidable induced subgraphs, and unavoidable subgraphs in …

Second Order Fully Discrete Energy Stable Methods On Staggered Grids For Hydrodynamic Phase Field Models Of Binary Viscous Fluids, Yuezheng Gong, Jia Zhao, Qi Wang

Mathematics and Statistics Faculty Publications

We present second order, fully discrete, energy stable methods on spatially staggered grids for a hydrodynamic phase field model of binary viscous fluid mixtures in a confined geometry subject to both physical and periodic boundary conditions. We apply the energy quadratization strategy to develop a linear-implicit scheme. We then extend it to a decoupled, linear scheme by introducing an intermediate velocity term so that the phase variable, velocity field, and pressure can be solved sequentially. The two new, fully discrete linear schemes are then shown to be unconditionally energy stable, and the linear systems resulting from the schemes are proved …

Creating A Predictive Model For Flowering Of Virginia Orchid, Cypripedium Pubescens, Emily Horton

Student Scholar Showcase

No abstract provided.

Correlations Of Co2 Levels, Brittney Nelson

Scholars Week

This project looks at the correlation between CO2 levels and human influences as well as the correlation between CO2 levels and global temperatures.

Applying The Mathematical Statistics Analysis Method To A Topic, A. V. Madraximova, S Kukiyeva

Scientific journal of the Fergana State University

Applying the mathematical statistics analysis method to a topic

Using Interactive Methods Of Teaching The Theme On Astronomy "The Moon Is The Natural Satellite Of The Earth" In General Schools, Z. Khusanov,, B Omonov

Scientific journal of the Fergana State University

Using interactive methods of teaching the theme on astronomy "The Moon is the natural satellite of the Earth" in general schools

The Basic Equation Of The Molecular-Kinetic Theory Of Gases, Sh Yakubova, N Nosirov,, O Tulanov

Scientific journal of the Fergana State University

The basic equation of the molecular-kinetic theory of gases

A Mixed Boundary-Value Problem For The Second Order Integral-Differential Equation, Akhmadjon Kushakovich Urinov, Maftuna Rakhimova

Scientific journal of the Fergana State University

A mixed boundary-value problem for the second order integral-differential equation

Professional Orientation Of Students Based On The Skills Of Mathematical Modeling, Z Siddikov

Scientific journal of the Fergana State University

Professional orientation of students based on the skills of mathematical modeling

Interdisciplinary Connection In The Theory Of Probability And Mathematical Statistics, A. Yusupova,, S. Oktamov

Scientific journal of the Fergana State University

Interdisciplinary connection in the theory of probability and mathematical statistics

The Basic Equation Of The Molecular-Kinetic Theory Of Gases, Sh Yakubova, N Nosirov,, O Tulanov

Scientific journal of the Fergana State University

The basic equation of the molecular-kinetic theory of gases