Mathematics Commons^™

Randomized Algorithms And How Society Uses Them Everyday, Rosaley Milano

Undergraduate Honors Thesis Projects

Randomness is an interesting and very beneficial phenomenon. In computer science randomness facilitates great advances in efficiency but topics like randomized algorithms aren’t taught until someone enters graduate school. This paper provides undergraduates as well as people unacquainted with computer science an opportunity to explore the topic of randomness by guiding them from essential topics all the way through the graduate level topic of randomized algorithms. Topics like what an algorithm is, how they are represented and the history that brought them into existence bring the reader up to speed before diving deeper into randomized algorithms. A discussion of complexity …

Guided Notes For College Algebra (Ggc), Rabia Shahbaz, Janice Alves

Mathematics Ancillary Materials

This collection of guided notes was created through a Round Fifteen Mini-Grant for Ancillary Materials Creation and Revision. Major topics include:

• Review Topics
• Equations and Inequalities
• Functions and Graphs
• Other Functions and Inequalities
• Exponentials and Logarithms

Infectious Disease Mortality Prediction, Kazi Tanvir Hasan

Mathematics

When mortality statistics are reported for infectious diseases, they commonly reflect the ratio for the entire population impacted from it. This causes an underestimation since the frail members of the population are impacted at a higher rate. With the remaining healthy members, the mortality rate becomes skewed. With this project, we study predicting mortality under varying frailty conditions to account for the hidden heterogeneity's impact on the parameter estimates.

A (2+1)-Dimensional Sine-Gordon And Sinh-Gordon Equations With Symmetries And Kink Wave Solutions, Gangwei Wang, Kaitong Yang, Haicheng Gu, Fei Guan, A. H. Kara

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, a (2+1)-dimensional sine-Gordon equation and a sinh-Gordon equation are derived from the well-known AKNS system. Based on the Hirota bilinear method and Lie symmetry analysis, kink wave solutions and travelingwave solutions of the (2+1)-dimensional sine-Gordon equation are constructed. The traveling wave solutions of the (2+1)-dimensional sinh-Gordon equation can also be provided in a similar manner. Meanwhile, conservation laws are derived.

Using Machine Learning Tools To Predict The Severity Of Osteoarthritis Based On Knee X-Ray Data, Yaorong Xiao

Master's Theses (2009 -)

Knee osteoarthritis(OA) is a very general joint disease that disturb many people especially people over 60. The severity of pain caused by knee OA is the most important portent to disable. Until now, the bad impact of osteoarthritis on health care and public health systems is still increasing.In this paper, we will build a machine learning model to detect the edge of the knee based on the X-ray image and predict the severity of OA. We use a clustering algorithm and machine learning tools to predict the severity of OA in knee X-ray images. The data is coming from …

Commutative Doubly-Idempotent Semirings Determined By Chains And By Preorder Forests, Natanael Alpay, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Books and Book Chapters

A commutative doubly-idempotent semiring (cdi-semiring) (S,V,·,0,1) is a semilattice (S,V,0) with x V 0 = x and a semilattices (S,·,1) with identity 1 such that x0 = 0, and x(y V z) = xy V xz holds for all x, y, z ϵ S. Bounded distributive lattices are cdi-semirings that satisfy xy = x ^ y, and the variety of cdi-semirings covers the variety of bounded distributive lattices. Chajda and Länger showed in 2017 that the variety of all cdi-semirings is generated by a 3-element cdi-semiring. We show that there are seven cdi-semirings with a V-semilattice of height …

Weakening Relation Algebras And Fl2-Algebras, Nikolaos Galatos, Peter Jipsen

Mathematics, Physics, and Computer Science Faculty Books and Book Chapters

FL²-algebras are lattice-ordered algebras with two sets of residuated operators. The classes RA of relation algebras and GBI of generalized bunched implication algebras are subvarieties of FL²-algebras. We prove that the congruences of FL²-algebras are determined by the congruence class of the respective identity elements, and we characterize the subsets that correspond to this congruence class. For involutive GBI-algebras the characterization simplifies to a form similar to relation algebras.

For a positive idempotent element p in a relation algebra A, the double division conucleus image p/A/p is an (abstract) weakening relation algebra, …

Ramanujan’S Theorem And Highest Abundant Numbers, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

In 1915, Ramanujan proved asymptotic inequalities for the sum of divisors function, assuming the Riemann hypothesis (RH). We consider a strong version of Ramanujan’s theorem and define highest abundant numbers that are extreme with respect to the Ramanujan and Robin inequalities. Properties of these numbers are very different depending on whether the RH is true or false.

Local And 2-Local Derivation On Solvable Leibniz Algebras Whose Nilradical Is A Quasi-Filiform Leibniz Algebra Of Maximum Length, Shavkat Ayupov, Bakhtiyor Yusupov

Karakalpak Scientific Journal

We show that any local derivation on the solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length with the maximal dimension of complementary space to the nilradical is a derivation. Moreover, a similar problem concerning 2-local derivations of such algebras is investigated.

How Emergent Social Patterns In Allogrooming Combat Parasitic Infections, Shelby N. Wilson, Suzanne S. Sindi, Heather Z. Brooks, Maryann E. Hohn, Candice R. Price, Ami E. Radunskaya, Nakeya D. Williams, Nina H. Fefferman

Mathematics Sciences: Faculty Publications

Members of social groups risk infection through contact with those in their social network. Evidence that social organization may protect populations from pathogens in certain circumstances prompts the question as to how social organization affects the spread of ectoparasites. The same grooming behaviors that establish social bonds also play a role in the progression of ectoparasitic outbreaks. In this paper, we model the interactions between social organization and allogrooming efficiency to consider how ectoparasitic threats may have shaped the evolution of social behaviors. To better understand the impacts of social grooming on organizational structure, we consider several dynamic models of …

The Application Of Late Acceptance Heuristic Method For The Tanzanian High School Timetabling Problem, Allen R. Mushi

Tanzania Journal of Science

High School timetabling is the problem of scheduling lessons of different subjects and teachers to timeslots within a week, while satisfying a set of constraints which are classified into hard and soft constraints. This problem is different from university course timetabling problem because of the differences in structures including classroom allocations and grouping of subject combinations. Given the scarce education resources in developing countries, high school timetabling problem plays a very important role in optimizing the use of meager resources and therefore contribute to improvement of quality of education. The problem has attracted attention of many researchers around the world; …

Bayesian Estimation Of Regression Quantiles In The Presence Of Autocorrelated Errors, Ayoade I. Adewole, Olusoga A. F Fasoranbaku

Tanzania Journal of Science

This is a study of  Bayesian quantile regression that broadly considered the estimation of regression quantiles in the presence of autocorrelated error. Regression models are based on several important statistical assumptions upon which their inferences rely. Autocorrelation of the error terms violates the ordinary least squares regression assumption that error terms are uncorrelated which invalidate Gauss Markov theorem. This study designed schemes for estimation and making inference of regression quantiles in the presence of autocorrelated errors using Bayesian approach. Bayesian method to quantile regression models regards unknown parameters as random variables and the parameter uncertainty was taken into account without …

Mapping Of The Geological Structures Using Digital Elevation Model (Dem)-Derived Flow Direction: A Case Study Of Rungwe Volcanic Province, Southwest Tanzania, Elisante Elisaimon Mshiu

Tanzania Journal of Science

This study aimed to assess the potentiality of Digital Elevation Model (DEM)-derived flow direction in mapping geologic structures, specifically in areas with thick overburden of soil or volcanic materials such as in the Rungwe Volcanic Province, SW Tanzania. Clustering of flow directions based on trends of structure sets found in the study area was applied and it successfully revealed a large number of geological structures through demarcated tectonic blocks from patterns created by flow directions. Northwest–southwest (NW-SE) and NE-SW- trending lineaments are the dominant structural sets in the area whereas N-S and E-W-trending lineaments constitute the minor sets. Moreover, the …

Recursive Formulas For Beans Functions Of Graphs, Kengo Enami, Seiya Negami

Theory & Applications of Graphs

In this paper, we regard each edge of a connected graph G as a line segment having a unit length, and focus on not only the "vertices" but also any "point" lying along such a line segment. So we can define the distance between two points on G as the length of a shortest curve joining them along G. The beans function B_G(x) of a connected graph G is defined as the maximum number of points on G such that any pair of points have distance at least x>0. We shall show a recursive formula for …

Higher Chow Cycles On The Jacobian Of Curves., Subham Sarkar Dr.

Doctoral Theses

The following formula, usually called Beilinson’s formula — though independently due to Deligne as well — describes the motivic cohomology group of a smooth projective variety X over a number field as the group of extensions in a conjectured abelian category of mixed motives, MMQ.The aim of this thesis is to describe this construction in the case of the motivic cohomology group of the Jacobian of a curve. The first work in this direction is due to Harris [Har83] and Pulte [Pul88], [Hai87]. They showed that the Abel-Jacobi image of the modified diagonal cycle on the triple product of a …

On Selected Subclasses Of Matroids, Tara Elizabeth Fife

LSU Doctoral Dissertations

Matroids were introduced by Whitney to provide an abstract notion of independence.

In this work, after giving a brief survey of matroid theory, we describe structural results for various classes of matroids. A connected matroid $M$ is unbreakable if, for each of its flats $F$, the matroid $M/F$ is connected%or, equivalently, if $M^*$ has no two skew circuits. . Pfeil showed that a simple graphic matroid $M(G)$ is unbreakable exactly when $G$ is either a cycle or a complete graph. We extend this result to describe which graphs are the underlying graphs of unbreakable frame matroids. A laminar family is …

Renewal Redundant Systems Under The Marshall–Olkin Failure Model. A Probability Analysis, Boyan Dimitrov, Vladimir Rykov, Tatiana Milovanova

Mathematics Publications

In this paper a two component redundant renewable system operating under the Marshall–Olkin failure model is considered. The purpose of the study is to find analytical expressions for the time dependent and the steady state characteristics of the system. The system cycle process characteristics are analyzed by the use of probability interpretation of the Laplace–Stieltjes transformations (LSTs), and of probability generating functions (PGFs). In this way the long mathematical analytic derivations are avoid. As results of the investigations, the main reliability characteristics of the system—the reliability function and the steady state probabilities—have been found in analytical form. Our approach can …

Avia 201 Project 1 Windtunnel Lab Form Ver 1.20 20200323, Nihad E. Daidzic

Aviation Department Publications

To introduce aviation/aeronautics/aerospace students to wind tunnel(s) and methods used in experimental identification of various aerodynamic (and stability) coefficients of airfoils (2D), wings (3D) and scale models.

Numerical Solution For Solving Two-Points Boundary Value Problems Using Orthogonal Boubaker Polynomials, Imad Noah Ahmed

Emirates Journal for Engineering Research

In this paper, a new technique for solving boundary value problems (BVPs) is introduced. An orthogonal function for Boubaker polynomial was utilizedand by the aid of Galerkin method the BVP was transformed to a system of linear algebraic equations with unknown coefficients, which can be easily solved to find the approximate result. Some numerical examples were added with illustrations, comparing their results with the exact to show the efficiency and the applicability of the method.

Block And Weddle Methods For Solving Nth Order Linear Retarded Volterra Integro-Differential Equations, Raghad Kadhim Salih

Emirates Journal for Engineering Research

A proposed method is presented to solve n^th order linear retarded Volterra integro-differential equations (RVIDE's) numerically by using fourth-order block and Weddle methods. Comparison between numerical and exact results has been given in numerical examples for conciliated the accuracy of the results of the proposed scheme.

Infusing Humanities In Stem Education: Student Opinions Of Disciplinary Connections In An Introductory Chemistry Course, Emily K. Faulconer, Beverly Wood, John C. Griffith

Publications

The Next Generation Science Standards and other educational reforms support the formation of deep connections across the STEM disciplines. Integrated STEM is considered as a best practice by the educational communities of the disparate disciplines. However, the integration of non-STEM disciplines is understudied and generally limited to the integration of art (STEAM). Humanistic STEM blends the study of STEM with interest in and concern for human affairs, welfare, values, or culture. This study looks at an infusion of the humanities into an online chemistry course to see if there is an influence on student connection between course content and cross-disciplinary …

A Mathematical Model Of Speeding, Jared Ott, Xavier Pérez Giménez

Honors Program: Senior Projects (Public)

Crime is often regarded as nonsensical, impulsive, and irrational. These conjectures are pointed, though conversation about the pros and cons of crime does not happen often. People point to harsh fines, jail times, and life restrictions as their reason for judgement, stating that the trade-offs are far too unbalanced to participate in illicit activity. Yet, everyday people commit small crimes, sometimes based on hedonistic desires, other times based on a rational thought process.

Speeding seems to be one of those that almost all people commit at least once during their life. Our work hopes to make an incremental improvement on …

Integer Versus Fractional Order Seir Deterministic And Stochastic Models Of Measles, Md Rafiul Islam, Angela Peace, Daniel Medina, Tamer Oraby

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations (FDEs) as approximations of some type of fractional nonlinear birth and death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While ordinary differential equations (ODEs) …

A Taxonomy Of Behaviors By Instructors That College Students Identified As Contributing To Their Math Anxiety, Matthew Allen Rhoads

Student Theses and Dissertations

Mathematics is considered one of the basics of education, but many have difficulty learning it. It is estimated that 25% of four- year college students and 80% of community college students have some degree of math anxiety. Several studies have identified math teachers as one of the primary causes of math anxiety. The purpose of this study was to identify, analyze, and classify those math instructors’ behaviors that are contributors to math anxiety. In short, what are the behaviors of a math instructor that leads to math anxiety? This study is phenomenological in nature with the goal of describing those …

On Persistence Of Superoscillations For Schrödinger Equation With Time-Dependent Quadratic Hamiltonians, Elijah Lee Hight, Jose Palacio, Tamer Oraby, Erwin Suazo

School of Mathematical & Statistical Sciences Faculty Publications

In this work, we prove the persistence in time of superoscillations for the Schrödinger equation with time-dependent coefficients. In order to prove the persistence of superoscillations, we have conditioned the coefficients to satisfy a Riccati system, and we have expressed the solution as a convolution operator in terms of solutions of this Riccati system. Further, we have solved explicitly the Cauchy initial value problem with three different kinds of superoscillatory initial data. The operator is defined on a space of entire functions. Particular examples include Caldirola-Kanai and degenerate parametric harmonic oscillator Hamiltonians, and other examples could include Hamiltonians not self-adjoint. …

Modeling And Visualizing Power Amplification In Fiber Optic Cables, Gil Parnon

University Honors Theses

Transverse mode instability in fiber optic cables causes power amplification to exhibit chaotic behavior. Due to this, numerical modeling of fiber optic power amplification is extremely computationally expensive. In this paper I work through modeling similar behavior in a simpler system. I also visualize the three-dimensional phase portrait of the system in order to better understand the behavior and hopefully relate it to more well-understood problems.

Memory-Modulated Cir Process With Discrete Delay Coefficients, Pathiranage Lochana Siriwardena, Harry Randolph Hughes, D. G. Wilathgamuwa

Journal of Stochastic Analysis

No abstract provided.

A Permutation Test And Spatial Cross-Validation Approach To Assess Models Of Interspecific Competition Between Trees, David Allen, Albert Y. Kim

Statistical and Data Sciences: Faculty Publications

Measuring species-specific competitive interactions is key to understanding plant communities. Repeat censused large forest dynamics plots offer an ideal setting to measure these interactions by estimating the species-specific competitive effect on neighboring tree growth. Estimating these interaction values can be difficult, however, because the number of them grows with the square of the number of species. Furthermore, confidence in the estimates can be overestimated if any spatial structure of model errors is not considered. Here we measured these interactions in a forest dynamics plot in a transitional oak-hickory forest. We analytically fit Bayesian linear regression models of annual tree radial …

Introductory Chapter: Dynamical Symmetries And Quantum Chaos, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

No abstract provided.

Alternating Connectivity In Random Graphs, Patrick Bennett, Ryan Cushman, Andrzej Dudek

Faculty Research and Creative Activities Award (FRACAA)

Many problems in graph theory are so hard in general that they seem hopeless. So sometimes mathematicians lower our expectations a bit, and try to prove that a statement is true for "almost all graphs" (for some reasonable interpretation of what that means) rather than insisting on proving it for all graphs. One way to address questions about about almost all graphs to use a random graph model, the first of which is due to Erdos, Rényi and Gilbert in the 1950's. Since then many more models have been introduced, but they all generate graphs according to the outcome of …