Mathematics Commons^™

Characterizations And Infinite Divisibility Of Certain Recently Introduced Distributions Iii, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work may be a source of preventing reinventing and duplicating the existing distributions and calling them newly proposed distributions.

On The Mixtures Of Weibull And Pareto (Iv) Distribution: An Alternative To Pareto Distribution, I. Ghosh, Gholamhossein G. Hamedani, Naveen K. Bansal, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Finite mixture models have provided a reasonable tool to model various types of observed phenomena, specially those which are random in nature. In this article, a finite mixture of Weibull and Pareto (IV) distribution is considered and studied. Some structural properties of the resulting model are discussed including estimation of the model parameters via expectation maximization (EM) algorithm. A real-life data application exhibits the fact that in certain situations, this mixture model might be a better alternative than the rival popular models.

On Characterizations Of Mcllog, Ellogw, Pthl And K-Ge Distributions, Gholamhossein G. Hamedani, Nadeem Shafique Butt

Mathematics, Statistics and Computer Science Faculty Research and Publications

Huang S. and Oluyede (2016), Oluyede et al. (2016), Krishnarani (2016) and Rather and Rather (2017) consider the "McDonald Log-Logistic", the "Exponentiated Log-Logistic Weibull", the "Power Transformation Half-Logistic" and "k-Generalized Exponential" distributions, respectively, and study certain properties and applications of these distributions. The present short note is intended to complete, in some way, the above mentioned works via establishing certain characterizations of these distributions in different directions.

A Bayesian Variable Selection Approach Yields Improved Detection Of Brain Activation From Complex-Valued Fmri, Cheng-Han Yu, Raquel Prado, Hernando Ombao, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Voxel functional magnetic resonance imaging (fMRI) time courses are complex-valued signals giving rise to magnitude and phase data. Nevertheless, most studies use only the magnitude signals and thus discard half of the data that could potentially contain important information. Methods that make use of complex-valued fMRI (CV-fMRI) data have been shown to lead to superior power in detecting active voxels when compared to magnitude-only methods, particularly for small signal-to-noise ratios (SNRs). We present a new Bayesian variable selection approach for detecting brain activation at the voxel level from CV-fMRI data. We develop models with complex-valued spike-and-slab priors on the activation …

Action Of The Symmetric Group On The Free Lanke: A Catalanke Theorem, Tamar Friedmann, Philip Hanlon, Richard P. Stanley, Michelle L. Wachs

Mathematics Sciences: Faculty Publications

We initiate a study of the representation of the symmetric group on the multilinear component of an n-ary generalization of the free Lie algebra, which we call a free LAnKe. Our central result is that the representation of the symmetric group S_2n−1 on the multilinear component of the free LAnKe with S_2n−1 generators is given by an irreducible representation whose dimension is the nth Catalan number. This leads to a more general result on eigenspaces of a certain linear operator. A decomposition, into irreducibles, of the representation of S_3n−2 on the multilinear component the free LAnKe …

Investigating Problems With Mathematical Proof Skills, Samantha Collier

The University Honors Program

This research paper is focused on identifying and exploring problems that high school students have with the mathematical proof process. The study described in this report was designed to answer the question, do students who tend to struggle with mathematical proofs also struggle with understanding what is known and unknown in a proof, making assumptions about figures, and understanding mathematical converses? To answer these questions, students at three Dayton area high schools completed tasks relating to proofs and converse statements as well as a questionnaire. Contrary to the initial hypothesis, students who were perceived to have greater proof abilities did …

Question 1: Iceberg To Los Angeles, Question 2: Lost Luggage, Larry Weinstein

Physics Faculty Publications

How much fuel would it take to tow a large enough iceberg to Los Angeles to provide fresh water for the city for an entire year? (Thanks to John Adam of Old Dominion University and co-author of Guesstimation for suggesting the question.)

U.S.-based airlines lost 1.7 million pieces of luggage in 2016. How tall a mountain will this make? What is the probability an airline will lose our luggage on our next flight? (Thanks to John Adam of Old Dominion University and co-author of Guesstimation for suggesting the question.)

Self-Assembly Of Dna Graphs And Postman Tours, Katie Bakewell

UNF Graduate Theses and Dissertations

DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graphs have previously been shown to give polynomial time solutions to hard computational problems such as 3-SAT and k-colorability problems. Jonoska et al. have proposed studying self-assembly of graphs topologically, considering the boundary components of their thickened graphs, which allows for reading the solutions to computational problems through reporter strands. We discuss weighting algorithms and consider applications of self-assembly of graphs and the boundary components of their thickened graphs to problems involving minimal weight Eulerian walks such as the Chinese Postman Problem and …

On Representations Of The Jacobi Group And Differential Equations, Benjamin Webster

UNF Graduate Theses and Dissertations

In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form .

Notions Of Rough Neutrosophic Digraphs, Florentin Smarandache, Nabeela Ishfaq, Sidra Sayed, Muhammad Akram

Branch Mathematics and Statistics Faculty and Staff Publications

Graph theory has numerous applications in various disciplines, including computer networks, neural networks, expert systems, cluster analysis, and image capturing. Rough neutrosophic set (NS) theory is a hybrid tool for handling uncertain information that exists in real life. In this research paper, we apply the concept of rough NS theory to graphs and present a new kind of graph structure, rough neutrosophic digraphs. We present certain operations, including lexicographic products, strong products, rejection and tensor products on rough neutrosophic digraphs. We investigate some of their properties. We also present an application of a rough neutrosophic digraph in decision-making.

Statistics And Biomechanics: An Interdisciplinary Evaluation Of The Mathematical, Practical, And Athletic Applications Of Principal Component Analysis, Sydney Grace Davis

Undergraduate Honors Theses

Excerpt from Introduction

Coaches and athletes around the world are in constant pursuit of improving their athletic performance. For some, a routine amount of weight lifting, cardiovascular exercise, agilities and flexibility training with gradual advancement may be enough to see growth. However, many are not satisfied and turn to in-depth analyses of their techniques in order to measure their progress. After an intense workout or competition, coaches spend time breaking down athletic performances based on major movements. By compartmentalizing these activities, they can identify which motions are efficient and which ones hinder fluid motion. From this evaluation and discernment, athletes …

A New Proof Of The Existence Of Embedded Surfaces With Anosov Geodesic Flow, Victor J. Donnay

Mathematics Faculty Research and Scholarship

We give a new proof of the existence of compact surfaces embedded in ℝ³ with Anosov geodesic flows. This proof starts with a noncompact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone condition. Using a sequence of explicit maps based on the standard torus embedding, we produce compact embedded surfaces that can be seen as small perturbations of the Anosov model system and hence are themselves Anosov.

In Quest Of Bernstein Inequalities Rational Functions, Askey-Wilson Operator, And Summation Identities For Entire Functions, Rajitha Puwakgolle Gedara

Electronic Theses and Dissertations

The title of the dissertation gives an indication of the material involved with the connecting thread throughout being the classical Bernstein inequality (and its variants), which provides an estimate to the size of the derivative of a given polynomial on a prescribed set in the complex plane, relative to the size of the polynomial itself on the same set. Chapters 1 and 2 lay the foundation for the dissertation. In Chapter 1, we introduce the notations and terminology that will be used throughout. Also a brief historical recount is given on the origin of the Bernstein inequality, which dated back …

Neutropsychic Personality / A Mathematical Approach To Psychology (Third Enlarged Edition), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutropsyche is the psychological theory that studies the soul or spirit using the neutrosophy and neutrosohic theories. In other words: Neutrosophic Psychological Theory. It is based on triadic neutrosophic psychological concepts of the form (A, neutA, antiA).

Neutropsychic Personality is a neutrosophic dynamic open psychological system of tendencies to feel, think, and act specific to each individual, based on

Neutrosophic Refined Memory: that restructured the division of memory into: consciousness, aconsciousness (which we introduce as a blend of consciousness and unconsciousness), and unconsciousness. Aconscious was further subdivided into preconscious, subconscious, semiconscious = semiunconscious, subunconscious, and preunconscious …

Neutrosophic Operational Research - Vol. 3., Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

Special Subset Vertex Subgraphs For Social Networks, Florentin Smarandache, W. B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the new notion of special subset vertex subgraph of subset vertex graphs introduced recently in [46]. These subset vertex graphs takes the vertex set values from the power set P(X) of any set X. The main speciality of these subset vertex graphs is that once a set of subsets from P(X) is given, the edges of the graph are fixed in a unique way, so for a given collection of subset vertices the graph is always unique [46]. The special subset vertex subgraphs of G are the ones, which have the …

New Trends In Neutrosophic Theory And Applications Volume Ii, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, …

Subset Vertex Graphs For Social Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of subset vertex graph using the vertex set as the subset of the power set P(S), S is assumed in this book to be finite; however it can be finite or infinite. We have defined two types of subset vertex graphs, one is directed and the other one is not directed. The most important fact which must be kept in record is that for a given set of vertices there exists one and only one subset vertex graph be it of type I or type II. Several important and …

Neutrosophic Logic: The Revolutionary Logic In Science And Philosophy -- Proceedings Of The National Symposium, Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa

Branch Mathematics and Statistics Faculty and Staff Publications

The first part of this book is an introduction to the activities of the National Symposium, as well as a presentation of Neutrosophic Scientific International Association (NSIA), based in New Mexico, USA, also explaining the role and scope of NSIA - Iraqi branch. The NSIA Iraqi branch presents a suggestion for the international instructions in attempting to organize NSIA's work. In the second chapter, the pivots of the Symposium are presented, including a history of neutrosophic theory and its applications, the most important books and papers in the advancement of neutrosophics, a biographical note of Prof. Florentin Smarandache in Arabic …

Mod Rectangular Natural Neutrosophic Numbers, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the new notion of MOD rectangular planes. The functions on them behave very differently when compared to MOD planes (square). These are different from the usual MOD planes. Algebraic structures on these MOD rectangular planes are defined and developed. However we have built only MOD interval natural neutrosophic products