Mathematics Commons^™

Complex Neutrosophic Soft Set, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mumtaz Ali, Ganeshsree Selvachandran

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we propose the complex neutrosophic soft set model, which is a hybrid of complex fuzzy sets, neutrosophic sets and soft sets. The basic set theoretic operations and some concepts related to the structure of this model are introduced, and illustrated. An example related to a decision making problem involving uncertain and subjective information is presented, to demonstrate the utility of this model.

Complex Neutrosophic Graphs Of Type 1, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we introduced a new neutrosophic graphs called complex neutrosophic graphs of type1 (CNG1) and presented a matrix representation for it and studied some properties of this new concept. The concept of CNG1 is an extension of generalized fuzzy graphs of type 1 (GFG1) and generalized single valued neutrosophic graphs of type 1 (GSVNG1).

Shortest Path Problem Under Trapezoidal Neutrosophic Information, Florentin Smarandache, Said Broumi, Mohamed Talea, Assia Bakali

Branch Mathematics and Statistics Faculty and Staff Publications

In this research paper, a new approach is proposed for computing the shortest path length from source node to destination node in a neutrosophic environment. The edges of the network are assigned by trapezoidal fuzzy neutrosophic numbers. A numerical example is provided to show the performance of the proposed approach.

A Critical Path Problem Using Triangular Neutrosophic Number, Florentin Smarandache, Mai Mohamed, Yongquan Zhou, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

The Critical Path Method (CPM) is one of several related techniques for planning and managing of complicated projects in real world applications. In many situations, the data obtained for decision makers are only approximate, which gives rise of neutrosophic critical path problem. In this paper, the proposed method has been made to find the critical path in network diagram, whose activity time uncertain. The vague parameters in the network are represented by triangular neutrosophic numbers, instead of crisp numbers. At the end of paper, two illustrative examples are provided to validate the proposed approach.

Educational Magic Tricks Based On Error-Detection Schemes, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

Magic tricks based on computer science concepts help grab student attention and can motivate them to delve more deeply. Error detection ideas long used by computer scientists provide a rich basis for working magic; probably the most well known trick of this type is one included in the CS Unplugged activities. This paper shows that much more powerful variations of the trick can be performed, some in an unplugged environment and some with computer assistance. Some of the tricks also show off additional concepts in computer science and discrete mathematics.

Patterns In Words Related To Dna Rearrangements, Lukas Nabergall

USF Tampa Graduate Theses and Dissertations

Patterns, sequences of variables, have traditionally only been studied when morphic images of them appear as factors in words. In this thesis, we initiate a study of patterns in words that appear as subwords of words. We say that a pattern appears in a word if each pattern variable can be morphically mapped to a factor in the word. To gain insight into the complexity of, and similarities between, words, we define pattern indices and distances between two words relative a given set of patterns. The distance is defined as the minimum number of pattern insertions and/or removals that transform …

The Fascinating Mathematical Beauty Of Triangular Numbers

Georgia Journal of Science

The abstract is available under additional files below.

An Optimal Execution Problem With S-Shaped Market Impact Functions, Takashi Kato

Communications on Stochastic Analysis

No abstract provided.

Multi-Type Display Calculus For Semi-De Morgan Logic, Giuseppe Greco, Fei Liang, M. Andrew Moshier, Alessandra Palmigiano

Mathematics, Physics, and Computer Science Faculty Articles and Research

We introduce a proper multi-type display calculus for semi De Morgan logic which is sound, complete, conservative, and enjoys cut-elimination and subformula property. Our proposal builds on an algebraic analysis of semi De Morgan algebras and applies the guidelines of the multi-type methodology in the design of display calculi.

The Mathematical Magic Of Perfect Numbers

Georgia Journal of Science

Mathematicians have been fascinated for centuries by the properties and patterns of numbers [2]. They have noticed that some numbers are equal to the sum of all of their factors (not including the number itself). Such numbers are called perfect numbers. Thus a positive integer is called a perfect number if it is equal to the sum of its proper positive divisors. The search for perfect numbers began in ancient times. The four perfect numbers 6, 28, 496, and 8128 seem to have been known from ancient times [2]. In this paper, we will investigate some important properties of perfect …

Lump, Complexiton And Algebro-Geometric Solutions To Soliton Equations, Yuan Zhou

USF Tampa Graduate Theses and Dissertations

In chapter 2, we study two Kaup-Newell-type matrix spectral problems, derive their soliton hierarchies within the zero curvature formulation, and furnish their bi-Hamiltonian structures by the trace identity to show that they are integrable in the Liouville sense. In chapter 5, we obtain the Riemann theta function representation of solutions for the first hierarchy of generalized Kaup-Newell systems.

In chapter 3, using Hirota bilinear forms, we discuss positive quadratic polynomial solutions to generalized bilinear equations, which generate lump or lump-type solutions to nonlinear evolution equations, and propose an algorithm for computing higher-order lump or lump-type solutions. In chapter 4, we …

Prevalence Of Typical Images In High School Geometry Textbooks, Megan N. Cannon

USF Tampa Graduate Theses and Dissertations

Visualization in mathematics can be discussed in many ways; it is a broad term that references physical visualization objects as well as the process in which we picture images and manipulate them in our minds. Research suggests that visualization can be a powerful tool in mathematics for intuitive understanding, providing and/or supporting proof and reasoning, and assisting in comprehension. The literature also reveals some difficulties related to the use of visualization, particularly how illustrations can mislead students if they are not comfortable seeing concepts represented in varied ways. However, despite the extensive research on the benefits and challenges of visualization …

Cybersecurity: Probabilistic Behavior Of Vulnerability And Life Cycle, Sasith Maduranga Rajasooriya

USF Tampa Graduate Theses and Dissertations

Analysis on Vulnerabilities and Vulnerability Life Cycle is at the core of Cybersecurity related studies. Vulnerability Life Cycle discussed by S. Frei and studies by several other scholars have noted the importance of this approach. Application of Statistical Methodologies in Cybersecurity related studies call for a greater deal of new information. Using currently available data from National Vulnerability Database this study develops and presents a set of useful Statistical tools to be applied in Cybersecurity related decision making processes.

In the present study, the concept of Vulnerability Space is defined as a probability space. Relevant theoretical analyses are conducted and …

Properties Enjoyed By The Highest Digit In A Base Other Than The Base 10, Sudhir Goel, Kathy Simons

Georgia Journal of Science

The number nine in base ten enjoys some nice arithmetic properties. In this paper, we show that these properties are not intrinsic to the number nine; in fact, they are true for the largest digit in any base b. Four properties involving the final sums of all the digits of a number in a non-decimal base are explored and proofs of these properties are given in the appendix.

Principle Components For Diagnosing Dispersion In Multivariate Statistical Process Control, Terrance E. Murphy, Mary Mcshane-Vaughn, Kwok Leung-Tsui

Georgia Journal of Science

We provide an easily implemented procedure to help data analysts systematically diagnose which quality characteristics may be driving the dispersion of a multivariate process out of control. Multivariate statistical process control commonly uses Hotelling's T² statistic to indicate when a multivariate observation goes out-of-control. Several techniques currently exist that accurately diagnose which specific variables are driving the T² statistic out-of-control. For subgroups of independently and identically distributed multivariate normal observations, we advocate decomposing the overall T² into independent T² statistics for separate monitoring of location and dispersion. We propose a procedure based on principle components to …

Conference Program, University Of Dayton

Summer Conference on Topology and Its Applications

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications.

Solving Liouville-Type Problems On Manifolds With Poincar´E-Sobolev Inequality By Broadening Q-Energy From Finite To Infinite, Lina Wu

Publications and Research

The aim of this article is to investigate Liouville-type problems on complete non-compact Riemannian manifolds with Poincar´e-Sobolev Inequality. Two significant technical breakthroughs are demonstrated in research findings. The first breakthrough is an extension from non-flat manifolds with non-negative Ricci curvatures to curved manifolds with Ricci curvatures varying among negative values, zero, and positive values. Poincar´e-Sobolev Inequality has been applied to overcome difficulties of an extension on manifolds. Poincar´e-Sobolev Inequality has offered a special structure on curved manifolds with a mix of Ricci curvature signs. The second breakthrough is a generalization of q-energy from finite to infinite. At this point, a …

Calculus Reform: Increasing Stem Retention And Post-Requisite Course Success While Closing The Retention Gap For Women And Underrepresented Minority Students, Doug Bullock, Janet Callahan, Jocelyn B. S. Cullers

Mathematics Faculty Publications and Presentations

Boise State University (BSU) implemented an across-the-board reform of calculus instruction during the 2014 calendar year. The details of the reform, described elsewhere (Bullock, 2015), (Bullock 2016), involve both pedagogical and curricular reform. Gains from the project have included a jump in Calculus I pass rate, greater student engagement, greater instructor satisfaction, a shift toward active learning pedagogies, and the emergence of a strong collaborative teaching community. This paper examines the effects of the reform on student retention. Since the curricular reform involved pruning some content and altering course outcomes, which could conceivably have negative downstream impacts, we report on …

Existence And Rapid Convergence Results For Nonlinear Caputo Nabla Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson

Department of Mathematics: Faculty Publications

This paper is concerned with finding properties of solutions to initial value problems for nonlinear Caputo nabla fractional difference equations. We obtain existence and rapid convergence results for such equations by use of Schauder’s fixed point theorem and the generalized quasi-linearization method, respectively. A numerical example is given to illustrate one of our rapid convergence results.

The Importance Of Mathematical Wording By Math Instructors, Sudhir Goel, Denise Reid

Georgia Journal of Science

At times we the math instructors in a classroom are not careful enough to use proper Mathematical wording, e.g. sin² + cos² = 1 without any reference to the angle. Improper Mathematical wording can be confusing to a student at any level, especially at high school and/or at a college freshman or sophomore level. It may hinder the students’ progress in the present and the subsequent math courses.

Connecting Algebra And Geometry For Extraneous Roots, Sudhir Goel, Iwan Elstak

Georgia Journal of Science

Extraneous roots are an unsolved mystery for our freshmen level college math students. The students are often confused and wonder what extraneous roots are and how do they suddenly appear while solving an algebraic equation. In this paper we clarify the idea of extraneous roots and connect the algebra and geometry behind extraneous roots.

Been There Done That Can We Connect?, Sudhir Goel, Patricia Bezona

Georgia Journal of Science

A standard topic in a College Algebra course is to find the coordinates of the midpoint of a line segment connecting two points. In the early twentieth century [1] and [2], in a few texts, this idea was extended to find the coordinates of a point that divides a line segment in any given ratio. In this paper, we present a neat application of this extended idea, and further use it to find the co-ordinates of the centroid of a triangle with vertices A(x₁, y₁), B(x₂, y₂) and …

Leslie Matrices And Women Population In The United States Of America, Brittney Nelson, Denise T. Reid, Antonija Tangar, Jose A. Velez-Marulanda

Georgia Journal of Science

This research tests the accuracy of the Leslie matrix, which is a discrete age-structured method that uses fertility and survival rates, as a tool for predicting women population. Based on available data for the year 2000, we have constructed a Leslie matrix that predicts female population in the United States for every five years from the years 2000 to 2020. To test the accuracy of this method, we compare the aforementioned obtained projected data for the year 2010 with the actual data for women population in the United States obtained by the 2010 U.S. Census.

College Algebra - Large Section Versus Traditional Size, Andreas Lazari, Denise Reid

Georgia Journal of Science

The economic crisis facing our nation forced many companies and universities to downsize and learn to operate with smaller budgets. Valdosta State University (VSU) was not immune to this economic crisis. To deal with this crisis VSU started offering large sections of core area courses, including College Algebra (MATH 1111). It is clear from a financial point of view that large sections will benefit the university during this financial crisis. What was not clear was the impact to student learning and success in College Algebra. In the fall 2010 and fall 2011 terms, VSU offered the first large sections of …

Vanishing Of Ext And Tor Over Fiber Products, Saeed Nasseh, Sean Sather-Wagstaff

Mathematical Sciences: Faculty Publications

Consider a non-trivial fiber product R=S×kT of local rings S, T with common residue field k. Given two finitely generate R-modules M and N, we show that if TorRi(M,N)=0=TorRi+1(M,N) for some i≥5, then pdR(M)≤1 or pdR(N)≤1. From this, we deduce several consequence, for instance, that R satisfies the Auslander-Reiten Conjecture.

Connecting Algebra And Geometry To Find Square And Higher Order Roots, Iwan R. Elstak, Sudhir Goel

Georgia Journal of Science

Unfortunately, the repeat rate for all core curriculum courses including calculus-I and II, and also math education courses is too high. K-12 students are barely able to do estimation, an important part of Mathematics, whether it is adding fractions or finding roots, or for that matter, simple percent problems. In this paper we present geometric ways to reason about approximation of square roots and cube roots that are not accessible with simple routine techniques. We combine graphical methods, the use of a geometry software (sketch pad) and convergence of sequences to find higher order roots of positive real numbers and …

Weak Factorizations Of The Hardy Space H1(RN) In Terms Of Multilinear Riesz Transforms, Ji Li, Brett D. Wick

Mathematics Faculty Research

This paper provides a constructive proof of the weak factorization of the classical Hardy space in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of (the dual of ) via commutators of the multilinear Riesz transforms.

Assessment Of The Effects Of Azimuthal Mode Number Perturbations Upon The Implosion Processes Of Fluids In Cylinders, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Highlights

• Implosion instabilities are studied by linearizing about a symmetric implosion.

• This suggests azimuthal instabilities decrease with time and mode number.

• Numerics capture the delta functions from linearized solutions of conservation laws.

• The mass of these delta functions is used to estimate perturbations in shock fronts.

• The linear Klein–Gordon equation in one dimension is solved via formal asymptotics.

Abstract

Fluid instabilities arise in a variety of contexts and are often unwanted results of engineering imperfections. In one particular model for a magnetized target fusion reactor, a pressure wave is propagated in a cylindrical annulus comprised of a dense fluid before …

Finding Fibonacci: The Quest To Rediscover The Forgotten Mathematical Genius Who Changed The World (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World by Keith Devlin. Princeton, NJ: Princeton University Press, 2017. 256 pp. ISBN: 9780691174860.

The Derivatives Of The Sine And Cosine Functions: A Mini_Primary Source Project For Calculus I Students, Dominic Klyve

Mathematics Faculty Scholarship

This curricular modular guides students through a method of calculating the derivative of the sine and cosine functions using differentials. It is based on one primary source: Leonhard Euler's Institutiones calculi differentialis (Foundations of Differential Calculus) [2], published in 1755.