Open Access. Powered by Scholars. Published by Universities.®

Physical Sciences and Mathematics Commons™

Open Access. Powered by Scholars. Published by Universities.®

2020

Mathematics

Nova Southeastern University

Articles 1 - 12 of 12

Full-Text Articles in Physical Sciences and Mathematics

Year 7 Students’ Interpretation Of Letters And Symbols In Solving Routine Algebraic Problems, Madihah Khalid Dr., Faeizah Yakop Dr., Hasniza Ibrahim Nov 2020

Year 7 Students’ Interpretation Of Letters And Symbols In Solving Routine Algebraic Problems, Madihah Khalid Dr., Faeizah Yakop Dr., Hasniza Ibrahim

The Qualitative Report

In this study wefocused on one of the recurring issues in the learning of mathematics, which is students’ errors and misconceptions in learning algebra. We investigated Year 7 students on how they manipulate and interpret letters in solving routine algebraic problems to understand their thinking process. This is a case study of qualitative nature, focusing on one pencil and paper test, observation, and in-depth interviews of students in one particular school in Brunei Darussalam. The themes that emerged from interviews based on the test showed students’ interpretation of letters categorized as “combining” - which involved the combining of numbers during …

Go to article

Classic/Quantum Harmonic Oscillator, Killian J. Hitsman Nov 2020

Classic/Quantum Harmonic Oscillator, Killian J. Hitsman

Mathematics Colloquium Series

A Harmonic Oscillator is an integral part of periodic motion in Classical and Quantum Theory. For systems with small fluctuations near stable points of equilibrium, the Harmonic Oscillator serves as a good approximation for measuring eigenstates and wave amplitudes of the particle(s). Aside from the classical version, this presentation will include the Lie Algebra of commutation relations as well as the ladder operators (Discrete and Continuous) as it pertains to a Quantum Harmonic Oscillator. After that, one of its' contributions to scalar fields in Quantum Field Theory, namely the Casimir Force, will be discussed. Whether it is a system of …

Go to article

Quaternions And Matrices Of Quaternions, Fuzhen Zhang Oct 2020

Quaternions And Matrices Of Quaternions, Fuzhen Zhang

Mathematics Colloquium Series

Quaternions comprise a noncommutative division algebra (skew field). As part of contemporary mathematics, they find uses not only in theoretical and applied mathematics but also in computer graphics, control theory, signal processing, physics, and mechanics. Speaker, N S U Professor, Fuzhen Zhang reviews basic theory on quaternions and matrices of quaternions, presents important results, proposes open questions, and surveys recent developments in the area.

Go to article

World Statistics Day: Malaria And Its Effects On The World: A Statistical Look, Aysha Nuhuman, Pola Naguib Oct 2020

World Statistics Day: Malaria And Its Effects On The World: A Statistical Look, Aysha Nuhuman, Pola Naguib

Mathematics Colloquium Series

As October 20, 2020 is designated United Nations World Statistics Day, we look at an important statistical problem using a data set collected by researchers from the United Nations. We have all heard about Malaria and seen the effects it could have on friends and family. Still, while we ponder on the who and why this could have occurred, we are here to tell you about the what and how. The severity of this disease can be seen throughout the world. In this presentation, we will look at the number of reported cases of Malaria worldwide and how they affected …

Go to article

Tridiagonal And Pentadiagonal Doubly Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker Sep 2020

Tridiagonal And Pentadiagonal Doubly Stochastic Matrices, Lei Cao, Darian Mclaren, Sarah Plosker

Mathematics Faculty Articles

We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix A is completely positive and provide examples including how one can change the initial conditions or deal with block matrices, which expands the range of matrices to which our decomposition can be applied. Our decomposition leads us to a number of related results, allowing us to prove that for tridiagonal doubly stochastic matrices, positive semidefiniteness is equivalent to complete positivity (rather than merely being implied by complete positivity). We then consider symmetric pentadiagonal matrices, proving some analogous results, and providing two different decompositions sufficient for complete …

Go to article

A Classification Of Hull Operators In Archimedean Lattice-Ordered Groups With Unit, Ricardo Enrique Carrera, Anthony W. Hager Jul 2020

A Classification Of Hull Operators In Archimedean Lattice-Ordered Groups With Unit, Ricardo Enrique Carrera, Anthony W. Hager

Mathematics Faculty Articles

The category, or class of algebras, in the title is denoted by W. A hull operator (ho) in W is a reflection in the category consisting of W objects with only essential embeddings as morphisms. The proper class of all of these is hoW. The bounded monocoreflection in W is denoted B. We classify the ho’s by their interaction with B as follows. A “word” is a function w : hoW → WW obtained as a finite composition of B and x a variable ranging in hoW. The set of these,“Word”, is in a natural …

Go to article

Phase-Adjusted Estimation Of The Covid-19 Outbreak In South Korea Under Multi-Source Data And Adjustment Measures: A Modelling Study, Xiaomei Feng, Jing Chen, Kai Wang, Lei Wang, Fengqin Zhang, Zhen Jin, Lan Zou, Xia Wang May 2020

Phase-Adjusted Estimation Of The Covid-19 Outbreak In South Korea Under Multi-Source Data And Adjustment Measures: A Modelling Study, Xiaomei Feng, Jing Chen, Kai Wang, Lei Wang, Fengqin Zhang, Zhen Jin, Lan Zou, Xia Wang

Mathematics Faculty Articles

Based on the reported data from February 16, 2020 to March 9, 2020 in South Korea including confirmed cases, death cases and recovery cases, the control reproduction number was estimated respectively at different control measure phases using Markov chain Monte Carlo method and presented using the resulting posterior mean and 95% credible interval (CrI). At the early phase from February 16 to February 24, we estimate the basic reproduction number R0 of COVID-19 to be 4.79(95% CrI 4.38 - 5.2). The estimated control reproduction number dropped rapidly to Rc ≈ 0.32(95% CrI …

Go to article

Pattern-Avoiding (0,1)-Matrices, Richard Brualdi, Lei Cao May 2020

Pattern-Avoiding (0,1)-Matrices, Richard Brualdi, Lei Cao

Mathematics Faculty Articles

We investigate pattern-avoiding (0,1)-matrices as generalizations of pattern-avoiding permutations. Our emphasis is on 123-avoiding and 321-avoiding patterns for which we obtain exact results as to the maximum number of 1's such matrices can have. We also give algorithms when carried out in all possible ways, construct all of the pattern-avoiding matrices of these two types.

Go to article

A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Emrah Paksoy Apr 2020

A Special Cone Construction And Its Connections To Structured Tensors And Their Spectra, Vehbi Emrah Paksoy

Mathematics Faculty Articles

In this work we construct a cone comprised of a group of tensors (hypermatrices) satisfying a special condition, and we study its relations to structured tensors such as M-tensors and H-tensors. We also investigate its applications to spectra of certain Z-tensors. We obtain an inequality for the spectral radius of certain tensors when the order m is odd.

Go to article

Tensor Eigenvalue Problems And Modern Medical Imaging, Vehbi Emrah Paksoy Feb 2020

Tensor Eigenvalue Problems And Modern Medical Imaging, Vehbi Emrah Paksoy

Mathematics Colloquium Series

Tensors (or hypermatrices) are multidimensional generalization of matrices. Although historically they are studied from the perspective of combinatorics and (hyper)graph theory, recent progress in the subject shows how useful they are in more applied sciences such as physics and medicine. In this presentation, I introduce a few tensor eigenvalue problems and their application to higher order diffusion tensor imaging such as diffusion-weighted magnetic resonance imaging (DW-MRI) and higher angular resolution diffusion imaging (HARDI).

Go to article

Soccer Tournament Matrices, Lei Cao Jan 2020

Soccer Tournament Matrices, Lei Cao

Mathematics Colloquium Series

In this talk, I will present a combinatorial object, soccer tournament matrices, which is understandable to undergraduate students and gives a taste of combinatorial matrix theory. Consider a round-robin tournament of n teams in which each team plays every other team exactly once and where ties are allowed. A team scores 3 points for a win, 1 point for a tie, and 0 point for a loss, then each particular result leads to a soccer tournament matrix. Let T(R, 3) denote the class of all soccer tournament matrices with the row sum vector R. In this talk, I will explore …

Go to article

A Short Note On Extreme Points Of Certain Polytopes, Lei Cao, Ariana Hall, Selcuk Koyuncu Jan 2020

A Short Note On Extreme Points Of Certain Polytopes, Lei Cao, Ariana Hall, Selcuk Koyuncu

Mathematics Faculty Articles

We give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly substochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

Go to article