Mathematics Commons^™

Covariant Quantum White Noise From Light-Like Quantum Fields, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

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 …

Development Of A Mobile Ten Frames App For Philippine K-12 Schools, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

This paper reports on the Quick Images app, whose design framework is informed by research on ten-structured thinking and gamification principles. Inclusivity was also a major consideration, especially in the context of a developing country. Thus, the app was made freely available and required only moderate system requirements. Pilot studies revealed that the app has the potential to promote children’s ability to see two-digit numbers in relation to tens and ones, which is a major goal of elementary school mathematics. Collaborations with the Philippine Department of Education to ensure the app’s sustained use are also discussed.

Grim Under A Compensation Variant, Aaron Davis, Aaron Davis

Honors College Theses

Games on graphs are a well studied subset of combinatorial games. Balance and strategies for winning are often looked at in these games. One such combinatorial graph game is Grim. Many of the winning strategies of Grim are already known. We note that many of these winning strategies are only available to the first player. Hoping to develop a fairer Grim, we look at Grim played under a slighlty different rule set. We develop winning strategies and known outcomes for this altered Grim. Throughout, we discuss whether our altered Grim is a fairer game then the original.

An Analysis Of Growth Of The Community Integration Psychological Score In An Ethnically Diverse Population Experiencing Homelessness In A Permanent Supportive Housing Program Using Hierarchical Mixed Modeling, Leah Hollis Puglisi

Mathematics & Statistics ETDs

Hierarchical models are becoming increasingly common in epidemiological and psychological research. When analyzing data from such studies, the nested structure of the data must be taken into account. Mixed modeling in conjunction with hierarchical mixed modeling allows researchers to ask broad questions about the population of interest. Modeling under restricted maximum likelihood estimation (REML), as opposed to full maximum likelihood estimation (ML), increases the accuracy of estimates for the random effects in the model. We use hierarchical mixed modeling under REML estimation to analyze which factors increase “community integration”, a concept and a construct developed and used in the mental …

Super Sudoku Squares, Dean Hoffman

Communications on Number Theory and Combinatorial Theory

We refer to a completed Sudoku puzzle as a Sudoku Square of order 3. We define a more restricted, but natural, extension --- a Super Sudoku Square of order n, and determine for which orders n one exists.

Crash Risk-Based Prioritization Of Basic Safety Message In Dsrc, Seungmo Kim, Byung Jun Kim

Michigan Tech Publications, Part 1

Dedicated short-range communications (DSRC) is one of the key technologies enabling safety-critical applications for intelligent transportation system (ITS). Considering the significance of such safety-of-life applications, it is of utmost importance to guarantee reliable delivery of basic safety messages (BSMs). However, in accordance with a V2X network being inherently dynamic in key aspects such as vehicle density and velocity, the networking behavior of a DSRC system is usually highly complicated to analyze. In addition, the United States Federal Communications Commission (US FCC) recently proposed the so-called “5.9 GHz band innovation”, which includes a plan to reduce bandwidth for DSRC to 10 …

On The Global Operator And Fueter Mapping Theorem For Slice Polyanalytic Functions, Daniel Alpay, Kamal Diki, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper, we prove that slice polyanalytic functions on quaternions can be considered as solutions of a power of some special global operator with nonconstant coefficients as it happens in the case of slice hyperholomorphic functions. We investigate also an extension version of the Fueter mapping theorem in this polyanalytic setting. In particular, we show that under axially symmetric conditions it is always possible to construct Fueter regular and poly-Fueter regular functions through slice polyanalytic ones using what we call the poly-Fueter mappings. We study also some integral representations of these results on the quaternionic unit ball.

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 …

A Posteriori Error Estimates For Maxwell's Equations Using Auxiliary Subspace Techniques, Ahmed El Sakori

Dissertations and Theses

The aim of our work is to construct provably efficient and reliable error estimates of discretization error for Nédélec (edge) element discretizations of Maxwell's equations on tetrahedral meshes. Our general approach for estimating the discretization error is to compute an approximate error function by solving an associated problem in an auxiliary space that is chosen so that:

-Efficiency and reliability results for the computed error estimates can be established under reasonable and verifiable assumptions.

-The linear system used to compute the approximate error function has condition number bounded independently of the discretization parameter.

In many applications, it is some functional …

Repeated Minimizers Of $P$-Frame Energies, Alexey Glazyrin, Josiah Park

School of Mathematical & Statistical Sciences Faculty Publications

For a collection of $N$ unit vectors ${X}=\{x_i\}_{i=1}^N$, define the $p$-frame energy of ${X}$ as the quantity $\sum_{i\neq j} |\langle x_i,x_j \rangle|^p$. In this paper, we connect the problem of minimizing this value to another optimization problem, thus giving new lower bounds for such energies. In particular, for $p<2$, we prove that this energy is at least $2(N-d) p^{-\frac p 2} (2-p)^{\frac {p-2} 2}$ which is sharp for $d\leq N\leq 2d$ and $p=1$. We also prove that for $1\leq m

Classical And Quantum Integrability: A Formulation That Admits Quantum Chaos, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

The concept of integrability of a quantum system is developed and studied. By formulating the concepts of quantum degree of freedom and quantum phase space, a realization of the dynamics is achieved. For a quantum system with a dynamical group G in one of its unitary irreducible representative carrier spaces, the quantum phase space is a finite topological space. It is isomorphic to a coset space G=R by means of the unitary exponential mapping, where R is the maximal stability subgroup of a fixed state in the carrier space. This approach has the distinct advantage of exhibiting consistency between classical …

An Agent-Based Simulator For The Gastrointestinal Pathway Of Listeria Monocytogenes, Ashrafur Rahman, Ali Asgary, Daniel Munther, Aamir Fazil, Ben A. Smith, Jianhong Wu

Mathematics and Statistics Faculty Publications

We developed an agent-based gastric simulator for a human host to illustrate the within host survival mechanisms of Listeria monocytogenes. The simulator incorporates the gastric physiology and digestion processes that are critical for pathogen survival in the stomach. Mathematical formulations for the pH dynamics, stomach emptying time, and survival probability in the presence of gastric acid are integrated in the simulator to evaluate the portion of ingested bacteria that survives in the stomach and reaches the small intestine. The parameters are estimated using in vitro data relevant to the human stomach and L. monocytogenes. The simulator predicts that 5%–29% of …

Deformed Gaussian Operators On Weighted Q-Fock Spaces, Nobuhiro Asai, Hiroaki Yoshida

Journal of Stochastic Analysis

No abstract provided.

Subproduct Systems And Cartesian Systems: New Results On Factorial Languages And Their Relations With Other Areas, Malte Gerhold, Michael Skeide

Journal of Stochastic Analysis

No abstract provided.

A Posteriori Error Estimates For Elliptic Eigenvalue Problems Using Auxiliary Subspace Techniques, Stefano Giani, Luka Grubišić, Harri Hakula, Jeffrey S. Ovall

Mathematics and Statistics Faculty Publications and Presentations

We propose an a posteriori error estimator for high-order p- or hp-finite element discretizations of selfadjoint linear elliptic eigenvalue problems that is appropriate for estimating the error in the approximation of an eigenvalue cluster and the corresponding invariant subspace. The estimator is based on the computation of approximate error functions in a space that complements the one in which the approximate eigenvectors were computed. These error functions are used to construct estimates of collective measures of error, such as the Hausdorff distance between the true and approximate clusters of eigenvalues, and the subspace gap between the corresponding true and approximate …

An Analysis Of Preservice Elementary Teachers’ Professional Noticing Skills In A Mathematics Education Setting, Liza Bondurant, Lisa Poling, Diana Moss

Journal of Practitioner Research

Prospective elementary mathematics teachers (PTs) were asked to analyze 28 videos of cognitive interviews. The purpose of this study was to determine if experiences analyzing videos would lead to improvements in PTs’ professional noticing skills. Using a coding schema that reflected three levels of understanding (periphery, transitional, and accomplished), a frequency table was constructed that allowed PTs’ use and understanding of a noticing framework to be analyzed. Findings indicate that experiences analyzing videos leads to improvements in PTs’ professional noticing skills.

Estimating The Number Of Discrete Models Of Biological Networks, Brandilyn Stigler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Nested Links, Linking Matrices, And Crushtaceans, Madeline Brown

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Covid-19 Mathematical Model Of At-Risk Populations With Non-Pharmaceutical Preventive Measures, Bismark Oduro

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.