Mathematics Commons^™

Mathematical Modeling Opportunities Reported By Secondary Mathematics Preservice Teachers And Instructors, Hyunyi Jung, Eryn Stehr, Jia He

Mathematical and Statistical Science Faculty Research and Publications

Engaging with mathematical modeling can support learners to collaboratively explore mathematics in integrated ways as well as generate mathematical ideas and representations that may be useful in everyday life. Although several studies provide diverse insights into teaching and learning mathematical modeling, research has yet to be conducted on the mathematical modeling learning opportunities available to secondary mathematics preservice teachers (PTs) in mathematics and education courses in teacher education programs. This study investigates the mathematical modeling learning opportunities reported by 48 instructors and ten focus groups of 37 PTs. Multiple data sources (e.g., interview transcripts, syllabi, tasks, and exams) collected from …

Numerical Methods For A Class Of Reaction-Diffusion Equations With Free Boundaries, Shuang Liu

Theses and Dissertations

The spreading behavior of new or invasive species is a central topic in ecology. The modelings of free boundary problems are widely studied to better understand the nature of spreading behavior of new species. From mathematical modeling point of view, it is a challenge to perform numerical simulations of free boundary problems, due to the moving boundary, the stiffness of the system and topological changes.

In this work, we design numerical methods to investigate the spreading behavior of new species for a diffusive logistic model with a free boundary and a diffusive competition system with free boundaries. We develop a …

Joint Spectra Of Spherical Aluthge Transforms Of Commuting N-Tuples Of Hilbert Space Operators, Chafiq Benhida, Raul E. Curto, Sang Hoon Lee, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

Let be a commuting n-tuple of operators on a Hilbert space , and let be its canonical joint polar decomposition (i.e. ⁎ ⁎ , a joint partial isometry, and ). The spherical Aluthge transform of T is the (necessarily commuting) n-tuple . We prove that , where denotes the Taylor spectrum. We do this in two stages: away from the origin, we use tools and techniques from criss-cross commutativity; at the origin, we show that the left invertibility of T or implies the invertibility of P. As a consequence, we can readily extend our main result to other spectral systems …

An Optimal Edg Method For Distributed Control Of Convection Diffusion Pdes, X. Zhang, Y. Zhang, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their uxes, and the control. Moreover, we prove the optimize-then-discretize (OD) and discrtize-then-optimize (DO) approaches coincide. Numerical results confirm our theoretical results.

Three-Dimensional Rotation Of Paramagnetic And Ferromagnetic Prolate Spheroids In Simple Shear And Uniform Magnetic Field, Christopher A. Sobecki, Yanzhi Zhang, Cheng Wang

Mathematics and Statistics Faculty Research & Creative Works

We examine a time-dependent, three-dimensional rotation of magnetic ellipsoidal particles in a two-dimensional, simple shear flow and a uniform magnetic field. We consider that the particles have paramagnetic and ferromagnetic properties, and we compare their rotational dynamics due to the strengths and directions of the applied uniform magnetic field. We determine the critical magnetic field strength that can pin the particles' rotations. Above the critical field strength, the particles' stable steady angles were determined. In a weak magnetic regime (below the critical field strength), a paramagnetic particle's polar angle will oscillate toward the magnetic field plane while its azimuthal angle …

Tick Control Methods For Amblyomma Americanum In Virginia: Applications And Modeling, Alexis Lynn White

Biological Sciences Theses & Dissertations

Tick-borne diseases continue to increase in the United States, and yet no comprehensive method of tick control currently exists. The lone star tick, Amblyomma americanum, is an aggressive human-biting tick and vector of several pathogens which effect both humans and other animals. Standard control methods do not work as well for A. americanum as they do for the more commonly studied blacklegged tick, Ixodes scapularis. TickBot, a tick-killing robot, is a potential method to control A. americanum that lures ticks to its path with carbon dioxide and the ticks die from contact with a permethrin-treated cloth that is …

Exercises Integrating High School Mathematics With Robot Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

This paper presents progress in developing exercises for high school students incorporating level-appropriate mathematics into robotics activities. We assume mathematical foundations ranging from algebra to precalculus, whereas most prior work on integrating mathematics into robotics uses only very elementary mathematical reasoning or, at the other extreme, is comprised of technical papers or books using calculus and other advanced mathematics. The exercises suggested are relevant to any differerential-drive robot, which is an appropriate model for many different varieties of educational robots. They guide students towards comparing a variety of natural navigational strategies making use of typical movement primitives. The exercises align …

Families Of Major Index Distributions: Closed Forms And Unimodality, William Keith

Michigan Tech Publications, Part 1

Closed forms for fλ,i(q):=∑τ∈SYT(λ):des(τ)=iqmaj(τ)fλ,i(q):=∑τ∈SYT(λ):des(τ)=iqmaj(τ), the distribution of the major index over standard Young tableaux of given shapes and specified number of descents, are established for a large collection of λλ and ii. Of particular interest is the family that gives a positive answer to a question of Sagan and collaborators. All formulas established in the paper are unimodal, most by a result of Kirillov and Reshetikhin. Many can be identified as specializations of Schur functions via the Jacobi-Trudi identities. If the number of arguments is sufficiently large, it is shown that any finite principal specialization of any Schur function sλ(1,q,q2,…,qn−1)sλ(1,q,q2,…,qn−1) …

A Note On Multilevel Toeplitz Matrices, Lei Cao, Selcuk Koyuncu

Mathematics Faculty Articles

Chien, Liu, Nakazato and Tam proved that all n × n classical Toeplitz matrices (one-level Toeplitz matrices) are unitarily similar to complex symmetric matrices via two types of unitary matrices and the type of the unitary matrices only depends on the parity of n. In this paper we extend their result to multilevel Toeplitz matrices that any multilevel Toeplitz matrix is unitarily similar to a complex symmetric matrix. We provide a method to construct the unitary matrices that uniformly turn any multilevel Toeplitz matrix to a complex symmetric matrix by taking tensor products of these two types of unitary …

On Three Possible Applications Of Neutrosophic Logic In Applied Sciences, Including Matter Creation, Victor Christianto, Robert N. Boyd, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In the same spirit with the theme of last issue of this SGJ journal (“Ongoing creation”), this paper shortly reviews a plausible mechanism from Aether to become ordinary matter from the perspective of Neutrosophic Logic. We also discuss two other possible applications of Neutrosophic Logic, including a resolution of conflicting paradigms in medicine. We hope that some ideas as outlined herein will be proved useful in the near future.

Fast Equilibration Dynamics Of Viscous Particle-Laden Flow In An Inclined Channel, Jeffrey Wong, Michael R. Lindstrom, Andrea L. Bertozzi

School of Mathematical & Statistical Sciences Faculty Publications

A viscous suspension of negatively buoyant particles released into a wide, open channel on an incline will stratify in the normal direction as it flows. We model the early dynamics of this stratification under the effects of sedimentation and shear-induced migration. Prior work focuses on the behaviour after equilibration where the bulk suspension either separates into two distinct fronts (settled) or forms a single, particle-laden front (ridged), depending on whether the initial concentration of particles exceeds a critical threshold. From past experiments, it is also clear that this equilibration time scale grows considerably near the critical concentration. This paper models …

Fractional Strong Matching Preclusion For Two Variants Of Hypercubes, Huifen Ge, Tianlong Ma, Miaolin Wu, Yuzhi Xiao

Theory & Applications of Graphs

Let F be a subset of edges and vertices of a graph G. If G-F has no fractional perfect matching, then F is a fractional strong matching preclusion set of G. The fractional strong matching preclusion number is the cardinality of a minimum fractional strong matching preclusion set. In this paper, we mainly study the fractional strong matching preclusion problem for two variants of hypercubes, the multiply twisted cube and the locally twisted cube, which are two of the most popular interconnection networks. In addition, we classify all the optimal fractional strong matching preclusion set of each.

Closed-Form Probability Distribution Of Number Of Infections At A Given Time In A Stochastic Sis Epidemic Model, Olusegun M. Otunuga

Mathematics Faculty Research

We study the effects of external fluctuations in the transmission rate of certain diseases and how these affect the distribution of the number of infected individuals over time. To do this, we introduce random noise in the transmission rate in a deterministic SIS model and study how the number of infections changes over time. The objective of this work is to derive and analyze the closed form probability distribution of the number of infections at a given time in the resulting stochastic SIS epidemic model. Using the Fokker-Planck equation, we reduce the differential equation governing the number of infections to …

9th Annual Postdoctoral Science Symposium, University Of Texas Md Anderson Cancer Center Postdoctoral Association

Annual Postdoctoral Science Symposium Abstracts

The mission of the Annual Postdoctoral Science Symposium (APSS) is to provide a platform for talented postdoctoral fellows throughout the Texas Medical Center to present their work to a wider audience. The MD Anderson Postdoctoral Association convened its inaugural Annual Postdoctoral Science Symposium (APSS) on August 4, 2011.

The APSS provides a professional venue for postdoctoral scientists to develop, clarify, and refine their research as a result of formal reviews and critiques of faculty and other postdoctoral scientists. Additionally, attendees discuss current research on a broad range of subjects while promoting academic interactions and enrichment and developing new collaborations.

On Cellular Automata Representation Of Submicroscopic Physics: From Static Space To Zuse’S Calculating Space Hypothesis, Victor Christianto, Volodymyr Krasnoholovets, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In some recent papers (G. ‘t Hooft and others), it has been argued that quantum mechanics can arise from classical cellular automata. Nonetheless, G. Shpenkov has proved that the classical wave equation makes it possible to derive a periodic table of elements, which is very close to Mendeleyev’s one, and describe also other phenomena related to the structure of molecules. Hence the classical wave equation complements Schrödinger’s equation, which implies the appearance of a cellular automaton molecular model starting from classical wave equation. The other studies show that the microworld is constituted as a tessellation of primary topological balls. The …

On Newtonian Dynamics With A Variable Earth Mass: Geodetic Evidence And Its Implications On Pioneer Spacecraft Anomaly And Lageos Satellite, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Around 3 decades ago, Jayant Narlikar & Halton Arp argued on possible variable mass hypothesis cosmology (VMH). In the meantime, the Earth expansion problem has attracted great interest, and recent study gives geodetic evidence that the Earth has been expanding, at least over the recent several decades. Therefore, in the present article discusses some interesting effects related to varying G, but here we argue that instead of varying G we can think of varying mass (M). Among other things we discuss receding planets from the Sun, calculation of Pioneer spacecraft anomaly as proposed by B.G. Sidharth, and also possible slight …

Fake News And Stem, Vikki French

The Liminal: Interdisciplinary Journal of Technology in Education

Based on over ten years teaching mathematics, statistics and science in universities, communities colleges, and for-profit universities, I have witnessed how Fake News is part of these disciplines and how students can easily be misled into accepting pseudoscience. This is a report of my findings.

Universal Rank-Order Transform To Extract Signals From Noisy Data, Glenn Ierley, Alexander Kostinski

Michigan Tech Publications, Part 1

We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric and objective, and the required data processing is parsimonious. The main ingredients include a rank-order data matrix and its transform to a stable form, which provide linear trends in excellent agreement with least squares regression, despite the loss of magnitude information. A group symmetry orthogonal decomposition of the 2D rank-order transform for iid (white) noise is further ordered by principal component analysis. This two-step procedure provides a noise “etalon” used to characterize arbitrary stationary stochastic processes. The …

On Nonoscillatory Solutions Of Three Dimensional Time-Scale Systems, Elvan Akin, Taher Hassan, Ozkan Ozturk, Ismail U. Tiryaki

Mathematics and Statistics Faculty Research & Creative Works

In this article, we classify nonoscillatory solutions of a system of three-dimensional time scale systems. We use the method of considering the sign of components of such solutions. Examples are given to highlight some of our results. Moreover, the existence of such solutions is obtained by Knaster's fixed point theorem.

Winnability Of The Group Labeling Lights Out Game On Complete Bipartite Graphs, Christian J. Miller

McNair Scholars Manuscripts

For an arbitrary graph, we can play Lights Out on it if we assign a number label to each of the vertices of a graph G, representing states of on/off in the original Lights Out game, with the edges connecting those vertices representing the buttons that are adjacent to each other. This project is focused on a slightly modifed version of the game's original rules, with the labels for the vertices coming from the group Zn. It is not always possible to win the game. We will be investigating the values of n for which this group labeling "Lights Out!" …

Preface, Hui-Hsiung Kuo, George Yin

Communications on Stochastic Analysis

No abstract provided.

Non-Nested Monte Carlo Dual Bounds For Multi-Exercisable Options, Xiang Cheng, Zhuo Jin

Communications on Stochastic Analysis

No abstract provided.

Subdifferentials Of Value Functions In Nonconvex Dynamic Programming For Nonstationary Stochastic Processes, Boris S. Mordukhovich, Nobusumi Sagara

Communications on Stochastic Analysis

No abstract provided.

Euler-Maruyama Method For Regime Switching Stochastic Differential Equations With Hölder Coefficients, Dung T. Nguyen, Son L. Nguyen

Communications on Stochastic Analysis

No abstract provided.

Totalitarian Random Tug-Of-War Games In Graphs, Marcos Antón, Fernando Charro, Peiyong Wang

Communications on Stochastic Analysis

No abstract provided.

Anticipating Exponential Processes And Stochastic Differential Equations, Chii Ruey Hwang, Hui-Hsiung Kuo, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Action Functionals For Stochastic Differential Equations With Lévy Noise, Shenglan Yuan, Jinqiao Duan

Communications on Stochastic Analysis

No abstract provided.

Stochastic Process And Its Role In The Development Of The Financial Market: Celebrating Professor Chow's Long And Successful Career, Xisuo L. Liu

Communications on Stochastic Analysis

No abstract provided.

Hybrid Models And Switching Control With Constraints, Jose L. Menaldi, Maurice Robin

Communications on Stochastic Analysis

No abstract provided.

Stochastic Partial Differential Equation Sis Epidemic Models: Modeling And Analysis, Nhu N. Nguyen, George Yin

Communications on Stochastic Analysis

No abstract provided.