Digital Commons Network^™

Flow And Stability Of Three-Dimensional Rotating Viscoelastic Jet, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

We consider rotationally driven nonlinear viscoelastic jet. In contrast to previous unrealistic planar studies with no gravity effect, we investigate here realistic three-dimensional jet with gravity effect. Using theoretical and computational methods, we develop models for such jet and its stability and determine the solutions. We find three-dimensional jet with gravity effect leads to faster and thinner jet. For jet arc length higher than its exit diameter, our calculation with typical parameter values shows that jet radius is smaller by a factor of more than 1.4 and jet speed is higher by factor of more than 2 as are compared …

Assessing Concepts, Procedures, And Cognitive Demand Of Chatgpt-Generated Mathematical Tasks, Bima Sapkota, Liza Bondurant

School of Mathematical & Statistical Sciences Faculty Publications

In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises concerns, such as outputs that are inaccurate, nonsensical, or vague. We, two mathematics teacher educators, engaged in a collaborative self-study using qualitative descriptive approaches to investigate the procedures, concepts, and cognitive demand of ChatGPT-generated mathematical tasks focused on fraction multiplication using the area model approach. We found that the ChatGPT-generated tasks were …

Exploring International Educators' Learning About Local And Global Social Justice In A Virtual Community Of Practice, Bima Sapkota, Xuwei Luo, Muna Sapkota, Murat Akarsu, Emmanuel Deogratias, Daphne Fauber, Rose Mbewe, Fidelis Mumba, Ram Krishna Panthi, Jill Newton

School of Mathematical & Statistical Sciences Faculty Publications

In this chapter, the authors report themes that emerged when a cross-cultural team of researchers involved in a virtual international community of practice (Global Social Justice in Education-GSJE) investigated reflections on activities focused on social justice in local and global contexts. The findings suggested that the activities elicited GSJE community members' understandings of the complexities of social justice associated with naming practices, privilege, and the arts within their own and across contexts. The authors discuss implications of the activities to advance diverse educators' understanding of social justice in global and local contexts. They also unpack the opportunities and challenges that …

Ivermectin, Colleen Aldous, Eleftherios Gkioulekas, Philip Oldfield

School of Mathematical & Statistical Sciences Faculty Publications

No abstract provided.

Brillouin Zones Of Integer Lattices And Their Perturbations, Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian, Mathijs Wintraecken

School of Mathematical & Statistical Sciences Faculty Publications

For a locally finite set, 𝐴⊆ℝ𝑑 , the 𝑘 th Brillouin zone of 𝑎∈𝐴 is the region of points 𝑥∈ℝ𝑑 for which ‖𝑥−𝑎‖ is the 𝑘 th smallest among the Euclidean distances between 𝑥 and the points in 𝐴 . If 𝐴 is a lattice, the 𝑘 th Brillouin zones of the points in 𝐴 are translates of each other, and together they tile space. Depending on the value of 𝑘 , they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our …

Enhanced Resolution Method For Electromagnetic Vortex Imaging Based On Electromagnetic Information Theory, Da Liu, Hongyin Shi, Ting Yang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The electromagnetic vortex imaging possesses independent orbital angular momentum with orthogonal degrees of freedom (DoF), which implies the existence of enhanced information capacity. However, high-mode orbital angular momentum (OAM) beams have stringent generation conditions and inefficient information carrying capacity, which results in limited resolution. This paper proposes a method to combine the electromagnetic information theory (EIT) with the traditional electromagnetic vortex imaging technique, which allows one may obtain more target azimuth information. The DoF, as the main component of information, has been increased to achieve higher azimuth resolution. First, the propagation and imaging model for the electromagnetic vortex with statistical …

Optimizing Energy Consumption In Smart Homes Using Ga-Lstm, Akibor Junior Chukwuka, Bakare-Bolaji Moyosoreoluwa, Baboucarr Dibba

School of Mathematical & Statistical Sciences Faculty Publications

The need to optimize energy consumption arises from the inadequate energy supply many homes face. However, to optimize energy consumption in a home, one must be equipped with the knowledge of the energy consumption rate and energy supply rate in the home. This paper proposed the use of a Long Short-Term Memory (LSTM) model optimized by Genetic Algorithm (GA) to optimize the energy consumption in a smart home. The model was designed using 8 input variables, which were observed weather information of a given region over a span of 350 days. The data set was split into a training data …

Investigating Preservice Teachers’ Conceptualizations Of Mathematical Knowledge For Teaching Through Video Analysis, Bima Sapkota

School of Mathematical & Statistical Sciences Faculty Publications

Mathematics Preservice Teachers’ (M-PSTs) conceptions of Mathematical Knowledge for Teaching (MKT) enhance their reflective skills because they utilize such conceptions to reflect on how to contextualize content knowledge during secondary mathematics teaching. While previous studies suggested M-PSTs develop MKT, including pedagogical content knowledge by analyzing teaching in video lessons, how M-PSTs enhance their conceptions of MKT through such analysis is underexplored. I used a collective case study approach to investigate how four secondary M-PSTs conceptualized MKT when they analyzed and discussed teaching represented in a video lesson using the MKT framework. The findings indicated that the M-PSTs often described teacher …

Use Of Hydroxychloroquine In Multidrug Protocols For Sars-Cov-2, Eleftherios Gkioulekas, Peter A. Mccullough

School of Mathematical & Statistical Sciences Faculty Publications

We review the available evidence supporting the use of hydroxychloroquine-based multidrug protocols in the treatment of COVID-19, in response to a recently published editorial in the Tasman Medical Journal.

Heuristics For Anti-Cyclotomic ℤp-Extensions, Debanjana Kundu, Lawrence C. Washington

School of Mathematical & Statistical Sciences Faculty Publications

This paper studies Iwasawa invariants in anti-cyclotomic towers. We do this by proposing two heuristics supported by computations. First we propose the Intersection Heuristics: these model “how often” the p-Hilbert class field of an imaginary quadratic field intersects the anti-cyclotomic tower and to what extent. Second we propose the Invariants Heuristics: these predict that the Iwasawa invariants 𝜆 and 𝜇 usually vanish for imaginary quadratic fields where p is non-split.

On The Center And The Antipode Of The Super-Yangian Of Q(1), Elena Poletaeva

School of Mathematical & Statistical Sciences Faculty Publications

For the queer Lie superalgebra Q(1), we explicitly describe the center of the super-Yangian Y Q(1) of Q(1) in terms of generators of Y Q(1). We also describe the square of the antipodal map on Y Q(1) and use the antipode to construct an involutive automorphism of Y Q(1).

On Combinatorics Of Voronoi Polytopes For Perturbations Of The Dual Root Lattices, Alexey Garber

School of Mathematical & Statistical Sciences Faculty Publications

The Voronoi conjecture on parallelohedra claims that for every convex polytope P that tiles Euclidean d-dimensional space with translations there exists a d-dimensional lattice such that P and the Voronoi polytope of this lattice are affinely equivalent. The Voronoi conjecture is still open for the general case but it is known that some combinatorial restrictions for the face structure of P ensure that the Voronoi conjecture holds for P. In this article, we prove that if P is the Voronoi polytope of one of the dual root lattices Dd*, E6*, E7* or E8*=E8 or their small perturbations, then every parallelohedron …

Logarithmic Algorithms For Fair Division Problems, Alexandr Grebennikov, Xenia Isaeva, Andrei V. Malyutin, Mikhail Mikhailov, Oleg R. Musin

School of Mathematical & Statistical Sciences Faculty Publications

We study the algorithmic complexity of fair division problems with a focus on minimizing the number of queries needed to find an approximate solution with desired accuracy. We show for several classes of fair division problems that under certain natural conditions on sets of preferences, a logarithmic number of queries with respect to accuracy is sufficient.

Signatures Of Time Interval Reproduction In The Human Electroencephalogram (Eeg), Harvey Mccone, John. S. Butler, Redmond. G. O'Connell

Articles

No abstract provided.

Probing A Neural Unreliability Account Of Auditory Sensory Processing Atypicalities In Rett Syndrome, Tufikameni Brima, Shlomit Beker, Kevin D. Prinsloo, John Butler, Aleksandra Djukic, Edward G. Freedman, Sophie Molholm, John J. Foxe

Articles

Background: In the search for objective tools to quantify neural function in Rett Syndrome (RTT), which are crucial in the evaluation of therapeutic efficacy in clinical trials, recordings of sensory-perceptual functioning using event-related potential (ERP) approaches have emerged as potentially powerful tools. Considerable work points to highly anomalous auditory evoked potentials (AEPs) in RTT. However, an assumption of the typical signal-averaging method used to derive these measures is “stationarity” of the underlying responses – i.e. neural responses to each input are highly stereotyped. An alternate possibility is that responses to repeated stimuli are highly variable in RTT. If so, this …

L∞ Bounds For Transient Growth In Repetitive And Iterative Learning Control Systems, Douglas A. Bristow, John R. Singler

Mechanical and Aerospace Engineering Faculty Research & Creative Works

This paper revisits the problem of large transient growth in Iterative Learning Control (ILC) and Repetitive Process Control (RPC) systems. In ILC and RPC problems a process is repeated iteratively, with new control calculations occurring in between each iteration. Large transient growth refers to the propensity of some control algorithms to grow error exponentially before eventually converging. While robust monotonic convergence algorithms (in which monotonic convergence is guaranteed usually in exchange for a small loss in performance) have largely eliminated the concern for large transient growth in ILC, similar results cannot always be obtained in RPC. The emergence of additive …

Extending Natural Mates In Euclidean 3-Space And Applications To Bertrand Pairs, Yun Myung Oh, Alexander Navarro

Faculty Publications

In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced in relation to the natural mate. A complete characterization of co-successors is proved, followed by an application of the co-successor towards describing Bertrand curves and their mates.

Maximizing The Number Of H-Colorings Of Graphs With A Fixed Minimum Degree, John Engbers

Mathematical and Statistical Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is an adjacency-preserving map from the vertex set of G to the vertex set of H.

On Cyclically 4-Connected Cubic Graphs, R. J. Kingan, S. R. Kingan

Publications and Research

A 3-connected cubic graph is cyclically 4-connected if it has at least n ≥ 8 vertices and when removal of a set of three edges results in a disconnected graph, only one component has cycles. By introducing the notion of cycle spread to quantify the distance between pairs of edges, we get a new characterization of cyclically 4-connected graphs. Let Q_n and V_n denote the ladder and Möbius ladder on n ≥ 8 vertices, respectively. We prove that a 3-connected cubic graph G is cyclically 4-connected if and only if G is either the Petersen graph, Q …

Quotients Of The Curve Complex, Joseph Maher, Hidetoshi Masai, Saul Schleimer

Publications and Research

We consider three kinds of quotients of the curve complex, which are obtained by coning off uniformly quasiconvex subspaces: symmetric curve sets, non-maximal train track sets, and compression body disc sets. We show that the actions of the mapping class group on those quotients are strongly weakly properly discontinuously (WPD), which implies that the actions are non-elementary and those quotients are of infinite diameter.

Time-Efficient Filtering Of Imaging Polarimetric Data By Checking Physical Realizability Of Experimental Mueller Matrices, Tatiana Novikova, Alexey Ovchinnikov, Gleb Pogudin, Jessica C. Ramella-Roman

Publications and Research

Motivation: Imaging Mueller polarimetry has already proved its potential for biomedicine, remote sensing, and metrology. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms. First, one must check the physical realizability of the experimental Mueller matrices in order to filter out non-physical data, i.e. to test the positive semi-definiteness of the 4 × 4 Hermitian coherency matrix calculated from the elements of corresponding Mueller matrix pixel-wise. For this purpose, we compared the execution time for the calculations of (i) eigenvalues, (ii) Cholesky decomposition, (iii) Sylvester’s criterion, and (iv) coefficients of the characteristic …

Identification Of Scientific Argumentation Ability Of High School Students On Optical Instrument Material, Rais Muktamar Amin, Parno Parno, Sentot Kusairi, Marlina Ali

Jurnal Pendidikan Sains

Optical instruments play a crucial role in physics education, providing essential material for students to understand complex concepts. This study aims to evaluate the scientific argumentation abilities of high school students regarding optical instruments. Conducted as a quantitative descriptive study, the research involved 60 eleventh-grade MIPA students from SMA Laboratorium UM. The research instrument was a scientific argumentation test comprising 12 essay questions, designed according to the Toulmin Argumentation Pattern (TAP) adaptation indicators, with a reliability coefficient of 0.332. Student responses were classified into five levels of scientific argumentation based on the TAP model, as developed by Sampson, Enderle, and …

Identifying Students’ Incorrect Common-Sense Knowledge In Forces And Motion: Recommendations For Developing Computer-Based Learning Media, Ahmad Ridlotul Adha, Sutopo Sutopo, Nasikhuddin Nasikhuddin

Jurnal Pendidikan Sains

Conceptual understanding is a crucial area in physics education research, focusing on students’ comprehension of fundamental principles. Force and motion, integral topics within this field, are inherently linked to students’ daily experiences. Numerous studies have identified the persistence of common sense knowledge among students. This research presents a literature review aimed at identifying such consistently held misconceptions. We analyzed 17 papers sourced from Publish or Perish 8, Google Scholar, and Scopus. Our analysis revealed that the concepts of impetus and active force are the most persistent forms of common sense knowledge, influenced by real-life experiences. Additionally, students’ difficulties with kinematics …

Analyzing Physics Students’ Misconceptions About Simple Electrical Circuits, Sapta Adiguna, Shinta Dewi Susanti, Sentot Kusairi, Iwan Setiawan

Jurnal Pendidikan Sains

This study investigates the prevalence and types of misconceptions among first-year Physics Education students regarding simple electrical circuits using the Simple Electric Circuits Diagnostic Test (SECDT). Employing a quantitative descriptive approach, the research analyzes responses from a sample of 42 students, selected through convenience sampling. The SECDT, a three-tier diagnostic instrument with a reliability of 0.69, identifies student misconceptions by categorizing responses into scientific knowledge, misconceptions, no understanding, and lack of knowledge. The results indicate significant gender differences in the types and prevalence of misconceptions. Male students exhibited a higher percentage of misconceptions (77.5%) compared to female students (62.8%). Notably, …

The Influence Of Predict, Observe, And Explain (Poe) Learning Accompanied By Formative Assessment On Misconceptions And Mastery Of Students’ Concepts Of Temperature And Heat Material, Ahmad Ilmar, Sentot Kusairi, Khusaini Khusaini

Jurnal Pendidikan Sains

High misconceptions and students’ mastery of concepts that are low enough are detected in temperature and heat material. To overcome this, teachers must apply learning strategies that are able to actively involve students in observation activities, namely the POE learning strategy. However, POE learning is not always easy to apply, students are still weak in communicating the results of their experiments. Therefore, a way is needed that helps students during the learning process to be more confident and not afraid when asked to argue, namely with formative assessment. POE learning accompanied by formative assessment aims to enable students to understand …

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

Sustainable Food House Area (Sfha): Analysis Of Community Knowledge And Behavior, Delvi Adri, Mimien Henie Irawati, Sueb Sueb

Jurnal Pendidikan Sains

This research aimed to assess the knowledge and behavior of the community regarding the Sustainable Reserve Food Garden (SRFG) program. The study was conducted in July 2016 in Jorong Lubuk Agam, Kenagarian Ampang Kuranji Koto Baru, Dharmasraya, West Sumatra. Utilizing a descriptive quantitative approach, data were collected using Accidental Random Sampling, involving 33 heads of families as respondents. The findings revealed that community knowledge and behavior related to the SRFG program were generally insufficient, with 44.1% and 47.27% of respondents, respectively, demonstrating a lack of understanding and practice. The study concludes that approximately one-third of the population has limited knowledge …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Modeling The Population Dynamics And Movement Of Zebra Mussels, Alexanderia Lacy, Yu Jin, David Strayer, Suzanne Lenhart

Department of Mathematics: Faculty Publications

Zebra mussels have caused significant damage in many lakes and rivers. By using a hybrid population model with discrete-time equations and ordinary differential equations, we represent the zebra mussel’s life cycle, growth, and population movement. The dynamics of the larvae (unsettled and settled larvae) are represented during the summer months in a system of two ordinary differential equations, while the juvenile, small adult, and large adult stages are represented by a discrete model with yearly time steps. The goal is to investigate the effects of zebra mussel movement between three different spatial locations and possible control measures. Zebra mussel data …

How To Intercept A High-Speed Rocket With A Pair Of Compasses And A Straightedge?, Yagub N. Aliyev

CODEE Journal

In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are …