Mathematics Commons^™

Affect Graphing: Leveraging Graphical Representations In The Study Of Students’ Affect In Mathematics, V. Rani Satyam, Younggon Bae, John P. Smith Iii, Mariana Levin

School of Mathematical & Statistical Sciences Faculty Publications

Affect (e.g., beliefs, attitudes, emotions) plays a crucial role in mathematics learning, but reliance on verbal and written responses (from surveys, interviews, etc.) limits students’ expression of their affective states. As a complement to existing methods that rely on verbal reports, we explore how graphing can be used to study affect during mathematical experiences. We analyze three studies that used graphing to represent, stimulate recall, and reflect on affect. In each, students were asked to draw their perception of an affective construct, such as confidence or intensity of emotion, against time. The studies differed in participant populations, target affect, timescales …

Directions For The Development Of Personal Subsidiary Farms And Increasing Sources Of Income In The Future, Yakupov Kabil

Karakalpak Scientific Journal

This article discusses the features of the development of personal subsidiary farms in modern conditions, defines their functions in the agrarian economy and in the life of society as a whole. Modern agrarian policy provides for the development of various forms of management, including personal subsidiary farms. Personal subsidiary farms are an organic part of the agricultural sectors and make a significant contribution to solving the food problem of the country. The provision of the population with food products is carried out by personal subsidiary farms through their own consumption, as well as the sale of surplus products.

Dynamic Correlation Estimators For Bivariate Brownian And Geometric Brownian Motions, Majnu John, Yihren Wu

Journal of Stochastic Analysis

No abstract provided.

Graphs, Local Zeta Functions, Log-Coulomb Gases, And Phase Transitions At Finite Temperature, Wilson A. Zuniga-Galindo, Brian A. Zambrano-Luna, E. León-Cardenal

School of Mathematical & Statistical Sciences Faculty Publications

We study a log-gas on a network (a finite, simple graph) confined in a bounded subset of a local field (i.e., R, C, and Qp being the field of p-adic numbers). In this gas, a log-Coulomb interaction between two charged particles occurs only when the sites of the particles are connected by an edge of the network. The partition functions of such gases turn out to be a particular class of multivariate local zeta functions attached to the network and a positive test function, which is determined by the confining potential. The methods and results of the theory of local …

Positivity Among P-Partition Generating Functions, Nathan R. T. Lesnevich, Peter R. W. Mcnamara

Faculty Journal Articles

We seek simple conditions on a pair of labeled posets that determine when the difference of their (P,ω)-partition enumerators is F-positive, i.e., positive in Gessel's fundamental basis. This is a quasisymmetric analogue of the extensively studied problem of finding conditions on a pair of skew shapes that determine when the difference of their skew Schur functions is Schur-positive. We determine necessary conditions and separate sufficient conditions for F-positivity, and show that a broad operation for combining posets preserves positivity properties. We conclude with classes of posets for which we have conditions that are both necessary and …

Educating Consumers And Producers Of Data: Review Of Making Sense Of Numbers By Jane E. Miller (2022), Andrew J. Miller

Numeracy

Author Jane E. Miller has brought her considerable experience writing and teaching about numerate communication to a new textbook, Making Sense of Numbers. Miller uses clear prose, timely and authentic examples, and thought-provoking exercises to educate the next generation of consumers and producers of data, students in introductory quantitative reasoning, research methods, or data analysis courses. While the textbook does not fit the mold of a "typical" quantitative literacy course, creative instructors may find ways to use it in innovative quantitative literacy, data literacy, or introductory data science courses.

The Zagreb Index Of Several Random Models, Panpan Zhang

Journal of Stochastic Analysis

No abstract provided.

Software For A Conformally Invariant Yang-Mills Type Energy And Equation On 6-Manifolds, Lawrence Peterson

Datasets

The author has developed some new computer software and has used it, together with Mathematica and John M. Lee's Ricci software package, to verify many of the results in the article "A Conformally Invariant Yang-Mills Type Energy and Equation on 6-Manifolds" (arXiv:2107.08515). The author's new software is posted here, along with the Ricci package and a special guidelines file. One should read this guidelines file before studying or using the software.

Using A Stochastic Continuous-Time Markov Chain Model To Examine Alternative Timing And Duration Of The Covid-19 Lockdown In Kuwait: What Can Be Done Now?, Mustafa Al-Zoughool, Tamer Oraby, Harri Vainio, Janvier Gasana, Joseph C. Longenecker, Walid Al Ali, Mohammad Alseaidan, Susie Elsaadany, Michael G. Tyshenko

School of Mathematical & Statistical Sciences Faculty Publications

Background

Kuwait had its first COVID-19 in late February, and until October 6, 2020 it recorded 108,268 cases and 632 deaths. Despite implementing one of the strictest control measures-including a three-week complete lockdown, there was no sign of a declining epidemic curve. The objective of the current analyses is to determine, hypothetically, the optimal timing and duration of a full lockdown in Kuwait that would result in controlling new infections and lead to a substantial reduction in case hospitalizations.

Methods

The analysis was conducted using a stochastic Continuous-Time Markov Chain (CTMC), eight state model that depicts the disease transmission and …

Generating B-Nomial Numbers, Ji Young Choi

Communications on Number Theory and Combinatorial Theory

This paper presents three new ways to generate each type of b-nomial numbers: We develop ordinary generating functions, we find a whole new set of recurrence relations, and we identify each b-nomial number as a single binomial coefficient or as an alternating sum of products of two binomial coefficients.

Hadamard’S Variational Formula In Terms Of Stress And Strain Tensors, Björn Gustafsson, Ahmed Sebbar

Mathematics, Physics, and Computer Science Faculty Articles and Research

Starting from a Lagrangian action functional for two scalar fields we construct, by variational methods, the Laplacian Green function for a bounded domain and an appropriate stress tensor. By a further variation, imposed by a given vector field, we arrive at an interior version of the Hadamard variational formula, previously considered by P. Garabedian. It gives the variation of the Green function in terms of a pairing between the stress tensor and a strain tensor in the interior of the domain, this contrasting the classical Hadamard formula which is expressed as a pure boundary variation.

Optimal Measures For P-Frame Energies On Spheres, Dmitriy Bilyk, Alexey Glazyrin, Ryan Matzke, Josiah Park, Oleksandr Vlasiuk

School of Mathematical & Statistical Sciences Faculty Publications

We provide new answers about the distribution of mass on spheres so as to minimize energies of pairwise interactions. We find optimal measures for the pp-frame energies, i.e., energies with the kernel given by the absolute value of the inner product raised to a positive power pp. Application of linear programming methods in the setting of projective spaces allows for describing the minimizing measures in full in several cases: we show optimality of tight designs and of the 600-cell for several ranges of pp in different dimensions. Our methods apply to a much broader class of potential functions, namely, those …

Saving, Investment, And Capital Markets In Developing Countries: A Look At Nepal And Tanzania, Aayush Aryal

CISLA Senior Integrative Projects

No abstract provided.

The Beverton-Hold Model On Isolated Time Scales, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

In this work, we formulate the Beverton-Holt model on isolated time scales and extend existing results known in the discrete and quantum calculus cases. Applying a recently introduced definition of periodicity for arbitrary isolated time scales, we discuss the effects of periodicity onto a population modeled by a dynamic version of the Beverton-Holt equation. The first main theorem provides conditions for the existence of a unique !-periodic solution that is globally asymptotically stable, which addresses the first Cushing-Henson conjecture on isolated time scales. The second main theorem concerns the generalization of the second Cushing-Henson conjecture. It investigates the effects of …

Optimal Equivalence Testing In Exponential Families, Renren Zhao, Robert L. Paige

Mathematics and Statistics Faculty Research & Creative Works

We develop uniformly most powerful unbiased (UMPU) two sample equivalence test for a difference of canonical parameters in exponential families. This development involves a non-unique reparameterization. We address this issue via a novel characterization of all possible reparameterizations of interest in terms of a matrix group. Furthermore, our procedure involves an intractable conditional distribution which we reproduce to a high degree of accuracy using saddle point approximations. The development of this saddle point-based procedure involves a non-unique reparameterization, but we show that our procedure is invariant under choice of reparameterization. Our real data example considers the mean-to-variance ratio for normally …

On The Hartogs Extension Theorem For Unbounded Domains In CN, Al Boggess, Roman Dwilewicz, Egmont Porten

Mathematics and Statistics Faculty Research & Creative Works

Let Ω ⊂ Cn, n > 2, be a domain with smooth connected boundary. If Ω is relatively compact, the Hartogs–Bochner theorem ensures that every CR distribution on ∂Ω has a holomorphic extension to Ω. For unbounded domains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extension property holds if and only if the envelope of holomorphy of Cn \ Ω is Cn. It seems that it is the first result in the literature which gives a geometric characterization of unbounded domains in Cn for which the …

Fundamental Structure Of General Stochastic Dynamical Systems: High-Dimension Case, Haoyu Wang, Xiaoliang Gan, Wenqing Hu, Ping Ao

Mathematics and Statistics Faculty Research & Creative Works

No one has proved that mathematically general stochastic dynamical systems have a special structure. Thus, we introduce a structure of a general stochastic dynamical system. According to scientific understanding, we assert that its deterministic part can be decomposed into three significant parts: the gradient of the potential function, friction matrix and Lorenz matrix. Our previous work proved this structure for the low-dimension case. In this paper, we prove this structure for the high-dimension case. Hence, this structure of general stochastic dynamical systems is fundamental.

Why Sine Membership Functions, Sofia Holguin, Javier Viaña, Kelly Cohen, Anca Ralescu, Vladik Kreinovich

Departmental Technical Reports (CS)

In applications of fuzzy techniques to several practical problems -- in particular, to the problem of predicting passenger flows in the airports -- the most efficient membership function is a sine function; to be precise, a portion of a sine function between the two zeros. In this paper, we provide a theoretical explanation for this empirical success.

Need To Combine Interval And Probabilistic Uncertainty: What Needs To Be Computed, What Can Be Computed, What Can Be Feasibly Computed, And How Physics Can Help, Julio Urenda, Vladik Kreinovich, Olga Kosheleva

Departmental Technical Reports (CS)

In many practical situations, the quantity of interest is difficult to measure directly. In such situations, to estimate this quantity, we measure easier-to-measure quantities which are related to the desired one by a known relation, and we use the results of these measurement to estimate the desired quantity. How accurate is this estimate?

Traditional engineering approach assumes that we know the probability distributions of measurement errors; however, in practice, we often only have partial information about these distributions. In some cases, we only know the upper bounds on the measurement errors; in such cases, the only thing we know about …

Σ-Ary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

The Effects Of Stem And Non-Stem Mathematics Corequisite Courses On Student Success At Public Institutions In West Virginia, Vanessa S. Keadle

Theses, Dissertations and Capstones

This study explored the differences in student success outcomes between students enrolled in non-STEM and STEM corequisite mathematics courses at 18 postsecondary institutions across five academic years in West Virginia, using de-identified student data. The researcher analyzed this extant data to determine if student characteristics were predictors of success, as defined as passing the mathematics corequisite course, retention to the next semester, and earning a GPA of 2.0 or higher. The researcher also conducted analyses to understand if the differences in those outcomes between STEM and non-STEM courses were significant. This study identified statistically significant gaps in success for students …

Implementing The Simplex Algorithm To Solve Zero-Sum Games, Chineng Vang

Senior Seminars and Capstones

The concept of a zero-sum game in Game Theory is widely studied in fields such as Mathematics and Economics in order to analyze situations and determine optimal courses of actions. Although a game or situation with fewer decisions can be solved by hand, we can turn to the Simplex Algorithm to efficiently solve larger games. This paper examines how the Simplex Algorithm can be implemented as a linear program in order to solve m x n zero-sum games.

Hypergeometric Motives, David P. Roberts, Fernando Rodriguez Villegas

Mathematics Publications

No abstract provided.

Asymptotic Properties Of Kneser Solutions To Third-Order Delay Differential Equations, Martin Bohner, John R. Graef, Irena Jadlovská

Mathematics and Statistics Faculty Research & Creative Works

The aim of this paper is to extend and complete the recent work by Graef et al. (J. Appl. Anal. Comput., 2021) analyzing the asymptotic properties of solutions to third-order linear delay differential equations. Most importantly, the authors tackle a particularly challenging problem of obtaining lower estimates for Kneser-type solutions. This allows improvement of existing conditions for the nonexistence of such solutions. As a result, a new criterion for oscillation of all solutions of the equation studied is established.

The Differentialgeometry Package, Ian M. Anderson, Charles G. Torre

Downloads

This is the entire DifferentialGeometry package, a zip file (DifferentialGeometry.zip) containing (1) a Maple Library file, DifferentialGeometryUSU.mla, (2) a Maple help file DifferentialGeometry.help, (3) a Maple Library file, DGApplicatons.mla. This is the latest version of the DifferentialGeometry software; it supersedes what is released with Maple.

Installation instructions

Reductions Of Some Two-Dimensional Crystalline Representations Via Kisin Modules, John Bergdall, Brandon Levin

Mathematics Faculty Research and Scholarship

We determine rational Kisin modules associated with 2-dimensional, irreducible, crystalline representations of Gal(Q¯p/Qp)" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;">Gal(ℚ⎯⎯⎯⎯⎯p/ℚp) of Hodge–Tate weights 0,k−1" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-family: inherit; font-variant-caps: inherit; font-stretch: inherit; line-height: normal; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;" …

Using Circle Packings To Approximate Harmonic Measure Distribution Functions, Ella Wilson

Undergraduate Mathematics Day: Past Content

Harmonic measure distribution functions, h-functions, encode information about the geometry of domains in the plane. Specifically, given a domain and a basepoint in the domain, for a fixed radius, r, the value h(r) is the probability that a Brownian particle first exits the domain within distance r of the basepoint. There are many domains for which we can compute h-functions, such as the disk and the inside and outside of a wedge. However, exact computation is often difficult or impossible for more complicated domains, so we need methods to approximate these h-functions. In this paper, we develop two methods for …

Why People Tend To Overestimate Joint Probabilities, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that, in general, people overestimate the probabilities of joint events. In this paper, we provide an explanation for this phenomenon -- as explanation based on Laplace Indeterminacy Principle and Maximum Entropy approach.

How To Deal With Conflict Of Interest Situations When Selecting The Best Submission, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations when we need to select the best submission -- the best paper, the best candidate, etc. -- there are so few experts that we cannot simply dismiss all the experts who have conflict of interest: we do not want them to judge their own submissions, but we would like to take into account their opinions of all other submissions. How can we take these opinions into account? In this paper, we show that a seemingly reasonable idea can actually lead to bias, and we explain how to take these opinions into account without biasing the final …

What Is A Natural Probability Distribution On The Class Of All Continuous Functions: Maximum Entropy Approach Leads To Wiener Measure, Vladik Kreinovich, Saeid Tizpaz-Niari

Departmental Technical Reports (CS)

While many data processing techniques assume that we know the probability distributions, in practice, we often only have a partial information about these probabilities -- so that several different distributions are consistent with our knowledge. Thus, to apply these data processing techniques, we need to select one of the possible probability distributions. There is a reasonable approach for such selection -- the Maximum Entropy approach. This approach selects a uniform distribution if all we know is that the random variable if located in an interval; it selects a normal distribution if all we know is the mean and the variance. …