Mathematics Commons^™

New Examples Of Self-Dual Near-Extremal Ternary Codes Of Length 48 Derived From 2-(47,23,11) Designs, Sanja Rukavina, Vladimir Tonchev

Michigan Tech Publications, Part 2

In a recent paper (Araya and Harada, 2023), Araya and Harada gave examples of self-dual near-extremal ternary codes of length 48 for 145 distinct values of the number A12 of codewords of minimum weight 12, and raised the question about the existence of codes for other values of A12. In this note, we use symmetric 2-(47,23,11) designs with an automorphism group of order 6 to construct self-dual near-extremal ternary codes of length 48 for 150 new values of A12.

Ramanujan Type Congruences For Quotients Of Klein Forms, Timothy Huber, Nathaniel Mayes, Jeffery Opoku, Dongxi Ye

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this work, Ramanujan type congruences modulo powers of primes p≥5 are derived for a general class of products that are modular forms of level p. These products are constructed in terms of Klein forms and subsume generating functions for t-core partitions known to satisfy Ramanujan type congruences for p=5,7,11. The vectors of exponents corresponding to products that are modular forms for Γ1(p) are subsets of bounded polytopes with explicit parameterizations. This allows for the derivation of a complete list of products that are modular forms for Γ1(p) of weights 1≤k≤5 for primes 5≤p≤19 and whose Fourier coefficients …

Increased Healthspan From Exercise, Nicholas Boros

Scholar Week 2016 - present

In this talk we discuss important factors for increased healthspan. Much of the discussion will focus on strength training and cardiovascular training. In particular we outline optimal ways to increase strength and VO₂ max, which are the largest contributors to increased healthspan. We will also explain what makes a strength training program “optimal” mathematically.

Rsa Algorithm, Evalisbeth Garcia Diazbarriga

ATU Research Symposium

I will be presenting about the RSA method in cryptology which is the coding and decoding of messages. My research will focus on proving that the method works and how it is used to communicate secretly.

Data Analytics Internship At Fastenal, Jacob J. Haines

Research & Creative Achievement Day

The poster will present the results from an analysis of Fastenal's customer base to find characteristics among them that serve as useful predictors of their spending habits. This will allow Fastenal to create more accurate control groups when assessing the effectiveness of various marketing initiatives. This poster acts as the communication of capstone experience outcomes which is required for Data Science majors in addition to the capstone experience.

Using Data Visualizations To Analyze Employee Performance At Xcel Energy, Abby Venz

Research & Creative Achievement Day

Companies often are curious about their employee performance. But how, exactly, do they analyze this? As a Data Analytics Intern for Xcel Energy, I was in charge of doing just this. This poster will walk you through the methods used to analyze and model employee performance, as well as the results found and the different ways managers at Xcel Energy used them

My Experience As An It Data Intern, Annajo V. Vonseth

Research & Creative Achievement Day

This poster presentation is focused on my internship as an IT Data Intern with B’nai B’rith Youth Organization (BBYO). I was able to use the skills already learned through courses here at WSU to help project and produce high-end reports. Additionally, I was in-charge of the creation of the survey all the way to creating the PowerPoint presentation with the results. I will also discuss how Microsoft Suites played a huge role in my day-to-day work, from large, complex data sets to cleaning and refining old data, I will be discussing the skills I learned during my time as an …

“Don’T Call On Me!”: Mediating Preservice Elementary Teachers’ Mathematics Anxiety In A Problem-Based Classroom, Christina Koehne, Wenyen Huang, Nataly Chesky

Excelsior: Leadership in Teaching and Learning

This study aims to understand the ways in which problem-based teaching in a mathematics content course can alleviate pre-service elementary school teachers' mathematics anxiety. The significance of this work is to help increase the content and pedagogical knowledge of mathematics education, as outlined in STEM policies. Using a mixed method approach, the teachers-researchers explore what methods, procedures, and other perhaps unknown variables, helped pre-service elementary teachers decrease their mathematics anxiety during two mathematics content courses. The findings illuminate five major themes the authors discuss, which are illustrated by rich descriptions of students’ narratives and interviews. Given the importance of mathematics …

Extensions Of Algebraic Frames, Papiya Bhattacharjee

Mathematics Colloquium Series

A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. …

Extensions Of Algebraic Frames, Papiya Bhattacharjee

Algebra Seminar

A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. …

Generalized Q-Fock Spaces And Structural Identities, Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using 𝑞-calculus we study a family of reproducing kernel Hilbert spaces which interpolate between the Hardy space and the Fock space. We give characterizations of these spaces in terms of classical operators such as integration and backward-shift operators, and their 𝑞-calculus counterparts. Furthermore, these new spaces allow us to study intertwining operators between classic backward-shift operators and the q-Jackson derivative.

Hgs-3 The Influence Of A Tandem Cycling Program In The Community On Physical And Functional Health, Therapeutic Bonds, And Quality Of Life For Individuals And Care Partners Coping With Parkinson’S Disease, Leila Djerdjour, Jennifer L. Trilk

SC Upstate Research Symposium

Purpose Statement: Several studies have shown that aerobic exercise can have a positive impact on alleviating symptoms experienced by individuals with Parkinson's disease (PD). Despite this evidence, the potential benefits of exercise for both PD patients and their care partners (PD dyad) remain unexplored. This research project investigates the effectiveness, therapeutic collaborations, and physical outcomes of a virtual reality (VR) tandem cycling program specifically designed for PD dyads.

Methods: Following approval from the Prisma Health Institutional Review Board, individuals with PD were identified and screened by clinical neurologists. The pre-testing measures for PD dyads (N=9) included emotional and cognitive status …

On Axially Rational Regular Functions And Schur Analysis In The Clifford-Appell Setting, Daniel Alpay, Fabrizio Colombo, Antonino De Martino, Kamal Diki, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we start the study of Schur analysis for Cauchy–Fueter regular quaternionic-valued functions, i.e. null solutions of the Cauchy–Fueter operator in . The novelty of the approach developed in this paper is that we consider axially regular functions, i.e. functions spanned by the so-called Clifford-Appell polynomials. This type of functions arises naturally from two well-known extension results in hypercomplex analysis: the Fueter mapping theorem and the generalized Cauchy–Kovalevskaya (GCK) extension. These results allow one to obtain axially regular functions starting from analytic functions of one real or complex variable. Precisely, in the Fueter theorem two operators play a …

Optimal Control Of Coefficients For The Second Order Parabolic Free Boundary Problems, Ali Hagverdiyev

Mathematics Colloquium Series

In this talk I will discuss Inverse Stefan type free boundary problem for the second order parabolic equation arising for instance, in modeling of laser ablation of biomedical tissues, where the information on the coefficients, heat flux on the fixed boundary, and density of heat sources are missing and must be found along with the temperature and free boundary. New PDE constrained optimal control framework is employed, where the missing data and the free boundary are components of the control vector, and optimality criteria are based on the final moment measurement of the temperature and position of the free boundary. …

Variable-Order Fractional Laplacian And Its Accurate And Efficient Computations With Meshfree Methods, Yixuan Wu, Yanzhi Zhang

Mathematics and Statistics Faculty Research & Creative Works

The variable-order fractional Laplacian plays an important role in the study of heterogeneous systems. In this paper, we propose the first numerical methods for the variable-order Laplacian (-Δ) α (x) / 2 with 0 < α (x) ≤ 2, which will also be referred as the variable-order fractional Laplacian if α(x) is strictly less than 2. We present a class of hypergeometric functions whose variable-order Laplacian can be analytically expressed. Building on these analytical results, we design the meshfree methods based on globally supported radial basis functions (RBFs), including Gaussian, generalized inverse multiquadric, and Bessel-type RBFs, to approximate the variable-order Laplacian (-Δ) α (x) / 2. Our meshfree methods integrate the advantages of both pseudo-differential and hypersingular integral forms of the variable-order fractional Laplacian, and thus avoid numerically approximating the hypersingular integral. Moreover, our methods are simple and flexible of domain geometry, and their computer implementation remains the same for any dimension d ≥ 1. Compared to finite difference methods, our methods can achieve a desired accuracy with much fewer points. This fact makes our method much attractive for problems involving variable-order fractional Laplacian where the number of points required is a critical cost. We then apply our method to study solution behaviors of variable-order fractional PDEs arising in different fields, including transition of waves between classical and fractional media, and coexistence of anomalous and normal diffusion in both diffusion equation and the Allen–Cahn equation. These results would provide insights for further understanding and applications of variable-order fractional derivatives.

How Difficult Is It To Comprehend A Program That Has Significant Repetitions: Fuzzy-Related Explanations Of Empirical Results, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In teaching computing and in gauging the programmers' productivity, it is important to property estimate how much time it will take to comprehend a program. There are techniques for estimating this time, but these techniques do not take into account that some program segments are similar, and this similarity decreases the time needed to comprehend the second segment. Recently, experiments were performed to describe this decrease. These experiments found an empirical formula for the corresponding decrease. In this paper, we use fuzzy-related ideas to provide commonsense-based theoretical explanation for this empirical formula.

Mcfadden's Discrete Choice And Softmax Under Interval (And Other) Uncertainty: Revisited, Bartlomiej Jacek Kubica, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Studies of how people actually make decisions have led to an empirical formula that predicts the probability of different decisions based on the utilities of different alternatives. This formula is known as McFadden's formula, after a Nobel prize winning economist who discovered it. A similar formula -- known as softmax -- describes the probability that the classification predicted by a deep neural network is correct, based on the neural network's degrees of confidence in the object belonging to each class. In practice, we usually do not know the exact values of the utilities -- or of the degrees of confidence. …

Why Bernstein Polynomials: Yet Another Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many computational situations -- in particular, in computations under interval or fuzzy uncertainty -- it is convenient to approximate a function by a polynomial. Usually, a polynomial is represented by coefficients at its monomials. However, in many cases, it turns out more efficient to represent a general polynomial by using a different basis -- of so-called Bernstein polynomials. In this paper, we provide a new explanation for the computational efficiency of this basis.

Somewhat Surprisingly, (Subjective) Fuzzy Technique Can Help To Better Combine Measurement Results And Expert Estimates Into A Model With Guaranteed Accuracy: Digital Twins And Beyond, Niklas Winnewisser, Michael Beer, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To understand how different factors and different control strategies will affect a system -- be it a plant, an airplane, etc. -- it is desirable to form an accurate digital model of this system. Such models are known as digital twins. To make a digital twin as accurate as possible, it is desirable to incorporate all available knowledge of the system into this model. In many cases, a significant part of this knowledge comes in terms of expert statements, statements that are often formulated by using imprecise ("fuzzy") words from natural language such as "small", "very possible", etc. To translate …

How To Gauge Inequality And Fairness: A Complete Description Of All Decomposable Versions Of Theil Index, Saeid Tizpaz-Niari, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In general, in statistics, the most widely used way to describe the difference between different elements of a sample if by using standard deviation. This characteristic has a nice property of being decomposable: e.g., to compute the mean and standard deviation of the income overall the whole US, it is sufficient to compute the number of people, mean, and standard deviation over each state; this state-by-state information is sufficient to uniquely reconstruct the overall standard deviation. However, e.g., for gauging income inequality, standard deviation is not very adequate: it provides too much weight to outliers like billionaires, and thus, does …