Tasks For Learning Trigonometry, 2024 Utah State University
Tasks For Learning Trigonometry, Sydnee Andreasen
All Graduate Reports and Creative Projects, Fall 2023 to Present
Many studies have been done using task-based learning within different mathematics courses. Within the field of trigonometry, task-based learning is lacking. The following research aimed to create engaging, mathematically rich tasks that meet the standards for the current trigonometry course at Utah State University and align with the State of Utah Core Standards for 7th through 12th grades. Four lessons were selected and developed based on the alignment of standards, the relevance to the remainder of the trigonometry course, and the relevance to courses beyond trigonometry. The four lessons that were chosen and developed were related to trigonometric ratios, graphing …
On Cheeger Constants Of Knots, 2024 California State University, San Bernardino
On Cheeger Constants Of Knots, Robert Lattimer
Electronic Theses, Projects, and Dissertations
In this thesis, we will look at finding bounds for the Cheeger constant of links. We will do this by analyzing an infinite family of links call two-bridge fully augmented links. In order to find a bound on the Cheeger constant, we will look for the Cheeger constant of the link’s crushtacean. We will use that Cheeger constant to give us insight on a good cut for the link itself, and use that cut to obtain a bound. This method gives us a constructive way to find an upper bound on the Cheeger constant of a two-bridge fully augmented link. …
Rsa Algorithm, 2024 Arkansas Tech University
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.
“Don’T Call On Me!”: Mediating Preservice Elementary Teachers’ Mathematics Anxiety In A Problem-Based Classroom, 2024 SUNY New Paltz
“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 …
Generalized Q-Fock Spaces And Structural Identities, 2024 Chapman University
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.
On Axially Rational Regular Functions And Schur Analysis In The Clifford-Appell Setting, 2024 Chapman University
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 …
Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, 2024 St. Mary's University
Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine
Honors Program Theses and Research Projects
Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …
Quasistationary Distribution For The Invasion Model On A Complete Bipartite Graph, 2024 University of British Columbia, Vancouver, BC V6T 1Z4, Canada
Quasistationary Distribution For The Invasion Model On A Complete Bipartite Graph, Clayton Allard, Iddo Ben-Ari, Shrikant Chand, Van Hovenga, Edith Lee, Julia Shapiro
Journal of Stochastic Analysis
No abstract provided.
A Characterization Of The Operator Entropy In Terms Of An Isometry Property Related To Trace Norms, 2024 Meijo University, Tenpaku, Nagoya 468- 8502, Japan
A Characterization Of The Operator Entropy In Terms Of An Isometry Property Related To Trace Norms, Ryo Inayoshi
Journal of Stochastic Analysis
No abstract provided.
A Bayesian Approach For Lifetime Modeling And Prediction With Multi-Type Group-Shared Missing Covariates, 2024 Communication University of Zhejiang
A Bayesian Approach For Lifetime Modeling And Prediction With Multi-Type Group-Shared Missing Covariates, Hao Zeng, Xuxue Sun, Kuo Wang, Yuxin Wen, Wujun Si, Mingyang Li
Engineering Faculty Articles and Research
In the field of reliability engineering, covariate information shared among product units within a specific group (e.g., a manufacturing batch, an operating region), such as operating conditions and design settings, exerts substantial influence on product lifetime prediction. The covariates shared within each group may be missing due to sensing limitations and data privacy issues. The missing covariates shared within the same group commonly encompass a variety of attribute types, such as discrete types, continuous types, or mixed types. Existing studies have mainly considered single-type missing covariates at the individual level, and they have failed to thoroughly investigate the influence of …
Pseudo-Differential Operators On The Circle, Bernoulli Polynomials, 2024 University Bordeaux
Pseudo-Differential Operators On The Circle, Bernoulli Polynomials, Roger Gay, Ahmed Sebbar
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show how the classical polylogarithm function Lis (z) and its relatives, the Hurwitz zeta function and the Lerch function are all of a spectral nature, and can explain many properties of the complex powers of the Laplacian on the circle and of the distribution (x +i0)s .We also make a relation with a result of Keiper [Fractional Calculus and its relationship to Riemann’s zeta function, Master of Science, Ohio State University, Mathematics (1975)].
Spacetime Geometry Of Acoustics And Electromagnetism, 2024 Chapman University
Spacetime Geometry Of Acoustics And Electromagnetism, Lucas Burns, Tatsuya Daniel, Stephon Alexander, Justin Dressel
Mathematics, Physics, and Computer Science Faculty Articles and Research
Both acoustics and electromagnetism represent measurable fields in terms of dynamical potential fields. Electromagnetic force-fields form a spacetime bivector that is represented by a dynamical energy–momentum 4-vector potential field. Acoustic pressure and velocity fields form an energy–momentum density 4-vector field that is represented by a dynamical action scalar potential field. Surprisingly, standard field theory analyses of spin angular momentum based on these traditional potential representations contradict recent experiments, which motivates a careful reassessment of both theories. We analyze extensions of both theories that use the full geometric structure of spacetime to respect essential symmetries enforced by vacuum wave propagation. The …
Two Non–*–Isomorphic *–Lie Algebra Structures On Sl(2,R) And Their Physical Origins, 2024 Università di Roma Tor Vergata, Roma I-00133, Italy
Two Non–*–Isomorphic *–Lie Algebra Structures On Sl(2,R) And Their Physical Origins, Luigi Accardi, Irina Ya. ArefʹEva, Yungang Lu, Igorʹ VasilʹEvich Volovich
Journal of Stochastic Analysis
No abstract provided.
New Effective Transformational Computational Methods, 2024 University of Maryland Eastern Shore
New Effective Transformational Computational Methods, Jun Zhang, Ruzong Fan, Fangyang Shen, Junyi Tu
Publications and Research
Mathematics serves as a fundamental intelligent theoretic basis for computation, and mathematical analysis is very useful to develop computational methods to solve various problems in science and engineering. Integral transforms such as Laplace Transform have been playing an important role in computational methods. In this paper, we will introduce Sumudu Transform in a new computational approach, in which effective computational methods will be developed and implemented. Such computational methods are straightforward to understand, but powerful to incorporate into computational science to solve different problems automatically. We will provide computational analysis and essentiality by surveying and summarizing some related recent works, …
The Frankensteinian Nature Of Mathematics, 2024 Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
The Frankensteinian Nature Of Mathematics, Ali Barahmand
Journal of Humanistic Mathematics
Frankenstein is a story about a scientist who creates a sapient creature that gets out of control and horrifies its creator by its unexpected behavior. In this note, we show that this type of undesirable behavior can reflect a part of the nature of mathematics, and that its origin is related to the ontological question of whether mathematics is invented or discovered. Based on a review of the relationship be- tween discovery and invention, we demonstrate that mathematics has similarities and differences with both discovery and invention. In the natural sciences, new instruments have to be invented to discover new …
Covariant Anyons Via Mackey Machinery, 2024 Army Research Laboratory Adelphi, MD, 21005-5069, USA
Covariant Anyons Via Mackey Machinery, Radhakrishnan Balu
Journal of Stochastic Analysis
No abstract provided.
Nonlinear Filtering Of Classical And Quantum Spin Systems, 2024 National Academies/Air Force Research Laboratory, Wright Patterson Air Force Base, Ohio 45433 USA
Nonlinear Filtering Of Classical And Quantum Spin Systems, Sivaguru S. Sritharan, Saba Mudaliar
Journal of Stochastic Analysis
No abstract provided.
Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being Through Hybrid Mathematical Modeling, 2024 University of Tennessee, Knoxville
Bridging Biological Systems With Social Behavior, Conservation, Decision Making, And Well-Being Through Hybrid Mathematical Modeling, Maggie Renee Sullens
Faculty Publications and Other Works -- Mathematics
This dissertation defense presentation highlights the power of hybrid mathematical modeling and addresses crucial issues such as:
1️. The Impact of Industry Collapse on Community Mental Health: A Complex Contagion ODE Model.
2️. Budget Allocation and Illegal Fishing: A Game Theoretic Model.
3️. Reactive Scope Model with an Energy Budget and Multiple Mediators: An ODE Model
The overarching theme of Hybrid Mathematical Modeling beautifully captures the essence of this work, demonstrating its potential to unravel ecological issues while addressing the intricate interactions between humans and the environment.
Reducing Food Scarcity: The Benefits Of Urban Farming, 2023 Brigham Young University
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 …
Convolution And Autoencoders Applied To Nonlinear Differential Equations, 2023 East Tennessee State University
Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye
Electronic Theses and Dissertations
Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to …