Mathematics Commons^™

Nidus Idearum. Scilogs, Xiv: Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this fourteenth book of scilogs – one may find topics on examples where neutrosophics works and others don’t, law of included infinitely-many-middles, decision making in games and real life through neutrosophic lens, sociology by neutrosophic methods, Smarandache multispace, algebraic structures using natural class of intervals, continuous linguistic set, cyclic neutrosophic graph, graph of neutrosophic triplet group , how to convert the crisp data to neutrosophic data, n-refined neutrosophic set ranking, adjoint of a square neutrosophic matrix, neutrosophic optimization, de-neutrosophication, the n-ary soft set relationship, hypersoft set, extending the hypergroupoid to the superhypergroupoid, alternative ranking, Dezert-Smarandache Theory (DSmT), reconciliation between …

Pt-Symmetry And Eigenmodes, Tamara Gratcheva

University Honors Theses

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration …

Representation Theory And Its Applications In Physics, Max Varverakis

Master's Theses

Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac …

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 …

Strategy-Proof Social Choice Functions On Condorcet Domains., Flannery Marie Musk Wells

Electronic Theses and Dissertations

A social choice function is said to be strategy-proof if no voter has any motivation to lie about their true preference. Strategy-proofness is a desirable property of social choice functions so we consider here functions that always satisfy this property. We add to this property the additional desirable conditions of anonymity and neutrality and present domains on which we can get a characterization of majority rule as the only social choice function that satisfies these three properties. Furthermore, we consider what functions look like when we drop the condition of anonymity.

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

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, Evalisbeth Garcia Diazbarriga

ATU Scholars 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, 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, 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, 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 …

Invariance Of Chsh Parameters When Projecting Weakly Signaling Distribution Into A No Signaling Subspace, Aaditya Paudel

LSU New Orleans Theses and Dissertations

The seminal 1935 paper by Einstein, Podolsky, and Rosen (EPR) sparked a fundamental debate in quantum mechanics about the completeness of physical reality through the EPR paradox. They questioned local realism by suggesting that particles could exhibit instantaneous correlations across any distance, challenging classical physics. Bell's theorem (1964) argued that no local hidden variable theory could replicate quantum predictions, introducing Bell's inequalities and their experimental tests. These tests, particularly through violations of Bell's inequalities, confirmed quantum predictions of non-local correlations that local realism could not account for. Quantum theory, while supporting such correlations, adheres to the no-signaling principle to prevent …

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, Ryo Inayoshi

Journal of Stochastic Analysis

No abstract provided.

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, Roger Gay, Ahmed Sebbar

Mathematics, Physics, and Computer Science Faculty Articles and Research

We show how the classical polylogarithm function Li_s (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, 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, Luigi Accardi, Irina Ya. ArefʹEva, Yungang Lu, Igorʹ VasilʹEvich Volovich

Journal of Stochastic Analysis

No abstract provided.

An Overview Of The Second-Previous Memory Effect In The Strictlyalternating Donation Game, Mohamed Zayet, Essam El-Seidy, Amira Abdel-Malek, Aya Rabie

Basic Science Engineering

Game theory delves into the examination of strategic behaviour across diverse domains such as insurance, business, military, biology, andmore,with the aim of deriving optimal decisions. Recent research focusing on the alteration of memory in the donation game with simultaneous iterated rounds has spurred our interest in investigating this phenomenon within the realm of the strictly alternating donation game. This study proposes a novel decision-making approach, utilising the previous unit instead of the most recent one. Thescopenarrowsdownto16employedstrategies,each definedbyfinitetwo-stateautomata,whileaccountingforpotentialimplementationerrorsinthe computationofstrategypayoffs.Dominant strategies are determined by assessing the interaction payoffs among strategy pairs. This article centres on the calculation of equilibrium points among heteroclinic …

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, 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, Radhakrishnan Balu

Journal of Stochastic Analysis

No abstract provided.

Nonlinear Filtering Of Classical And Quantum Spin Systems, Sivaguru S. Sritharan, Saba Mudaliar

Journal of Stochastic Analysis

No abstract provided.

Bounded Point Derivations On Roadrunner Sets, Evan Abshire

Theses, Dissertations and Capstones

This paper is concerned primarily with a type of subset of the complex plane known as a Roadrunner set, and its admittance of a bounded point derivation with respect to a given norm on the complex plane. The four norms we are concerned with are the Uniform norm, Lipschitz norm, L^p norm, and Campanato semi-norm. The purpose of this thesis is to provide researchers in approximation theory with more tools for them to accomplish their goals such as the proof of theorems regarding generalized derivatives. A connection has historically been established between the existence of bounded point derivations and …

Cats, Dogs, And Roll Waves: Solutions For Fermi Questions, April 2024, John Adam

Mathematics & Statistics Faculty Publications

On a hot afternoon in western North Carolina, the heavens opened and (to mix metaphors) it started raining “cats and dogs.” The rain was torrential, and soon a river of water was flowing downhill into the parking lot. In rivers and dam spillways, these are known as flood waves. The picture shows a particular type of flood waves known s roll waves—shock-like patterns separated by smooth profiles. In a steady-state situation, the drag forces on the water in the channel are balanced by the down-slope gravitational force. The dimensionless friction coefficient is C, the stream depth is h, v is …

Orthogonal Single-View And Multi-View Feature Selection Models Via Spectral Theory Based Methods, Zachary Chairez

Mathematics Dissertations - Archive

As the digital world continues to grow in the age of big data, there beckons a need for efficient and robust methods for data exploration. Under the umbrella of machine learning, feature selection positions itself as a fruitful approach that uncovers buried truths and illuminates important features of data, all while minimizing long-term storage requirements. In this work, we introduce a set of novel single-view and multi-view supervised feature selection models which are embedded with orthogonality constraints to maintain data's structural integrity while confining the optimal solution's search space.

Taking advantage of the underlying framework of these types of models, …

Sky Smiley Face: Solutions For Fermi Questions, November 2024, John Adam

Mathematics & Statistics Faculty Publications

Question 2(a): By rotating Fig. 2 counterclockwise by 90°, explain why circumhorizontal arcs (CHAs) [Figs. 1(b) and (c)] form (under favorable conditions) only when the solar altitude exceeds 58° of arc. (In this case, the incoming ray enters a vertical face of an ice crystal and exits via the lower horizontal face.)Question 2(b): By considering the tilt of Earth’s imaginary N–S axis toward the plane of its orbit around the Sun (∼23.5°), explain why in the northern hemisphere CHAs cannot be seen above about latitude 56° N.

Manifold Learning In Robotics: A Tutorial And Survey, Marcus Hawkins

Computer Science and Engineering Theses - Archive

In this article, we hope to represent the current state of the art of manifold learning in an understandable and approachable way. The authors will present a general overview core algorithms associated with linear and nonlinear dimensionality reduction techniques, give rudimentary definitions from differential geometry, and tenets of robotic perception, manipulation and path planning. Some of the historical applications of these algorithms will be presented, as well as conjectures about future uses, through examples from peer-reviewed journals.

Calculus Students’ Problem-Solving Strategies On Related Rates Of Change Problems Appearing In Online Versus Paper-And-Pencil Format, Tyson Bailey

Mathematics Dissertations - Archive

This study explores first-semester calculus students’ use of mathematical problem-solving strategies while working related rates of change problems in both an online homework format and a traditional pencil-paper format. We address two research questions: (1) How do students’ mathematical problem-solving strategies when working online homework on related rates of change problems compare with their problem-solving strategies when working paper-and-pencil homework related rates of change problems? (2) What influence does the ‘view an example’ feature in online homework have on a student’s problem-solving strategies when working an online RRC homework problem? Using scores on free-response midterm exam problems on related rates …

The Direct And Inverse Scattering Problems For The Third-Order Operator, Ivan Toledo

Mathematics Dissertations - Archive

We consider the full-line direct and inverse scattering problems for the third-order ordinary differential equation containing two potentials decaying sufficiently fast at infinity. The direct scattering problem consists of the determination of the scattering data set when the two potentials are known. The scattering data set is made up of the corresponding scattering coefficients and the bound-state information. On the other hand, the inverse scattering problem involves the recovery of the two potentials when the scattering data set is available. We formulate the inverse scattering problem via a related Riemann--Hilbert problem on the complex plane. We describe the recovery of …