Superoscillations And Analytic Extension In Schur Analysis, 2021 Chapman University

#### Superoscillations And Analytic Extension In Schur Analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

We give applications of the theory of superoscillations to various questions, namely extension of positive definite functions, interpolation of polynomials and also of Rfunctions; we also discuss possible applications to signal theory and prediction theory of stationary stochastic processes. In all cases, we give a constructive procedure, by way of a limiting process, to get the required results.

New Representations For A Semi-Markov Chain And Related Filters, 2021 University of South Australia, Campus Central - City West, GPO Box 2471

#### New Representations For A Semi-Markov Chain And Related Filters, Robert J. Elliott, W. P. Malcolm

*Journal of Stochastic Analysis*

No abstract provided.

Math Escape Rooms: A Novel Approach For Engaging Learners In Math Circles, 2021 University of Nebraska at Omaha

#### Math Escape Rooms: A Novel Approach For Engaging Learners In Math Circles, Janice F. Rech, Paula Jakopovic, Hannah Seidl, Greg Lawson, Rachel Pugh

*Journal of Math Circles*

Engaging middle and high school students in Math Circles requires time, planning and creativity. Finding novel approaches to maintain the interest of a variety of learners can be challenging. This paper outlines a model for developing and implementing math escape rooms as a unique structure for facilitating collaborative problem solving in a Math Circle. These escape rooms were designed and hosted by undergraduate secondary mathematics education majors. We provide possible structures for hosting escape rooms that could translate to a range of settings, as well as reflections and lessons learned through our experiences that could inform practitioners in other settings.

Wild Randomness And The Application Of Hyperbolic Diffusion In Financial Modelling, 2021 Memorial University of Newfoundland, St Johns, NL A1C 5S7, Canada

#### Wild Randomness And The Application Of Hyperbolic Diffusion In Financial Modelling, Will Hicks

*Journal of Stochastic Analysis*

No abstract provided.

Linear Decomposition And Anticipating Integral For Certain Random Variables, 2021 National Taitung University, No 369, University Road, Sec. 2, Taitung, Taiwan

#### Linear Decomposition And Anticipating Integral For Certain Random Variables, Ching-Tang Wu, Ju-Yi Yen

*Journal of Stochastic Analysis*

No abstract provided.

Group Theory Visualized Through The Rubik's Cube, 2021 Portland State University

#### Group Theory Visualized Through The Rubik's Cube, Ashlyn Okamoto

*University Honors Theses*

In my thesis, I describe the work done to implement several Group Theory concepts in the context of the Rubik’s cube. A simulation of the cube was constructed using Processing-Java and with help from a YouTube series done by TheCodingTrain. I reflect on the struggles and difficulties that came with creating this program along with the inspiration behind the project. The concepts that are currently implemented at this time are: Identity, Associativity, Order, and Inverses. The functionality of the cube is described as it moves like a regular cube but has extra keypresses that demonstrate the concepts listed. Each ...

First Exit-Time Analysis For An Approximate Barndorff-Nielsen And Shephard Model With Stationary Self-Decomposable Variance Process, 2021 North Dakota State University, Fargo, North Dakota 58108-6050, USA

#### First Exit-Time Analysis For An Approximate Barndorff-Nielsen And Shephard Model With Stationary Self-Decomposable Variance Process, Shantanu Awasthi, Indranil Sengupta

*Journal of Stochastic Analysis*

No abstract provided.

Quantum Theories Associated To Increasing Hilbert Space Filtrations And Generalized Jacobi 3–Diagonal Relation, 2021 Università di Roma "Tor Vergata," via Columbia, 2, 00133 Roma, Italy

#### Quantum Theories Associated To Increasing Hilbert Space Filtrations And Generalized Jacobi 3–Diagonal Relation, Luigi Accardi, Yun Gang Lu

*Journal of Stochastic Analysis*

No abstract provided.

Rate Of Convergence In The Central Limit Theorem For Iid Pareto Variables, 2021 Hochschule RheinMain, 65022 Wiesbaden, Germany

#### Rate Of Convergence In The Central Limit Theorem For Iid Pareto Variables, Claas Becker, Manuel Bohnet, Sarah Kummert

*Journal of Stochastic Analysis*

No abstract provided.

Noncentral Limit Theorem For Large Wishart Matrices With Hermite Entries, 2021 CNRS, Université de Lille, Laboratoire Paul Painlevé UMR 8524, F-59655 Villeneuve d’Ascq, France

#### Noncentral Limit Theorem For Large Wishart Matrices With Hermite Entries, Charles-Philippe Diez, Ciprian A. Tudor

*Journal of Stochastic Analysis*

No abstract provided.

The Surface Area Of A Scalene Cone As Solved By Varignon, Leibniz, And Euler, 2021 Northern Kentucky University

#### The Surface Area Of A Scalene Cone As Solved By Varignon, Leibniz, And Euler, Daniel J. Curtin

*Euleriana*

In a 1727 mathematical compendium, Pierre Varignon (1654-1722) published his solution to the problem of finding the surface area of a scalene (oblique) cone, one whose base is circular but whose vertex is off-center. The article after Varignon's in that publication was by Gottfried Leibniz (1646-1716), who proposed improvements and even extended the solution to a base with any curve. When Leonhard Euler (1707-1783) published on the subject [E133] in 1750, he gently pointed out an error in Leibniz's solution, which he corrected, after extending Varignon's solution in the case of circular base. Euler then used Leibniz ...

Fuzzy P-Value Of Hypotheses Tests With Crisp Data Using Non-Asymptotic Fuzzy Estimators, 2021 Democritus University of Thrace, Kimeria, Xanthi, 67100, Greece

#### Fuzzy P-Value Of Hypotheses Tests With Crisp Data Using Non-Asymptotic Fuzzy Estimators, Nikos Mylonas, Basil K. Papadopoulos

*Journal of Stochastic Analysis*

No abstract provided.

Once Upon A Party - An Anecdotal Investigation, 2021 Ariana Investment Management

#### Once Upon A Party - An Anecdotal Investigation, Vijay Fafat

*Journal of Humanistic Mathematics*

Mathematicians and Physicists attending let-your-hair-down parties behave exactly like their own theories. They live by their theorems, they jive by their theorems. Life imitates their craft, and we must simply observe the deep truths hiding in their party-going behavior...

Mathematical Zendo: A Game Of Patterns And Logic, 2021 Westfield State University

#### Mathematical Zendo: A Game Of Patterns And Logic, Philip Deorsey, Corey Pooler, Michael Ferrara

*Journal of Math Circles*

Mathematical Zendo is a logic game that actively engages participants in pattern recognition, problem solving, and critical thinking while providing a fun opportunity to explore all manner of mathematical objects. Based upon the popular game of Zendo, created by Looney Labs, Mathematical Zendo centers on a secret rule, chosen by the leader, that must be guessed by teams of players. In each round of the game, teams provide examples of the mathematical object of interest (e.g. functions, numbers, sets) and receive information about whether their guesses do or do not satisfy the secret rule. In this paper, we introduce ...

Total Differentiability And Monogenicity For Functions In Algebras Of Order 4, 2021 Politecnico di Milano

#### Total Differentiability And Monogenicity For Functions In Algebras Of Order 4, I. Sabadini, Daniele C. Struppa

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper we discuss some notions of analyticity in associative algebras with unit. We also recall some basic tool in algebraic analysis and we use them to study the properties of analytic functions in two algebras of dimension four that played a relevant role in some work of the Italian school, but that have never been fully investigated.

Review Of Social Workers Count: Numbers And Social Issues By Michael Anthony Lewis, 2021 Dakota Wesleyan University

#### Review Of Social Workers Count: Numbers And Social Issues By Michael Anthony Lewis, Michael T. Catalano

*Numeracy*

Lewis, Michael Anthony. 2017. *Social Workers Count: Numbers and Social Issues*. 2019. New York: Oxford University Press. 223 pp. ISBN 978-019046713-5

The numeracy movement, although largely birthed within the mathematics community, is an outside-the-box endeavor which has always sought to break down or at least transgress traditional disciplinary boundaries. Michael Anthony Lewis’s book is a testament that this effort is succeeding. Lewis is a social worker and sociologist with an impressive resume, author of *Economics for Social Workers*, co-editor of *The Ethics and Economics of the Basic Income Guarantee,* and member of the faculty at the Silberman School of ...

Green's Function For The Schrodinger Equation With A Generalized Point Interaction And Stability Of Superoscillations, 2021 Chapman University

#### Green's Function For The Schrodinger Equation With A Generalized Point Interaction And Stability Of Superoscillations, Yakir Aharonov, Jussi Behrndt, Fabrizio Colombo, Peter Schlosser

*Mathematics, Physics, and Computer Science Faculty Articles and Research*

In this paper we study the time dependent Schrödinger equation with all possible self-adjoint singular interactions located at the origin, which include the *δ* and *δ*'-potentials as well as boundary conditions of Dirichlet, Neumann, and Robin type as particular cases. We derive an explicit representation of the time dependent Green's function and give a mathematical rigorous meaning to the corresponding integral for holomorphic initial conditions, using Fresnel integrals. Superoscillatory functions appear in the context of weak measurements in quantum mechanics and are naturally treated as holomorphic entire functions. As an application of the Green's function we study ...

Numerical Integration Through Concavity Analysis, 2021 Embry-Riddle Aeronautical University

#### Numerical Integration Through Concavity Analysis, Daniel J. Pietz

*Rose-Hulman Undergraduate Mathematics Journal*

We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.

Linear Combinations Of Harmonic Univalent Mappings, 2021 California State University, Stanislaus

#### Linear Combinations Of Harmonic Univalent Mappings, Dennis Nguyen

*Rose-Hulman Undergraduate Mathematics Journal*

Many properties are known about analytic functions, however the class of harmonic functions which are the sum of an analytic function and the conjugate of an analytic function is less understood. We wish to find conditions such that linear combinations of univalent harmonic functions are univalent. We focus on functions whose image is convex in one direction i.e. each line segment in that direction between points in the image is contained in the image. M. Dorff proved sufficient conditions such that the linear combination of univalent harmonic functions will be univalent on the unit disk. The conditions are: the ...

Mathematical Magic: A Study Of Number Puzzles, 2021 Maryville College

#### Mathematical Magic: A Study Of Number Puzzles, Nicasio M. Velez

*Rose-Hulman Undergraduate Mathematics Journal*

Within this paper, we will briefly review the history of a collection of number puzzles which take the shape of squares, polygons, and polyhedra in both modular and nonmodular arithmetic. Among other results, we develop construction techniques for solutions of both Modulo and regular Magic Squares. For other polygons in nonmodular arithmetic, specifically of order 3, we present a proof of why there are only four Magic Triangles using linear algebra, disprove the existence of the Magic Tetrahedron in two ways, and utilizing the infamous 3-SUM combinatorics problem we disprove the existence of the Magic Octahedron.