Alòs Type Decomposition Formula For Barndorff-Nielsen And Shephard Model, 2021 Keio University, 2-15-45 Mita, Minato-ku, Tokyo, 108-8345, Japan

#### Alòs Type Decomposition Formula For Barndorff-Nielsen And Shephard Model, Takuji Arai

*Journal of Stochastic Analysis*

No abstract provided.

Mixed Generalized Fractional Brownian Motion, 2021 Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam, Saudi Arabia

#### Mixed Generalized Fractional Brownian Motion, Shaykhah Alajmi, Ezzedine Mliki

*Journal of Stochastic Analysis*

No abstract provided.

Understanding The Effect Of Adaptive Mutations On The Three-Dimensional Structure Of Rna, 2021 Duquesne University

#### Understanding The Effect Of Adaptive Mutations On The Three-Dimensional Structure Of Rna, Justin Cook

*Undergraduate Research and Scholarship Symposium*

Single-nucleotide polymorphisms (SNPs) are variations in the genome where one base pair can differ between individuals.^{1} SNPs occur throughout the genome and can correlate to a disease-state if they occur in a functional region of DNA.^{1}According to the central dogma of molecular biology, any variation in the DNA sequence will have a direct effect on the RNA sequence and will potentially alter the identity or conformation of a protein product. A single RNA molecule, due to intramolecular base pairing, can acquire a plethora of 3-D conformations that are described by its structural ensemble. One SNP, rs12477830, which ...

Application Of Randomness In Finance, 2021 CUNY New York City College of Technology

#### Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh

*Publications and Research*

Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.

Exact Solutions To Optimal Control Problems For Wiener Processes With Exponential Jumps, 2021 Polytechnique Montréal, Montréal, Québec H3C 3A7, Canada

#### Exact Solutions To Optimal Control Problems For Wiener Processes With Exponential Jumps, Mario Lefebvre

*Journal of Stochastic Analysis*

No abstract provided.

Zeta Function Regularization And Its Relationship To Number Theory, 2021 East Tennessee State University

#### Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang

*Electronic Theses and Dissertations*

While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to ...

Constructions & Optimization In Classical Real Analysis Theorems, 2021 East Tennessee State University

#### Constructions & Optimization In Classical Real Analysis Theorems, Abderrahim Elallam

*Electronic Theses and Dissertations*

This thesis takes a closer look at three fundamental Classical Theorems in Real Analysis. First, for the Bolzano Weierstrass Theorem, we will be interested in constructing a convergent subsequence from a non-convergent bounded sequence. Such a subsequence is guaranteed to exist, but it is often not obvious what it is, e.g., if an = sin n. Next, the H¨older Inequality gives an upper bound, in terms of p ∈ [1,∞], for the the integral of the product of two functions. We will find the value of p that gives the best (smallest) upper-bound, focusing on the Beta and Gamma integrals ...

Determining Quantum Symmetry In Graphs Using Planar Algebras, 2021 William & Mary

#### Determining Quantum Symmetry In Graphs Using Planar Algebras, Akshata Pisharody

*Undergraduate Honors Theses*

A graph has quantum symmetry if the algebra associated with its quantum automorphism group is non-commutative. We study what quantum symmetry means and outline one specific method for determining whether a graph has quantum symmetry, a method that involves studying planar algebras and manipulating planar tangles. Modifying a previously used method, we prove that the 5-cycle has no quantum symmetry by showing it has the generating property.

Markov Chains And Their Applications, 2021 University of Texas at Tyler

#### Markov Chains And Their Applications, Fariha Mahfuz

*Math Theses*

Markov chain is a stochastic model that is used to predict future events. Markov chain is relatively simple since it only requires the information of the present state to predict the future states. In this paper we will go over the basic concepts of Markov Chain and several of its applications including Google PageRank algorithm, weather prediction and gamblers ruin.

We examine on how the Google PageRank algorithm works efficiently to provide PageRank for a Google search result. We also show how can we use Markov chain to predict weather by creating a model from real life data.

Free Semigroupoid Algebras From Categories Of Paths, 2021 University of Nebraska-Lincoln

#### Free Semigroupoid Algebras From Categories Of Paths, Juliana Bukoski

*Dissertations, Theses, and Student Research Papers in Mathematics*

Given a directed graph *G*, we can define a Hilbert space *H _{G}* with basis indexed by the path space of the graph, then represent the vertices of the graph as projections on

*H*and the edges of the graph as partial isometries on

_{G}*H*. The weak operator topology closed algebra generated by these projections and partial isometries is called the free semigroupoid algebra for

_{G}*G*. Kribs and Power showed that these algebras are reflexive, and that they are semisimple if and only if each path in the graph lies on a cycle. We extend the free semigroupoid ...

An Astronomer’S Journey Into Quantitative Reasoning, 2021 Big Kid Science

#### An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

*Numeracy*

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

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.