Numeric And Dynamic B-Stability, Exact-Monotone And Asymptotic Two-Point Behavior Of Theta Methods For Stochastic Differential Equations, 2021 Southern Illinois University, Carbondale, IL 62901, USA

#### Numeric And Dynamic B-Stability, Exact-Monotone And Asymptotic Two-Point Behavior Of Theta Methods For Stochastic Differential Equations, Henri Schurz

*Journal of Stochastic Analysis*

No abstract provided.

A Math Without Words Puzzle, 2021 Stephen F. Austin State University

#### A Math Without Words Puzzle, Jane H. Long, Clint Richardson

*Journal of Math Circles*

A visual puzzle by James Tanton forms the basis for a session that has been successfully implemented with various audiences. Designed to be presented with no directions or description, the puzzle requires participants to discover the goals themselves and to generate their own questions for investigation. Solutions, significant facilitation suggestions, and possibilities for deep mathematical extensions are discussed; extensive illustrations are included.

On Distributions Of Self-Adjoint Extensions Of Symmetric Operators, 2021 Politecnico di Milano, Milan, 20133, Italy

#### On Distributions Of Self-Adjoint Extensions Of Symmetric Operators, Franco Fagnola, Zheng Li

*Journal of Stochastic Analysis*

No abstract provided.

Anticipating Linear Stochastic Differential Equations With Adapted Coefficients, 2021 Louisiana State University, Baton Rouge, LA 70803, USA

#### Anticipating Linear Stochastic Differential Equations With Adapted Coefficients, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha

*Journal of Stochastic Analysis*

No abstract provided.

A New Method To Generate Superoscillating Functions And Supershifts, 2021 Chapman University

#### A New Method To Generate Superoscillating Functions And Supershifts, Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen

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

Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as optics, signal processing and antenna theory. In this paper, we introduce a new method to generate superoscillatory functions that allows us to construct explicitly a very large class of superoscillatory functions.

The Edwards Model For Fractional Brownian Loops And Starbursts, 2021 Technische Universität Kaiserslautern, Technomathematics Group, 67663 Kaiserslautern, Germany

#### The Edwards Model For Fractional Brownian Loops And Starbursts, Wolfgang Bock, Torben Fattler, Ludwig Streit

*Journal of Stochastic Analysis*

No abstract provided.

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 ...

A Component-Wise Approach To Smooth Extension Embedding Methods, 2021 The University of Southern Mississippi

#### A Component-Wise Approach To Smooth Extension Embedding Methods, Vivian Montiforte

*Dissertations*

Krylov Subspace Spectral (KSS) Methods have demonstrated to be highly scalable methods for PDEs. However, a current limitation of these methods is the requirement of a rectangular or box-shaped domain. Smooth Extension Embedding Methods (SEEM) use fictitious domain methods to extend a general domain to a simple, rectangular or box-shaped domain. This dissertation describes how these methods can be combined to extend the applicability of KSS methods, while also providing a component-wise approach for solving the systems of equations produced with SEEM.

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.

Interfacial Dynamics And Ionic Transport Of Radiologic Contrast Media In Carbohydrate Matrix: Utility And Limits Of X-Ray Imaging, 2021 CUNY New York City College of Technology

#### Interfacial Dynamics And Ionic Transport Of Radiologic Contrast Media In Carbohydrate Matrix: Utility And Limits Of X-Ray Imaging, Lin Mousa, Hayley Sanchez, Subhendra Sarkar, Zoya Vinokur

*Publications and Research*

Hello, our names are Lin Mousa and Hayley Sanchez, this semester we participated in a research project dedicated to analyzing the interactions of contrast media with the molecular components of fruits to compare how they would react with the human brain. This project involved the injection of fruits with varying contrasts and the imaging of the diffusion and interactions of the contrast within the fruits with X-rays. With setup technical parameters on the x-ray equipment images were taken with identical setups at an hourly rate for several days. The final results of this experiment indicated that contrasts such as Gadolinium ...

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.

A Survey Of Methods To Determine Quantum Symmetry Of Graphs, 2021 William & Mary

#### A Survey Of Methods To Determine Quantum Symmetry Of Graphs, Samantha Phillips

*Undergraduate Honors Theses*

We introduce the theory of quantum symmetry of a graph by starting with quantum permutation groups and classical automorphism groups. We study graphs with and without quantum symmetry to provide a comprehensive view of current techniques used to determine whether a graph has quantum symmetry. Methods provided include specific tools to show commutativity of generators of algebras of quantum automorphism groups of distance-transitive graphs; a theorem that describes why nontrivial, disjoint automorphisms in the automorphism group implies quantum symmetry; and a planar algebra approach to studying symmetry.

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.

Ready To Engage? Urban Middle School Teachers’ Responsiveness To Targeted Engagement Interventions On Their Virtual Instructional Practices: An Action Research Study, 2021 University of Missouri Saint Louis

#### Ready To Engage? Urban Middle School Teachers’ Responsiveness To Targeted Engagement Interventions On Their Virtual Instructional Practices: An Action Research Study, Svetlana Nikic

*Dissertations*

Teachers’ effectiveness is associated with their instructional practices and is ultimately linked to students’ learning outcomes. In order to impact teachers’ effectiveness, schools focus substantial effort and resources on professional development led by an assumption that teachers’ classroom practices can be improved through targeted interventions. Even if this premise is correct, little information is available about how much a teacher’s practice may change through interventions, or which aspects of instructional practice are more receptive to improving teacher effectiveness (Garret et al., 2019).

This study took place at an urban middle school and examined teachers’ responsiveness to targeted engagement intervention ...

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 ...