Hierarchical Hyperbolicity Of Graph Products And Graph Braid Groups, 2021 The Graduate Center, City University of New York

#### Hierarchical Hyperbolicity Of Graph Products And Graph Braid Groups, Daniel James Solomon Berlyne

*Dissertations, Theses, and Capstone Projects*

This thesis comprises three original contributions by the author concerning hierarchical hyperbolicity, a coarse geometric tool developed by Behrstock, Hagen, and Sisto to provide a common framework for studying aspects of non-positive curvature in a wide variety of groups and spaces.

We show that any graph product of finitely generated groups is hierarchically hyperbolic relative to its vertex groups. We apply this to answer two questions of Genevois about the electrification of a graph product of finite groups. We also answer two questions of Behrstock, Hagen, and Sisto: we show that the syllable metric on a graph product forms a ...

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.

Knowing What We Know: Leveraging Community Knowledge Through Automated Text-Mining, 2021 Rochester Institute of Technology

#### Knowing What We Know: Leveraging Community Knowledge Through Automated Text-Mining, Justin Gardner, Jonathan Tory Toole, Hemant Kalia, Garry Spink Jr., Gordon Broderick

*Advances in Clinical Medical Research and Healthcare Delivery*

No abstract provided.

Applications Of Nonstandard Analysis In Probability And Measure Theory, 2021 Louisiana State University and Agricultural and Mechanical College

#### Applications Of Nonstandard Analysis In Probability And Measure Theory, Irfan Alam

*LSU Doctoral Dissertations*

This dissertation broadly deals with two areas of probability theory and investigates how methods from nonstandard analysis may provide new perspectives in these topics. In particular, we use nonstandard analysis to prove new results in the topics of limiting spherical integrals and of exchangeability.

In the former area, our methods allow us to represent finite dimensional Gaussian measures in terms of marginals of measures on hyperfinite-dimensional spheres in a certain strong sense, thus generalizing some previously known results on Gaussian Radon transforms as limits of spherical integrals. This first area has roots in the kinetic theory of gases, which is ...

Developing Mathematical Flexible Thinking In Students With Disabilities, 2021 The College at Brockport: State University of New York

#### Developing Mathematical Flexible Thinking In Students With Disabilities, Bridget Sadler

*Education and Human Development Master's Theses*

This curriculum project was designed to improve mathematical flexible thinking skills, with a focus on students with disabilities. This is achieved through the integration of inquiry-based learning activities and mathematical discourse throughout each lesson. This collection of lessons is not a unit, rather it is a collection of exemplar lessons which detail how to embed these strategies to develop students mathematical fleible thinking skills. Hoever, all lessons are from Alegbra I and Geometry. Teachers can use this curriculum as it is, or as a model of how to support the development of flexible thinking skills for all students ...

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.

Association Of Hypothermia With Increased Mortality Rate In Sars-Cov-2 Infection, 2021 Broward Health Medical Center

#### Association Of Hypothermia With Increased Mortality Rate In Sars-Cov-2 Infection, Naaz Fatteh, Glen E. Sutherland, Radleigh Santos, Rita Zeidan, Alexandra P. Gastesi, Christopher D. Naranjo

*Mathematics Faculty Articles*

### Objective

We observed patients to have variable temperatures. The objective of the study was to identify if hypothermia in a patient infected with SARS-CoV-2 is associated with a higher than expected mortality.

### Methods

We reviewed 331 charts from patients hospitalized with SARS-CoV-2 between March 9 to April 20, 2020.

### Results

The probability of death was 2.06 times higher for those with hypothermia than those without [95% C.I. (1.25, 3.38)]. In ventilated patients, there were 32 deaths. Of those, 75% had been hypothermic. In a prior review of 10,000 non-SARS-CoV-2 patients with sepsis, the mortality rate ...

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.

Интегрирование Модифицированного Уравнения Кортевега-Де Фриза С Нагруженным Членом И Источником В Виде Суммы, 2021 Каракалпакский государственный университет имени Бердаха

#### Интегрирование Модифицированного Уравнения Кортевега-Де Фриза С Нагруженным Членом И Источником В Виде Суммы, Т.Ж. Алланазарова Ассистент Преподаватель

*Science and Society*

** **This paper considers the method of the inverse spectral problem for integrating the modified Korteweg-de Vries equation (mKdV) with a loaded term and a source in the form of a sum in the class of infinite-gap periodic functions.

** **

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.

Streaming Down The Stern-Brocot Tree: Finding And Expressing Solutions To Pell's Equation In Sl(2,Z), 2021 Jacksonville State University

#### Streaming Down The Stern-Brocot Tree: Finding And Expressing Solutions To Pell's Equation In Sl(2,Z), Marcus L. Shell

*Theses*

This paper explores and elaborates on a method of solving Pell’s equation as introduced by Norman Wildberger. In the first chapters of the paper, foundational topics are introduced in expository style including an explanation of Pell’s equation. An explanation of continued fractions and their ability to express quadratic irrationals is provided as well as a connection to the Stern-Brocot tree and a convenient means of representation for each in terms of 2×2 matrices with integer elements. This representation will provide a useful way of navigating the Stern-Brocot tree computationally and permit us a means of computing continued ...

Qualitative Analysis Of Corequisite Instruction In A Quantitative Reasoning Course, 2021 Piedmont Virginia Community College

#### Qualitative Analysis Of Corequisite Instruction In A Quantitative Reasoning Course, Zachary Beamer

*Inquiry: The Journal of the Virginia Community Colleges*

In corequisite models of instruction, marginally prepared students are placed directly into college-level coursework, taught with a paired support course. Initial research suggests that such models yield significant improvements in the number of students passing credit-level mathematics when compared to previous models of prerequisite remediation. The present study employs qualitative methods to investigate methods of instruction at one community colleges to understand how instructors identify and respond to student needs. It concludes with recommendations for practice and highlights advantages of small format corequisite classes taught by the same instructor.

Simulations Of An Attack On Rsa, 2021 University of Mary Washington

#### Simulations Of An Attack On Rsa, Makayla Ferrell

*Student Research Submissions*

We introduce a variation of Shanks’ baby-step/giant-step (BSGS) to carry out a chosen plaintext attack on RSA. The original usage of BSGS is to find a solution to the discrete log problem. Although BSGS is guaranteed to find a solution, it is not guaranteed to find the matching RSA private key. Our variation of BSGS finds the matching private key d by using the order of the plaintext message to generate a set of solutions. We then use the length of this set to determine the most likely candidate for φ(n). We use a large data set to ...

Parameter Estimation In Nonlinear Regression: Exploring Confidence Intervals For Estimated Coefficients, 2021 University of Mary Washington

#### Parameter Estimation In Nonlinear Regression: Exploring Confidence Intervals For Estimated Coefficients, Brandon Williams

*Student Research Submissions*

Previously, we explored generating data using four different curved source functions with normally distributed errors and then fitting various curved models to this generated data. This research aimed to study the reliability of the goodness-of-fit measures, such as R^{2} and AIC, when the data originates from a curved source model. Ultimately, we found that, for logarithmic source models, AIC picks the correct source model most often, while R^{2} selects either the logarithmic or quadratic source models. For quadratic source models, AIC picks the power source model most often, whereas R^{2} selects the correct source model. Lastly, we ...

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.