Mathematics Commons^™

Hessenberg Varieties Of Parabolic Type, Martha Precup, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

This paper studies the geometry and combinatorics of three interrelated varieties: Springer fibers, Steinberg varieties, and parabolic Hessenberg varieties. We prove that each parabolic Hessenberg variety is the pullback of a Steinberg variety under the projection of the flag variety to an appropriate partial flag variety and we give three applications of this result. The first application constructs an explicit paving of all Steinberg varieties in Lie type A in terms of semistandard tableaux. As a result, we obtain an elementary proof of a theorem of Steinberg and Shimomura that the well-known Kostka numbers count the maximal-dimensional irreducible components of …

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.

2-Adic Valuations Of Quadratic Sequences, Will Boultinghouse, Jane H. Long, Olena Kozhushkina, Justin Trulen

Faculty Publications

We determine properties of the 2-adic valuation sequences for general quadratic polynomials with integer coefficients directly from the coefficients. These properties include boundedness or unboundedness, periodicity, and valuations at terminating nodes. We completely describe the periodic sequences in the bounded case. Throughout, we frame results in terms of trees and sequences.

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, 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 in patients with hypothermia was …

Weighted Inequalities On Spaces Of Homogeneous Type, Naga Manasa Vempati

Arts & Sciences Graduate Student Theses and Dissertations

Let $(X,d,\mu )$ be a space of homogeneous type in the sense of Coifman andWeiss, i.e. $d$ is a quasi metric on $X$ and $\mu $ is a nonzero measure satisfying the doubling condition. Suppose that $u$ and $v$ are two locally finite positive Borel measures on $(X,d,\mu )$, the two weight inequality for the Calder\'on-Zygmund operator is of the form \begin{align*} & \|T(f\cdot u)\|_{L^2(v)}\lesssim \|f\|_{L^2(u)}. \end{align*} Subject to the pair of weights satisfying a side condition, we have given a characterization of the boundedness of a Calder\'{o}n-Zygmund operator $T$ from $L^{2}(u)$ to $L^{2}(v)$ in terms of the $A_{2}$ condition …

Spring 2021

Scientia

From the Dean: A Decade of Purpose and Progress; Lab Notes: Alumna Wins Gordon Bell Special Prize, New Scholarships, Vaccination Site Volunteers; Women in Science Lecture, National Institutes of Health Grants, "Unequal Cities" Research; All Hands on Deck: Inspired pandemic approaches showcase interdisciplinary acumen in action; Unlocking Potential: Christopher Beasley thinks psychology is key to academic transformation for the formerly incarcerated; Puzzle Master: Bridget Tenner goes to pieces solving problems in cutting-edge mathematics

Interpolating Matrices, Alberto Dayan

Arts & Sciences Graduate Student Theses and Dissertations

This Thesis work aims to extend the notion of interpolating sequences to objects having a non-trivial algebraic structure, such as a sequence of square matrices A (of eventually unbounded dimensions). First, we will consider the case in which the spectra of A lie in the unit disc, a necessary assumption if we want to apply to each matrix of the sequence a bounded holomorphic function on the unit disc. Since analytic functions preserve algebraic properties of square matrices, such as their eigenspaces, we can't extend the definition of interpolating sequences to matrices by just considering targets which are bounded in …

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, 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.

An Exploration Of Manipulatives In Math Education, Jade Monte

Honors Program Theses and Projects

Pre-existing literature has shown that the education system needs to re-evaluate mathematical teaching practices in a manner that can boost students’ confidence in mathematics. Thus, the research is to investigate the use of manipulatives in reducing students’ anxiety by increasing their learning experience and engagement in mathematics. Furthermore, the purpose of this thesis is to explain the interconnectedness of math manipulatives, student engagement, and problem-solving. An in-depth literature review is conducted, which contains definitions, important benefits and methodologies of manipulatives, as well as the teacher’s role regarding these three terms. When manipulatives, student engagement, and problem-solving are in harmony, students …

We’Re Here To Get You There: A Statistical Analysis Of Bridgewater State University’S Transit System, Abigail Adams

Honors Program Theses and Projects

Bridgewater State University first established its on-campus transportation service in January of 1984. While it began only running as an on-campus service for students throughout the day, the service grew to expand by offering an off-campus connection to the neighboring city of Brockton and absorbed the night service system from the campus safety team. As BSU Transit continues to grow, the organization is seeking ways to improve their overall service and better prepare their fleet and driver pool to accommodate this growth. The purpose of this research is to analyze trends among the data collected by BSU Transit and assist …

Mixed Generalized Fractional Brownian Motion, Shaykhah Alajmi, Ezzedine Mliki

Journal of Stochastic Analysis

No abstract provided.

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 fractions without the …

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

Departmental Honors & Graduate Capstone Projects

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 R² 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 R² selects either the logarithmic or quadratic source models. For quadratic source models, AIC picks the power source model most often, whereas R² selects the correct source model. Lastly, we …

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, Makayla Ferrell

Departmental Honors & Graduate Capstone Projects

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 test the …

Krein Reproducing Kernel Modules In Clifford Analysis, Daniel Alpay, Paula Cerejeiras, Uwe Kähler

Mathematics, Physics, and Computer Science Faculty Articles and Research

Classic hypercomplex analysis is intimately linked with elliptic operators, such as the Laplacian or the Dirac operator, and positive quadratic forms. But there are many applications like the crystallographic X-ray transform or the ultrahyperbolic Dirac operator which are closely connected with indefinite quadratic forms. Although appearing in many papers in such cases Hilbert modules are not the right choice as function spaces since they do not reflect the induced geometry. In this paper we are going to show that Clifford-Krein modules are naturally appearing in this context. Even taking into account the difficulties, e.g., the existence of different inner products …

Second-Order Semi-Discretized Schemes For Solving Stochastic Quenching Models On Arbitrary Spatial Grids, Nina Garcia-Montoya, Julienne Kabre, Jorge E. Macías-Díaz, Qin Sheng

Mathematics Faculty Articles

Reaction-diffusion-advection equations provide precise interpretations for many important phenomena in complex interactions between natural and artificial systems. This paper studies second-order semi-discretizations for the numerical solution of reaction-diffusion-advection equations modeling quenching types of singularities occurring in numerous applications. Our investigations particularly focus at cases where nonuniform spatial grids are utilized. Detailed derivations and analysis are accomplished. Easy-to-use and highly effective second-order schemes are acquired. Computational experiments are presented to illustrate our results as well as to demonstrate the viability and capability of the new methods for solving singular quenching problems on arbitrary grid platforms.

Time Series Forecasting Of Covid-19 Deaths In Massachusetts, Andrew Disher

Honors Program Theses and Projects

The aim of this study was to use data provided by the Department of Public Health in the state of Massachusetts on its online dashboard to produce a time series model to accurately forecast the number of new confirmed deaths that have resulted from the spread of CoViD-19. Multiple different time series models were created, which can be classified as either an Auto-Regressive Integrated Moving Average (ARIMA) model or a Regression Model with ARIMA Errors. Two ARIMA models were created to provide a baseline forecasting performance for comparison with the Regression Model with ARIMA Errors, which used the number of …