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Articles 1 - 30 of 1580

Full-Text Articles in Other Mathematics

Numeric And Dynamic B-Stability, Exact-Monotone And Asymptotic Two-Point Behavior Of Theta Methods For Stochastic Differential Equations, Henri Schurz Jun 2021

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, Jane H. Long, Clint Richardson Jun 2021

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, Franco Fagnola, Zheng Li Jun 2021

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, Hui-Hsiung Kuo, Pujan Shrestha, Sudip Sinha May 2021

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, Yakir Aharonov, Fabrizio Colombo, Irene Sabadini, Tomer Shushi, Daniele C. Struppa, Jeff Tollaksen May 2021

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, Wolfgang Bock, Torben Fattler, Ludwig Streit May 2021

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, Takuji Arai May 2021

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

Journal of Stochastic Analysis

No abstract provided.


Mixed Generalized Fractional Brownian Motion, Shaykhah Alajmi, Ezzedine Mliki May 2021

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, Justin Cook May 2021

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.1According 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, Vivian Montiforte May 2021

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, Jose Sanchez, Daanial Ahmad, Satyanand Singh May 2021

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, Lin Mousa, Hayley Sanchez, Subhendra Sarkar, Zoya Vinokur May 2021

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, Mario Lefebvre May 2021

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, Stephen Wang May 2021

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, Abderrahim Elallam May 2021

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, Akshata Pisharody May 2021

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, Samantha Phillips May 2021

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, Fariha Mahfuz Apr 2021

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, Svetlana Nikic Apr 2021

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, Juliana Bukoski Apr 2021

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 HG with basis indexed by the path space of the graph, then represent the vertices of the graph as projections on HG and the edges of the graph as partial isometries on HG. The weak operator topology closed algebra generated by these projections and partial isometries is called the free semigroupoid algebra for 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 ...


Superoscillations And Analytic Extension In Schur Analysis, Daniel Alpay, Fabrizio Colombo, Irene Sabadini Mar 2021

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, Robert J. Elliott, W. P. Malcolm Mar 2021

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, Janice F. Rech, Paula Jakopovic, Hannah Seidl, Greg Lawson, Rachel Pugh Mar 2021

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, Will Hicks Mar 2021

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, Ching-Tang Wu, Ju-Yi Yen Mar 2021

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, Ashlyn Okamoto Feb 2021

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, Shantanu Awasthi, Indranil Sengupta Feb 2021

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, Luigi Accardi, Yun Gang Lu Feb 2021

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, Claas Becker, Manuel Bohnet, Sarah Kummert Feb 2021

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, Charles-Philippe Diez, Ciprian A. Tudor Feb 2021

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

Journal of Stochastic Analysis

No abstract provided.