Analysis Commons^™

Quantization Of The Poisson Type Central Limit Theorem (1), Yungang Lu

Journal of Stochastic Analysis

No abstract provided.

Commutative C*-Algebras Generated By Toeplitz Operators On The Fock Space, Vishwa Nirmika Dewage

LSU Doctoral Dissertations

The Fock space $\mathcal{F}(\mathbb{C}^n)$ is the space of holomorphic functions on $\mathbb{C}^n$ that are square-integrable with respect to the Gaussian measure on $\mathbb{C}^n$. This space plays an essential role in several subfields of analysis and representation theory. In particular, it has for a long time been a model to study Toeplitz operators. Grudsky and Vasilevski showed in 2002 that radial Toeplitz operators on $\mathcal{F}(\mathbb{C})$ generate a commutative $C^*$-algebra $\mathcal{T}^G$, while Esmeral and Maximenko showed that $C^*$-algebra $\mathcal{T}^G$ is isometrically isomorphic to the $C^*$-algebra $C_{b,u}(\mathbb{N}_0,\rho_1)$. In this thesis, we extend the result to $k$-quasi-radial symbols acting on the Fock space $\mathcal{F}(\mathbb{C}^n)$. …

A Closed Form Formula For The Stochastic Exponential Of A Matrix-Valued Semimartingale, Peter Kern, Christian Müller

Journal of Stochastic Analysis

No abstract provided.

Understanding Compactness Through Primary Sources: Early Work Uniform Continuity To The Heine-Borel Theorem, Naveen Somasunderam

Analysis

No abstract provided.

Self-Repelling Elastic Manifolds With Low Dimensional Range, Carl Mueller, Eyal Neumann

Journal of Stochastic Analysis

No abstract provided.

Induced Matrices: Recurrences And Markov Chains, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Preconditioned Iteractive Solvers For The 2d Helmholtz Equation Via Radial Basis Functions, Lina Wu

Publications and Research

In this paper, we discuss the solution solver for the linear system of equations arising from the discretized 2D Helmholtz equation using the radial basis functions. The coefficient matrix A that is generated from the discretization is dense and often ill-conditioned. This paper uses preconditioned iterative methods such as the General Minimal Residual method (GMRES) to solve the linear system. Different preconditioners are compared. Numerical experiments are conducted in order to provide a comparison of the convergence rates among various preconditioned linear systems. A further observation is made into the eigenvalue distributions and the choice of the shaping parameters during …

Unomaha Problem Of The Week (2021-2022 Edition), Brad Horner, Jordan M. Sahs

UNO Student Research and Creative Activity Fair

The University of Omaha math department's Problem of the Week was taken over in Fall 2019 from faculty by the authors. The structure: each semester (Fall and Spring), three problems are given per week for twelve weeks, with each problem worth ten points - mimicking the structure of arguably the most well-regarded university math competition around, the Putnam Competition, with prizes awarded to top-scorers at semester's end. The weekly competition was halted midway through Spring 2020 due to COVID-19, but relaunched again in Fall 2021, with massive changes.

Now there are three difficulty tiers to POW problems, roughly corresponding to …

(R1517) Asymptotical Stability Of Riemann-Liouville Fractional Neutral Systems With Multiple Time-Varying Delays, Erdal Korkmaz, Abdulhamit Ozdemir

Applications and Applied Mathematics: An International Journal (AAM)

In this manuscript, we investigate the asymptotical stability of solutions of Riemann-Liouville fractional neutral systems associated to multiple time-varying delays. Then, we use the linear matrix inequality (LMI) and the Lyapunov-Krasovskii method to obtain sufficient conditions for the asymptotical stability of solutions of the system when the given delays are time dependent and one of them is unbounded. Finally, we present some examples to indicate the efficacy of the consequences obtained.

(R1521) On Weighted Lacunary Interpolation, Swarnima Bahadur, Sariya Bano

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we considered the non-uniformly distributed zeros on the unit circle, which are obtained by projecting vertically the zeros of the derivative of Legendre polynomial together with x=1 and x=-1 onto the unit circle. We prescribed the function on the above said nodes, while its second derivative at all nodes except at x=1 and x=-1 with suitable weight function and obtained the existence, explicit forms and establish a convergence theorem for such interpolatory polynomial. We call such interpolation as weighted Lacunary interpolation on the unit circle.

(R1516) Results On Fekete-Szegö Problem For Some New Subclasses Of Univalent Analytic Functions With Fractional-Order Operators, N. Singha, R. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

We introduce some new subclasses of analytic functions which are univalent in an open unit disk by means of fractional calculus. The elemental interest is to explore the significance of fractional-order operators while formulating a few distinct subclasses of univalent analytic functions. Present work establishes the Fekete-Szegö inequality for the proposed subclasses. In addition, some classical Fekete-Szegö problems have also been retrieved and discussed as particular cases of the presented work. To make the suggested work more evident, an extremal function is also provided for which a sharp upper bound is attained.

An Investigation Into Crouzeix's Conjecture, Timothy T. Royston

Master's Theses

We will explore Crouzeix’s Conjecture, an upper bound on the norm of a matrix after the application of a polynomial involving the numerical range. More formally, Crouzeix’s Conjecture states that for any n × n matrix A and any polynomial p from C → C,
∥p(A)∥ ≤ 2 sup_{z∈W (A)} |p(z)|.
Where W (A) is a set in C related to A, and ∥·∥ is the matrix norm. We first discuss the conjecture, and prove the simple case when the matrix is normal. We then explore a proof for a class of matrices given by Daeshik Choi. We expand …

Exploring The Numerical Range Of Block Toeplitz Operators, Brooke Randell

Master's Theses

We will explore the numerical range of the block Toeplitz operator with symbol function \(\phi(z)=A_0+zA_1\), where \(A_0, A_1 \in M_2(\mathbb{C})\). A full characterization of the numerical range of this operator proves to be quite difficult and so we will focus on characterizing the boundary of the related set, \(\{W(A_0+zA_1) : z \in \partial \mathbb{D}\}\), in a specific case. We will use the theory of envelopes to explore what the boundary looks like and we will use geometric arguments to explore the number of flat portions on the boundary. We will then make a conjecture as to the number of flat …

On The Numerical Range Of Compact Operators, Montserrat Dabkowski

Master's Theses

One of the many characterizations of compact operators is as linear operators which
can be closely approximated by bounded finite rank operators (theorem 25). It is
well known that the numerical range of a bounded operator on a finite dimensional
Hilbert space is closed (theorem 54). In this thesis we explore how close to being
closed the numerical range of a compact operator is (theorem 56). We also describe
how limited the difference between the closure and the numerical range of a compact
operator can be (theorem 58). To aid in our exploration of the numerical range of
a compact …

A New Model For Predicting The Drag And Lift Forces Of Turbulent Newtonian Flow On Arbitrarily Shaped Shells On The Seafloor, Carley R. Walker, James V. Lambers, Julian Simeonov

Dissertations

Currently, all forecasts of currents, waves, and seafloor evolution are limited by a lack of fundamental knowledge and the parameterization of small-scale processes at the seafloor-ocean interface. Commonly used Euler-Lagrange models for sediment transport require parameterizations of the drag and lift forces acting on the particles. However, current parameterizations for these forces only work for spherical particles. In this dissertation we propose a new method for predicting the drag and lift forces on arbitrarily shaped objects at arbitrary orientations with respect to the direction of flow that will ultimately provide models for predicting the sediment sorting processes that lead to …

Data And Algorithmic Modeling Approaches To Count Data, Andraya Hack

Honors College Theses

Various techniques are used to create predictions based on count data. This type of data takes the form of a non-negative integers such as the number of claims an insurance policy holder may make. These predictions can allow people to prepare for likely outcomes. Thus, it is important to know how accurate the predictions are. Traditional statistical approaches for predicting count data include Poisson regression as well as negative binomial regression. Both methods also have a zero-inflated version that can be used when the data has an overabundance of zeros. Another procedure is to use computer algorithms, also known as …

Identifying How Home Advantage Manifests In Butler Basketball Using Sfa, Emily M. Shoemaker

Undergraduate Honors Thesis Collection

Butler University’s basketball team has been in the Big East Conference since 2013 and is known for having a distinct home court advantage named ‘Hinkle Magic’ by fans. It is of interest to identify how home court advantage affects a Big East team’s ability to play to its full potential for generating wins and what factors are most accurate in measuring this potential. This project will utilize the Stochastic Frontier Approach (SFA) model to identify a team’s efficiency when playing at home vs. away in order to identify when teams meet their potential and if game location has an effect …

Dimension Theory Of Conformal Iterated Function Systems, Sharon Sneha Spaulding

Honors Scholar Theses

This thesis is an expository investigation of the conformal iterated function system (CIFS) approach to fractals and their dimension theory. Conformal maps distort regions, subject to certain constraints, in a controlled way. Let $\mathcal{S} = (X, E, \{\phi_e\}_{e \in E})$ be an iterated function system where $X$ is a compact metric space, $E$ is a countable index set, and $\{\phi_e\}_{e \in E}$ is a family of injective and uniformly contracting maps. If the family of maps $\{\phi_e\}_{e \in E}$ is also conformal and satisfies the open set condition, then the distortion properties of conformal maps can be extended to the …

Lattice Reduction Algorithms, Juan Ortega

Electronic Theses, Projects, and Dissertations

The purpose of this thesis is to propose and analyze an algorithm that follows
similar steps of Guassian Lattice Reduction Algorithm in two-dimensions and applying
them to three-dimensions. We start off by discussing the importance of cryptography in
our day to day lives. Then we dive into some linear algebra and discuss specific topics that
will later help us in understanding lattice reduction algorithms. We discuss two lattice
problems: the shortest vector problem and the closest vector problem. Then we introduce
two types of lattice reduction algorithms: Guassian Lattice Reduction in two-dimensions
and the LLL Algortihm. We illustrate how both …

Error Terms For The Trapezoid, Midpoint, And Simpson's Rules, Jessica E. Coen

Electronic Theses, Projects, and Dissertations

When it is not possible to integrate a function we resort to Numerical Integration. For example the ubiquitous Normal curve tables are obtained using Numerical Integration. The antiderivative of the defining function for the normal curve involves the formula for antiderivative of e^{-x^2} which can't be expressed in the terms of basic functions.

Simpson's rule is studied in most Calculus books, and in all undergraduate Numerical Analysis books, but proofs are not provided. Hence if one is interested in a proof of Simpson's rule, either it can be found in advanced Numerical Analysis books as a special case …