Analysis Commons^™

Elements Of Functional Analysis And Applications, Chengting Yin

Graduate Theses/Dissertations

Functional analysis is a branch of mathematical analysis that studies vector spaces with a limit structure (such as a norm or inner product), and functions or operators defined on these spaces. Functional analysis provides a useful framework and abstract approach for some applied problems in variety of disciplines. In this thesis, we will focus on some basic concepts and abstract results in functional analysis, and then demonstrate their power and relevance by solving some applied problems under the framework. We will give the definitions and provide some examples of some different spaces (such as metric spaces, normed spaces and inner …

Design Of Metamaterials For Optics, Abiti Adili

LSU Doctoral Dissertations

First part of this dissertation studies the problem of designing metamaterial crystals with double negative effective properties for applications in optics by investigating the conditions necessary for generating novel dispersion properties in a metamaterial crystal with subwavelength microstructure. This provides novel optical properties created through local resonances tied to the geometry of the media in subwavelength regime.

In the second part, this dissertation studies the representation formula used to describe band structures in photonic crystals with plasmonic inclusions. By using layer potential techniques, a magnetic dipole operator describing the tangential component of the electrical field generated by magnetic distribution is …

Increasing C-Additive Processes, Nadjib Bouzar

Communications on Stochastic Analysis

No abstract provided.

A Limiting Process To Invert The Gauss-Radon Transform, Jeremy J. Becnel

Communications on Stochastic Analysis

No abstract provided.

Spectral Theorem Approach To The Characteristic Function Of Quantum Observables, Andreas Boukas, Philip J. Feinsilver

Communications on Stochastic Analysis

No abstract provided.

Smoothing Parameters For Recursive Kernel Density Estimators Under Censoring, Yousri Slaoui

Communications on Stochastic Analysis

No abstract provided.

Strong Convergence Rate In Averaging Principle For The Heat Equation Driven By A General Stochastic Measure, Vadym Radchenko

Communications on Stochastic Analysis

No abstract provided.

Integral Inequalities Of Hermite-Hadamard Type Via Green Function And Applications, Tuba Tunç, Sümeyye Sönmezoğlu, Mehmet Z. Sarıkaya

Applications and Applied Mathematics: An International Journal (AAM)

In this study, we establish some Hermite- Hadamard type inequalities for functions whose second derivatives absolute value are convex. In accordance with this purpose, we obtain an identity using Green's function. Then using this equality we get our main results.

Generalized Bagley-Torvik Equation And Fractional Oscillators, Mark Naber, Lucas Lymburner

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the driving force. The properties of the effective decay rate and the oscillation frequency with respect to the order of the fractional damping are also studied. It is found that the effective decay rate and oscillation frequency have a complex dependency on the order of the derivative of the damping term and exhibit properties one might expect of a thermodynamic Equation of …

Generalized Differential Transform Method For Solving Some Fractional Integro-Differential Equations, S. Shahmorad, A. A. Khajehnasiri

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we use a generalized form of two-dimensional Differential Transform (2D-DT) to solve a new class of fractional integro-differential equations. We express some useful properties of the new transform as a proposition and prove a convergence theorem. Then we illustrate the method with numerical examples.

Transient Thermal Stresses Due To Axisymmetric Heat Supply In A Semi-Infinite Thick Circular Plate, S. D. Warbhe, K. C. Deshmukh

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with the determination of thermal stresses in a semi-infinite thick circular plate of a finite length and infinite extent subjected to an axisymmetric heat supply. A thick circular plate is considered having constant initial temperature and arbitrary heat flux is applied on the upper and lower face. The governing heat conduction equation has been solved by using integral transform technique. The results are obtained in terms of Bessel’s function. The thermoelastic behavior has been computed numerically and illustrated graphically for a steel plate.

Generalized Growth And Faber Polynomial Approximation Of Entire Functions Of Several Complex Variables In Some Banach Spaces, Devendra Kumar, Manisha Vijayran

Applications and Applied Mathematics: An International Journal (AAM)

In this paper the relationship between the generalized order of growth of entire functions of many complex variables m(m ≥ 2) over Jordan domains and the sequence of Faber polynomial approximations in some Banach spaces has been investigated. Our results improve the various results shown in the literature.

Unified Ball Convergence Of Inexact Methods For Finding Zeros With Multiplicity, Ioannis K. Argyros, Santhosh George

Applications and Applied Mathematics: An International Journal (AAM)

We present an extended ball convergence of inexact methods for approximating a zero of a nonlinear equation with multiplicity m; where m is a natural number. Many popular methods are special cases of the inexact method.

Functional Dimension Of Solution Space Of Differential Operators Of Constant Strength, Morteza Shafii-Mousavi

Applications and Applied Mathematics: An International Journal (AAM)

A differential operator with constant coefficients is hypoelliptic if and only if its solution space is of finite functional dimension. We extend this property to operators with variable coefficient. We prove that an equally strong differential operator with variable coefficients has the same property. In addition, we extend the Zielezny’s result to operators with variable coefficients; prove that an operator with analytic coefficients on ℝⁿ is elliptic if and only if locally the functional dimension of its solution space is the same as the Euclidean dimension n.

Study Of Specially And Temporally Dependent Adsorption Coefficient In Heterogeneous Porous Medium, Dilip K. Jaiswal, Gulrana _

Applications and Applied Mathematics: An International Journal (AAM)

One-dimensional advection-dispersion equation (ADE) is studied along unsteady longitudinal flow through a semi-infinite heterogeneous medium. Adsorption coefficient is considered temporally and spatially–dependent function i.e., expressed in degenerate form. The dispersion parameter is considered as inversely proportional to adsorption coefficient. The input source is of pulse type. The Laplace Transformation Technique (LTT) is used to obtain the analytical solution by introducing certain new independent variables through separate transformations. The effects of adsorption, heterogeneity and unsteadiness are investigated and discussed with the help of various graphs.

Extracting Signal From The Noisy Environment Of An Ecosystem, Emily Wefelmeyer, Pranita Pramod Patil, Sridhar Reddy Ravula, Kevin M. Purcell, Ziyuan Huang, Igor Pilja

Other Student Works

The collection and storage of environmental and ecological data by researchers, government agencies and stewardship groups over the last decade has been remarkable. The proportional challenge to this data accretion lies in capitalizing on these resources for significant gain for both stewards and stakeholders. These trends highlight the role of data science as a critical component to the future of data-driven environmental management. Most critical are models of how data scientists can collaborate with policy makers and stewards to offer tools that leverage data and facilitate decisions. Our project aims to show how a successful collaboration between a management group, …

Survey Of Lebesgue And Hausdorff Measures, Jacob N. Oliver

Graduate Theses/Dissertations

Measure theory is fundamental in the study of real analysis and serves as the basis for more robust integration methods than the classical Riemann integrals. Measure theory allows us to give precise meanings to lengths, areas, and volumes which are some of the most important mathematical measurements of the natural world. This thesis is devoted to discussing some of the major proofs and ideas of measure theory. We begin with a study of Lebesgue outer measure and Lebesgue measurable sets. After a brief discussion of non-measurable sets, we define Lebesgue measurable functions and the Lebesgue integral. In the last chapter …

Black Swamp Pub And Bistro Analysis, Sara Aniol

Honors Projects

The Black Swamp Pub and Bistro is a full-service restaurant located in the Union on the Bowling Green State University Campus. We mainly do sit-down service, but we also do take-out orders and have a full bar with draft beers as well as mixed drinks. Our menu tends to change a lot, with new additions as well as some of the items being deleted. My goal of this project is to try to give some insight on the patterns that are too big to see with day-to-day operations as well as give some recommendations for the future that is backed …

Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert

Department of Mathematics: Dissertations, Theses, and Student Research

This dissertation investigates the properties of unbounded derivations on C*-algebras, namely the density of their analytic vectors and a property we refer to as "kernel stabilization." We focus on a weakly-defined derivation δ_D which formalizes commutators involving unbounded self-adjoint operators on a Hilbert space. These commutators naturally arise in quantum mechanics, as we briefly describe in the introduction.

A first application of kernel stabilization for δ_D shows that a large class of abstract derivations on unbounded C*-algebras, defined by O. Bratteli and D. Robinson, also have kernel stabilization. A second application of kernel stabilization provides a sufficient condition …

Admissibility Of C*-Covers And Crossed Products Of Operator Algebras, Mitchell A. Hamidi

Department of Mathematics: Dissertations, Theses, and Student Research

In 2015, E. Katsoulis and C. Ramsey introduced the construction of a non-self-adjoint crossed product that encodes the action of a group of automorphisms on an operator algebra. They did so by realizing a non-self-adjoint crossed product as the subalgebra of a C*-crossed product when dynamics of a group acting on an operator algebra by completely isometric automorphisms can be extended to self-adjoint dynamics of the group acting on a C*-algebra by ∗-automorphisms. We show that this extension of dynamics is highly dependent on the representation of the given algebra and we define a lattice structure for an operator algebra's …

Dynamic Attribute-Level Best Worst Discrete Choice Experiments, Amanda Working, Mohammed Alqawba, Norou Diawara

Mathematics & Statistics Faculty Publications

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are …

An Anatomical And Functional Analysis Of Digital Arteries, Katie Highsmith

Student Scholar Showcase

Blood flow to the tissue of the hands and digits is efficiently regulated by vasoconstriction and vasodilation. Through a series of cadaveric dissection, we examined arteries in the hands and digits, including ulnar artery, radial artery, palmar arteries, and digital arteries, for their distribution (branching) patterns and morphological parameters (e.g., thickness, length between branches, external and internal diameters). Using data directly collected from three female cadavers as input variables to our mathematical model, we simulated vasoconstriction (-20% and -10% diameter) and vasodilation (+10% and +20 diameter) to evaluate the extent of changes in blood volume and flow within the arteries. …

Making The Cut: Receivers Of The National Football League, Anthony Kent Davis

Mathematics Senior Capstone Papers

In this paper the prospects of the National Football League, or NFL, are studied in order to determine the relationships between past college statistics, other “measurables,” and how they translate to successful careers in the league. When referring to measurables, this consists of all of the numerical data from each player that should, in theory, help teams get an idea of the players strengths or weaknesses. The data being used comes from an annual scouting combine for NFL teams that is held prior to each season. Information about the player’s college statistics and pre-draft measurables are being compared to several …

The Hyperreals: Do You Prefer Non-Standard Analysis Over Standard Analysis?, Chloe Munroe

Mathematics Undergraduate Theses

The hyperreal number system *ℝ forms an ordered field that contains ℝ as a subfield as well as infinitely many large and small numbers. A number is defined to be infinitely large if |ω| > n for all n = 1, 2, 3, ... and infinitely small if |ε| < 1/n for all n = 1, 2, 3... This number system is built out of the real number system analogous to Cantor’s construcion of ℝ out of ℚ. The new entities in *ℝ and the relationship between the reals and hyperreals provides an appealing alternate approach to real (standard) analysis …

Time Series Analysis Of Stochastic Networks With Correlated Random Arcs, Brendon T. Sands

Theses and Dissertations

While modern day weather forecasting is not perfect, there are many benefits given by the multitude and variety of predictive models. In the interest of routing airplanes, this paper uses time series analysis on successive weather forecasts to predict the optimal path and fuel burn of wind-based, fuel-burn networks with stochastic correlated arcs. Networks are populated with either deterministic or ensemble-based weather data, and the two data sources with and without time series analysis are compared. Methods were compared by fuel burn prediction accuracy and ability to predict a future optimal path. Of the four options, the ensemble-based methods were …

Fourier Series Expansion Methods For The Heat And Wave Equations In Two And Three Dimensions On Spherical Domains, Matthew Eller

UNO Student Research and Creative Activity Fair

Description: The Fourier series expansion method is an invaluable approach to solving partial differential equations, including the heat and wave equations. For homogeneous heat and wave equations, the solution can readily be found through separation of variables and then expansion of the solution in terms of the eigenfunctions. Solutions to inhomogeneous heat and wave equations through Fourier series expansion methods were not readily available in the literature for two- and three-dimensional cases. In my previous paper, I developed an approach for solving inhomogeneous heat and wave equations on cubic domains using Fourier series expansion methods. I shall extend my …

On The Adjoint Markov Policies In Stochastic Differential Games, Nicolai V. Krylov

Communications on Stochastic Analysis

No abstract provided.

A Nonlocal Approach To The Quantum Kolmogorov Backward Equation And Links To Noncommutative Geometry, Will Hicks

Communications on Stochastic Analysis

No abstract provided.

Regularity Of The Local Time Of Diffusions On The Positive Real Line With Reflection At Zero, Masafumi Hayashi

Communications on Stochastic Analysis

No abstract provided.

On The Spectrum Of Self-Adjoint Lévy Generators, David Applebaum

Communications on Stochastic Analysis

No abstract provided.