Analysis Commons^™

Computing Homology Of Hypergraphs, Jackson Earl

STAR Program Research Presentations

In the modern age of data science, the necessity for efficient and insightful analytical tools that enable us to interpret large data structures inherently presents itself. With the increasing utility of metrics offered by the mathematics of hypergraph theory and algebraic topology, we are able to explore multi-way relational datasets and actively develop such tools. Throughout this research endeavor, one of the primary goals has been to contribute to the development of computational algorithms pertaining to the homology of hypergraphs. More specifically, coding in python to compute the homology groups of a given hypergraph, as well as their Betti numbers …

Radial Solutions To Semipositone Dirichlet Problems, Ethan Sargent

HMC Senior Theses

We study a Dirichlet problem, investigating existence and uniqueness for semipositone and superlinear nonlinearities. We make use of Pohozaev identities, energy arguments, and bifurcation from a simple eigenvalue.

Approximations In Reconstructing Discontinuous Conductivities In The Calderón Problem, George H. Lytle

Theses and Dissertations--Mathematics

In 2014, Astala, Päivärinta, Reyes, and Siltanen conducted numerical experiments reconstructing a piecewise continuous conductivity. The algorithm of the shortcut method is based on the reconstruction algorithm due to Nachman, which assumes a priori that the conductivity is Hölder continuous. In this dissertation, we prove that, in the presence of infinite-precision data, this shortcut procedure accurately recovers the scattering transform of an essentially bounded conductivity, provided it is constant in a neighborhood of the boundary. In this setting, Nachman’s integral equations have a meaning and are still uniquely solvable.

To regularize the reconstruction, Astala et al. employ a high frequency …

Random Matrices, Continuous Circular Systems And The Triangular Operator, Romuald Lenczewski

Communications on Stochastic Analysis

No abstract provided.

Exponential Inequalities For Exit Times For Stochastic Navier-Stokes Equations And A Class Of Evolutions, Po-Han Hsu, Padamanbhan Sundar

Communications on Stochastic Analysis

No abstract provided.

Global Strong Solutions Of The Stochastic Three Dimensional Inviscid Simplified Bardina Turbulence Model, Manil T. Mohan

Communications on Stochastic Analysis

No abstract provided.

Normally Ordered Disentanglement Of Multi-Dimensional Schrödinger Algebra Exponentials, Luigi Accardi, Andreas Boukas

Communications on Stochastic Analysis

No abstract provided.

Injective Tensor Products Of Tree Spaces, Milena Venkova, Christopher Boyd, Costas Poulios

Articles

We study tensor products on tree spaces; in particular, we give necessary and sufficient conditions for the n-fold injective tensor product of tree spaces to contain a copy of l_1.

Improving Access To Clean Water In Rural Ecuador: The Connection Between Willingness To Pay And Population Health, Micalea Leaska

Capstone Collection

Climate change is affecting social and environmental determinants of health through access to safe drinking water, safely managed sanitation systems, and access to health care services and the ability for individuals to break free from unsuitable circumstances. Ecological disturbances such as those caused by climate change can cause a shift in host vectors or a change in habitat that results in a greater likelihood of the pathogen coming in contact with humans. Water, sanitation, and hygiene (WASH) services and their accessibility to populations can directly impact a community’s vulnerability to diseases and limiting factors to increase economic growth. If rural …

Boundary Layers In Periodic Homogenization, Jinping Zhuge

Theses and Dissertations--Mathematics

The boundary layer problems in periodic homogenization arise naturally from the quantitative analysis of convergence rates. Formally they are second-order linear elliptic systems with periodically oscillating coefficient matrix, subject to periodically oscillating Dirichelt or Neumann boundary data. In this dissertation, for either Dirichlet problem or Neumann problem, we establish the homogenization results and obtain the nearly sharp convergence rates, provided the domain is strictly convex. Also, we show that the homogenized boundary data is in W^1,p for any p ∈ (1,∞), which implies the C^α-Hölder continuity for any α ∈ (0,1).

Composition Of Gaussian Noises From Successive Convex Integrations, Amites Dasgupta

Communications on Stochastic Analysis

No abstract provided.

Limiting Means For Spherical Slices, Amy Peterson, Ambar Sengupta

Communications on Stochastic Analysis

No abstract provided.

Generalized Stochastic Burgers' Equation With Non-Lipschitz Diffusion Coefficient, Vivek Kumar, Ankik Kumar Giri

Communications on Stochastic Analysis

No abstract provided.

Eigenvalues And Approximation Numbers, Ryan Chakmak

CMC Senior Theses

While the spectral theory of compact operators is known to many, knowledge regarding the relationship between eigenvalues and approximation numbers might be less known. By examining these numbers in tandem, one may develop a link between eigenvalues and l^p spaces. In this paper, we develop the background of this connection with in-depth examples.

Perturbed Obstacle Problems In Lipschitz Domains: Linear Stability And Nondegeneracy In Measure, Ivan Blank, Jeremy Lecrone

Department of Math & Statistics Faculty Publications

We consider the classical obstacle problem on bounded, connected Lipschitz domains D⊂Rⁿ. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right-hand side and the boundary data for obstacle problems. In particular, we show that the Lebesgue measure of the symmetric difference between two contact sets is linearly comparable to the L¹-norm of perturbations in the data.

The Encyclopedia Of Neutrosophic Researchers - Vol. 3, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: …

Neutrosophic Triplet Structures - Vol. 1, Florentin Smarandache, Memet Sahin

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs, the properties of neutrosophic sets …

Plithogenic Fuzzy Whole Hypersoft Set, Construction Of Operators And Their Application In Frequency Matrix Multi Attribute Decision Making Technique, Florentin Smarandache, Shazia Rana, Madiha Qayyum, Muhammad Saeed, Bakhtawar Ali Khan

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, initially a matrix representation of Plithogenic Hypersoft Set (PHSS) is introduced and then with the help of this matrix some local operators for Plithogenic Fuzzy Hypersoft set (PFHSS) are developed. These local operators are used to generalize PFHSS to Plithogenic Fuzzy Whole Hypersoft set (PFWHSS). The generalized PFWHSS set is hybridization of Fuzzy Hypersoft set (which represent multiattributes and their subattributes as a combined whole membership i.e. case of having an exterior view of the event) and the Plithogenic Fuzzy Hypersoft set (in which multi attributes and their subattributes are represented with individual memberships case of having …

Global Existence And Asymptotic Behaviors For Some Nonlinear Partial Differential Equations., Ismahan Dhaw Binshati

Graduate Theses, Dissertations, and Problem Reports (ETD)

We study global existence and asymptotic behavior of the solutions for two-fluid compressible isentropic Euler-Maxwell equations by the Fourier transform and energy method. We discuss the case when the pressure for two fluids is not identical and we also add the friction between two fluids. In addition, we discuss the rates of decay of $L^{p}-L^{q}$ norms for a linear system. Moreover, we use the result for $L^{p}-L^{q}$ estimates to prove the decay rates for the nonlinear systems. In addition, we prove existence of heteroclinic orbits for the nonlinear Vlasov and the one-dimensional Vlasov-Poisson systems. In the nonlinear Vlasov case with …

Primes In Arithmetical Progression, Edward C. Wessel

Honors Theses

This thesis will tackle Dirichlet’s Theorem on Primes in Arithmetical Progressions. The majority of information that follows below will stem from Tom M. Apostol’s Introduction to Analytical Number Theory. This is the main source of all definitions, theorems, and method. However, I would like to assure the reader that prior knowledge of neither the text nor analytical number theory in general is needed to understand the result. A rough background in Abstract Algebra and a moderate grasp on Complex and Real Analysis are more than sufficient. In fact, my project’s intent is to introduce Dirichlet’s ideas to the mathematics student …

The Relationship Between Housing Affordability And Demographic Factors: Case Study For The Atlanta Beltline, Chapman T. Lindstrom

College of Graduate Studies: Theses & Dissertations

Housing affordability has been a widely examined subject for populations residing in major metropolitan regions around the world. The relationship between housing affordability and the city’s demographics and its volume of urban development are important to take into consideration. In the past two decades there has been an increasing volume of literature detailing Atlanta Georgia’s large-scale redevelopment project, the Atlanta BeltLine (ABL), and its relationship with Atlanta’s Metropolitan population and housing affordability. The first objective of this paper is to study the relationship between housing affordability at two scales within the Atlanta Metropolitan Area (AMA) for both renters and homeowners. …

Invariant Subspaces Of Compact Operators And Related Topics, Weston Mckay Grewe

Mathematics

The invariant subspace problem asks if every bounded linear operator on a Banach space has a nontrivial closed invariant subspace. Per Enflo has shown this is false in general, however it is known that every compact operator has an invariant subspace. The purpose of this project is to explore introductory results in functional analysis. Specifically we are interested in understanding compact operators and the proof that all compact operators on a Hilbert space have an invariant subspace. In the process of doing this we build up many examples and theorems relating to operators on a Hilbert or Banach space. Continuing …

Approximate Analytical Solutions Of Space-Fractional Telegraph Equations By Sumudu Adomian Decomposition Method, Hasib Khan, Cemil Tunç, Rahmat A. Khan, Akhtyar G. Shirzoi, Aziz Khan

Applications and Applied Mathematics: An International Journal (AAM)

The main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases.

Functional Central Limit Theorem For Additive Functionals Associated To The Generalized Nelson Hamiltonian, Soumaya Gheryani, Achref Majid, Habib Ouerdiane

Communications on Stochastic Analysis

No abstract provided.

Stochastic Differential Equations With Anticipating Initial Conditions, Hui-Hsiung Kuo, Sudip Sinha, Jiayu Zhai

Communications on Stochastic Analysis

No abstract provided.

Stochastic Lagrangian Formulations For Damped Navier-Stokes Equations And Boussinesq System, With Applications, Kazuo Yamazaki

Communications on Stochastic Analysis

No abstract provided.

Generalized Random Fields And Lévy's Continuity Theorem On The Space Of Tempered Distributions, Hermine Biermé, Olivier Durieu, Yizao Wang

Communications on Stochastic Analysis

No abstract provided.

On A Stochastic 2d Simplified Liquid Crystal Model Driven By Jump Noise, T. Tachim Medjo

Communications on Stochastic Analysis

No abstract provided.

New Filters For The Calibration Of Regime Switching Beta Dynamics, Robert J. Elliott, Carlton Osakwe

Communications on Stochastic Analysis

No abstract provided.

Non-Continuous Double Barrier Reflected Bsdes With Jumps Under A Stochastic Lipschitz Coefficient, Mohamed Marzougue, Mohamed El Otmani

Communications on Stochastic Analysis

No abstract provided.