Applied Mathematics Commons^™

Rigidity And Nonrigidity Of Corona Algebras, Paul Mckenney, Alessandro Vignati

Summer Conference on Topology and Its Applications

Shelah proved in the 1970s that there is a model of ZFC in which every homeomorphism of the Cech-Stone remainder of the natural numbers is induced by a function on the natural numbers. More recently, Farah proved that in essentially the same model, every automorphism of the Calkin algebra on a separable Hilbert space must be induced by a linear operator on the Hilbert space. I will discuss a common generalization of these rigidity results to a certain class of C*-algebras called corona algebras. No prerequisites in C*-algebra will be assumed.

Balanced And Functionally Balanced P-Groups, Menachem Shlossberg

Summer Conference on Topology and Its Applications

In relation to Itzkowitz's problem, we show that a c-bounded P-group is balanced if and only if it is functionally balanced. We prove that for an arbitrary P-group, being functionally balanced is equivalent to being strongly functionally balanced. A special focus is given to the uniform free topological group defined over a uniform P-space. In particular, we show that this group is (functionally) balanced precisely when its subsets B_n, consisting of words of length at most n, are all (resp., functionally) balanced.

Compactly Supported Homeomorphisms As Long Direct Limits, Rafael Dahmen, Gábor Lukács

Summer Conference on Topology and Its Applications

Let λ be a limit ordinal and consider a directed system of topological groups (G_α)_{α < λ} with topological embeddings as bonding maps and its directed union G=∪_{α < λ}G_α. There are two natural topologies on G: one that makes G the direct limit (colimit) in the category of topological spaces and one which makes G the direct limit (colimit) in the category of topological groups.

For λ = ω it is known that these topologies almost never coincide (Yamasaki's Theorem).

In my talk last year, I introduced the Long Direct Limit Conjecture, stating that …

Uncountable Discrete Sets And Forcing, Akira Iwasa

Summer Conference on Topology and Its Applications

Suppose that a space X has no uncountable discrete subspace. We will discuss if forcing can create an uncountable discrete subspace of X.

Locally Compact Groups: Traditions And Trends, Karl Heinrich Hofmann, Wolfgang Herfort, Francesco G. Russo

Summer Conference on Topology and Its Applications

For a lecture in the Topology+Algebra and Analysis section, the subject of locally compact groups appears particularly fitting: Historically and currently as well, the structure and representation theory of locally compact groups draws its methods from each of theses three fields of mathematics. Nowadays one might justifiably add combinatorics and number theory as sources. The example of a study of a class of locally compact groups called “near abelian,” undertaken by W. Herfort, K. H. Hofmann, and F. G. Russo, may be used to illustrate the liaison of topological group theory with this different areas of interest. Concepts like the …

Disjoint Infinity Borel Functions, Daniel Hathaway

Summer Conference on Topology and Its Applications

Consider the statement that every uncountable set of reals can be surjected onto R by a Borel function. This is implied by the statement that every uncountable set of reals has a perfect subset. It is also implied by a new statement D which we will discuss: for each real a there is a Borel function f_a : RtoR and for each function g : RtoR there is a countable set G(g) of reals such that the following is true: for each a in R and for each function g : R to R, if f_a is disjoint …

Dense Subsets Of Function Spaces With No Non-Trivial Convergent Sequences, Vladimir V. Tkachuk

Summer Conference on Topology and Its Applications

We will show that a monolithic compact space X is not scattered if and only if C_p(X) has a dense subset without non-trivial convergent sequences. Besides, for any cardinal κ ≥ c, the space R^κ has a dense subspace without non-trivial convergent sequences. If X is an uncountable σ-compact space of countable weight, then any dense set Y ⊂ C_p(X) has a dense subspace without non-trivial convergent sequences. We also prove that for any countably compact sequential space X, if C_p(X) has a dense k-subspace, then X is scattered.

Compactness Via Adherence Dominators, Bhamini M. P. Nayar, Terrence A. Edwards, James E. Joseph, Myung H. Kwack

Summer Conference on Topology and Its Applications

This talk is based on a joint work by T. A. Edwards, J. E. Joseph, M. H. Kwack and B. M. P. Nayar that apperared in the Journal of Advanced studies in Topology, Vol. 5 (4), 2014), 8 - 15. B

An adherence dominator on a topological space X is a function π from the collection of filterbases on X to the family of closed subsets of X satisfying A(Ω) ⊆ π(Ω) where A(Ω) is the adherence of Ω. The notations π(Ω) and A(Ω) are used for the values of the functions π and A and π(Ω) =⋂_Ω π F= …

Entropy In Topological Groups, Part 2, Dikran Dikranjan

Summer Conference on Topology and Its Applications

Entropy was introduced first in thermodynamics and statistical mechanics, as well as information theory. In the last sixty years entropy made its way also in topology, ergodic theory, as well as other branches of mathematics as algebra, geometry and number theory where dynamical systems appear in one way or another.

Roughly speaking, entropy is a non-negative real number or infinity assigned to a "selfmap" T of a "space" X, where the "space" X can be a topological or uniform space, a measure space, an abstract or topological group (or vector space) or just a set. The "selfmap" T can be, …

On Cardinality Bounds Involving The Weak Lindelöf Degree And H-Closed Spaces, Nathan Carlson, Angelo Bella, Jack Porter

Summer Conference on Topology and Its Applications

1. Bella and Carlson give several classes of spaces X for which |X| ≤ 2^wL(X)χ(X). This includes locally compact spaces and, more recently, extremally disconnected spaces. Three proofs of the former lead to more general results. One such result is that any regular space X with a π-base consisting of elements with compact closure satisfies |X| ≤ 2^wL(X)χ(X). It is also shown that if X is locally compact and power homogeneous that |X| ≤ 2^wL(X)t(X), an extension of De la Vega's Theorem.

2. Porter and Carlson give a new cardinality bound for any Hausdorff …

Paper Abstracts (2017), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

No abstract provided.

Thermal Stress Analysis In A Functionally Graded Hollow Elliptic-Cylinder Subjected To Uniform Temperature Distribution, V. R. Manthena, N. K. Lamba, G. D. Kedar

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, an analytical method of a thermoelastic problem for a medium with functionally graded material properties is developed in a theoretical manner for the elliptic-cylindrical coordinate system under the assumption that the material properties except for Poisson’s ratio and density are assumed to vary arbitrarily with the exponential law in the radial direction. An attempt has been made to reconsider the fundamental system of equations for functionally graded solids in a two-dimensional state under thermal and mechanical loads. The general solution of displacement formulation is obtained by the introduction of appropriate transformation and carried out the analysis by …

Some Relations On Generalized Rice's Matrix Polynomials, Ayman Shehata

Applications and Applied Mathematics: An International Journal (AAM)

The main aim of this paper is to obtain certain properties of generalized Rice’s matrix polynomials such as their matrix differential equation, generating matrix functions, an expansion for them. We have also deduced the various families of bilinear and bilateral generating matrix functions for them with the help of the generating matrix functions developed in the paper and some of their applications have also been presented here.

Numerical Solution Of Fractional Elliptic Pde's By The Collocation Method, Fuat Usta

Applications and Applied Mathematics: An International Journal (AAM)

In this presentation a numerical solution for the solution of fractional order of elliptic partial differential equation in R² is proposed. In this method we use the Radial basis functions (RBFs) method to benefit the desired properties of mesh free techniques such as no need to generate any mesh and easily applied to multi dimensions. In the numerical solution approach the RBF collocation method is used to discrete fractional derivative terms with the Gaussian basis function. Two dimensional numerical examples are presented and discussed, which conform well with the corresponding exact solutions.

A Novel Approach For Solving Volterra Integral Equations Involving Local Fractional Operator, Hassan K. Jassim

Applications and Applied Mathematics: An International Journal (AAM)

The paper presents an approximation method called local fractional variational iteration method (LFVIM) for solving the linear and nonlinear Volterra integral equations of the second kind with local fractional derivative operators. Some illustrative examples are discussed to demonstrate the efficiency and the accuracy of the proposed method. Furthermore, this method does not require spatial discretization or restrictive assumptions and therefore reduces the numerical computation significantly. The results reveal that the local fractional variational iteration method is very effective and convenient to solve linear and nonlinear integral equations within local fractional derivative operators.

Some Properties Of Certain Mixed Type Special Matrix Functions And Polynomials, Ahmed A. Al-Gonah, Fatima M. Al-Samadi

Applications and Applied Mathematics: An International Journal (AAM)

By using certain operational methods, the authors introduce some new mixed type special matrix functions and polynomials. Some properties of these matrix functions and polynomials are established.

Application Of Kudryashov Method For The Ito Equations, Mozhgan Akbari

Applications and Applied Mathematics: An International Journal (AAM)

In this present work, the Kudryashov method is used to construct exact solutions of the (1+1)- dimensional and the (1+2)-dimensional form of the generalized Ito integro-differential equation. The Kudryashov method is a powerful method for obtaining exact solutions of nonlinear evolution equations. This method can be applied to non-integrable equations as well as integrable ones.

Highly Hamiltonian Graphs And Digraphs, Zhenming Bi

Dissertations

A cycle that contains every vertex of a graph or digraph is a Hamiltonian cycle. A graph or digraph containing such a cycle is itself called Hamiltonian. This concept is named for the famous Irish physicist and mathematician Sir William Rowan Hamilton. These graphs and digraphs have been the subject of study for over six decades. In this dissertation, we study graphs and digraphs with even stronger Hamiltonian properties, namely highly Hamiltonian graphs and digraphs.

Conference Schedule (2017), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

No abstract provided.

Table Of Contents (2017), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

No abstract provided.

Association Of Christians In The Mathematical Sciences Proceedings 2017, Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

The conference proceedings of the Association of Christians in the Mathematical Sciences biannual conference, May 31-June 2, 2017 at Charleson Southern University.

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.

Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.

Tropical Algebra, Graph Theory, & Foreign Exchange Arbitrage, Bradley A. Mason

Senior Honors Projects, 2010-2019

We answer the question, given n currencies and k trades, how can a maximal arbitrage opportunity be found and what is its value? To answer this question, we use techniques from graph theory and employ a max-plus algebra (commonly known as tropical algebra). Further, we show how the tropical eigenvalue of a foreign exchange rate matrix relates to arbitrage among the currencies and can be found algorithmically. We finish by employing time series techniques to study the stability of maximal, high-currency arbitrage opportunities.

Detecting Finite Flat Dimension Of Modules Via Iterates Of The Frobenius Endomorphism, Douglas J. Dailey, Srikanth B. Iyengar, Thomas Marley

Department of Mathematics: Faculty Publications

It is proved that a module M over a Noetherian ring R of positive characteristic p has finite flat dimension if there exists an integer t > 0 such that Tor R (M, fe R) = 0 for t < i< t + dim R and infinitely many e. This extends results of Herzog, who proved it when M is finitely generated. It is also proved that when R is a Cohen-Macaulay local ring, it suffices that the Tor vanishing holds for one e > logp e(R) is the multiplicity of R.

Shortest Path Problem On Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Mohamed Talea, Assia Bakali, Kishore Kumar

Branch Mathematics and Statistics Faculty and Staff Publications

A single valued neutrosophic graph is a generalized structure of fuzzy graph, intuitionistic fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs and intuitionistic fuzzy graphs. This paper addresses for the first time, the shortest path in an acyclic neutrosophic directed graph using ranking function. Here each edge length is assigned to single valued neutrosophic numbers instead of a real number. The neutrosophic number is able to represent the indeterminacy in the edge (arc) costs of neutrosophic graph. A proposed algorithm gives the shortest path and shortest …

Krylov Subspace Spectral Methods For Pdes In Polar And Cylindrical Geometries, Megan Richardson

Dissertations

As a result of stiff systems of ODEs, difficulties arise when using time stepping methods for PDEs. Krylov subspace spectral (KSS) methods get around the difficulties caused by stiffness by computing each component of the solution independently. In this dissertation, we extend the KSS method to a circular domain using polar coordinates. In addition to using these coordinates, we will approximate the solution using Legendre polynomials instead of Fourier basis functions. We will also compare KSS methods on a time-independent PDE to other iterative methods. Then we will shift our focus to three families of orthogonal polynomials on the interval …

Differentiating Between A Protein And Its Decoy Using Nested Graph Models And Weighted Graph Theoretical Invariants, Hannah E. Green

Electronic Theses and Dissertations

To determine the function of a protein, we must know its 3-dimensional structure, which can be difficult to ascertain. Currently, predictive models are used to determine the structure of a protein from its sequence, but these models do not always predict the correct structure. To this end we use a nested graph model along with weighted invariants to minimize the errors and improve the accuracy of a predictive model to determine if we have the correct structure for a protein.

Application Of Symplectic Integration On A Dynamical System, William Frazier

Electronic Theses and Dissertations

Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic …

A Stochastic Model For Water-Vegetation Systems And The Effect Of Decreasing Precipitation On Semi-Arid Environments, Shannon A. Dixon

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Current climate change trends are affecting the magnitude and recurrence of extreme weather events. In particular, several semi-arid regions around the planet are confronting more intense and prolonged lack of precipitation, slowly transforming these regions into deserts. Many mathematical models have been developed for purposes of analyzing vegetation-water interactions, particularly in semi-arid landscapes. Most models are based on the average behavior of the system as a whole, and how it is influenced by external changes. These models may be termed "macro-scale" models. Other models have concerned themselves with the interactions between individuals, in this case the interactions between individual plants …