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Using Canalization For The Control Of Discrete Networks, David Murrugarra 2018 University of Kentucky

Using Canalization For The Control Of Discrete Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng 2018 Air Force Institute of Technology

Radial Basis Function Generated Finite Differences For The Nonlinear Schrodinger Equation, Justin Ng

Theses and Dissertations

Solutions to the one-dimensional and two-dimensional nonlinear Schrodinger (NLS) equation are obtained numerically using methods based on radial basis functions (RBFs). Periodic boundary conditions are enforced with a non-periodic initial condition over varying domain sizes. The spatial structure of the solutions is represented using RBFs while several explicit and implicit iterative methods for solving ordinary differential equations (ODEs) are used in temporal discretization for the approximate solutions to the NLS equation. Splitting schemes, integration factors and hyperviscosity are used to stabilize the time-stepping schemes and are compared with one another in terms of computational efficiency and accuracy. This thesis shows ...


On Generalizations Of P-Adic Weierstrass Sigma And Zeta Functions, Clifford Blakestad 2018 University of Colorado at Boulder

On Generalizations Of P-Adic Weierstrass Sigma And Zeta Functions, Clifford Blakestad

Mathematics Graduate Theses & Dissertations

We generalize a paper of Mazur and Tate on p-adic sigma functions attached to elliptic curves of ordinary reduction over a p-adic field.

We begin by generalizing the theory of division polynomials attached to an isogeny of elliptic curves, developed by Mazur and Tate, to isogenies of prinicipally polarized abelian varieties.

As an application, we produce a notion of a p-adic sigma function attached to a prinicipally polarized abelian variety of good ordinary reduction over a complete non-archimedean field of residue characteristic p.

Furthermore, we derive some the properties of the sigma function, many of which uniquely characterize ...


Positive Definite Functions And Dual Pairs Of Locally Convex Spaces, Daniel Alpay, Saak Gabriyelyan 2018 Chapman University

Positive Definite Functions And Dual Pairs Of Locally Convex Spaces, Daniel Alpay, Saak Gabriyelyan

Mathematics, Physics, and Computer Science Faculty Articles and Research

Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.


Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo 2017 Cylance, Inc.

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Conference Program, University of Dayton 2017 University of Dayton

Conference Program, University Of Dayton

Summer Conference on Topology and Its Applications

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications.


Elliptic Curve Cryptology, Francis Rocco 2017 Union College - Schenectady, NY

Elliptic Curve Cryptology, Francis Rocco

Honors Theses

In today's digital age of conducting large portions of daily life over the Internet, privacy in communication is challenged extremely frequently and confidential information has become a valuable commodity. Even with the use of commonly employed encryption practices, private information is often revealed to attackers. This issue motivates the discussion of cryptology, the study of confidential transmissions over insecure channels, which is divided into two branches of cryptography and cryptanalysis. In this paper, we will first develop a foundation to understand cryptography and send confidential transmissions among mutual parties. Next, we will provide an expository analysis of elliptic curves ...


Cohen Reals And The Sequential Order Of Groups, Alexander Shibakov 2017 Tennessee Technological University

Cohen Reals And The Sequential Order Of Groups, Alexander Shibakov

Summer Conference on Topology and Its Applications

We show that adding uncountably many Cohen reals to a model of diamond results in a model with no countable sequential group with an intermediate sequential order. The same model has an uncountable group of sequential order 2. We also discuss related questions.


Sequential Order Of Compact Scattered Spaces, Alan Dow 2017 University of North Carolina at Charlotte

Sequential Order Of Compact Scattered Spaces, Alan Dow

Summer Conference on Topology and Its Applications

A space is sequential if the closure of set can be obtained by iteratively adding limits of converging sequences. The sequential order of a space is a measure of how many iterations are required. A space is scattered if every non-empty set has a relative isolated point. It is not known if it is consistent that there is a countable (or finite) upper bound on the sequential order of a compact sequential space. We consider the properties of compact scattered spaces with infinite sequential order.


Revelation Of Nano Topology In Cech Rough Closure Spaces, V. Antonysamy, Llellis Thivagar, Arockia Dasan 2017 Madurai Kamaraj University

Revelation Of Nano Topology In Cech Rough Closure Spaces, V. Antonysamy, Llellis Thivagar, Arockia Dasan

Summer Conference on Topology and Its Applications

The concept of Cech closure space was initiated and developed by E. Cech in 1966. Henceforth many more research scholars set their minds in this theory and developed it to a new height. Pawlak.Z derived and gave shape to Rough set theory in terms of approximation using equivalence relation known as indiscernibility relation. Further Lellis Thivagar enhanced rough set theory into a topology, called Nano Topology, which has at most five elements in it and he also extended this into multi granular nano topology. The purpose of this paper is to derive Nano topology in terms of Cech rough ...


Totally Geodesic Surfaces In Arithmetic Hyperbolic 3-Manifolds, Benjamin Linowitz, Jeffrey S. Meyer 2017 Oberlin College

Totally Geodesic Surfaces In Arithmetic Hyperbolic 3-Manifolds, Benjamin Linowitz, Jeffrey S. Meyer

Summer Conference on Topology and Its Applications

In this talk we will discuss some recent work on the problem of determining the extent to which the geometry of an arithmetic hyperbolic 3-manifold M is determined by the geometric genus spectrum of M (i.e., the set of isometry classes of finite area, properly immersed, totally geodesic surfaces of M, considered up to free homotopy). In particular, we will give bounds on the totally geodesic 2-systole, construct infinitely many incommensurable manifolds with the same initial geometric genus spectrum and analyze the growth of the genera of minimal surfaces across commensurability classes. These results have applications to the study ...


On The Chogoshvili Homology Theory Of Continuous Maps Of Compact Spaces, Anzor Beridze, Vladimer Baladze 2017 Batumi Shota Rustaveli State University

On The Chogoshvili Homology Theory Of Continuous Maps Of Compact Spaces, Anzor Beridze, Vladimer Baladze

Summer Conference on Topology and Its Applications

In this paper an exact homology functor from the category MorC of continuous maps of compact Hausdorff spaces to the category LES of long exact sequences of abelian groups is defined (cf. [2], [3], [5]). This functor is an extension of the Hu homology theory, which is uniquely defined on the category of continuous maps of finite CW complexes and is constructed without the relative homology groups [9]. To define the given homology functor we use the Chogoshvili construction of projective homology theory [7], [8]. For each continuous map f:X → Y of compact spaces, using the notion of ...


Compactness Via Adherence Dominators, Bhamini M. P. Nayar, Terrence A. Edwards, James E. Joseph, Myung H. Kwack 2017 Morgan State University

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 ...


Some New Completeness Properties In Topological Spaces, Cetin Vural, Süleyman Önal 2017 Gazi University

Some New Completeness Properties In Topological Spaces, Cetin Vural, Süleyman Önal

Summer Conference on Topology and Its Applications

One of the most widely known completeness property is the completeness of metric spaces and the other one being of a topological space in the sense of Cech. It is well known that a metrizable space X is completely metrizable if and only if X is Cech-complete. One of the generalisations of completeness of metric spaces is subcompactness. It has been established that, for metrizable spaces, subcompactness is equivalent to Cech-completeness. Also the concept of domain representability can be considered as a completeness property. In [1], Bennett and Lutzer proved that Cech-complete spaces are domain representable. They also proved, in ...


Some Applications Of The Point-Open Subbase Game, David Guerrero Sanchez 2017 Universidad Autonoma Metropolitana - Iztapalapa

Some Applications Of The Point-Open Subbase Game, David Guerrero Sanchez

Summer Conference on Topology and Its Applications

Given a subbase S of a space X, the game PO(S,X) is defined for two players P and O who respectively pick, at the n-th move, a point xn 2 X and a set Un 2 S such that xn 2 Un . The game stops after the moves {xn, Un : n 2 !} have been made and the player P wins if the union of the Un’s equals X; otherwise O is the winner. Since PO(S,X) is an evident modification of the well-known point-open game PO(X), the primary line of research is to describe the ...


Disjoint Infinity Borel Functions, Daniel Hathaway 2017 University of Denver

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 fa : 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 fa is disjoint from g ...


On Di-Injective T0-Quasi-Metric Spaces, Collins Amburo Agyingi 2017 North-West University (South Africa)

On Di-Injective T0-Quasi-Metric Spaces, Collins Amburo Agyingi

Summer Conference on Topology and Its Applications

We prove that every q-hyperconvex T0-quasi-metric space (X, d) is di-injective without appealing to Zorn’s lemma. We also demonstrate that QX as constructed by Kemajou et al. and Q(X) (the space of all Katˇetov function pairs on X) are di-injective. Moreover we prove that di-injective T0-quasi-metric spaces do not contain proper essential extensions. Among other results, we state a number of ways in which the the di-injective envelope of a T0-quasi-metric space can be characterized.


On A Construction Of Some Class Of Metric Spaces, Dariusz Bugajewski 2017 Adam Mickiewicz University of Poznan

On A Construction Of Some Class Of Metric Spaces, Dariusz Bugajewski

Summer Conference on Topology and Its Applications

In this talk we are going to describe Sz´az’s construction of some class of metric spaces. Most of all we will analyze topological properties of metric spaces obtained by using Sz´az’s construction. In particular, we provide necessary and sufficient conditions for completeness of metric spaces obtained in this way. Moreover, we will discuss the relation between Sz´az’s construction and the “linking construction”. A particular attention will be drawn to the “floor” metric, the analysis of which provides some interesting observations.


Hausdorff Dimension Of Kuperberg Minimal Sets, Daniel Ingbretson 2017 University of Illinois at Chicago

Hausdorff Dimension Of Kuperberg Minimal Sets, Daniel Ingbretson

Summer Conference on Topology and Its Applications

The Seifert conjecture was answered negatively in 1994 by Kuperberg who constructed a smooth aperiodic flow on a three-manifold. This construction was later found to contain a minimal set with a complicated topology. The minimal set is embedded as a lamination by surfaces with a Cantor transversal of Lebesgue measure zero. In this talk we will discuss the pseudogroup dynamics on the transversal, the induced symbolic dynamics, and the Hausdorff dimension of the Cantor set.


A New Class Of Dendrites Having Unique Second Symmetric Product, David Maya, José G. Anaya, Fernando Orozco Zitli 2017 Universidad Autonoma del Estado de Mexico

A New Class Of Dendrites Having Unique Second Symmetric Product, David Maya, José G. Anaya, Fernando Orozco Zitli

Summer Conference on Topology and Its Applications

The second symmetric product of a continuum X, F2(X), is the hyperspace consisting of all nonempty subsets of X having at most two points. A continuum X has unique hyperspace F2(X) provided that each continuum Y satisfying that F2(X) and F2(Y) are homeomorphic must be homeomorphic to X. In this talk, a new class of dendrites having unique F2(X) will be presented.


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