Using Canalization For The Control Of Discrete Networks, 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, 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 ...

Positive Definite Functions And Dual Pairs Of Locally Convex Spaces, 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.

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

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

On Roitman's Principle For Box Products, 2017 Universidad Nacional Autonoma de Mexico

#### On Roitman's Principle For Box Products, Hector Alonso Barriga-Acosta

*Summer Conference on Topology and Its Applications*

One of the oldest problems in box products is if the countable box product of the convergent sequence is normal. It is known that consistenly (e.g., b=d, d=c) the answer is affirmative. A recent progress is due to Judy Roitman that states a combinatorial principle which also implies the normality and holds in many models.

Although the countable box product of the convergent sequence is normal in some models of b < d < c, Roitman asked what happen with her principle in this models. We answer that Roitman's principle is true in some models of b < d < c.

The Isbell-Hull Of An Asymmetrically Normed Space, 2017 North-West University (South Africa)

#### The Isbell-Hull Of An Asymmetrically Normed Space, Olivier Olela Otafudu, Jurie Conradie, Hans-Peter Künzi

*Summer Conference on Topology and Its Applications*

In this talk, we discuss an explicit method to define the linear structure of the Isbell-hull of an asymmetrically normed space.

Fiber Strong Shape Theory For Topological Spaces, 2017 Batumi Shota Rustaveli State University

#### Fiber Strong Shape Theory For Topological Spaces, Ruslan Tsinaridze, Vladimer Baladze

*Summer Conference on Topology and Its Applications*

The purpose of this paper is the construction and investigation of fiber strong shape theory for compact metrizable spaces over a fixed base space B_{0} , using the fiber versions of cotelescop, fibrant space and SSDR-map. In the paper obtained results containing the characterizations of fiber strong shape equivalences, based on the notion of double mapping cylinder over a fixed space B_{0}. Besides, in the paper we construct and develop a fiber strong shape theory for arbitrary spaces over fixed metrizable space B_{0}. Our approach is based on the method of Mardešić-Lisica and instead of resolutions, introduced by ...

A Compact Minimal Space Whose Cartesian Square Is Not Minimal, 2017 AGH University of Science and Technology, Krakow

#### A Compact Minimal Space Whose Cartesian Square Is Not Minimal, Jan P. Boronski, Alex Clark, Piotr Oprocha

*Summer Conference on Topology and Its Applications*

A compact metric space X is called *minimal* if it admits a minimal homeomorphism; i.e. a homeomorphism h:X→ X such that the forward orbit {h^{n}(x):n=1, 2, ...} is dense in X, for every x ∈ X. In my talk I shall outline a construction of a family of 1-dimensional minimal spaces from "A compact minimal space Y such that its square YxY is not minimal" whose existence answer the following long standing problem in the negative.

**Problem.** Is minimality preserved under Cartesian product in the class of compact spaces?

Note that for the fixed point property ...

Compactly Supported Homeomorphisms As Long Direct Limits, 2017 Technische Universitat Darmstadt

#### 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 for λ = ω_{1 ...}

Virtual Seifert Surfaces And Slice Obstructions For Knots In Thickened Surfaces, 2017 Monmouth University

#### Virtual Seifert Surfaces And Slice Obstructions For Knots In Thickened Surfaces, Micah Chrisman, Hans U. Boden, Robin Gaudreau

*Summer Conference on Topology and Its Applications*

Here we introduce the notion of virtual Seifert surfaces. Virtual Seifert surfaces may be thought of as a generalization of Gauss diagrams of virtual knots to spanning surfaces of a knot. This device is then employed to extend the Tristram-Levine signature function to AC knots. Using the AC signature functions and Tuarev’s graded genus invariant, we determine the slice status of all 76 almost classical knots having at most six crossings. The slice obstructions for AC knots are then extended to all virtual knots via the parity projection map. This map, which is computable from a Gauss diagram, sends ...

Pseudo-Contractibility, 2017 Universidad Autonoma del Estado de Mexico

#### Pseudo-Contractibility, Felix Capulín, Leonardo Juarez-Villa, Fernando Orozco

*Summer Conference on Topology and Its Applications*

Let X, Y be topological spaces and let f, g:X→ Y be mappings, we say that f is pseudo-homotopic to g if there exist a continuum C, points a, b ∈ C and a mapping H:X ×C → Y such that H(x, a)=f(x) and H(x, b)=g(x) for each x ∈ X. The mapping H is called a pseudo-homotopy between f and g. A topological space X is said to be pseudo-contractible if the identity mapping is pseudo-homotopic to a constant mapping in X. i.e., if there exist a continuum C, points a, b ∈ C ...

Quotients Of N-Fold Hyperspaces, 2017 Universidad Autonoma del Estado de Mexico

#### Quotients Of N-Fold Hyperspaces, Sergio Macías, Javier Camargo

*Summer Conference on Topology and Its Applications*

iven a continuum X and an integer n ≥ 2, let C_{n}(X) be the n-fold hyperspace of X consisting of all nonempty closed subsets of X with at most n components. We consider the quotient space C^{n}_{1}(X)=C_{n}(X)/C_{1}(X) with the quotient topology. We prove several properties. For example: C^{n}_{1}(X) is unicoherent; if X has the property of Kelley, C^{n}_{1}(X) is contractible; dim(C_{n}(X))=dim(C^{n}_{1}(X)); both C^{n}_{1}([0, 1]) and C^{n}_{1}(S^{1}) are Cantor manifolds ...

On A Construction Of Some Class Of Metric Spaces, 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.

Disjoint Infinity Borel Functions, 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 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 from g ...

Cohen Reals And The Sequential Order Of Groups, 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.

On Di-Injective T0-Quasi-Metric Spaces, 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.

Entropy Of Induced Continuum Dendrite Homeomorphisms, 2017 Universidade Federal do Rio de Janeiro

#### Entropy Of Induced Continuum Dendrite Homeomorphisms, Jennyffer Bohorquez, Alexander Arbieto

*Summer Conference on Topology and Its Applications*

Let f: D → D be a dendrite homeomorphism. Let C(D) denote the hyperspace of all nonempty connected compact subsets of D endowed with the Hausdorff metric. Let C(f):C(D) → C(D) be the induced continuum homeomorphism. In this talk we sketch the proof of the following result: If there exists a nonrecurrent branch point then the topological entropy of C(f) is ∞.

Uncountably Many Quasi-Isometry Classes Of Groups Of Type Fp, 2017 University of Oklahoma

#### Uncountably Many Quasi-Isometry Classes Of Groups Of Type Fp, Ignat Soroko, Robert Kropholler, Ian Leary

*Summer Conference on Topology and Its Applications*

An interplay between algebra and topology goes in many ways. Given a space X, we can study its homology and homotopy groups. In the other direction, given a group G, we can form its Eilenberg-Maclane space K(G, 1). It is natural to wish that it is `small' in some sense. If K(G, 1) space has n-skeleton with finitely many cells, then G is said to have type F_{n}. Such groups act naturally on the cellular chain complex of the universal cover for K(G, 1), which has finitely generated free modules in all dimensions up to n ...