Geometry and Topology Commons^™

On Integrability Of Semi-Invariant Submanifolds Of Trans-Sasakian Finsler Manifolds, Nesrin Caliskan, Ayse F. Saglamer, Nurten Kilic

Applications and Applied Mathematics: An International Journal (AAM)

We introduce the notion of trans-Sasakian Finsler manifold, then study semi-invariant submanifold F^m = (Y, Y', F) of a trans-Sasakian Finsler manifold F^{2n+1} + (bar-Y, bar-Y', bar-F) and we discuss the integrability conditions of the distrubitions of the semi-invariant submanifolds of the trans-Sasakian Finsler manifold.

A Comparison Of Original And Inverse Motion In Minkowski Plane, Kemal Eren, Soley Ersoy

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate the inflection circle, circling-point curve, and center-point curve for the original and inverse motion of Minkowski planes, and we also deal with their degenerate cases individually. For this purpose, we consider the trajectory of origin with respect to the instantaneous invariants of Bottema in Minkowski plane by using hyperbolic numbers. Finally, we give the geometric interpretation of the circling-point and center-point curves by comparing the original and inverse motion in Minkowski planes.

Optimal Inequalities For Submanifolds Of An Indefinite Space Form, Rıfat Güneş, Mehmet Gülbahar, Sadık Keleş, Erol Kılıç

Applications and Applied Mathematics: An International Journal (AAM)

Optimal inequalities involving the scalar curvature, the mean curvature vector and the second fundamental form for pseudo Riemannian submanifolds are proved and the equality cases of these inequalities are discussed. These results are studied for submanifolds of various indefinite contact space forms.

The T3,T4-Conjecture For Links, Katie Tucker

Department of Mathematics: Dissertations, Theses, and Student Research

An oriented n-component link is a smooth embedding of n oriented copies of S¹ into S³. A diagram of an oriented link is a projection of a link onto R² such that there are no triple intersections, with notation at double intersections to indicate under and over strands and arrows on strands to indicate orientation. A local move on an oriented link is a regional change of a diagram where one tangle is replaced with another in a way that preserves orientation. We investigate the local moves t₃ and t₄, which are …

Merge Trees In Discrete Morse Theory, Benjamin Johnson

Mathematics Summer Fellows

The field of topological data analysis seeks to use techniques in topology to study large data sets. The hope is that rather than single quantities that summarize the data, such as mean or standard deviation, information about the data can be learned by studying the overall ``shape” of the data. One way to summarize this data is through a merge tree. Merge trees can be thought of as keeping track of certain clusters of data and determining when they merge together. In this paper, we will study merge trees induced by a discrete Morse function on a tree. Under a …

Mathematics And Programming Exercises For Educational Robot Navigation, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

This paper points students towards ideas they can use towards developing a convenient library for robot navigation, with examples based on Botball primitives, and points educators towards mathematics and programming exercises they can suggest to students, especially advanced high school students.

Properties Of Functionally Alexandroff Topologies And Their Lattice, Jacob Scott Menix

Masters Theses & Specialist Projects

This thesis explores functionally Alexandroff topologies and the order theory asso- ciated when considering the collection of such topologies on some set X. We present several theorems about the properties of these topologies as well as their partially ordered set.

The first chapter introduces functionally Alexandroff topologies and motivates why this work is of interest to topologists. This chapter explains the historical context of this relatively new type of topology and how this work relates to previous work in topology. Chapter 2 presents several theorems describing properties of functionally Alexandroff topologies ad presents a characterization for the functionally Alexandroff topologies …

Dehn Functions Of Bestvina-Brady Groups, Yu-Chan Chang

LSU Doctoral Dissertations

In this dissertation, we prove that if the flag complex on a finite simplicial graph is a 2-dimensional triangulated disk, then the Dehn function of the associated Bestvina--Brady group depends on the maximal dimension of the simplices in the interior of the flag complex. We also give some examples where the flag complex on a finite simplicial graph is not 2-dimensional, and we establish a lower bound for the Dehn function of the associated Bestvina--Brady group.

On Nonlinear Contractions In New Extended 𝒃-Metric Spaces, Hassen Aydi, Abdelbasset Felhi, Tayyab Kamran, Erdal Karapınar, Muhammad U. Ali

Applications and Applied Mathematics: An International Journal (AAM)

Very recently, the notion of extended 𝑏-metric spaces was introduced by replacing the modified triangle inequality with a functional triangle inequality and the analog of the renowned Banach fixed point theorem was proved in this new structure. In this paper, continuing in this direction, we further refine the functional inequality and establish some fixed point results for nonlinear contractive mappings in the new setting. A nontrivial example for the new extended 𝑏-metric space is given.

Fuchsian Groups, Bob Anaya

Electronic Theses, Projects, and Dissertations

Fuchsian groups are discrete subgroups of isometries of the hyperbolic plane. This thesis will primarily work with the upper half-plane model, though we will provide an example in the disk model. We will define Fuchsian groups and examine their properties geometrically and algebraically. We will also discuss the relationships between fundamental regions, Dirichlet regions and Ford regions. The goal is to see how a Ford region can be constructed with isometric circles.

Geodesics On Generalized Plane Wave Manifolds, Moises Pena

Electronic Theses, Projects, and Dissertations

A manifold is a Hausdorff topological space that is locally Euclidean. We will define the difference between a Riemannian manifold and a pseudo-Riemannian manifold. We will explore how geodesics behave on pseudo-Riemannian manifolds and what it means for manifolds to be geodesically complete. The Hopf-Rinow theorem states that,“Riemannian manifolds are geodesically complete if and only if it is complete as a metric space,” [Lee97] however, in pseudo-Riemannian geometry, there is no analogous theorem since in general a pseudo-Riemannian metric does not induce a metric space structure on the manifold. Our main focus will be on a family of manifolds referred …

Network Analyses Of Glomerular Capillaries, Jason Cory Brunson, Justin Sardi, Mark Terasaki

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mental Geometry For Estimating Relative 3d Size, Akihito Maruya, Qasim Zaidi Dr.

MODVIS Workshop

No abstract provided.

Geometric Aspects Of Wound Healing, Julio Urenda, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we show that many aspects of complex biological processes related to wound healing can be explained in terms of the corresponding geometric symmetries.

On The Fundamental Group Of Plane Curve Complements, Mitchell Scofield

Boise State University Theses and Dissertations

Given a polynomial f(x,y) monic in y of degree d, we study the complement ℂ²-C, where C is the curve defined by the equation f(x,y)=0. The Zariski-Van Kampen theorem gives a presentation of the fundamental group of the complement ℂ²-C. Let NT be be the set of complex numbers x for which f(x,y) has multiple roots (as a polynomial in y). Let : ℂ − NT → ℂ^d − Δ be the map that …

Connectedness- Its Evolution And Applications, Nicholas A. Scoville

Topology

No abstract provided.

Integrating Mathematics And Educational Robotics: Simple Motion Planning, Ronald I. Greenberg, George K. Thiruvathukal, Sara T. Greenberg

Computer Science: Faculty Publications and Other Works

This paper shows how students can be guided to integrate elementary mathematical analyses with motion planning for typical educational robots. Rather than using calculus as in comprehensive works on motion planning, we show students can achieve interesting results using just simple linear regression tools and trigonometric analyses. Experiments with one robotics platform show that use of these tools can lead to passable navigation through dead reckoning even if students have limited experience with use of sensors, programming, and mathematics.

Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo

The Transdisciplinary STEAM+ Journal

The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of …

Parametric Natura Morta, Maria C. Mannone

The Transdisciplinary STEAM+ Journal

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.

Differential Invariants Of Non-Degenerate Surfaces, Yasemin Sağıroğlu, Djavvat Khadjiev, Uğur Gözütok

Applications and Applied Mathematics: An International Journal (AAM)

This paper aims to prove that the set {g_{ij}(x), L_{ij} (x), i, j = 1, 2} is a complete system of the SM(3)- invariants of a nondegenerate surface in R3, where {g_{ij}(x)} and {L_{ij}(x)}, 1, j = 1, 2 are the sets of all coefficients of the first and second fundamental forms of a surface x in R3. A similar result was obtained for the group M(3).