Physical Sciences and Mathematics Commons^™

Intersecting Circles And Their Inner Tangent Circle, Max Tran

Publications and Research

We derive the general equation for the radius of the inner tangent circle that is associated with three pairwise intersecting circles. We then look at three special cases of the equation.

Splitting Of Vector Bundles On Punctured Spectrum Of Regular Local Rings, Mahdi Majidi-Zolbanin

Dissertations, Theses, and Capstone Projects

In this dissertation we study splitting of vector bundles of small rank on punctured spectrum of regular local rings. We give a splitting criterion for vector bundles of small rank in terms of vanishing of their intermediate cohomology modules Hⁱ(U, E)_{2_i_n−3}, where n is the dimension of the regular local ring. This is the local analog of a result by N. Mohan Kumar, C. Peterson, and A. Prabhakar Rao for splitting of vector bundles of small rank on projective spaces.

As an application we give a positive answer (in a special case) to a conjecture …

Robustly Transitive Sets And Heterodimensional Cycles, Christian Bonatti, Lorenzo J. Díaz, Enrique R. Pujals, Jorge Rocha

Publications and Research

It is known that all non-hyperbolic robustly transitive sets Λ_φ have a dominated splitting and, generically, contain periodic points of different indices. We show that, for a C¹-dense open subset of diffeomorphisms φ, the indices of periodic points in a robust transitive set Λ_φ form an interval in ℕ. We also prove that the homoclinic classes of two periodic points in Λ_φ are robustly equal. Finally, we describe what sort of homoclinic tangencies may appear in Λ_φ by studying its dominated splittings.

On String Topology Of Three Manifolds, Hossein Abbaspour

Dissertations, Theses, and Capstone Projects

In this dissertation we establish a connection between some aspects of the string topology of three dimensional manifolds and their topology and geometry using the theory of the prime decomposition and characteristic surfaces.

On C^1 Robust Singular Transitive Sets For Three-Dimensional Flows, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

The main goal of this paper is to study robust invariant transitive sets containing singularities for C¹ flows on three-dimensional compact boundaryless manifolds:they are partially hyperbolic with volume expanding central direction. Moreover, they are either attractors or repellers. Robust here means that this property cannot be destroyed by small C¹-perturbations of the flow.

Résumé:

Le but de ce travail est d'étudier des ensembles invariants robustes ayant des singularités pour des flots C¹ sur des variétés tridimensionelles : ce sont des ensembles hyperboliques singuliers. << Robuste >> veut dire ici que cette propriété ne peut être détruite par des …

Global Attractors From The Explosion Of Singular Cycles, Carlos Arnoldo Morales, Maria José Pacífico, Enrique Ramiro Pujals

Publications and Research

Abstract:

In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

Résumé:

Nous présentons dans cette Note des résultats récents concernant l’existence et les bifurcations d’un nouvel attracteur global chaotique.

Difference Equations, Isoperimetric Inequality And Transience Of Certain Random Walks, Jozef Dodziuk

Publications and Research

No abstract provided.

Finite-Difference Approach To The Hodge Theory Of Harmonic Forms, Jozef Dodziuk

Publications and Research

No abstract provided.

Class Groups Of Real Quadratic Number Fields, Paul B. Massell

Dissertations, Theses, and Capstone Projects

No abstract provided.

D-Structures And Their Semantics, Rohit J. Parikh

Publications and Research

"Many logicians are familiar with the game theoretic approach to semantics, due to Jaakko Hintikka. This paper by me contains class notes of a logic course at Boston University in fall 1972. It has similar game theoretic ideas, developed quite independently, but influenced by the work of A. Ehrenfeucht. It applies to a larger class of logics, including classical logic, intuitionistic logic and the *-semantics of Ehrenfeucht. The treatment is via D-structures which are finite approximations of infinite structures. For various reasons I did not publish this paper then, but some abstracts, both by myself as well as joint abstracts …