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TOPOLOGICAL SYMMETRY GROUPS OF COMPLETE GRAPHS IN THE 3-SPHERE
TOPOLOGICAL SYMMETRY THE 3-SPHERE
2015/12/17
The orientation preserving topological symmetry group of
a graph embedded in the 3-sphere is the subgroup of the automorphism
group of the graph consisting of those automorphisms which can be
induc...
FINITE-SIDED DEFORMATION SPACES OF COMPLETE AFFINE 3-MANIFOLDS
3-MANIFOLDS DEFORMATION SPACES
2015/9/29
A Margulis spacetime is a complete affine 3-manifold
M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S.
We show that eve...
The elementary diagram of a trivial, weakly minimal structure is near model complete
elementary diagram model complete
2015/9/28
We prove that if M is any model of a trivial, weakly minimal theory,
then the elementary diagram T(M) eliminates quantifiers down
to Boolean combinations of certain existential formulas.
Trivial, strongly minimal theories are model complete after naming constants
model complete naming constants
2015/9/25
We prove that if M is any model of a trivial, strongly
minimal theory, then the elementary diagram Th(MM ) is a model
complete LM -theory. We conclude that all countable models of
a trivial, strong...
Borel complexity of complete, first order theories(status report)
first order theories status report
2015/9/25
Borel complexity of complete, first order theories(status report).
Equidistribution of Horocyclic Flows on Complete Hyperbolic Surfaces of Finite Area
Horocyclic Flows Complete Hyperbolic Surfaces Finite Area
2015/8/26
We provide a self-contained, accessible introduction to Ratner’s Equidistribution Theorem in the special case of horocyclic flow on a complete hyperbolic surface of finite area. This equidistribution ...
PARALLEL CHIP-FIRING ON THE COMPLETE GRAPH;DEVIL’S STAIRCASE AND POINCARE ROTATION NUMBER
PARALLEL CHIP-FIRING COMPLETE GRAPH DEVIL’S STAIRCASE POINCARE ROTATION NUMBER
2015/8/14
We study how parallel chip-firing on the complete graph Kn changes behavior as we vary the total number of chips. Surprisingly,the activity of the system, defined as the average number of firings per ...
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3
Allen-Cahn Equation Embedded Minimal Surfaces Finite Total Curvature in R3
2015/4/3
Entire Solutions of the Allen-Cahn Equation and Complete Embedded Minimal Surfaces of Finite Total Curvature in R3.
A Complete Catalog of Geometrically Non-Is omorphic 18-run Orthogonal Ar rays
Orthogonal Ar rays Complete Catalog
2015/3/18
Factorial designs have w ide applications in industrial and scie ntific studies.
Traditionally, they are class ifie d based their combinatoric prop ertie s. Two
designs are considered to b e isomorp...
The KH-Theory of Complete Simplicial Toric Varieties and the Algebraic K-Theory of Weighted Projective Spaces
Toric Varieties Algebraic K-Theory Weighted Projective Spaces K-regularity
2012/7/11
We show that, for a complete simplicial toric variety $X$, we can determine its homotopy $\K$-theory (denoted $\KH$-theory) entirely in terms of the torus pieces of open sets forming an open cover of ...
ON THE INJECTIVITY RADIUS GROWTH OF COMPLETE NONCOMPACT RIEMANNNIAN MANIFOLDS
INJECTIVITY RADIUS GROWTH COMPLETE NONCOMPACT RIEMANNNIAN MANIFOLDS
2018/4/19
In this paper we introduce a global geometric invariant (M) related to injectivityradius to complete non-compact Riemannian manifolds and prove: If (Mn) > 1,then Mn is isometric to Rn when Ricci curva...
On complete constant mean curvature vertical multigraphs in E(κ,τ)
multigraphs constant mean curvature homogeneous spaces
2012/6/29
We prove that any complete surface with constant mean curvature in a homogeneous space E(\kappa,\tau) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a cons...
Constructing graphs with no immersion of large complete graphs
Graph immersion minimum degree chromatic number edgeconnectivity Hajos Conjecture Hadwiger Conjecture graph minor
2012/6/29
In 1989, Lescure and Meyniel proved, for $d=5, 6$, that every $d$-chromatic graph contains an immersion of $K_d$, and in 2003 Abu-Khzam and Langston conjectured that this holds for all $d$. In 2010, D...
Complete Residue Systems: A Primer and an Application
Complete Residue Systems A Primer and an Application Number Theory
2012/6/19
Complete residue systems play an integral role in abstract algebra and number theory, and a description is typically found in any number theory textbook. This note provides a concise overview of compl...
Optimal Riemannian metric for a volumorphism and a mean ergodic theorem in complete global Alexandrov nonpositively curved spaces
Optimal Riemannian metric volumorphism mean ergodic theorem complete global Alexandrov nonpositively curved spaces Differential Geometry
2012/6/15
In this paper we give a natural condition for when a volumorphism on a Riemannian manifold $(M,g)$ is actually an isometry with respect to some other, optimal, Riemannian metric $h$. We consider the n...