Equivalence classes of codimension-one cut-and-project nets

The graph of equivalence classes and Isoclinism of groups

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

Equivalence Classes of Latin Squares and Nets in Cp

The fundamental combinatorial structure of a net in CP is its associated set of mutually orthogonal latin squares. We define equivalence classes of sets of orthogonal Latin squares by label equivalences of the lines of the corresponding net in CP. Then we count these equivalence classes for small cases. Finally, we prove that the realization spaces of these classes in CP are empty to show some ...

Some equivalence classes of operators on B(H)

Codimension One Symplectic Foliations

We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.

Codimension One Branes

We study codimension one branes, i.e. p-branes in (p + 2)-dimensions, in the superembedding approach for the cases where the worldvolume superspace is embedded in a minimal target superspace with half supersymmetry breaking. This singles out the cases p = 1, 2, 3, 5, 9. For p = 3, 5, 9 the superembedding geometry naturally involves a fundamental super 2-form potential on the worldvolume whose g...