The universal n-pointed surface bundle only has n sections

A Universal Investigation of $n$-representations of $n$-quivers

noindent We have two goals in this paper. First, we investigate and construct cofree coalgebras over $n$-representations of quivers, limits and colimits of $n$-representations of quivers, and limits and colimits of coalgebras in the monoidal categories of $n$-representations of quivers. Second, for any given quivers $mathit{Q}_1$,$mathit{Q}_2$,..., $mathit{Q}_n$, we construct a new quiver $math...

The Lie Algebra of Smooth Sections of a T-bundle

In this article, we generalize the concept of the Lie algebra of vector fields to the set of smooth sections of a T-bundle which is by definition a canonical generalization of the concept of a tangent bundle. We define a Lie bracket multiplication on this set so that it becomes a Lie algebra. In the particular case of tangent bundles this Lie algebra coincides with the Lie algebra of vector fie...

Who has the “Right” to Use the N-Word? A Survey of Attitudes about the Acceptability of Using the N-Word and its Derivatives

The N-word is the ultimate insult that has tormented generations of African-Americans. Yet over time, N-word derivatives have become popular terms of endearment by the descendants of the very people who once had to endure the N-word. Therein lies the root of an ongoing argument in society today: Who has the ‘right’ to use the N-word and N-word derivatives?  A quota sample (N=347) of undergradua...

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

Counting Rooted Trees: The Universal Law t(n)~C ρ-n n-3/2

Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series T(z) with a positive radius of convergence; for most of these a simple test can be used to quickly show that the form of the asymptotics is the same as that for the class of rooted trees: Cρn , where ρ ...