States and regions around the US are readying their bids to host centers for hydrogen production, distribution, end uses.

A multigraph drawn in the plane is called non-homotopic if no pair of its edges connecting same vertices can be continuously transformed into each other without passing through a vertex, and loop shrunk to end-vertex way. Edges are allowed intersect themselves. It easy see that on n>1 have arbitrarily many edges. We prove number crossings between with n m>4n larger than cm2n for some constant c...

The WZW models describe the dynamics of edge modes Chern-Simons theories in three dimensions. We explore which can be mapped to supersymmetric via generalized Jordan-Wigner transformation. Some such have Ramond vacua, but others break supersymmetry spontaneously. also make a comment on recent proposals that Read-Rezayi states at filling fraction \nu=1/2,~2/3 <mml:math xmlns:mml="http://www.w3.o...

A geometric graph is a drawn in the plane so that its vertices and edges are represented by points general position straight line segments, respectively. vertex of called pointed if it lies outside convex hull neighbours. We show for with $$n$$ $$e$$ there at least $$\frac{n}{2}\left(\begin{array}{cc}2e/n\\3\end{array}\right)$$ pairs disjoint provided $$2e\ge n$$ all pointed. Besides, we prove ...