So far in the course we have been concerned almost exclusively with functions on the set {−1, 1}n (sometimes written F2 ). What about other product spaces? As alluded to in Problem #1 on Homeworks #4 and #5, we can develop some kind of “orthogonal decomposition” for functions on any product probability space X. This will give us some subset of our Fourier analysis, and it’s useful when one does...

Abstract A squaregraph is a plane graph in which each internal face 4‐cycle and vertex has degree at least 4. This paper proves that every isomorphic to subgraph of the semistrong product an outerplanar path. We generalise this result for infinite squaregraphs, show best possible sense “outerplanar graph” cannot be replaced by “forest”.

A Riemannian manifold endowed with k>2 orthogonal complementary distributions (called here an almost multi-product structure) appears in such topics as multiply twisted or warped products and the webs nets composed of foliations. In this article, we define mixed scalar curvature structure a linear connection, represent kind using fundamental tensors divergence geometrically interesting vecto...

We consider the unit tangent sphere bundle of Riemannian manifold ( M, g ) with g-natural metric G̃ and we equip it to an almost contact B-metric structure. Considering this structure, we show that there is a direct correlation between the Riemannian curvature tensor of ( M, g ) and local symmetry property of G̃. More precisely, we prove that the flatness of metric g is necessary and sufficien...