In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere Sn ≃ SO(n + 1)/SO(n) and the spherical functions of the n-dimensional real projective space P n(R) ≃ SO(n + ...

Starting from the planar molecule 1,3,5-trihydroxybenzene, Du et al reported synthesizing one of a couple of possible 2D materials: graphenylene or 3-carbophene [1]. 3-carbophene is a member of a novel class of two-dimensional ...

In this paper we establish a close relationship between the spherical functions of the n-dimensional sphere $S^n\simeq\SO(n+1)/\SO(n)$ and the spherical functions of the n-dimensional real projective space $P^n(\mathbb{R ...

Cohomology groups H(s)(Z(n), Z(m)) are studied to describe all groups up to isomorphism which are (central) extensions of the cyclic group Z(n) by the Z(n)-module Z(m). Further, for each such a group the number of ...

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X ...

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X ...

Organic compounds owe their diversity to the amount of carbons and to the atomic types that are part of their structure, also called functional groups. According to the functional group, the organic compounds present ...