Let $G$ be a connected graph, and let $D[G]$ denote the double graph of $G$. In this paper, we first derive closed-form formulas for different distance based topological indices for $D[G]$ in terms of that of $G$. Finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topologica...

NNIL-formulas are propositional formulas that do not allow nesting of implication to the left. These formulas were introduced in [16], where it was shown that NNIL-formulas are (up to provable equivalence) exactly the formulas that are preserved under taking submodels of Kripke models. In this paper we show that NNIL-formulas are up to frame equivalence the formulas that are preserved under tak...

Extensions of the Stirling numbers of the second kind and Dobinski-like formulas are proposed in a series of exercises for graduetes. Some of these new formulas recently discovered by me are to be found in A.K.Kwaśniewski’s source paper [1]. These extensions naturally encompass the well known q-extensions.The indicatory references are to point at a part of the vast domain of the foundations of ...

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

Given a symplectic space, equipped with a line bundle and a Hamiltonian group action satisfying certain compatibility conditions, it is a basic question to understand the decomposition of the quantization space in irreducible representations of the group. We derive weight multiplicity formulas for the quantization space in terms of data at the fixed points on the symplectic space, which apply t...