In the last article on square-root palindromes [1], we investigated constant square-root palindromes (those in which all terms are the same) using a combination of programs, guesses, and deduction. In this article, we’ll take a different approach: solving continued fractions to get data from which to derive more information about square-root palindromes. In a previous article [2], we showed a m...

The stress of a vertex is node centrality index, which has been introduced by Shimbel (1953). in graph the number geodesics (shortest paths) passing through it. In this paper, we introduce new topological index for graphs called square root sum using stresses vertices. Further, establish some inequalities, prove results and compute stress-sum standard graphs.

Let $$L(t) = - \mathrm{div} \left( A(x,t) \nabla _x \right) $$ for $$t \in (0, \tau )$$ be a uniformly elliptic operator with boundary conditions on domain $$\Omega of $$\mathbb {R}^d$$ and $$\partial \frac{\partial }{\partial t}$$ . Define the parabolic $${{\mathcal {L}}}= \partial + L$$ $$L^2(0, , L^2(\Omega ))$$ by $$({{\mathcal {L}}}u)(t) := u(t)}{\partial t} L(t)u(t)$$ We assume very littl...