In the paper, we present sufficient conditions of boundedness L-index in joint variables for a sum entire functions, where L : C n → R + is continuous function, R+ = (0, +∞). They are applicable to very wide class functions because every function F with bounded multiplicities zero points there exists positive such that has variables. Our propositions generalizations Pugh’s result obtained one v...

Statistical literacy depends on the ability to read and compare data presented in tables and graphs. Tables of rates and percentages are very useful in supporting arguments, but these tables are often difficult to decode. This paper presents rules for determining whether an index variable in such a table is part or whole depending on whether the associated margin value is an average, a sum or a...

The Balaban index of a connected graph G is defined as J(G) = |E(G)| μ+ 1 ∑ e=uv∈E(G) 1 √ DG(u)DG(v) , and the Sum-Balaban index is defined as SJ(G) = |E(G)| μ+ 1 ∑ e=uv∈E(G) 1 √ DG(u)+DG(v) , where DG(u) = ∑ w∈V (G) dG(u,w), and μ is the cyclomatic number of G. In this paper, the unicyclic graphs with the maximum Balaban index and the maximum Sum-Balaban index among all unicyclic graphs on n v...

As highly discriminant distance-based topological indices, the Balaban index and the sum-Balaban index of a graph $G$ are defined as $J(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)D_{G}(v)}}$ and $SJ(G)=frac{m}{mu+1}sumlimits_{uvin E} frac{1}{sqrt{D_{G}(u)+D_{G}(v)}}$, respectively, where $D_{G}(u)=sumlimits_{vin V}d(u,v)$ is the distance sum of vertex $u$ in $G$, $m$ is the n...

In the modern era, many research works are being carried out throughout the world for finding out a suitable cementitious material for the replacement of cement. The supplementary cementitious materials (SCM) can be used as a replacement of cement in the construction industry to minimize the carbon dioxide emission which is implicated in global warming and climatic changes in the environment. T...