Compression boosting (Ferragina & Manzini, SODA 2004) is a new technique to enhance zeroth order entropy compressors’ performance to k-th order entropy. It works by constructing the BurrowsWheeler transform of the input text, finding optimal partitioning of the transform, and then compressing each piece using an arbitrary zeroth order compressor. The optimal partitioning has the property that t...

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

We study the finite horizonMerton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the ‘implied Sharpe ratio’ and derive a series approximation for this quantity. The zeroth-order approximation of the value fu...

In a study on the structure–dependency of the total π-electron energy from 1972, Trinajstić and one of the present authors have shown that it depends on the sums ∑ v∈V d(v) 2 and ∑ v∈V d(v) , where d(v) is the degree of a vertex v of the underling molecular graph G. The first sum was later named first Zagreb index and over the years became one of the most investigated graph–based molecular stru...

The Generalised Randić index R−α(T ) of a tree T is the sum over the edges uv of T of (d(u)d(v))−α where d(x) is the degree of the vertex x in T . For all α > 0, we find the minimal constant βc = βc(α) such that for all trees on at least 3 vertices R−α(T ) ≤ βc(n + 1) where n = |V (T )| is the number of vertices of T . For example, when α = 1, βc = 15 56 . This bound is sharp up to the additive...

A real-number to molecular structure mapping is a topological index. It graph invariant method for describing physico-chemical properties of structures specific substances. In that article, We examined pentacene’s chemical composition. The research on the subsequent indices reflected in our paper, we conducted an analysis several including general randic connectivity index, first zagreb sum-con...

We derive sharp lower bounds for the first and the second Zagreb indices (M1 and M2 respectively) for trees and chemical trees with the given number of pendent vertices and find optimal trees. M1 is minimized by a tree with all internal vertices having degree 4, while M2 is minimized by a tree where each “stem” vertex is incident to 3 or 4 pendent vertices and one internal vertex, while the res...