ABSTRACT
In this article, we study the degree-based topological indices in a random polyomino chain. The key purpose of this manuscript is to obtain the asymptotic distribution, expected value and variance for the degree-based topological indices in a random polyomino chain by using a martingale approach. Consequently, we compute the degree-based topological indices in a polyomino chain, hence some known results from the existing literature about polyomino chains are obtained as corollaries. Also, in order to apply the results, we obtain the expected value of several degree-based topological indices such as Sombor, Forgotten, Zagreb, atom-bond-connectivity, Randic and geometric-arithmetic index of a random polyomino chain.
ABSTRACT
This work examines aquaculture-related activities in the commercial exploitation of fish reproduction. Fisheries' problem of maximizing utility is modeled for the state of Puebla, Mexico, to determine optimal fish production. The problem of maximizing utility subject to the fish production function is solved using an approach based on Euler's equation. The theoretical results are then applied, using data on aquaculture production and tilapia sales prices in the state of Puebla, Mexico. A logarithmic regression is used to approximate the utility function. The optimal fishing production and utility functions are thus explicitly obtained. Furthermore, this work shows how to obtain greater profits from the amount of fish that can be extracted without reducing the fish population.
