Objective: Since orthodontic and orthognathic treatment planningin each ethnic group must be done according to the soft tissue facial characteristicsregarded as beauty,they thus vary from country to country.The main purpose of this articlewas to determine the mean range of the middle third of soft tissue facial profile and anteroposterior lip positioningusing 3angular and 2 linear measurement...

The Merrifield-Simmons index i G of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, that is, the number of independent vertex sets of G The Hosoya index z G of a graph G is defined as the total number of independent edge subsets, that is, the total number of its matchings. By C n, k, λ we denote the set of graphs with n vertices, k cyc...

Abstract Many chemical indices have been invented in theoretical chemistry, such as Wiener index, Merrifield-Simmons index, Hosoya index, spectral radius and Randić index, etc. The extremal trees and unicyclic graphs for these chemical indices are interested in existing literature. Let G be a molecular graph (called a cacti), which all of blocks of G are either edges or cycles. Denote G (n, r) ...

We study the number of independent vertex subsets (known as the MerrifieldSimmons index in mathematical chemistry) and the number of independent edge subsets (called the Hosoya index) for trees whose vertex degrees are restricted to 1 or d (for some d ≥ 3), a natural restriction in the chemical context. We find that the minimum of the Merrifield-Simmons index and the maximum of the Hosoya index...

The synthesis of diverse substituted indole structures on solid supports is described. The immobilization of nitrobenzoic acid onto Merrifield resin and the subsequent treatment with alkenyl Grignard reagents delivered indole carboxylates bound to solid supports. In contrast to results in the liquid phase, ortho,ortho-unsubstituted nitroarenes also delivered indole moieties in good yields. Subs...

Abstract Bruce Merrifield (1921‒2006) was an American biochemist who, at the Rockefeller Institute, invented a highly efficient technique for producing peptides and proteins in early 1960s. He awarded Nobel Prize Chemistry 1984. We remember this original, low-profile contributor to chemistry on occasion of one hundredth anniversary his birth.