Incorporation of green chemistry techniques in undergraduate (UG) laboratories has a great demand. The challenge is to select and modify the known fundamental reactions in a greener way to implement into UG laboratories. A practical, two-step synthesis of 4-bromoacetanilide from aniline through a greener approach is described. Design of the synthetic route is based on the fundamental concepts of green chemistry. It can be adapted in most of the UG laboratories, including those with limited facilities. In the first step, aniline is converted to acetanilide using Zn dust/Fe powder−acetic acid instead of conventional acetic anhydride. In the second step, acetanilide is brominated using ceric ammonium nitrate−KBr combination in ethanolic−aqueous medium instead of bromine. The overall concept of modification could be useful to teach students about the concept of green chemistry, functional group protection, aromatic electrophilic substitution, and laboratory techniques such as reaction setup, isolation, purification, and product analysis.

We present a unifying approach to studying the replica symmetric solution in general diluted spin glass models on random p-uniform hypergraphs with sparsity parameter α. Our result shows that there exist two key regimes in which the model exhibits replica symmetry and the free energy can be explicitly represented as the evaluation of an energy functional at the unique fixed point of a recursive distributional equation. One is called the high temperature regime, where the temperature and the sparsity parameter are essentially inversely proportional to each other; the other is the subcritical regime defined as αp(p − 1) ≤ 1. In particular, the fact that the second regime is independent of the temperature parameter further allows us to deduce an analogous representation of the ground state energy in the subcritical regime. Along the way, we revisit several well-known formulas and also derive new ones for the free and ground state energies in the constraint satisfaction problem, Potts model, XY model, and continuous hardcore model.

We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of the spins in the system with varying edge connectivity. The key ingredient in our argument is played by the identification of these random variables as the unique solution to a recursive distributional equation. Our results in particular provide the first example of the diluted Shcherbina-Tirozzi model, whose limiting free energy can be derived at any inverse temperature and external field.