We present an exact computation of effective Hamiltonians for elementary model obtained from the Yukawa theory by going to limit bare fermions being infinitely heavy and bosons at rest with respect that emit or absorb them. The coupling constant can be arbitrarily large. are computed solving differential equation renormalization group procedure particles (RGPEP). Physical fermions, defined in a...

A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.

  The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...

The idea is to start with a microscopic Hamiltonian describing the “actual” system and to find a reduced description on as subspace. For example, starting with a set of sites with various energies and hopping elements, we might want an effective description between a subset of them — which will make sense if they different energies — and to find the effective on-site and hopping elements for th...