In the thermodynamic limit, the ground state of a system with these entities and the ground state in the absence of these entities are orthogonal according to Anderson’s orthogonality theorem. Numerical renormalization group method was developed to explain the existence of minimum resistivity due to these entities. Conduction electrons scattering of these entities in a metal contribute a term proportional to log of inverse temperature to the resistivity in the Kondo effect. (*) Neodymium serves as one of these entities to YAG crystal structure used in a laser medium. These entities are added to change the conductivity of semiconductors (10[1])in the process of doping. For 10 points, identify these substances in which parts of its compositions are substituted with foreign atoms. ■END■