This paper presents new explicit formulae for the point doubling, tripling and addition for ordinary Weierstraß elliptic curves with a point of order 3 and their equivalent Hessian curves over finite fields of characteristic three. The cost of basic point operations is lower than that of all previously proposed ones. The new doubling, mixed addition and tripling formulae in projective coordinat...

Attention is drawn to the observation that in many correlated systems (e.g. 3He, heavy fermion systems and Hubbard models) the specific heat curves, when plotted for different values of some thermodynamic variable (e.g. pressure, magnetic field, interaction), cross almost precisely at one or two characteristic temperatures. A quantitative explanation of this phenomenon, based on the temperature...