scalar expansion
2.In connection with the researches carried out in our laboratory, the description is concentrated on the high accurate four-component relativistic density functional methods with relativistic effects taken into account strictly, and the two-component or scalar relativistic density functional methods with relativistic effects considered approximately, involving the zero-order regular approximation (ZORA) method and its improved variants, the singularity excluded approximate expansion (SEAX) method, and the jointed two component-scalar relativistic (or non-relativistic) approach applicable to the calculations of large systems locally containing heavy elements.
5.A simple two-dimensional lattice Boltzmann model with three speeds is studied. The local equilibrium distribution functions are determined under the restrained conditions of fluid dynamics by connecting the discrete model with the continuum macro-models. Euler equation and Navier--Stokes equation are derived by using Chapman Enskog expansion and multi-scalar technique, and the viscosity formula is also provided.
6.When a message is encrypted in (H)ECC, there will be a large amount of message expansion. Due to this fact, (H)ECC is often applied in Diffie-Hellman key agreement protocols and digital signature schemes, though ECC encrypting cards have appeared but only devised for some special kind of small data area. In the application of hyperelliptic curve cryptosystems, the key operation is divisor scalar multiplication.
