In a recent paper, Dave Benson and Peter Symonds defined new invariant ?G(M) for finite dimensional module M of group G which attempts to quantify how close is being projective. this we determine permutation modules the symmetric corresponding two-part partitions using tools from representation theory combinatorics.

This letter revisits the energy quadratization (EQ) method by introducing a novel and essential relaxation technique to improve its accuracy consistency. The EQ has witnessed significant popularity in past few years. Though we acknowledge effectiveness designing energy-stable schemes for thermodynamically consistent models, primary known drawback is apparent, i.e., it respects “modified” law re...