Second generation intact stability criteria for few past years had been under development by International Maritime Organization (IMO). Since the draft proposed amendments shall be amended to International code on Intact Stability (IS code 2008), new regulations shall enter into force for ships of length more than 24 meter. Generally second generation intact stability criteria (SGISC) refers to...

We prove some criteria for uniform K-stability of log Fano pairs. In particular, we show that is equivalent to $\beta$-invariant having a positive lower bound. Then study the relation between optimal destabilization conjecture and conjectural equivalence in twisted setting.