This note explores the analogy between the dynamics of the interest rate term structure and the implied volatility surface of a stock. In particular, we prove an impossibility theorem conjectured by Steve Ross. Implied volatility and smile asymptotics and long rates JEL Classification: G13 Mathematics Subject Classification (2000): 60G44, 91B70

G13 signaling pathway is closely related with differentiation of neural stem cells. RhoGDIγ is a key factor in this pathway. When Rho-GDIγ is silenced by using RNAi, the neural stem cell appears distinguished morphological change. The results indicate that the silenced cells showed the tendency of stimulative differentiation of neural stem cells.

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.