The complete interpretation of the fractions in quantum Hall effect

We propose that the modified cyclotron energy is given by (h/2$\pi )\omega _{c}$(1/2)g(n+1/2) so that the fractional charge is given by the angular momentum with both signs of spin, j = $l \pm $ s. In addition to the (i) principal fractions given by (1/2)g our theory with effective charge e*=(1/2)ge, has (ii) resonances at $\nu _{1}-\nu _{2}$ and (iii) two-particle states at $\nu _{1}+\nu _{2}$ and there are (iv) clusters with spin $>$1/2, where $\nu $ is a filling factor. This theory explains all of the 101 fractions and full graphene series. The fractional charges of graphene [2] are also explained. The series also explains the even denominators for S=0,1,2, {\ldots}, as in electron clusters. The S=0, L=0, corresponds to half filled Landau level. S=1/2, L=0 with negative sign before s in j gives the zero-energy state. All of the predicted fractions agree with the data. \\[4pt] [1] K. N. Shrivastava, AIP Conf. Proc. 1150, 59-67 (2009). \\[0pt] [2] K. I. Bolotin, et al, Nature 462, 196(2009).