We obtain two fixed point theorems for a kind of $varphi $-contractions incomplete fuzzy metric spaces, which are applied to easily deduceintuitionistic versions that improve and simplify the recent results of X.Huang, C. Zhu and X. Wen.

we obtain two fixed point theorems for a kind of $varphi $-contractions incomplete fuzzy metric spaces, which are applied to easily deduceintuitionistic versions that improve and simplify the recent results of x.huang, c. zhu and x. wen.

Using a description of the Levin-Wen model excitations in terms Wilson lines, we compute degeneracy energy levels for any input anyon theory and trivalent graph embedded on (orientable) compact surface. This result allows one to obtain finite-size finite-temperature partition function show that there are no thermal phase transitions.