We perform a comprehensive study of the homogeneous finite modular group ${A}_{5}^{\ensuremath{'}}$ which is double covering ${A}_{5}$. The integral weight and level 5 forms have been constructed up to 6 they are decomposed into irreducible representations ${A}_{5}^{\ensuremath{'}}$. Then we systematical analysis models for lepton masses mixing. phenomenologically viable with minimal number fre...

The optimal path cover problem is to find a minimum number of vertex disjoint paths which together cover all the vertices of the graph. Finding an optimal path cover for an arbitrary graph is known to be NP-complete [3]. However, polynornial-time algorithms exist for trees [4], cacti [4] and for interval graphs [9]. The solution presented in [2] For circular-arc graphs is known to be wrong. In ...

The nonarchimedean local analogues of modular forms of half-integral weight with level and character are certain vectors in irreducible, admissible, genuine representations of the metaplectic group over a nonarchimedean local field of characteristic zero. Two natural level raising operators act on such vectors, leading to the concepts of oldforms and newforms. We prove that the number of newfor...