in this paper, an attempt is made to present an extension of darbo's theorem, and its applicationto study the solvability of a functional integral equation of volterra type.

In this work, we classify all the effective $U(1)$ symmetries and their associated Noether charges in standard model (SM) its minimal supersymmetric extension (MSSM) from highest scale after inflation down to weak scale. We then demonstrate that discovery of violation baryon minus lepton number ($B\ensuremath{-}L$), which pinpoints primordial Universe at any cosmic temperature above 30 TeV, wil...