Relation between quark masses and weak mixings
  Simple transformation formulas between fermion matrices and observables, and numerical values of quark matrices, are obtained on a particular weak basis with one quark matrix diagonal and the other with vanishing elements 1-1, 1-3 and 3-1, and with only the element 2-2 complex. When we choose $M_u$ diagonal, then $M_d$ shows intriguing numerical properties which suggest a four parameter description of it, which implies $V_{us}\simeq \sqrt{m_d/m_s}$, $V_{cb}\simeq (3/\sqrt{5})(m_s/m_b)$ and $V_{ub}\simeq (1/\sqrt{5})(\sqrt{m_d m_s}/m_b)$. Few comments on mass-mixing relations are added. 
D. Falcone and F. Tramontano