Maximization of a Superconductor's Transition Temperature in a Boson - Fermion Model by Variation of the Boson Density of States and the Boson - Fermion Coupling Constants or for Spin Vector or Scalar Couplings Respective

We have solved the problem of maximizing a superconductors transition temperature $T_c $ by varying the Boson (spin fluctuation or phonon) density of states $N_B \left( \omega \right)$ and coupling constants, $J_q $ or$g_{kq\lambda } $. We find that $T_c \sim 10^9\;{ }^0K$ can be obtained, for example in Heusler alloys, such as$Au_2 \left( {Mn_{2-x} \;A\ell _x } \right)$, with$x\sim 0.1-0.5$. Also values of $H_{c2} \sim 10^{13}T$ and$j_c \sim 10^{13}\,Amps/cm^2$are predicted. Additionally results for the tunneling density of states$N_T \left( {eV} \right)$, the arpes cross section,${d\Delta } \mathord{\left/ {\vphantom {{d\Delta } {d\Omega d\omega }}} \right. \kern-\nulldelimiterspace} {d\Omega d\omega }$, $e.m.,{\kern 1pt}\,I.R.$ and transport coefficients arising from these models will be presented. Also we will present a discussion of the 36 Leggett modes which our theory predicts to exist, whose energies are in the optical frequency range$\left[ {\omega \sim 1-3eV} \right]$, versus the microwave frequency range for superfluid $^{3}$He-A phase.