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The effect of the domain wall (DW) on the conductance in a ballistic ferromagnetic nanowire (FMNW) is revisited by exploiting a specific perturbation theory which is effective for a thin DW; the thinness is often the case in currently interested conductance measurements on FMNWs. Including the Hund coupling between carrier spins and local spins in a DW, the conductance of a FMNW in the presence of a very thin DW is calculated within the Landauer-B\"{u}ttiker formalism. It is revealed that the conductance plateaus are modified significantly, and the switching of the quantization unit from $e^2/h$ to ``about $2e^2/h$'' is produced in a FMNW by the introduction of a thin DW. This accounts well for recent observations in a FMNW., Comment: 5 pages, 2 figures, Corrected typos and added references

Two-dimensional Eliashberg equations have been solved by use of a mixed interaction with $s$- and $d$-channels. It is discussed what kind of pairing symmetry of the superconducting state can be realized when the channel mixing parameters and the band-filling are varied. By changing the mixing parameters and varying the chemical potential $\mu$ between zero- and half-filling, the pairing symmetry is determined and summarized into a phase diagram of the symmetry. It is revealed that there is an effective threshold in $\mu$ for the appearance of the d-wave superconductivity regardless of the strength of the $d$-channel interaction. It is also shown that, although the s-wave superconductivity can occur for any value of $\mu$ if the $s$-channel interaction is mixed sufficiently, the d-wave superconductivity has the advantage of achieving a high $T_{c}$ over the s-wave one, once it occurs., Comment: 11 pages, LaTeX