  The low-temperature behavior of the asymmetric single-impurity
  Anderson model is studied by diagrammatic methods resulting in analytically
controllable approximations. We first discuss the ways one can simplify parquet
equations in critical regions of singularities in the two-particle vertex. The
scale vanishing at the critical point defines the Kondo temperature at which
the electron-hole correlation function saturates. We show that the Kondo
temperature exists at any filling of the impurity level. A quasiparticle
resonance peak in the spectral function, however, forms only in almost
electron-hole symmetric situations. We relate the Kondo temperature with the
width of the resonance peak. Finally we discuss the existence of satellite
Hubbard bands in the spectral function.
