A short review on recent works on the analytic properties of perturbation expansions including those of Tarski, Eden is given. In the appendix, a number of related problems are discussed. In appendix 1, it is explicitly shown that for N-π, N-N scattering, the critical α for all points on the surface of singularities for the simplest 4-pt diagram lies entirely outside the interval (01) of the real axis, except those α corresponding to points on the curve of singularities as required by the Mandelstamm's theory. In appendix 2, a heuristic proof of the single dispersive relation independent of the momentum trausfer is provided. The proof rests on averaging over the azimuthal augle of meson momentum while the unclear momentum is oriented along the polar axis (here Breit system is emple-yed). In appendix 3, it is shown that hermiticity of certain variables leads to unitarity condition and thus one may hope to formulate the unitarity condition without encoanlering quadratic terms in the scattering amplitudes.