  In the quasilinear Regge trajectory ansatz, some useful linear mass
inequalities, quadratic mass inequalities and quadratic mass equalities are
derived for mesons and baryons. Based on these relations, mass ranges of some
mesons and baryons are given. The masses of bc-bar and ss-bar belonging to the
pseudoscalar, vector and tensor meson multiplets are also extracted. The J^P of
the baryon Xi_cc(3520) is assigned to be 1/2^+. The numerical values for Regge
slopes and intercepts of the 1/2^+ and 3/2^+ SU(4) baryon trajectories are
extracted and the masses of the orbital excited baryons lying on the 1/2^+ and
3/2^+ trajectories are estimated. The J^P assignments of baryons Xi_c(2980),
Xi_c(3055), Xi_c(3077) and Xi_c(3123) are discussed. The predictions are in
reasonable agreement with the existing experimental data and those suggested in
many other different approaches. The mass relations and the predictions may be
useful for the discovery of the unobserved meson and baryon states and the J^P
assignment of these states.
