  Magnetic and superconducting pairing correlation functions in a general class
of Hubbard models, the t-J model and a single-band Hubbard model with
additional bond-charge interaction are investigated, respectively. Some
rigorous upper bounds of the corresponding correlation functions are obtained.
It is found that the decay of the spin-spin correlation function with
temperature in the general Hubbard models can not be slower than the squared
inverse law at low temperatures and the inverse law at high temperatures, while
the on-site pairing correlation function can not be slower than the inverse
law. An upper bound for the average energy of the t-J model is found. The upper
bounds for the spin-spin and the electron pairing correlation functions in the
t-J model as well as in the Hubbard model with bond-charge interaction are also
obtained. These bounds are expected to provide certain standards for
approximate methods. In some special cases, these bounds rule out the
possibility of corresponding magnetic and pairing long-range order.
