  We study an array of cigar-like Bose atom condensates confined in a cylinder
and examine the competition between the dipole-dipole and the short range
interactions. The system is effectively reduced to a one-dimensional boson one
with a contact and inverse square interactions. We call this system the
Calogero-Sutherland-Lieb-Liniger gas. The universal properties of the ground
state are analyzed by the renormalization group theory. By using the
bosonization techniques to the excluson gas, we calculate the non-universal
exponent depending on the microscopic parameters. This exponent may be
experimentally measurable.
