  We present new data obtained with the Submillimeter Array for a sample of
fourteen nearby luminous and ultraluminous infrared galaxies. The galaxies were
selected to have luminosity distances D < 200 Mpc and far-infrared luminosities
log(L_FIR) > 11.4. The galaxies were observed with spatial resolutions of order
1 kpc in the CO J=3-2, CO J=2-1, 13CO J=2-1, and HCO+ J=4-3 lines as well as
the continuum at 880 microns and 1.3 mm. We have combined our CO and continuum
data to measure an average gas-to-dust mass ratio of 120 +/- 28 (rms deviation
109) in the central regions of these galaxies, very similar to the value of 150
determined for the Milky Way. This similarity is interesting given the more
intense heating from the starburst and possibly accretion activity in the
luminous infrared galaxies compared to the Milky Way. We find that the peak H_2
surface density correlates with the far-infrared luminosity, which suggests
that galaxies with higher gas surface densities inside the central kiloparsec
have a higher star formation rate. The lack of a significant correlation
between total H_2 mass and far-infrared luminosity in our sample suggests that
the increased star formation rate is due to the increased availability of
molecular gas as fuel for star formation in the central regions. In contrast to
previous analyses by other authors, we do not find a significant correlation
between central gas surface density and the star formation efficiency, as trace
by the ratio of far-infrared luminosity to nuclear gas mass. Our data show that
it is the star formation rate, not the star formation efficiency, that
increases with increasing central gas surface density in these galaxies.
