  The X-ray luminosity-temperature relation for nearby T=3.5-10 keV clusters is
rederived using new ASCA temperatures and ROSAT luminosities. Both quantities
are derived by directly excluding the cooling flow regions. This correction
results in a greatly reduced scatter in the Lx-T relation; cooling flow
clusters are similar to others outside the small cooling flow regions. For a
fit of the form L_bol ~ T^alpha, we obtain alpha=2.64+-0.27 (90%) and a
residual rms scatter in log L_bol of 0.10. The derived relation can be directly
compared to theoretical predictions that do not include radiative cooling. It
also provides an accurate reference point for future evolution searches and
comparison to cooler clusters.
  The new temperatures together with a newly selected cluster sample are used
to update the temperature function at z~0.05. The resulting function is
generally higher and flatter than the previous estimates by Edge et al (1990)
and Henry & Arnaud (1991, corrected). For a qualitative estimate of constraints
that the new data place on the density fluctuation spectrum, we apply the
Press-Schechter formalism for Omega=1 and 0.3. For Omega=1, assuming cluster
isothermality, the temperature function implies sigma_8=0.55+-0.03, while
taking into account the observed cluster temperature profiles,
sigma_8=0.51+-0.03, consistent with the previously derived range. The
dependence of sigma_8 on Omega differs from earlier findings, because of our
treatment of n as a free parameter. We find n=-(2.0-2.3)+-0.3, somewhat steeper
than derived from the earlier temperature function data, in agreement with the
local slope of the galaxy fluctuation spectrum from the APM survey, and
significantly steeper than the standard CDM prediction.
