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We report I-band observations of the GRB 980329 field made on 1998 March 29 with the 1.34 m Tautenberg Schmidt telescope, R-, J- and K-band observations made on 1998 April 1 with the APO 3.5 m telescope, R- and I-band observations made on 1998 April 3 with the Mayall 4 m telescope at KPNO, and J- and K-band observations made 1998 April 6-8 with the Keck-I 10 m telescope. We show that these and other reported measurements are consistent with a power-law fading of the optical/near-infrared source that is coincident with the variable radio source VLA J0702+3850. This firmly establishes that this source is the afterglow of GRB 980329.

From the Press-Schechter mass function and the empirical X-ray cluster luminosity-temperature (L-T) relation, we construct an X-ray cluster luminosity function that can be applied to the growing number of high-redshift, X-ray cluster luminosity catalogs to constrain cosmological parameters. In this paper, we apply this luminosity function to the Einstein Medium Sensitivity Survey (EMSS) and the ROSAT Brightest Cluster Sample (BCS) luminosity function to constrain the value of Ωm. In the case of the EMSS, we find a factor of 4-5 fewer X-ray clusters at redshifts above z = 0.4 than below this redshift at luminosities above LX = 7 × 1044 ergs s-1 (0.3-3.5 keV), which suggests that the X-ray cluster luminosity function has evolved above L(Black star). At lower luminosities, this luminosity function evolves only minimally, if at all. Using Bayesian inference, we find that the degree of evolution at high luminosities suggests that Ωm = 0.96+0.36-0.32, given the best-fit L-T relation of Reichart, Castander, & Nichol. When we account for the uncertainty in how the empirical L-T relation evolves with redshift, we find that Ωm ≈ 1.0 ± 0.4. However, it is unclear to what degree systematic effects may affect this and similarly obtained results.