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jul### Abstract:

{We have developed a technique to systematically discover and study high-redshift supernovae that can be used to measure the cosmological parameters. We report here results based on the initial seven of more than 28 supernovae discovered to date in the high-redshift supernova search of the Supernova Cosmology Project. We find an observational dispersion in peak magnitudes of sigma \_$\{$M$_{B}$$\}$=0.27 ; this dispersion narrows to sigma \_$\{$M$_{B}$,$\{$corr$\}$$\}$=0.19 after ''correcting'' the magnitudes using the light-curve ''width-luminosity'' relation found for nearby (z łt}= 0.1) Type Ia supernovae from the Calan/Tololo survey (Hamuy et al.). Comparing light-curve width–corrected magnitudes as a function of redshift of our distant (z = 0.35–0.46) supernovae to those of nearby Type Ia supernovae yields a global measurement of the mass density, Omega \_$\{$$\{$M$\}$$\}$=0.88\^{}$\{$+0.69$\}$\_$\{$-0.60$\}$ for a Lamda = 0 cosmology. For a spatially flat universe (i.e., Omega M + Omega Lamda = 1), we find Omega \_$\{$$\{$M$\}$$\}$=0.94\^{}$\{$+0.34$\}$\_$\{$-0.28$\}$ or, equivalently, a measurement of the cosmological constant, Omega \_$\{$ Lamda $\}$=0.06\^{}$\{$+0.28$\}$\_$\{$-0.34$\}$ (łt}0.51 at the 95% confidence level). For the more general Friedmann-Lemaitre cosmologies with independent Omega M and Omega Lamda , the results are presented as a confidence region on the Omega M- Omega Lamda plane. This region does not correspond to a unique value of the deceleration parameter q0. We present analyses and checks for statistical and systematic errors and also show that our results do not depend on the specifics of the width-luminosity correction. The results for Omega Lamda -versus- Omega M are inconsistent with Lamda -dominated, low-density, flat cosmologies that have been proposed to reconcile the ages of globular cluster stars with higher Hubble constant values. }