| his thesis is divided into two parts, the first part (chapters 2-4) is on gravitational lensing, and the second part (chapters 5-8) on gamma-ray bursts (GRBs).;In chapter 2, the assumptions in the analysis of gravitational lensing statistics are examined. It is shown that a redshift cutoff model, which may result from galaxy evolution, can reduce the lensing probability and explain the large mean separation of gravitational lenses. We show that the reduction of the lensing probability due to the finite core radii of galaxies is likely to be no more than a factor of 2 and the most recent galaxy luminosity function gives a lensing probability that is smaller than previously estimated by a factor of ;In chapter 3, gravitational microlensing by a single star plus external shear is discussed. It is shown analytically that for a general cusp the magnification probability distribution follows ;In chapter 4, gravitational microlensing by double lenses is applied to the galactic bulge stars. We estimate that ;In chapter 5, statistical properties of GRBs are calculated for a large number of luminosity functions and density profiles assuming that the sources are galactic. We find that no galactic disk model can be reconciled with the statistical properties observed by the Burst and Transient Source Experiment (BATSE), and a galactic halo distribution must have a core radius ;In chapter 6, statistical properties of GRBs are analyzed assuming that the sources are cosmological. The range of observations is estimated to be ;In chapters 7 and 8, gravitational lensing of GRBs is studied. The lensing frequency of GRBs by galaxies is... |
