We study several aspects of the formation of galaxies, using numerical simulations. We investigate the influence of about thirty different sub-grid physics recipes for cooling, star formation,... Show moreWe study several aspects of the formation of galaxies, using numerical simulations. We investigate the influence of about thirty different sub-grid physics recipes for cooling, star formation, supernova feedback, AGN feedback etc. on the resulting galaxy populations with large SPH simulations. We investigate several parameters that quantify the environment of galaxies and present the strongest measure of halo mass and a new parameter that is insensitive to halo mass. We look at the effects of input physics and dust attenuation on the simulated luminosity functions and compare luminosity functions directly obtained from simulations, with those using observers' tools on mock images. Regardless of most parameters used for the mock image creation and the detection of sources, these two LFs agree well. The last chapter compares several ways of sampling stellar IMFs in clusters that follow a cluster mass function in order to see how the choice of CMF and sampling method influence the resulting integrated galactic initial mass function. The effects are only significant if the CMF extends as a steep power-law down to a few solar masses. We study the effects of these IGIMFs on the galaxies' integrated photometry and metal and O-star content. Show less
Factorization methods, such as the quadratic sieve and the number field sieve, spend a lot of time on the sieving step, in which the necessary relations are collected for factoring the given number... Show moreFactorization methods, such as the quadratic sieve and the number field sieve, spend a lot of time on the sieving step, in which the necessary relations are collected for factoring the given number N. Relations are smooth or k-semismooth numbers (numbers with either all prime factors below some bound or all with the exception of at most k prime factors that do not exceed a second bound) or pairs of these type of numbers. In this thesis, we predict the amount of k-semismooth numbers needed to factor N, based on asymptotic approximation formulas (these formulas generalize the published results), and compare them with the amount of k-semismooth numbers found during the factorization of N. Furthermore, for the number field sieve we propose a method for predicting the number of necessary relations for factoring N with given parameters, and the corresponding sieving time. The basic idea is to do a small but representative amount of sieving and analyze the relations in this sample. We randomly generate relations according to the relevant distribution as observed in the sample and process these relations. Experiments show that our predictions of the number of necessary relations are within 2% of the number of relations needed in the real factorization. Show less
