16,942 research outputs found
Computing A Glimpse of Randomness
A Chaitin Omega number is the halting probability of a universal Chaitin
(self-delimiting Turing) machine. Every Omega number is both computably
enumerable (the limit of a computable, increasing, converging sequence of
rationals) and random (its binary expansion is an algorithmic random sequence).
In particular, every Omega number is strongly non-computable. The aim of this
paper is to describe a procedure, which combines Java programming and
mathematical proofs, for computing the exact values of the first 64 bits of a
Chaitin Omega:
0000001000000100000110001000011010001111110010111011101000010000. Full
description of programs and proofs will be given elsewhere.Comment: 16 pages; Experimental Mathematics (accepted
Two-component model for the chemical evolution of the Galactic disk
In the present paper, we introduce a two-component model of the Galactic disk
to investigate its chemical evolution. The formation of the thick and thin
disks occur in two main accretion episodes with both infall rates to be
Gaussian. Both the pre-thin and post-thin scenarios for the formation of the
Galactic disk are considered. The best-fitting is obtained through
-test between the models and the new observed metallicity distribution
function of G dwarfs in the solar neighbourhood (Hou et al 1998). Our results
show that post-thin disk scenario for the formation of the Galactic disk should
be preferred. Still, other comparison between model predictions and
observations are given.Comment: 23 pages, 7 figure
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