arXiv subjects
Publications and source records attributed to Germano D'Abramo.
In this paper we provide a straightforward proof that if a pair of amicable numbers with different parity exists (one number odd and the other one even), then the odd amicable number must be a perfect square, while the even amicable number has to be equal to the product of a power of 2 and an odd perfect square.
In this paper we present three simple applications of probability and highlight and discuss their paradoxical flavour.
This paper has been withdrawn. See published paper http://arxiv.org/math.HO/0512390
Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the probability that such a program will halt after that time is smaller than any arbitrary fixed value. Consistency with known results and consequences are also discussed.
The Mind-Body Problem, which constitutes the starting point for a large part of the speculations about consciousness and conscious experience, can be re-stated in an equivalent way, using the `brain duplication' argument described in this paper. If we assume that consciousness follows from a peculiar organization of physical matter and energy, namely that it does not transcend physical reality, then the brain duplication argument gives a possible interesting physical characterization of the mind: namely, a sort of extensive interdependence of the brain with the whole surrounding physical world in giving rise to consciousness.
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that though they evoke suggestive scenarios, they are still quite speculative.
In this paper we briefly review and analyze three published proofs of Chaitin's theorem, the celebrated information-theoretic version of Gödel's incompleteness theorem. Then, we discuss our main perplexity concerning a key step common to all these demonstrations.
In this paper we develop a simple model of the penetration process of a long rod through an uniform target. Applying the momentum and energy conservation laws, we derive an analytical relation which shows how the penetration depth depends upon the density of the rod, given a fixed kinetic energy. This work was sparked off by the necessity of understanding the effectiveness of high density penetrators (e.g. depleted uranium penetrators) as anti-tank weapons.
Dimensional analysis techniques are used to describe (not only qualitatively) some interesting features of two specific physical processes: the kinematics of moving objects on the surface of a planet (e.g. the walking pace of a man on the Moon) and the run-up process of a tsunami wave approaching the shore.
In this paper we define the a posteriori probability W. This quantity is introduced with the aim of suggesting a reliable interpretation of the actual threat posed by a newly discovered Near Earth Asteroid (NEA), for which impacting orbital solutions (now commonly known as Virtual Impactors or VIs) can not be excluded on the basis of the available astrometric observations. The probability W is strictly related to the so-called background impact probability (that extrapolated through a statistical analysis from close encounters of the known NEA population) and to the annual frequency with which the impact monitoring systems (currently NEODyS-CLOMON at University of Pisa and SENTRY at NASA-JPL) find VIs among newly discovered asteroids. Of W we also provide a conservative estimate, which turns out to be of nearly the same order of the background impact probability. This eventually says to us what we already know: the fact that nowadays monitoring systems frequently find VIs among newly discovered asteroids does not make NEAs more threatening than they have ever been.