1,721,079 research outputs found
Computations Concerning Primes and Powers of Two
No full textThe problem of representing odd integers as the sum of a prime and a power of two is investigated using numerical computations. The density of representable numbers is calculated up to 231 and the results are extrapolated in order to estimate the asymptotic density. A probabilistic model (suggested by Bombieri) is used to get an independent estimate for the asymptotic density. Either approach suggests 0.434... as a reasonable approximation for the asymptotic density
ON THE ADDITIVE STRUCTURE OF THE INVERSES OF BANDED MATRICES
No full textAbstractThe additive structure of the inverses of banded matrices is investigated. Under certain conditions, the inverse of a (2k+1)-diagonal symmetric banded matrix can be expressed as a sum of k symmetric matrices belonging to the class of inverses of symmetric irreducible tridiagonal matrices. In the nonsymmetric case, a more complicated structure is obtained. Applications are mentioned for the resolution of constant coefficient banded linear systems in VLSI models
The Parallelism Principle: Speeding up the Cellular Automata Synchronization
No full textIn recent years we have seen many generalizations of the well-known Firing Squad Synchronization problem. Now it is possible to synchronize networks of finite automata arbitrarily connected. This paper shows a general principle according to which synchronization time of figures with particular symmetry properties will decrease considerably
On the Fast Synchronization of Tree Connected Networks
No full textIn extending the Firing Squad Synchronization problem to the case of tree connected networks and applying the controlled synchronization of linear arrays, we obtain the optimal time for trees with a bounded number of nodes.
We also investigate methods for synchronizing general trees and show how to apply them to networks arbitrarily connected
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