General Taylor configuration expansion revisited

General Taylor configuration expansion revisited

The validity of a series expansion proposed previously @T. H. Jensen and M. S. Chu, Phys. Fluids 27, 2881 ~1984!# for describing general Taylor configurations of magnetized plasmas has been reexamined because an apparent paradox was realized. From analyses of simple cases which can be dealt with mostly analytically, it is concluded that the paradox is a Gibbs phenomenon, and that the series exp...

Taylor Expansion for the Entropy Rate of Hidden Markov Chains

We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...

Note Pointed Taylor Bubble Revisited

Taylor's Expansion Revisited: A General Formula for the Remainder

Taylor’s polynomial is a central tool in any elementary course in mathematical analysis. Nowadays, its importance is centred on its applications, for instance, to asymptotic analysis or to obtain satisfactory numerical or integral inequalities see, e.g., 1–5 . The core of these results comes from manipulations on the explicit formula of the remainder, that is, the error estimation when consider...

Firewall Configuration Errors Revisited

Practically every corporation that is connected to the Internet uses firewalls as the first line of its cyber-defense. However, the protection that these firewalls provide is only as good as the policy they are configured to implement. The first quantitative evaluation of the quality of corporate firewall configurations appeared in 2004, based on Check Point FireWall-1 rule-sets. In general tha...