Two classical, damped and driven spin oscillators with an isotropic exchange interaction are considered. They represent a nontrivial physical system whose equations of motion are shown to allow for an analytic treatment of local codi-mension 1 and 2 bifurcations. In addition, numerical results are presented which exhibit a Feigenbaum route to chaos.

Remotely keyed encryption schemes (RKESs) support fast encryption and decryption using low-bandwidth devices, such as secure smartcards. The long-lived secret keys never leave the smartcard, but most of the encryption is done on a fast untrusted device, such as the smartcard’s host. This paper describes an new scheme, the length-preserving “accelerated remotely keyed” (ARK) encryption scheme an...

Analogy between an approximate version of Feigenbaum renormalization group analysis in complex domain and the phase transition theory of Yang-Lee (based on consideration of formally complexified thermodynamic values) is discussed. It is shown that the Julia sets of the renormal-ization transformation correspond to the approximation of Mandelbrot set of the original map. New aspects of analogy b...

The renormalization of a quadratic-like map is studied. The threedimensional Yoccoz puzzle for an infinitely renormalizable quadratic-like map is discussed. For an unbranched quadratic-like map having the a priori complex bounds, the local connectivity of its Julia set is proved by using the three-dimensional Yoccoz puzzle. The generalized version of Sullivan’s sector theorem is discussed and i...

A mathematical model to explain cations’ solubility of both protic and aprotic ionic liquids in a wide range hydrochloric acid solutions has been developed. The concept this is based on an assumption the mineral extraction into organic phase, formation salt there between liquid cation chloride-anion due ions recombination partial back-extraction. proposed approach allows estimating correspondin...