martindale proved that under some conditions every multiplicative isomorphism between two rings is additive. in this paper, we extend this theorem to a larger class of mappings and conclude that every multiplicative $(alpha, beta)-$derivation is additive.

A method for adapting HMMs to additive noise and multiplicative distortion at the same time is proposed. This method first creates a noise HMM for additive noise, then composes HMMs for noisy and distorted speech data from this HMM and speech HMMs so that these composed HMMs become the functions of signal-to-noise (SIN) ratio and multiplicative distortion. S/N ratio and multiplicative distortio...

Our purpose is to relate the Fokker-Planck formalism proposed by [Friedrich et al., Phys. Rev. Lett. 84, 5224 (2000)] for the distribution of stock market returns to the empirically well-established power law distribution with an exponent in the range 3− 5. We show how to use Friedrich et al.’s formalism to predict that the distribution of returns is indeed asymptotically a power law with an ex...