. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

We introduce a new Markov chain Monte Carlo (MCMC) sampler called the Markov Interacting Importance Sampler (MIIS). The MIIS sampler uses conditional importance sampling (IS) approximations to jointly sample the current state of the Markov Chain and estimate conditional expectations, possibly by incorporating a full range of variance reduction techniques. We compute Rao-Blackwellized estimates ...

In this paper we present criteria for an n-quasigroup to be isotopic to an n-group. We call a such n-quasigroup G−n-quasigroup. Applications to functional equations on quasigroups are presented in a subsequent paper. 2000 Mathematics Subject Classification: 20N15. Some important n-quasigroup classes are the following. An n-quasigroup (A,α) of the form α(x1 ) = n ∑ i=1 fi(xi)+a, where (A,+) is a...