### Asymptotic formulae concerning arithmetical functions defined by cross-convolutions. VI: $A$-$k$-free integers.

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The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.

The currently dominant speech recognition technology, hidden Mar-kov modeling, has long been criticized for its simplistic assumptions about speech, and especially for the naive Bayes combination rule inherent in it. Many sophisticated alternative models have been suggested over the last decade. These, however, have demonstrated only modest improvements and brought no paradigm shift in technology. The goal of this paper is to examine why HMM performs so well in spite of its incorrect bias due to...

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