1 Basic inequality For any real numbers ρ d satisfying ρ 1 = 1, and for any natural number m, we have d|m µ(d) d|m ρ d 2 = e|m λ e , λ e = [d 1 ,d 2 ]=e ρ d 1 ρ d 2. Our goal is to optimize the choice of (ρ d) d1. Let m = (n, P (z)), multiply by a n and sum over n using (g): say. Minimizing XG + R is quite difficult. However, if we restrict the support of ρ to d √ D, it is relatively easy to mi...

This paper first establishes the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi-nonparametric time series models. We show that, even when the sieve score process is not a martingale difference, the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals are the same as those for independent da...

Although the enucleate conducting cells of the phloem are incapable of protein synthesis, phloem exudates characteristically contain low concentrations of soluble proteins. The role of these proteins and their movement into and out of the sieve tubes poses important questions for phloem physiology and for cell-to-cell protein movement via plasmodesmata. The occurrence of protein turnover in sie...

The sieve method is a classic one in number theory (see, for example, [FI]). Recently it found some applications in a non-commutative setting. On the one hand, Bourgain-Gamburd-Sarnak [BGS1] applied it in studying almost-prime vectors in orbits of non-commutative groups acting on Z. On the other hand, Rivin [Ri] and Kowalski [Ko] used it to study generic properties of elements in the mapping cl...

We study a bootstrap method which is based on the method of sieves. A linear process is approximated by a sequence of autoregressive processes of order p = pn, where pn ! 1 ; p n = on as the sample size n ! 1. F or given data, we t h e n estimate such a n A R pn model and generate a bootstrap sample by resampling from the residuals. This sieve bootstrap enjoys a nice nonparametric property. We ...

Because sieve elements are generally regarded as the specialized conducting cells in the phloem tissue, their structure in relation to function has been the subject of many studies and discussions. ' Both the protoplast and the walls of sieve elements have distinctive characteristics, some of which are difficult to relate to the rapid flow of materials-at the rate of up to 100 cm. per hour-reco...