Let $$(R,\mathfrak {m})$$ be a Noetherian local ring of prime characteristic p and Q an $$\mathfrak {m}$$ -primary parameter ideal. We give criteria for F-rationality R using the tight Hilbert function $$H^*_Q(n)=\ell (R/(Q^n)^*)$$ coefficient $$e_1^*(Q)$$ polynomial $$P^*_Q(n)=\sum _{i=0}^d(-1)^ie_i^*(Q)\left( {\begin{array}{c}n+d-1-i\\ d-i\end{array}}\right) .$$ obtain lower bound equidimensi...

We present a general technique for obtaining permutation polynomials over a finite field from permutations of a subfield. By applying this technique to the simplest classes of permutation polynomials on the subfield, we obtain several new families of permutation polynomials. Some of these have the additional property that both f(x) and f(x) + x induce permutations of the field, which has combin...

This article describes the asymptotic properties of local polynomial regression estimators for univariate and additive models when observation weights are included. The implications of these ndings are discussed for local scoring estimators, a widely used class of estimators for generalized additive models described in Hastie and Tibshirani (1990).

so far several methods have been developed for mapping and interpolation of isohyets.one of the recently accepted methods is geographically weighting regression which is suitable for evaluation of spatial heterogeneity of dependent variable by using local regressions. in order to evaluate annually precipitation spatial variation, this study was conducted in gilan province which precipitation is...

In this paper, we introduce a new class of estimators of jump size in a nonparametric regression model and apply it to the estimation of local average treatment effect (LATE). We refer members of this class as local polynomial wavelet estimators and show that all the existing estimators, including estimators constructed from differencing two nonparametric estimates and partial linear estimators...