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Kernel Regression Estimation for Permutation Fixed Design Additive Models
Baek, Jangsun,Wehrly, Thomas E. The Korean Statistical Society 1996 Journal of the Korean Statistical Society Vol.25 No.4
Consider an additive regression model of Y on X = (X$_1$,X$_2$,. . .,$X_p$), Y = $sum_{j=1}^pf_j(X_j) + $\varepsilon$$, where $f_j$s are smooth functions to be estimated and $\varepsilon$ is a random error. If $X_j$s are fixed design points, we call it the fixed design additive model. Since the response variable Y is observed at fixed p-dimensional design points, the behavior of the nonparametric regression estimator depends on the design. We propose a fixed design called permutation fixed design, and fit the regression function by the kernel method. The estimator in the permutation fixed design achieves the univariate optimal rate of convergence in mean squared error for any p $\geq$ 2.
Co-Re-based alloys a new class of material for gas turbine applications at very high temperatures
Mukherji, D.,Rosler, J.,Wehrs, J.,Eckerlebe, H.,Gilles, R. Techno-Press 2012 Advances in materials research Vol.1 No.3
Co-Re alloy development is prompted by the search for new materials for future gas turbines which can be used at temperatures considerably higher than the present day single crystal Ni-based superalloys. The Co-Re based alloys are designed to have very high melting range. Although Co-alloys are used in gas turbine applications today, the Co-Re system was never exploited for structural applications and basic knowledge on the system is lacking. The alloy development strategy therefore is based on studying alloying additions on simple model alloy compositions of ternary and quaternary base. Various strengthening possibilities have been explored and precipitation hardening through fine dispersion of MC type carbides was found to be a promising route. In the early stages of the development we are mainly dealing with polycrystalline alloys and therefore the grain boundary embrittlement needed to be addressed and boron addition was considered for improving the ductility. In this paper recent results on the effect of boron on the strength and ductility and the stability of the fine structure of the strengthening TaC precipitates are presented. In the beginning the alloy development strategy is briefly discussed.