Transverse vibration of clamped trapezoidal plates having rectangular orthotropy

This paper deals with the free transverse vibration of orthotropic trapezoidal plates clamped at the edges. A series-type method is applied for obtaining an analytical solution of the problem, and the resulting frequency equation is presented for symmetric trapezoids. In the numerical study, accurate frequency parameters and mode shapes of the plates are calculated for the first several modes, and the effects of the orthotropy are discussed.     

Electronic structure of black phosphorus studied by X-ray photoelectron spectroscopy

The X-ray photoelectron spectrum of black phosphorus has been measured for the first time. The features in the valence band spectrum are found to be in good agreement with those of the valence state density recently calculated on the basis of a pseudopotential method. The 2s and 2p core spectrum of black phosphorus is also discussed.     

Ce 5d and Fe 3d magnetic profiles in CeH2/Fe multilayers probed by XRMS

The element and electronic shell specificities of X-ray resonant magnetic scattering have been used to investigate the magnetization of Ce 5d and Fe 3d states in [CeH₂(19.6 ?)/Fe(25.4 ?)]*38 a multilayer. We show that the measurement of the magnetic contribution to the intensities reflected at low angles at the Ce L₂ and Fe L_2,3 edges allows us to investigate the profile of the Ce 5d and Fe 3d magnetic polarization. The Fe 3d polarization is found to be uniform across the Fe layer and the Ce 5d polarization appears to be restricted close to the interface with Fe. Received: 22 May 2001 / Accepted: 4 July 2001 / Published online: 5 October 2001     

Localization and completion of nilpotent groups of automorphisms

We study nilpotent subgroups of automorphism groups in the category of groups and the homotopy category of spaces. We establish localization and completion theorems for nilpotent groups of automorphisms of nilpotent groups. We then apply these algebraic theorems to prove analogous results for certain groups of self-homotopy equivalences of spaces.     

Admissibility and minimaxity of generalized Bayes estimators for spherically symmetric family

We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. Compared to the known results for the multivariate normal case, our sufficient condition is very tight and is close to being a necessary condition. In particular, we establish the admissibility of generalized Bayes estimators with respect to the harmonic prior and priors with slightly heavier tail than the harmonic prior. We use the theory of regularly varying functions to construct a sequence of smooth proper priors approaching an improper prior fast enough for establishing the admissibility. We also discuss conditions of minimaxity of the generalized Bayes estimator with respect to the harmonic prior.     

An extended class of minimax generalized Bayes estimators of regression coefficients

We derive minimax generalized Bayes estimators of regression coefficients in the general linear model with spherically symmetric errors under invariant quadratic loss for the case of unknown scale. The class of estimators generalizes the class considered in Maruyama and Strawderman [Y. Maruyama, W.E. Strawderman, A new class of generalized Bayes minimax ridge regression estimators, Ann. Statist., 33 (2005) 1753–1770] to include non-monotone shrinkage functions.     

Stein's idea and minimax admissible estimation of a multivariate normal mean

We consider estimation of a multivariate normal mean vector under sum of squared error loss.We propose a new class of minimax admissible estimator which are generalized Bayes with respect to a prior distribution which is a mixture of a point prior at the origin and a continuous hierarchical type prior. We also study conditions under which these generalized Bayes minimax estimators improve on the James–Stein estimator and on the positive-part James–Stein estimator.