We give a sufficient condition for the 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 necessary. In particular we establish the admissibility of generalized Bayes estimators with respect...

Thyristor rectifiers are widely used in electric railways in order to control the speed. As a consequence of their usage in addition to substantial input lead current, an enormous amount of harmonics is injected into the grid. To avoid such harmonics as well as reactive power compensation, reactive power hybrid filters consisting of active and passive filters are utilized. Regarding different p...

Harmonic univalent mappings have attracted the serious attention of complex analysts only after the appearance of a basic paper by Clunie and Sheil-Small [4] in 1984. These researchers laid the foundation for the study of harmonic univalent mappings over the unit disk as a generalization of analytic univalent functions. Interestingly, almost at the same time, the famous Bieberbach conjecture wh...

Due to the unbalanced features of distribution systems, a three-phase harmonic analysis method is essential to accurately analyze the harmonic impact on distribution systems. Moreover, harmonic analysis is the basic tool for harmonic filter design and harmonic resonance mitigation; therefore, the computational performance should also be efficient. An accurate and efficient three-phase harmonic ...

We present the first analysis of harmonic generation data where the full potential of the generalized nonlinear Kramers-Krönig (KK) relations and sum rules is exploited. We consider two published sets of wide spectral range experimental data of third harmonic generation susceptibility on different polymers, the polysilane (frequency

This note studies the fourth-order generalized Hartree equation$ i\dot u+\Delta^2 u\pm|u|^{p-2}(J_\gamma*|u|^p)u = 0,\quad p\geq2. $Indeed, for both attractive and repulsive sign, scattering is obtained in inter-critical regime, which given by $ 0<s_c<2 $, where critical Sobolev exponent equality \kappa^\frac{4+\gamma}{2(p-1)}\|u(\kappa^4\cdot,\kappa t)\|_{\dot H^{s_c}} \|u(\kappa $. In f...