this study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. a least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. the proposed approach, which can deal with both symmetric and non-symmetric fuzzy observations, is compared with several existing models by...

The purpose of this research is to provide a deeper understanding of the planar high- symmetry configuration instability. In the ideal case, the distortion corresponds to the movements of nuclei along normal modes that belong to non-totally symmetric irreps of the high symmertry (HS) point group of molecule. The analysis of the structural distortion from the HS nuclear arrangements of the JT ac...

The change in phase factor of the wavefunction does not affect the absolute value of the matrix element, but does change the phase factor of the off-diagonal matrix element. This phase dependence causes a serious confusion in the sign of some parameters in the molecular Hamiltonian, which appear only in the off-diagonal matrix element; for example, the sign of the /-type doubling constant q of ...

Assuming the low molecular reorientation approximation, the formulae for the third-order electric polarization induced in liquids composed of rigid noninteracting dipolar, symmetric-top molecules in spherical solvents were derived. Our medium is acted on by a strong external dc bias electric field superimposed on a weak ac electric field, and the classical Smoluchowski– Debye equation for rotat...