Universal Inequalities for Eigenvalues of the Buckling Problem of Arbitrary Order

We investigate the eigenvalues of the buckling problem of arbitrary order on compact domains in Euclidean spaces and spheres. We obtain universal bounds for the $k$th eigenvalue in terms of the lower eigenvalues independently of the particular geometry of the domain.Comment: 24 page

Sn(II)-containing phosphates as optoelectronic materials

We theoretically investigate Sn(II) phosphates as optoelectronic materials using first principles calculations. We focus on known prototype materials Sn$_n$P$_2$O$_{5+n}$ (n=2, 3, 4, 5) and a previously unreported compound, SnP$_2$O$_6$ (n=1), which we find using global optimization structure prediction. The electronic structure calculations indicate that these compounds all have large band gaps above 3.2 eV, meaning their transparency to visible light. Several of these compounds show relatively low hole effective masses ($\sim$2-3 m$_0$), comparable the electron masses. This suggests potential bipolar conductivity depending on doping. The dispersive valence band-edges underlying the low hole masses, originate from the anti-bonding hybridization between the Sn 5s orbitals and the phosphate groups. Analysis of structure-property relationships for the metastable structures generated during structure search shows considerable variation in combinations of band gap and carrier effective masses, implying chemical tunability of these properties. The unusual combinations of relatively high band gap, low carrier masses and high chemical stability suggests possible optoelectronic applications of these Sn(II) phosphates, including p-type transparent conductors. Related to this, calculations for doped material indicate low visible light absorption, combined with high plasma frequencies.Comment: 10 pages, 10 figures, Supplementary informatio