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

Faithful teleportation with arbitrary pure or mixed resource states

We study faithful teleportation systematically with arbitrary entangled states as resources. The necessary conditions of mixed states to complete perfect teleportation are proved. Based on these results, the necessary and sufficient conditions of faithful teleportation of an unknown state |\phi> in C^d with an entangled resource {\rho} in C^m \otimes C^d and C^d \otimes C^n are derived. It is shown that for {\rho} in C^m\otimesC^d, {\rho} must be a maximally entangled state, while for {\rho} in C^d \otimes C^n, {\rho} must be a puremaximally entangled state. Moreover, we show that the sender's measurements must be all projectors of maximally entangled pure states. The relations between the entanglement of the formation of the resource states and faithful teleportation are also discussed.Comment: 9 page

Detrital heavy minerals constraints on the Triassic tectonic evolution of the West Qinling terrane, NW China: implications for understanding subduction of the Paleotethyan Ocean

We have examined the Triassic sediments in the west Qinling terrane, northeastern Tibet. These sediments consist mainly of flysch and shallow-sea and fluvial deposits with abundant lithic and heavy mineral detritus, sandwiched between and overlying Late Paleozoic and Early-Middle Triassic ophiolitic mélanges. Volcanic and metamorphic detritus dominates the lithic component of Lower Triassic sandstones accompanied by high Cr-spinel, pyroxene, and magnetite contents, indicating a mixed ophiolite and metamorphic source. Detrital mineral geochemistry further suggests that ophiolitic, high-grade metamorphic, basic, and intermediate-acidic igneous rocks must have been exposed and deeply eroded in their source area. Abundances of zircon, rutile, garnet, tourmaline, and epidote are greater in the Middle Triassic samples, and granitic and volcanic sources are the major contributors of detrital clasts. Considering these new observations on sedimentary petrography and detrital heavy mineral geochemistry, along with published data on paleocurrents, detrital zircon U-Pb ages, sedimentary facies, and regional magmatism, we suggest that these Triassic sediments represent the sedimentary fill of a forearc basin that overlies a late Paleozoic ophiolitic complex. A south-facing Andean-type convergent continental margin system developed along the southern margin of the North China block during the Triassic, in response to northward subduction of the Paleotethyan Ocean

A Note on Hierarchy of Quantum Measurement Incompatibilities

The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators we present a complete classification of the incompatibility of a given measurement assemblage with $n$ members. Detailed examples are given to the incompatibility for unbiased qubit measurements based on semidefinite programm.Comment: 11pages,0 figure

Uncertainty Relations Based on Modified Wigner-Yanase-Dyson Skew Information

Uncertainty relation is a core issue in quantum mechanics and quantum information theory. We introduce modified generalized Wigner-Yanase-Dyson (MGWYD) skew information and modified weighted generalizedWigner-Yanase-Dyson (MWGWYD) skew information, and establish new uncertainty relations in terms of the MGWYD skew information and MWGWYD skew information.Comment: 16 page