Full pseudoscalar mesonic chiral Lagrangian at p6 order under the unitary group

We construct the full p6 order chiral Lagrangians for the unitary group and special unitary groups, including nf-, three- and two-flavor cases, all bilinear currents (scalar, pseudoscalar, vector, axial-vector and tensor currents) and theta parameter. The number of independent operators are 1391, 1326 and 969 for each of the flavor unitary groups. From these results, we find one extra linear relation among the traditional p4 order low-energy constants under the U(3) group, and some more linear relations with tensor sources for the p6 order low-energy constants in the special unitary groups. We develop a scheme to obtain the relations for the dependent operators in terms of independent operators.Comment: 23 page

Achieving acoustic cloak by using compressible background flow

We propose a scheme of acoustic spherical cloaking by means of background irrotational flow in compressible fluid. The background flow forms a virtual curved spacetime and guides the sound waves bypass the cloaked objects. To satisfy the laws of real fluid, we show that spatially distributed mass source and momentum source are necessary to supply. The propagation of sound waves in this system is studied via both geometric acoustics approximation and full wave approach. The analytic solution of sound fields is obtained for plane wave incidence. The results reveal the effect of phase retardation (or lead) in comparison with the ordinary transformation-acoustic cloak. In addition, the ability of cloaking is also evaluated for unideal background flows by analyzing the scattering cross section.Comment: 15 pages, 6 figure

Partitioning Clustering Based on Support Vector Ranking

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