Stability of Multiplier Ideal Sheaves

Chinese Annals of Mathematics, Series B - In the present article, the authors find and establish stability of multiplier ideal sheaves, which is more general than strong openness.     

Ideal optomechanically induced transparency generation in a cavity optoelectromechanical system

The ideal optomechanically induced transparency effects of an output probe field are investigated in a cavity optoelectromechanical system, which is composed of an optical cavity, a charged mechanical resonator, and a charged object.Although the charged mechanical resonator damping rate is nonzero, the ideal optomechanically induced transparency can still appear due to the non-rotating wave approximation effect in the system. The location of optomechanically induced transparency dip can be controlled via the Coulomb coupling strength. In addition, we find that both the transparency window width and the maximum dispersion curve slope are closely related to the optical cavity decay rate.     

Powers of edge ideals with linear resolutions

We show that if G is a gap-free and diamond-free graph, then I(G)^s has a linear minimal free resolution for every s≥2.     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.