I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are pr...I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are proposed, referring to Anderson, for example.展开更多
The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addit...The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addition to two different modes coupling,a nonuniform distribution of gain and loss leads to an offset from the original propagation constants,including both real and imaginary parts,resulting in the absence of EP.These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations,which yields results that are more accurate than those from the classical coupled-mode theory.Numerical verification via the finite element method is provided.In the end,we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘I. INTRODUCTIONIt is well-known that the usual estimator, the sample mean, for the mean of a multivariate normal distribution is inadmissible. After the improvement of the original proof, several concise proofs are proposed, referring to Anderson, for example.
基金National Natural Science Foundation of China(NSFC)(11274083,61405067)Guandong Natural Science Foundation(2015A030313748)Shenzhen Municipal Science and Technology Plan(JCYJ20150513151706573)
文摘The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addition to two different modes coupling,a nonuniform distribution of gain and loss leads to an offset from the original propagation constants,including both real and imaginary parts,resulting in the absence of EP.These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations,which yields results that are more accurate than those from the classical coupled-mode theory.Numerical verification via the finite element method is provided.In the end,we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.
