Improving entanglement of assistance by local parity–time symmetric operation

We investigate entanglement of assistance without and with decoherence using a local non-Hermitian operation, i.e.,parity–time(PT) symmetric operation. First we give the explicit expressions of entanglement of assistance for a general W-like state of a three-qubit system under a local parity–time symmetric operation. Then for a famous W state without decoherence, we find that entanglement of assistance shared by two parties can be obviously enhanced with the assistance of the third party by a local parity–time symmetric operation. For the decoherence case, we provide two schemes to show the effects of local parity–time symmetric operation on improvement of entanglement of assistance against amplitude damping noise. We find that for the larger amplitude damping case the scheme of PT symmetric operation performed on one of two parties with the influence of noise is superior to that of PT symmetric operation performed on the third party without the influence of noise in suppressing amplitude damping noise. However, for the smaller amplitude damping case the opposite result is given. The obtained results imply that the local PT symmetric operation method may have potential applications in quantum decoherence control.

A Fault Feature Extraction Model in Synchronous Generator under Stator Inter-Turn Short Circuit Based on ACMD and DEO3S

This paper proposed a new diagnosis model for the stator inter-turn short circuit fault in synchronous generators.Different from the past methods focused on the current or voltage signals to diagnose the electrical fault,the sta-tor vibration signal analysis based on ACMD(adaptive chirp mode decomposition)and DEO3S(demodulation energy operator of symmetrical differencing)was adopted to extract the fault feature.Firstly,FT(Fourier trans-form)is applied to the vibration signal to obtain the instantaneous frequency,and PE(permutation entropy)is calculated to select the proper weighting coefficients.Then,the signal is decomposed by ACMD,with the instan-taneous frequency and weighting coefficient acquired in the former step to obtain the optimal mode.Finally,DEO3S is operated to get the envelope spectrum which is able to strengthen the characteristic frequencies of the stator inter-turn short circuit fault.The study on the simulating signal and the real experiment data indicates the effectiveness of the proposed method for the stator inter-turn short circuit fault in synchronous generators.In addition,the comparison with other methods shows the superiority of the proposed model.

Medical Waste Treatment Station Selection Based on Linguistic q-Rung Orthopair Fuzzy Numbers

During the COVID-19 outbreak,the use of single-use medical supplies increased significantly.It is essential to select suitable sites for establishing medical waste treatment stations.It is a big challenge to solve the medical waste treatment station selection problem due to some conflicting factors.This paper proposes a multi-attribute decision-making(MADM)method based on the partitioned Maclaurin symmetric mean(PMSM)operator.For the medical waste treatment station selection problem,the factors or attributes(these two terms can be interchanged.)in the same clusters are closely related,and the attributes in different clusters have no relationships.The partitioned Maclaurin symmetric mean function(PMSMF)can handle these complex attribute relationships.Hence,we extend the PMSM operator to process the linguistic q-rung orthopair fuzzy numbers(Lq-ROFNs)and propose the linguistic q-rung orthopair fuzzy partitioned Maclaurin symmetric mean(Lq-ROFPMSM)operator and its weighted form(Lq-ROFWPMSM).To reduce the negative impact of unreasonable data on the final output results,we propose the linguistic q-rung orthopair fuzzy partitioned dual Maclaurin symmetric mean(Lq-ROFPDMSM)operator and its weighted form(Lq-ROFWPDMSM).We also discuss the characteristics and typical examples of the above operators.A novel MADM method uses the Lq-ROFWPMSM operator and the Lq-ROFWPDMSM operator to solve the medical waste treatment station selection problem.Finally,the usability and superiority of the proposed method are verified by comparing it with previous methods.

The Symmetry of Singular Hamiltonian Differential Operators and Properties of Deficiency Indices

The symmetry of singular Hamiltonian differential operators is proved under the standard ＂definiteness condition＂, which is strictly weaker than the densely definite condition used by A. M. Krall. Meanwhile, some properties of deficiency indices are given.

Inverse-Definiteness of the Fourth-Order Symmetric Differential Operator(Ⅰ)

We give a linear symmetric differential operator L defined by

THE SYMMETRY DESCRIPTION OF A CLASS OF FRACTIONAL STURM-LIOUVILLE OPERATOR

This paper studies the symmetry of a class of tractional Sturm-Liouville differential equations with right and left fractional derivatives. We give the Hermitian boundary condition description of this problem. Furthermore, the density of minimal operator is given. Then the symmetry of this problem is obtained.