Monogamy and polygamy relations are important properties of entanglement,which characterize the entanglement distribution of multipartite systems.We explore monogamy and polygamy relations of entanglement in multipart...Monogamy and polygamy relations are important properties of entanglement,which characterize the entanglement distribution of multipartite systems.We explore monogamy and polygamy relations of entanglement in multipartite systems by using two newly derived parameterized mathematical inequalities,and establish classes of parameterized monogamy and polygamy relations of multiqubit entanglement in terms of concurrence and entanglement of formation.We show that these new parameterized monogamy and poelygamy inequalities are tighter than the existing ones by detailed examples.展开更多
BACKGROUND Mycosis fungoides(MF)is a form of lymphoma derived from heterogeneous T cells,and eyelid involvement is extremely rare.The common methods to treat eyelid involvement are radiotherapy and chemotherapy,but th...BACKGROUND Mycosis fungoides(MF)is a form of lymphoma derived from heterogeneous T cells,and eyelid involvement is extremely rare.The common methods to treat eyelid involvement are radiotherapy and chemotherapy,but their efficacies are limited.Herein,we report a case of advanced-stage MF eyelid involvement,propose ultrasound(US)-guided microwave ablation(MWA)therapy and present a literature review.CASE SUMMARY A male patient was admitted to our hospital in June 2018 and diagnosed with MF via radiological and histopathological examinations.The patient’s condition was not well controlled by various conventional chemotherapies.US-guided MWA was performed to relieve the patient’s symptoms and improve his quality of life,showing satisfactory efficacy.CONCLUSION Eyelid involvement is one of the most troublesome clinical problems for advanced-stage MF patients.This is the first report on the use of US-guided MWA as a palliative therapy for MF eyelid involvement;the treatment successfully relieved the patient’s clinical symptoms and reduced his anxiety behaviours.Our study sheds new light on methods for improving the clinical management of eyelid involvement in MF.展开更多
Let G be a multigraph.Suppose that e=u1v1 and e′=u2v2 are two edges of G.If e≠e′,then G(e,e′)is the graph obtained from G by replacing e=u1v1 with a path u1vev1 and by replacing e′=u2v2 with a path u2ve′v2,where...Let G be a multigraph.Suppose that e=u1v1 and e′=u2v2 are two edges of G.If e≠e′,then G(e,e′)is the graph obtained from G by replacing e=u1v1 with a path u1vev1 and by replacing e′=u2v2 with a path u2ve′v2,where ve,ve′are two new vertices not in V(G).If e=e′,then G(e,e′),also denoted by G(e),is obtained from G by replacing e=u1v1 with a path u1vev1.A graph G is strongly spanning trailable if for any e,e′∈E(G),G(e,e′)has a spanning(ve,ve′)-trail.The design of n processor network with given number of connections from each processor and with a desirable strength of the network can be modelled as a degree sequence realization problem with certain desirable graphical properties.A sequence d=(d1,d2,⋯,dn)is multigraphic if there is a multigraph G with degree sequence d,and such a graph G is called a realization of d.A multigraphic degree sequence d is strongly spanning trailable if d has a realization G which is a strongly spanning trailable graph,and d is line-hamiltonian-connected if d has a realization G such that the line graph of G is hamiltonian-connected.In this paper,we prove that a nonincreasing multigraphic sequence d=(d1,d2)⋯,dn)is strongly spanning trailable if and only if either n=1 and d1=0 or n≥2 and dn≥3.Applying this result,we prove that for a nonincreasing multigraphic sequence d=(d1,d2,⋯,dn),if n≥2 and dn≥3,then d is line-hamiltonian-connected.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.12075159 and 12171044)the Beijing Natural Science Foundation (Grant No.Z190005)the Academician Innovation Platform of Hainan Province。
文摘Monogamy and polygamy relations are important properties of entanglement,which characterize the entanglement distribution of multipartite systems.We explore monogamy and polygamy relations of entanglement in multipartite systems by using two newly derived parameterized mathematical inequalities,and establish classes of parameterized monogamy and polygamy relations of multiqubit entanglement in terms of concurrence and entanglement of formation.We show that these new parameterized monogamy and poelygamy inequalities are tighter than the existing ones by detailed examples.
基金Supported by Zhenjiang Social Development Fund,No.SH2021028Zhenjiang Social Development Fund,No.SH2018035the“169”Project of Zhenjiang City,No.YLJ201931.
文摘BACKGROUND Mycosis fungoides(MF)is a form of lymphoma derived from heterogeneous T cells,and eyelid involvement is extremely rare.The common methods to treat eyelid involvement are radiotherapy and chemotherapy,but their efficacies are limited.Herein,we report a case of advanced-stage MF eyelid involvement,propose ultrasound(US)-guided microwave ablation(MWA)therapy and present a literature review.CASE SUMMARY A male patient was admitted to our hospital in June 2018 and diagnosed with MF via radiological and histopathological examinations.The patient’s condition was not well controlled by various conventional chemotherapies.US-guided MWA was performed to relieve the patient’s symptoms and improve his quality of life,showing satisfactory efficacy.CONCLUSION Eyelid involvement is one of the most troublesome clinical problems for advanced-stage MF patients.This is the first report on the use of US-guided MWA as a palliative therapy for MF eyelid involvement;the treatment successfully relieved the patient’s clinical symptoms and reduced his anxiety behaviours.Our study sheds new light on methods for improving the clinical management of eyelid involvement in MF.
基金This paper is supported by the National Natural Science Foundation of China(Nos.11771039,11971054)Fundamental Research Funds for the Central Universities of China(No.2015JBM107)the 111 Project of China(No.B16002)。
文摘Let G be a multigraph.Suppose that e=u1v1 and e′=u2v2 are two edges of G.If e≠e′,then G(e,e′)is the graph obtained from G by replacing e=u1v1 with a path u1vev1 and by replacing e′=u2v2 with a path u2ve′v2,where ve,ve′are two new vertices not in V(G).If e=e′,then G(e,e′),also denoted by G(e),is obtained from G by replacing e=u1v1 with a path u1vev1.A graph G is strongly spanning trailable if for any e,e′∈E(G),G(e,e′)has a spanning(ve,ve′)-trail.The design of n processor network with given number of connections from each processor and with a desirable strength of the network can be modelled as a degree sequence realization problem with certain desirable graphical properties.A sequence d=(d1,d2,⋯,dn)is multigraphic if there is a multigraph G with degree sequence d,and such a graph G is called a realization of d.A multigraphic degree sequence d is strongly spanning trailable if d has a realization G which is a strongly spanning trailable graph,and d is line-hamiltonian-connected if d has a realization G such that the line graph of G is hamiltonian-connected.In this paper,we prove that a nonincreasing multigraphic sequence d=(d1,d2)⋯,dn)is strongly spanning trailable if and only if either n=1 and d1=0 or n≥2 and dn≥3.Applying this result,we prove that for a nonincreasing multigraphic sequence d=(d1,d2,⋯,dn),if n≥2 and dn≥3,then d is line-hamiltonian-connected.
