A property(C) for permutation pairs is introduced. It is shown that if a pair{π_1, π_2} of permutations of(1,2,…,n) has property(C),then the D-type map Φ_(π_1,π_2) on n× n complex matrices constructed from ...A property(C) for permutation pairs is introduced. It is shown that if a pair{π_1, π_2} of permutations of(1,2,…,n) has property(C),then the D-type map Φ_(π_1,π_2) on n× n complex matrices constructed from {π_1,π_2} is positive. A necessary and sufficient condition is obtained for a pair {π_1,π_2} to have property(C),and an easily checked necessary and sufficient condition for the pairs of the form {π~p,π~q} to have property(C) is given, whereπ is the permutation defined by π(i) = i + 1 mod n and 1≤ p < q≤ n.展开更多
For n≥3,we construct a class{Wn,π1,π2}of n^(2)×n^(2) hermitian matrices by the permutation pairs and show that,for a pair{π1,π2}of permutations on(1,2,…,n),Wn,π1,π2 is an entanglement witness of the n⊗n s...For n≥3,we construct a class{Wn,π1,π2}of n^(2)×n^(2) hermitian matrices by the permutation pairs and show that,for a pair{π1,π2}of permutations on(1,2,…,n),Wn,π1,π2 is an entanglement witness of the n⊗n system if{π1,π2}has the property(C).Recall that a pair{π1,π2}of permutations of(1,2,…,n)has the property(C)if,for each i,one can obtain a permutation of(1,…,i−1,i+1,…,n)from(π1(1),…,π1(i−1),π1(i+1),…,π1(n))and(π2(1),…,π2(i−1),π2(i+1),…,π2(n)).We further prove that Wn,π1,π2 is not comparable with Wn,π,which is the entanglement witness constructed from a single permutationπ;Wn,π1,π2 is decomposable ifπ1π2=id orπ21=π22=id.For the low dimensional cases n∈{3,4},we give a sufficient and necessary condition onπ1,π2 for Wn,π1,π2 to be an entanglement witness.We also show that,for n∈{3,4},Wn,π1,π2 is decomposable if and only ifπ1π2=id orπ21=π22=id;W3,π1,π2 is optimal if and only if(π1,π2)=(π,π2),whereπ=(2,3,1).As applications,some entanglement criteria for states and some decomposability criteria for positive maps are established.展开更多
Tin-based sulfides have attracted increasing attention as anodes for sodium-ion batteries(SIBs) owing to their high theoretical capacity;however, the poor rate capability and inferior cycling stability caused by the l...Tin-based sulfides have attracted increasing attention as anodes for sodium-ion batteries(SIBs) owing to their high theoretical capacity;however, the poor rate capability and inferior cycling stability caused by the low electrical conductivity, sluggish kinetics and drastic volume variations during cycling have greatly hampered their practical applications. Herein, heterostructured NiS_(2)@SnS_(2) hybrid spheres were delicately designed and constructed by anchoring interconnected SnS_(2) nanosheets on metalorganic frameworks(MOFs)-derived Ni S_(2) hollow spheres coupled with N-doped carbon skeleton through facile solvothermal and sulfurization/carbonization processes. The unique hollow heterostructure with highly conductive carbon matrix can effectively facilitate the charge transfer kinetics and ensure the desired buffer space while endowing more active sites and enhanced structural integrity, as demonstrated by the experimental and density functional theory(DFT) results. Benefitting from these merits, the NiS_(2)@SnS_(2) hybrid composite displays a high reversible capacity of 820 m Ah g^(-1) after 250 cycles at 1 A g^(-1), and retains a value of 673 m Ah g^(-1)after 1,300 cycles at 5 A g^(-1), manifesting the excellent high-rate and durable sodium storage behaviors when applied in SIBs. This study shall shed more light on the fabricating and interface engineering of other transition metal-based composite anodes for high-performance SIBs.展开更多
In order to provide direct evidence for the use of fire by humans at Locality 1,Zhoukoudian,we examine the burnt and unburnt sediments of newly excavated area in Layer 4 by detailed measurements of magnetic susceptibi...In order to provide direct evidence for the use of fire by humans at Locality 1,Zhoukoudian,we examine the burnt and unburnt sediments of newly excavated area in Layer 4 by detailed measurements of magnetic susceptibility,color,and diffuse reflectance spectrum.Results show that the magnetic susceptibility and redness of the burnt sediments are remarkably higher than those of other areas on the same level:up to*22 times for magnetic susceptibility and*3 times for redness of those of the adjacent unburnt sediments.Fine-grained(superparamagnetic/stable single-domain)magnetite and hematite grains make dominant contributions to the distinctly high values of magnetic susceptibility and redness in the burnt sediments.Diffuse reflectance spectroscopy results show that the burnt sediments contain more hematite than those of other areas and localities 2 and 3.High-temperature magnetic susceptibility measurements demonstrate that the burnt sediments have been heated above 700°C.Those changes in low-frequency magnetic susceptibility and redness are impossibly resulted from natural fires,thus most likely signaling the human activities of controlled use of fire.However,further work is needed to confirm whether or not these heat-affected sediments were produced in situ.展开更多
The positive partial transposition(PPT)criterion and the realignment criterion constitute two of the most important criteria for detecting entanglement.The generalized partial transposition(GPT)criterion which contain...The positive partial transposition(PPT)criterion and the realignment criterion constitute two of the most important criteria for detecting entanglement.The generalized partial transposition(GPT)criterion which contains the PPT criterion and the realignment criterion as special cases,provides a necessary condition for a multipartite state to be separable.Here we extend the GPT criterion to the infinitedimensional multipartite(bipartite)case and show that it includes multipartite(bipartite)PPT criterion and multipartite(bipartite)realignment criterion as special cases as well.展开更多
基金partially supported by National Natural Science Foundation of China(11671294)
文摘A property(C) for permutation pairs is introduced. It is shown that if a pair{π_1, π_2} of permutations of(1,2,…,n) has property(C),then the D-type map Φ_(π_1,π_2) on n× n complex matrices constructed from {π_1,π_2} is positive. A necessary and sufficient condition is obtained for a pair {π_1,π_2} to have property(C),and an easily checked necessary and sufficient condition for the pairs of the form {π~p,π~q} to have property(C) is given, whereπ is the permutation defined by π(i) = i + 1 mod n and 1≤ p < q≤ n.
基金partially supported by National Natural Science Foundation of China(11671294,12071336)。
文摘For n≥3,we construct a class{Wn,π1,π2}of n^(2)×n^(2) hermitian matrices by the permutation pairs and show that,for a pair{π1,π2}of permutations on(1,2,…,n),Wn,π1,π2 is an entanglement witness of the n⊗n system if{π1,π2}has the property(C).Recall that a pair{π1,π2}of permutations of(1,2,…,n)has the property(C)if,for each i,one can obtain a permutation of(1,…,i−1,i+1,…,n)from(π1(1),…,π1(i−1),π1(i+1),…,π1(n))and(π2(1),…,π2(i−1),π2(i+1),…,π2(n)).We further prove that Wn,π1,π2 is not comparable with Wn,π,which is the entanglement witness constructed from a single permutationπ;Wn,π1,π2 is decomposable ifπ1π2=id orπ21=π22=id.For the low dimensional cases n∈{3,4},we give a sufficient and necessary condition onπ1,π2 for Wn,π1,π2 to be an entanglement witness.We also show that,for n∈{3,4},Wn,π1,π2 is decomposable if and only ifπ1π2=id orπ21=π22=id;W3,π1,π2 is optimal if and only if(π1,π2)=(π,π2),whereπ=(2,3,1).As applications,some entanglement criteria for states and some decomposability criteria for positive maps are established.
基金funded by Zhejiang Provincial Natural Science Foundation of China (LY21E020010)the National Natural Science Foundation of China (52102315)the Fundamental Research Fund of Zhejiang Sci-Tech University (2021Y005)。
文摘Tin-based sulfides have attracted increasing attention as anodes for sodium-ion batteries(SIBs) owing to their high theoretical capacity;however, the poor rate capability and inferior cycling stability caused by the low electrical conductivity, sluggish kinetics and drastic volume variations during cycling have greatly hampered their practical applications. Herein, heterostructured NiS_(2)@SnS_(2) hybrid spheres were delicately designed and constructed by anchoring interconnected SnS_(2) nanosheets on metalorganic frameworks(MOFs)-derived Ni S_(2) hollow spheres coupled with N-doped carbon skeleton through facile solvothermal and sulfurization/carbonization processes. The unique hollow heterostructure with highly conductive carbon matrix can effectively facilitate the charge transfer kinetics and ensure the desired buffer space while endowing more active sites and enhanced structural integrity, as demonstrated by the experimental and density functional theory(DFT) results. Benefitting from these merits, the NiS_(2)@SnS_(2) hybrid composite displays a high reversible capacity of 820 m Ah g^(-1) after 250 cycles at 1 A g^(-1), and retains a value of 673 m Ah g^(-1)after 1,300 cycles at 5 A g^(-1), manifesting the excellent high-rate and durable sodium storage behaviors when applied in SIBs. This study shall shed more light on the fabricating and interface engineering of other transition metal-based composite anodes for high-performance SIBs.
文摘In order to provide direct evidence for the use of fire by humans at Locality 1,Zhoukoudian,we examine the burnt and unburnt sediments of newly excavated area in Layer 4 by detailed measurements of magnetic susceptibility,color,and diffuse reflectance spectrum.Results show that the magnetic susceptibility and redness of the burnt sediments are remarkably higher than those of other areas on the same level:up to*22 times for magnetic susceptibility and*3 times for redness of those of the adjacent unburnt sediments.Fine-grained(superparamagnetic/stable single-domain)magnetite and hematite grains make dominant contributions to the distinctly high values of magnetic susceptibility and redness in the burnt sediments.Diffuse reflectance spectroscopy results show that the burnt sediments contain more hematite than those of other areas and localities 2 and 3.High-temperature magnetic susceptibility measurements demonstrate that the burnt sediments have been heated above 700°C.Those changes in low-frequency magnetic susceptibility and redness are impossibly resulted from natural fires,thus most likely signaling the human activities of controlled use of fire.However,further work is needed to confirm whether or not these heat-affected sediments were produced in situ.
基金partially supported by the National Natural Science Foundation of China(11171249,11301312,11101250)Research Fund for the Doctoral Program of Higher Education of China(20101402110012)+1 种基金China Postdoctoral Science Foundation funded project the Natural Science Foundation of Shanxi(2013021001-1)Research Start-up Fundfor Doctors of Shanxi Datong University(2011-B-01)
文摘The positive partial transposition(PPT)criterion and the realignment criterion constitute two of the most important criteria for detecting entanglement.The generalized partial transposition(GPT)criterion which contains the PPT criterion and the realignment criterion as special cases,provides a necessary condition for a multipartite state to be separable.Here we extend the GPT criterion to the infinitedimensional multipartite(bipartite)case and show that it includes multipartite(bipartite)PPT criterion and multipartite(bipartite)realignment criterion as special cases as well.
