In this paper, we consider the ground-states of the following M-coupled system:where p_(ij)+q_(ij)=2*:=2 N/(N-2)(N≥3). We prove the existence of ground-states to the M-coupled system. At the same time, we not only gi...In this paper, we consider the ground-states of the following M-coupled system:where p_(ij)+q_(ij)=2*:=2 N/(N-2)(N≥3). We prove the existence of ground-states to the M-coupled system. At the same time, we not only give out the characterization of the ground-states, but also study the number of the ground-states, containing the positive ground-states and the semi-trivial ground-states, which may be the first result studying the number of not only positive ground-states but also semi-trivial ground-states.展开更多
Rational design of solid-state electrolytes(SSEs)with high ionic conductivity and low activation energy(Ea)is vital for all solid-state batteries.Machine learning(ML)techniques have recently been successful in predict...Rational design of solid-state electrolytes(SSEs)with high ionic conductivity and low activation energy(Ea)is vital for all solid-state batteries.Machine learning(ML)techniques have recently been successful in predicting Li^(+) conduction property in SSEs with various descriptors and accelerating the development of SSEs.In this work,we extend the previous efforts and introduce a framework of ML prediction for E_(a) in SSEs with hierarchically encoding crystal structure-based(HECS)descriptors.Taking cubic Li-argyrodites as an example,an Ea prediction model is developed to the coefficient of determination(R^(2))and rootmean-square error(RMSE)values of 0.887 and 0.02 eV for training dataset,and 0.820 and 0.02 eV for test dataset,respectively by partial least squares(PLS)analysis,proving the prediction power of HECSdescriptors.The variable importance in projection(VIP)scores demonstrate the combined effects of the global and local Li^(+) conduction environments,especially the anion size and the resultant structural changes associated with anion site disorder.The developed E_(a) prediction model directs us to optimize and design new Li-argyrodites with lower Ea,such as Li_(6–x)PS_(5–x)Cl_(1+x)(<0.322 eV),Li_(6+x)PS_(5+x)Br_(1–x)(<0.273 eV),Li_(6+x)PS_(5+x)Br_(0.25)I_(0.75–x)(<0.352 eV),Li_(6+(5–n)y)P_(1–y)N_(y)S_(5)I(<0.420 eV),Li_(6+(5–n)y)As_(1–y)N_(y)S_(5)I(<0.371 eV),Li_(6+(5–n)y)As_(1–y)NySe_(5)I(<0.450 eV),by broadening bottleneck size,invoking site disorder and activating concerted Li+conduction.This analysis shows great potential in promoting rational design of advanced SSEs and the same approach can be applied to other types of materials.展开更多
In this article,we take the Zc(3900) and Z(4430) as the ground state and the first radial excited state of the axial-vector tetraquark states with J^(PC) = 1^(+-),respectively,and study their masses and pole residues ...In this article,we take the Zc(3900) and Z(4430) as the ground state and the first radial excited state of the axial-vector tetraquark states with J^(PC) = 1^(+-),respectively,and study their masses and pole residues with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in a consistent way in the operator product expansion.The numerical result favors assigning the Z_c(3900) and Z(4430) as the ground state and first radial excited state of the axial-vector tetraquark states,respectively.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11601194)PhD Start-Up Funds of Jiangsu University of Science and Technology (Grant Nos. 1052931601 and 1052921513)
文摘In this paper, we consider the ground-states of the following M-coupled system:where p_(ij)+q_(ij)=2*:=2 N/(N-2)(N≥3). We prove the existence of ground-states to the M-coupled system. At the same time, we not only give out the characterization of the ground-states, but also study the number of the ground-states, containing the positive ground-states and the semi-trivial ground-states, which may be the first result studying the number of not only positive ground-states but also semi-trivial ground-states.
基金the National Key Research and Development Program of China(2017YFB0701600)the National Natural Science Foundation of China(11874254,51622207,and U1630134)。
文摘Rational design of solid-state electrolytes(SSEs)with high ionic conductivity and low activation energy(Ea)is vital for all solid-state batteries.Machine learning(ML)techniques have recently been successful in predicting Li^(+) conduction property in SSEs with various descriptors and accelerating the development of SSEs.In this work,we extend the previous efforts and introduce a framework of ML prediction for E_(a) in SSEs with hierarchically encoding crystal structure-based(HECS)descriptors.Taking cubic Li-argyrodites as an example,an Ea prediction model is developed to the coefficient of determination(R^(2))and rootmean-square error(RMSE)values of 0.887 and 0.02 eV for training dataset,and 0.820 and 0.02 eV for test dataset,respectively by partial least squares(PLS)analysis,proving the prediction power of HECSdescriptors.The variable importance in projection(VIP)scores demonstrate the combined effects of the global and local Li^(+) conduction environments,especially the anion size and the resultant structural changes associated with anion site disorder.The developed E_(a) prediction model directs us to optimize and design new Li-argyrodites with lower Ea,such as Li_(6–x)PS_(5–x)Cl_(1+x)(<0.322 eV),Li_(6+x)PS_(5+x)Br_(1–x)(<0.273 eV),Li_(6+x)PS_(5+x)Br_(0.25)I_(0.75–x)(<0.352 eV),Li_(6+(5–n)y)P_(1–y)N_(y)S_(5)I(<0.420 eV),Li_(6+(5–n)y)As_(1–y)N_(y)S_(5)I(<0.371 eV),Li_(6+(5–n)y)As_(1–y)NySe_(5)I(<0.450 eV),by broadening bottleneck size,invoking site disorder and activating concerted Li+conduction.This analysis shows great potential in promoting rational design of advanced SSEs and the same approach can be applied to other types of materials.
基金Supported by National Natural Science Foundation under Grant No.11375063Natural Science Foundation of Hebei Province under Grant No.A2014502017
文摘In this article,we take the Zc(3900) and Z(4430) as the ground state and the first radial excited state of the axial-vector tetraquark states with J^(PC) = 1^(+-),respectively,and study their masses and pole residues with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in a consistent way in the operator product expansion.The numerical result favors assigning the Z_c(3900) and Z(4430) as the ground state and first radial excited state of the axial-vector tetraquark states,respectively.
