Based on the generalized Dikin-type direction proposed by Jansen et al in 1997, we give out in this paper a generalized Dikin-type affine scaling algorithm for solving the P-*(kappa)-matrix linear complementarity prob...Based on the generalized Dikin-type direction proposed by Jansen et al in 1997, we give out in this paper a generalized Dikin-type affine scaling algorithm for solving the P-*(kappa)-matrix linear complementarity problem (LCP). Form using high-order correctors technique and rank-one updating, the iteration complexity and the total computational turn out asymptotically O((kappa + 1)root nL) and O((kappa + 1)n(3)L) respectively.展开更多
Symmetryandaxialityarethought tobeguides toward the pursuit of high energy barrier and blocking temperature for thedysprosium(Ⅲ)(Dy^(Ⅲ))single-molecule magnets(SMMs).The Dy^(Ⅲ)complexeswith low coordination numbers...Symmetryandaxialityarethought tobeguides toward the pursuit of high energy barrier and blocking temperature for thedysprosium(Ⅲ)(Dy^(Ⅲ))single-molecule magnets(SMMs).The Dy^(Ⅲ)complexeswith low coordination numbers are intended to satisfy axial symmetry.Here,we report four four-coordinate Dy^(Ⅲ)SMMs based on bis(arylamido)dysprosium building block{Dy(N^(RR’))2(μ-Cl)_(2)K}(N^(RR’)={N(SiMe_(3))(C_(6)H_(3)iPr_(2)-2,6)}^(−)),with two strong Dy–N and twoweak Dy–Cl bonds.Through fine-tuning of axial anisotropy,the SMM with the largest N–Dy–N angle of 139.24(15)°displayed magnetic hysteresis with a coercive field(H_(c))of 18.6 kOe at 2 K,which kept opening up to 35 K.Alternating current susceptibility measurement showed that the relaxation energy barrier reached as high as 1578 K,which is among the highest reported Dy^(Ⅲ)SMMs.Ab initio calculations revealed strong anisotropy and crystal-field axiality of the compound,despite the low symmetry,and provided a synthetically workable approach to construct high-performance SMMs useful in applications such as digital processing,transport electronics,quantumcomputing,and ultra-high-density data storage.展开更多
文摘Based on the generalized Dikin-type direction proposed by Jansen et al in 1997, we give out in this paper a generalized Dikin-type affine scaling algorithm for solving the P-*(kappa)-matrix linear complementarity problem (LCP). Form using high-order correctors technique and rank-one updating, the iteration complexity and the total computational turn out asymptotically O((kappa + 1)root nL) and O((kappa + 1)n(3)L) respectively.
基金supported by the National Natural Science Foundation of China(21971006)National Key R&D Program of China(2018YFA0306003,2017YFA0206301,and 2017YFA0204903)High-Performance Computing Platform at Peking University.
文摘Symmetryandaxialityarethought tobeguides toward the pursuit of high energy barrier and blocking temperature for thedysprosium(Ⅲ)(Dy^(Ⅲ))single-molecule magnets(SMMs).The Dy^(Ⅲ)complexeswith low coordination numbers are intended to satisfy axial symmetry.Here,we report four four-coordinate Dy^(Ⅲ)SMMs based on bis(arylamido)dysprosium building block{Dy(N^(RR’))2(μ-Cl)_(2)K}(N^(RR’)={N(SiMe_(3))(C_(6)H_(3)iPr_(2)-2,6)}^(−)),with two strong Dy–N and twoweak Dy–Cl bonds.Through fine-tuning of axial anisotropy,the SMM with the largest N–Dy–N angle of 139.24(15)°displayed magnetic hysteresis with a coercive field(H_(c))of 18.6 kOe at 2 K,which kept opening up to 35 K.Alternating current susceptibility measurement showed that the relaxation energy barrier reached as high as 1578 K,which is among the highest reported Dy^(Ⅲ)SMMs.Ab initio calculations revealed strong anisotropy and crystal-field axiality of the compound,despite the low symmetry,and provided a synthetically workable approach to construct high-performance SMMs useful in applications such as digital processing,transport electronics,quantumcomputing,and ultra-high-density data storage.
