The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian ...The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.展开更多
Using the theory of derivations on finitely generated and graded Lie algebras, we determine that derivations of the BMS-Weyl algebra are all inner. On this basis, it is proved that every 2-local derivation of the BMS-...Using the theory of derivations on finitely generated and graded Lie algebras, we determine that derivations of the BMS-Weyl algebra are all inner. On this basis, it is proved that every 2-local derivation of the BMS-Weyl algebra is a derivation.展开更多
The chiral magnetic effect (CME) refers to a charge separation along a strong magnetic field due to an imbalanced chirality of quarks from interactions with the vacuum topological gluon field. This chiral anomaly is a...The chiral magnetic effect (CME) refers to a charge separation along a strong magnetic field due to an imbalanced chirality of quarks from interactions with the vacuum topological gluon field. This chiral anomaly is a fundamental property of quantum chromodynamics (QCD) and, therefore, an observation of the CME would have far-reaching impact on our understanding of QCD and Nature. The measurements of the CME-sensitive azimuthal correlator Δγ observable in heavy-ion collisions are contaminated by a major background induced by elliptic flow anisotropy. Several novel approaches have been carried out, including a dedicated isobar collision program, to address this flow-induced background. Further background effects, arising from nonflow correlations, have been studied. While the isobar data are consistent with zero CME signal with an upper limit of 10% of the measured Δγ, the Au+Au midcentral data suggest a positive CME signal on the order of 10% of the measured Δγ with a significance of ~2 standard deviations. Future increased statistics and improved detector capability should yield a firm conclusion on the existence (or the lack) of the CME in relativistic heavy-ion collisions.展开更多
基金The National Natural Science Foundation of China(No.11371089)the China Postdoctoral Science Foundation(No.2016M601688)
文摘The range and existence conditions of the Hermitian positive definite solutions of nonlinear matrix equations Xs+A*X-tA=Q are studied, where A is an n×n non-singular complex matrix and Q is an n×n Hermitian positive definite matrix and parameters s,t>0. Based on the matrix geometry theory, relevant matrix inequality and linear algebra technology, according to the different value ranges of the parameters s,t, the existence intervals of the Hermitian positive definite solution and the necessary conditions for equation solvability are presented, respectively. Comparing the existing correlation results, the proposed upper and lower bounds of the Hermitian positive definite solution are more accurate and applicable.
基金National Natural Science Foundation of China(10771064)Natural Science Foundation of Zhejiang Province(Y7080197,Y6090036)+1 种基金Characteristic Subject of China"Mathematics and applied mathematics",Delicate Course of China"theory of functions of a complex variable",Educational Innovation of Zhejiang province(yb07109)Foundation of Creative Group in Colleges and Universities of Zhejiang Province(T200924)
基金National Natural Science Foundation of China(11971315)。
文摘Using the theory of derivations on finitely generated and graded Lie algebras, we determine that derivations of the BMS-Weyl algebra are all inner. On this basis, it is proved that every 2-local derivation of the BMS-Weyl algebra is a derivation.
文摘The chiral magnetic effect (CME) refers to a charge separation along a strong magnetic field due to an imbalanced chirality of quarks from interactions with the vacuum topological gluon field. This chiral anomaly is a fundamental property of quantum chromodynamics (QCD) and, therefore, an observation of the CME would have far-reaching impact on our understanding of QCD and Nature. The measurements of the CME-sensitive azimuthal correlator Δγ observable in heavy-ion collisions are contaminated by a major background induced by elliptic flow anisotropy. Several novel approaches have been carried out, including a dedicated isobar collision program, to address this flow-induced background. Further background effects, arising from nonflow correlations, have been studied. While the isobar data are consistent with zero CME signal with an upper limit of 10% of the measured Δγ, the Au+Au midcentral data suggest a positive CME signal on the order of 10% of the measured Δγ with a significance of ~2 standard deviations. Future increased statistics and improved detector capability should yield a firm conclusion on the existence (or the lack) of the CME in relativistic heavy-ion collisions.
