再论随机变量的相关性与因果性

随机变量之间的关系一直是统计学研究中的重要问题之一.在面对不同的问题时,选取合适的方法去判断随机变量间的关系已成为解决实际问题的关键所在.针对这一现状,从概率论中的条件概率和条件分布出发,对随机变量的相关性理论与格兰杰的因果性理论进行了详细的讨论和分析,给出了判断随机变量由相关性(线性到非线性演化)到格兰杰因果性的方法.结果对于理解和把握随机变量的关系,给出恰当的判断,是有益的一种探索.     

2-(Ⅳ,Ⅳ-二羧甲基)-氨甲基4-氯酚铜(Ⅱ)的合成、结构与催化降解聚丙烯酰胺性能研究

合成了2-(N,N-二羧甲基)氨甲基4-氯酚,进而在水溶液中合成了其铜(Ⅱ)配合物,通过X-射线单晶衍射法测定了晶体结构.配合物中心Cu(Ⅱ)为五配位四方锥结构,在该配合物的晶体结构中存在两种构象异构体,相互问隔通过分子问氢键连接,延伸为一维链状结构.催化性能研究表明该配合物对H<,2>O<,2>的氧化降解聚丙烯酰胺有...     

2-(N,N-二羧甲基)-氨甲基-4-氯酚铜(Ⅱ)的合成、结构与催化降解聚丙烯酰胺性能研究

合成了2-(N,N-二羧甲基)氨甲基4-氯酚,进而在水溶液中合成了其铜(Ⅱ)配合物,通过X-射线单晶衍射法测定了晶体结构.配合物中心Cu(Ⅱ)为五配位四方锥结构,在该配合物的晶体结构中存在两种构象异构体,相互问隔通过分子问氢键连接,延伸为一维链状结构.催化性能研究表明该配合物对H<,2>O<,2>的氧化降解聚丙烯酰胺有一定的催化作用,可以使分子量由6.1×10<'6>降低至1.66×10<'5>.     

Legendre transformations and the thermodynamic geometry of 5D black holes

This paper studies the thermodynamic properties of the 5D black hole in Einstein-Gauss-Bonnet gravity from the viewpoint of geometrothermodynamics. It is found that the Legendre invariant metrics of the 5D black holes in Einstein-Yang-Mills-Gauss-Bonnet theory and Einstein-Maxwell-Gauss-Bonnet theory reproduce the behavior of the thermodynamic interaction and phase transition structure of the corresponding black hole configurations correctly. It is shown that they are both curved and that the curvature scalar provides information about the phase transition point.     

ICF激光驱动器间接驱动兼顾直接驱动打靶角度的优化设计

为了增加ICF激光驱动器的灵活性,使其可满足多种聚变点火方式,激光驱动器激光打靶角度的优化设计应以间接驱动为主,同时兼顾直接驱动。以神光Ⅲ主机装置为例,基于已有的间接驱动激光打靶角度设计,用球谐模和三维辐照场方法,完成了兼顾直接驱动打靶角度的优化,结果表明优化设计的打靶角度可实现小于1%的球靶表面辐照均匀性。同时分析了激光参数对辐照性能的影响,并获得了满足直接驱动要求的陡边小焦斑设计。     

具有高斯过程误差的函数型线性模型的统计诊断

提出了具有高斯过程误差的函数型回归模型的几种诊断方法.在此模型中,首先,在样条基的基础上,推导了回归系数函数的估计.随后,证明了数据删失模型和均值漂移模型的等价性.然后,研究了三种诊断方法,即残差分析、Cook距离和似然距离来诊断异常和强影响数据.最后,通过一个模拟例子和一个实例来阐述方法的有效性.     

一类关于正规三角函数基的标准模糊系统逼近误差公式的讨论

在标准模糊系统的基础上提出了以正规三角函数为基函数的一类模糊系统.通过采用数值分析中的余项与辅助函数方法,对该类模糊系统进行了逼近误差精度的分析,给出了从SISO到MISO的误差界公式.最后,指出了这些公式在模糊系统的理论研究与实际应用的意义.     

SU(3) spin-orbit coupled fermions in an optical lattice

We propose a scheme to realize the SU(3)spin-orbit coupled three-component fermions in an one-dimensional optical lattice.The topological properties of the single-particle Hamiltonian are studied by calculating the Berry phase,winding number and edge state.We also investigate the effects of the interaction on the ground-state topology of the system,and characterize the interaction-induced topological phase transitions,using a state-of-the-art density-matrix renormalization-group numerical method.Finally,we show the typical features of the emerging quantum phases,and map out the many-body phase diagram between the interaction and the Zeeman field.Our results establish a way for exploring novel quantum physics induced by the SOC with SU(N)symmetry.     

Topological phases and type-II edge state in two-leg-coupled Su-Schrieffer-Heeger chains

Topological quantum states have attracted great attention both theoretically and experimentally.Here,we show that the momentum-space lattice allows us to couple two Su-Schrieffer-Heeger(SSH)chains with opposite dimerizations and staggered interleg hoppings.The coupled SSH chain is a four-band model which has sublattice symmetry similar to the SSH4.Interestingly,the topological edge states occupy two sublattices at the same time,which can be regarded as a one-dimension analogue of the type-II corner state.The analytical expressions of the edge states are also obtained by solving the eigenequations.Finally,we provide a possible experimental scheme to detect the topological winding number and corresponding edge states.     

Hard-core Hall tube in superconducting circuits

The Hall tube as a minimum model to simulate the integer quantum Hall effect is essential for exploring topological physics, while it has not been constructed in the recent developing successfully experiments on superconducting circuits. In this work, we propose a feasible experiment scheme using three legs superconducting circuits with transmon qubits to realize a Hall tube. Then we first investigate its topological properties. Since the time-reversal, particle-hole, and chiral symmetries are all broken for the system, the Hall tube belongs to the A class of the Altland-Zirnbauer classification. We obtain the corresponding topological phase transition both numerically and analytically. Since the chirality is a key character of the quantum Hall effect, we secondly investigate the chiral physics in the Hall tube. We find the topological protected chiral edge currents and discuss its robustness. Finally, we give the possible experimental observations of the topological state and topological protected chiral edge currents.