On the k-sample Behrens-Fisher problem for high-dimensional data

For several decades, much attention has been paid to the two-sample Behrens-Fisher (BF) problem which tests the equality of the means or mean vectors of two normal populations with unequal variance/covariance structures. Little work, however, has been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal populations with unequal covariance structures. In this paper we study this challenging problem via extending the famous Scheffe’s transformation method, which reduces the k-sample BF problem to a one-sample problem. The induced one-sample problem can be easily tested by the classical Hotelling’s T ² test when the size of the resulting sample is very large relative to its dimensionality. For high dimensional data, however, the dimensionality of the resulting sample is often very large, and even much larger than its sample size, which makes the classical Hotelling’s T ² test not powerful or not even well defined. To overcome this difficulty, we propose and study an L ²-norm based test. The asymptotic powers of the proposed L ²-norm based test and Hotelling’s T ² test are derived and theoretically compared. Methods for implementing the L ²-norm based test are described. Simulation studies are conducted to compare the L ²-norm based test and Hotelling’s T ² test when the latter can be well defined, and to compare the proposed implementation methods for the L ²-norm based test otherwise. The methodologies are motivated and illustrated by a real data example. The work was supported by the National University of Singapore Academic Research Grant (Grant No. R-155-000-085-112)     

P2型钠离子电池正极材料Na0.66Mn0.675Ni0.1625Co0.1625O2的表面重构及其演变的电子显微表征

采用球差校正扫描透射电子显微镜(STEM)、X射线能谱(EDS)等分析手段表征了高温固相法合成的Na_0.66Mn_0.675Ni_0.1625Co_0.1625O₂钠离子过渡金属氧化物正极材料。X射线衍射(XRD)结果表明该材料为结晶性良好的P2型钠离子层状氧化物(P6₃/mmc)。原子尺度的结构与成分分析显示材料表面存在宽度约为1-2 nm的表面重构层,重构区域内存在大量晶格畸变与反位缺陷,并伴有一定程度的成分偏析——表面富钴(Co)、缺镍(Ni)。进一步研究表明这些表面重构区域在时效过程中会发生明显的“退化”,即初始表面重构层宽度会进一步扩展至5-10 nm,部分区域钠离子耗尽,由层状结构转变为尖晶石(Spinel,Fd3m)与岩盐相(rocksalt,Fm3m)共存的结构。     

不同的烧结工艺对Sm-Co2:17型高温磁体性能的影响

采用中频感应熔炼法制备了Sm(Co0.79Fe0.09Cu0.085Zr0.032)7.95合金,采用传统烧结工艺,在1200～1240℃烧结1 h,1165～1190℃固溶处理3 h,快速风冷淬火后在840℃保温12 h,以0.4℃.min-1的冷速冷却至420℃,保温10 h,最后随炉冷却。磁体经过加工后,采用不同的磁性测试手段对磁体进行测试。结果表明,磁体的剩磁随烧结温度的升高而增大,矫顽力最好的工艺为1230℃烧结1 h,然后在1180℃固溶3 h。将此工艺制备的磁体采用中国计量科学院NIM-500C超高温永磁测量仪测试,磁体在773 K时的最大磁能积为10.94 MGOe,高于已经报道的同Z值的2∶17型永磁体。磁体的磁滞回线通过振动样品磁强计(VSM)测得,室温下Br=10.5 kGs,Hcj=30.21 kOe,(BH)max=25.60MGOe;773 K时磁体Br=7.45 kGs,Hcj=6.02 kOe,(BH)max=9.85 MGOe。剩磁温度系数α=-0.0624%.℃-1,矫顽力温度系数β=-0.169%.℃-1。     

Ⅰ型拉伸试样金属注射成形多相流动的三维数值模拟

将粉末注射成形充模过程视为粘结剂、粉末和空气的三相流动过程,基于多相流理论给出金属注射成形的多相流动控制方程。根据金属注射成形的工艺特点确定多相流动控制方程的初边界条件,用多相流数值分析软件CFX对Ⅰ型拉伸试样的铁粉注射成形充模流动过程实现了三维数值模拟,分析了模腔中不同位置处粘结剂一粉末流动的速度曲线。数值模拟结果表明在Ⅰ型拉伸试样金属注射成形充模流动过程中发生过两相分离的现象,数值模拟的瞬态信息可用于金属注射成形产品缺陷的分析与控制。     

A Protocol for Bidirectional Quantum Secure Communication Based on Genuine Four-Particle Entangled States

By swapping the entanglement of genuine four-particle entangled states, we propose a bidirectional quantum secure communication protocol. The biggest merit of this protocol is that the information leakage does not exist. In addition, the ideas of the ``two-step" transmission and the block transmission are employed in this protocol. In order to analyze the security of the second sequence transmission, decoy states are used.     

利用Raman型的Jaynes-Cummings模型传送光场的福克叠加态

提出了一种利用Λ型三能级原子与光场Raman相互作用来传送光场的福克叠加态的方案.     

Convergence of Rational Interpolants with Preassigned Poles

Let Ω be a domain in the extended complex plane such that ∞∈Ω . Further, let K= C / Ω and, for each n , let Q _n be a monic polynomial of degree n with all its zeros in K . This paper is concerned with whether (Q _n ) can be chosen so that, if f is any holomorphic function on Ω and P _n is the polynomial part of the Laurent expansion of Q _n f at ∞ , then (P _n /Q _n ) converges to f locally uniformly on Ω . It is shown that such a sequence (Q _n ) can be chosen if and only if either K has zero logarithmic capacity or Ω is regular. January 21, 1999. Date accepted: August 17, 1999.     

利用破坏对称性的超导人造原子制备χ型四比特纠缠态

提出了利用在一维传输线共振器中的破坏对称性的超导人造原子来制备χ型四比特纠缠态的方案. 方案中所用到的Δ型三能级人造原子不同于自然的原子, 它可以产生循环跃迁. 经过适当时间的相互作用和简单的操作, 可以得到想要制备的纠缠态. 由于人造原子的激发态和光子态被绝热消除, 所以该方案对于人造原子的自发辐射和传输线共振器的衰减是鲁棒的.     

Novel structurally characterized hetero-bimetallic [Zn(II)2M(II)] (M = Ca and Sr) bis(salamo)-type complexes: DFT calculation,Hirshfeld analyses,antimicrobial and fluorescent properties

Two hetero-bimetallic [Zn(II)₂M(II)] (M = Ca and Sr) complexes [Zn₂Ca(L)(OAc)₂] ( 1 ) and [Zn₂Sr(L)(OAc)₂] ( 2 ) with a novel asymmetrical bis(salamo)-type tetraoxime ligand (H₅L) were designed and synthesized, and characterized by elemental analyses, FT-IR spectra, UV–vis absorption spectra, Density Functional Theory (DFT) calculation, Hirshfeld surface analyses and X-ray single crystal diffractions. Compared with the symmetric bis(salamo)-type ligands, the ligand H₅L and its [Zn(II)₂M(II)] (M = Ca and Sr) asymmetrical bis(salamo)-type complexes synthesized for the first time in this paper have more novel structures and better properties. The results of ultraviolet titration show that the coordination ratio of ligand, alkaline earth metal and transition metal is 1:1:2. Complexes 1 and 2 have good luminescent properties and obvious antimicrobial activities.     

利用V型三能级原子与相干态光场Raman相互作用传送未知奇偶相干态

描述了简并V型三能级原子与单模相干态光场的Raman相互作用，获得了处于激发态单态的原子与相干态光场相互作用的结果。利用探测原子与光场的相互作用将原子和探测光场制备成最大纠缠态，并将原子注入待测任一奇偶相干叠加态，通过原子与待测腔模构成的Bell基矢演化，对原子进行选择性探测，获得奇偶相干叠加态与原子相互作用后可能的量子状态，然后对待测腔场与原子进行联合探测，接着对所测奇偶相干态腔场的量子状态实施么正变换，就将探测腔场制备到待测腔场的初始量子态上，从而实现未知奇偶相干态的隐形传送。