Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated based on the effective score, which is obtained by determining the component of the parametric score orthogonal to the space generated by the infinite-dimensional nuisance parameter. The asymptotic distributions of the maximum pseudolikelihood and related estimators in an i.i.d. setting show that these estimators do not achieve the computed asymptotic lower bound. Simple guidelines are provided to determine in which instances such estimators are close enough to efficient for practical purposes.     

Structures and syntheses of layered and framework amine-bearing uranyl phosphate and uranyl arsenates

Two hydrated uranyl arsenates and a uranyl phosphate were synthesized by hydrothermal methods in the presence of amine structure-directing agents and their structures determined: (N₂C₆H₁₄)[(UO₂)(AsO₄)]₂(H₂O)₃, DabcoUAs, {NH(C₂H₅)₃}[(UO₂)₂(AsO₄)(AsO₃OH)], TriethUAs, and (N₂C₄H₁₂)(UO₂)[(UO₂)(PO₄)]₄(H₂O)₂, PiperUP. Intensity data were collected at room temperature using MoKα X-radiation and a CCD-based area detector. The crystal structures were refined by full-matrix least-squares techniques on the basis of F² to agreement indices (DabcoUAs, TriethUAs, PiperUP) wR₂=5.6%, 8.3%, 7.2% for all data, and R₁=2.9%, 3.3%, 4.0%, calculated for 1777, 5822, 9119 unique observed reflections (|F_o|?4σ_F), respectively. DabcoUAs is monoclinic, space group C2/m, Z=2, a=18.581(1), b=7.1897(4), c=7.1909(4) Å, β=102.886(1)°, V=936.43(9) Å³, D_calc=3.50 g/cm³. TriethUAs is monoclinic, space group P2₁/n, Z=4, a=9.6359(4), b=18.4678(7), c=10.0708(4) Å, β=92.282(1)°, V=1790.7(1) Å³, D_calc=3.41 g/cm³. PiperUP is monoclinic, space group Pn, Z=2, a=9.3278(4), b=15.5529(7), c=9.6474(5) Å, β=93.266(1)°, V=1397.3(1) Å³, D_calc=4.41 g/cm³. The structure of DabcoUAs contains the autunite-type sheet formed by the sharing of vertices between uranyl square bipyramids and arsenate tetrahedra. The triethylenediammonium cations are located in the interlayer along with two H₂O groups and are disordered. Both TriethUAs and PiperUP contain sheets formed of uranyl pentagonal bipyramids and tetrahedra (arsenate and phosphate, respectively) with the uranophane sheet-anion topology. In TriethUAs, triethlyammonium cations are located in the interlayer. In PiperUP, the sheets are connected by a uranyl pentagonal bipyramid that shares corners with phosphate tetrahedra of adjacent sheets, resulting in a framework with piperazinium cations and H₂O groups in the cavities of the structure.     

Coherent quantum transport in normal-metal/d-wave superconductor/normal-metal double tunnel junctions

Taking into account the effects of quantum interference and interface scattering, combining the electron current with hole current contribution to tunnel current,we study the coherent quantum transport in normal-metal/d-wave superconductor/normal-metal (NM/d-wave SC/NM) double tunnel junctions by using extended Blonder-Tinkham-Klapwijk (BTK) approach. It is shown that all quasiparticle transport coefficients and conductance spectrum exhibit oscillating behavior with the energy, in which periodic vanishing of Andreev reflection (AR) above superconducting gap is found.In tunnel limit for the interface scattering strength taken very large, there are a series of bound states of quasiparticles formed in SC.     

双（十二烷基亚磺酰）乙烷溶剂萃取钯及其机理的研究

本文研究用双（十二烷基亚磺酰）乙烷萃取钯的性能，在ＫＩ存在下从７ｍｏｌ／Ｌ盐酸介质中用含有ＢＤＳＥ的氯仿能定量萃取钯，有机的钯可被硫脲或氨溶液反萃继之用ＴＭＫ－ＴｒｉｔｏｎＸ－１００光度法测定，研究了萃取的最佳条件及干扰情况，斜率法测得萃合物组成为Ｐｄ：Ｉ：ＢＤＳＥ＝１：２：１，红外光谱证实萃合物中ＢＤＳＥ的二个亚砜以硫原子与钯配位，萃合物为异位体络合物，提出了选择性萃取分离钯的新方法。     

Bounding multi-stage stochastic programs from above

The purpose of this paper is to present general approaches for bounding some multi-stage stochastic programs from above. The results are based on restricting the solution set, such that the remaining multi-stage stochastic program is easy to solve. An example where the methods can be applied is presented.Supported in part by NATO Collaborative Research Grant No. 0785/87.     

若干有关欧阳不等式的非线性积分不等式和离散不等式

获得几个非线性的积分不等式及离散不等式．它们和近期Ｐａｃｈｐａｔｅ［１］中欧阳亮不等式［２］的推广有关．作为特殊情形还导出了一些具有幂非线性的新不等式．为说明结果的有用性，讨论了某个非线性差分方程解的有界性．     

苯对N,N-二甲基甲酰胺化合物1H NMR的影响研究

本文研究了N,N-二甲基甲酰胺(DMF)在四氯化碳和苯混合溶剂中的¹H NMR。观察到N,N-二甲基甲酰胺(DMF)分子中两个甲基和混合溶剂中苯的共振吸收峰的化学位移随苯的摩尔分数增加而逐渐移向高场,而且两个甲基共振吸收峰向高场移动的程度不同,α甲基较β甲基为甚。DMF分子中两个甲基和混合溶剂中苯的化学位移可以用线性方程表示(δ=A+Bx),这里x是混合溶剂中苯的摩尔分数。相关系数R接近于-1。     

On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

电荷量子比特与量子化光场之间的纠缠

研究了初态为混合态的电荷量子比特与量子化光场之间的纠缠.通过求解系统的concurrence下限, 研究初态的混合度λ和失谐量Δ对系统纠缠随时间演化的影响. 在弱场中, 电荷量子比特初始是激发态的系统, 其纠缠度远远大于电荷量子比特初始是基态的系统, 并且Δ对系统的纠缠有明显的抑制作用. 在强场中, 电荷量子比特初始分别为激发态和基态时系统的纠缠演化接近一致, 初态混合度最高时系统的纠缠度最小, 并且Δ对系统纠缠的影响变弱. 关键词： 约瑟夫森结 纠缠 混合态 concurrence下限     

Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]