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.     

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.     

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．     

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]     

The logarithmic norm. History and modern theory

In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities that distinguished between forward and reverse time integration. Originally defined for matrices, the logarithmic norm can be extended to bounded linear operators, but the extensions to nonlinear maps and unbounded operators have required a functional analytic redefinition of the concept.This compact survey is intended as an elementary, but broad and largely self-contained, introduction to the versatile and powerful modern theory. Its wealth of applications range from the stability theory of IVPs and BVPs, to the solvability of algebraic, nonlinear, operator, and functional equations. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05     

ENSTAR detector forη- mesic studies

We have initiated a search for a new type of nuclear matter, theη-mesic nucleus, using beams from the multi-GeV hadron facility, COSY at Juelich, Germany. A large acceptance scintillator detector, ENSTAR has been designed and built at BARC, Mumbai and fully assembled and tested at COSY. A test run for calibration and evaluation has been completed. In this contribution we present the design and technical details of the ENSTAR detector and how it will be used to detect protons and pions (the decay products ofη-mesic bound state). The detector is made of plastic scintillators arranged in three concentric cylindrical layers. The readout of the detectors is by means of optical fibres. The layers are used to generate ΔE –E spectra for particle identification and total energy information of stopped particles. The granularity of the detector allows for position (θ and ?ø determination making the event reconstruction kinematically complete     

Calorimetric approach to tetronic/water interactions

Tetronic^®comprises X-shaped copolymers formed by four poly(propylene oxide) (PPO) andpoly(ethylene oxide) (PEO) block chains bonded to an ethylene diamine centralgroup. Micellization behaviour of three representative Tetronics (T304, T904and T1307) was characterized to gain an insight into the interactions betweenthe copolymer unimers and the state of water in their solutions. The enthalpyof demicellization, recorded at 37°C in an isoperibol microcalorimeter,indicated that the process was in all cases exothermic and the enthalpy rankedin the order T1307≥T904>>T304. Micellization is entropy-driven owing tohydrophobic interactions between the PPO chains.DSC analysisshowed that the crystallization and melting peaks of the free water remainingin T304 and T904 solutions were progressively shifted toward lower temperaturesas the surfactant proportion increased, owing to a colligative effect. Boundwater corresponded to 3 water molecules per EO repeating unit. In the caseof T1307, which has longer PEO chains, a splitting of the melting peak wasobserved, one peak appearing around 0°C due to free water and anotherat –15°C due to interfacial water. As T1307 proportion raised, theenthalpy of the former decreased, whilst the enthalpy of the latter increased.In 40% T1307 solutions, interfacial water overcame the proportion of freewater; there being 1 interfacial and 3 bound water molecules per EO repeatingunit. Gaussian deconvolution of FTIR spectra also enabled to characterizethe evolution of free water as a function of Tetronic proportion. The dependenceof micellization and water interaction behaviour on Tetronics structure shouldbe taken into account to use these copolymers as drug solubilizers and micellarcarriers.