A Practical Protocol for Advantage Distillation and Information Reconciliation

Information-theoretic secret key agreement generally consists of three phases, namely, advantage distillation information reconciliation and privacy amplification. Advantage distillation is needed in the case when two legitimate users, Alice and Bob, start in a situation which is inferior to that of the adversary Eve. The aim for them is to gain advantage over Eve in terms of mutual information between each other. Information reconciliation enables Alice and Bob to arrive at a common string by error correction techniques. Finally they distill a highly secret string from the common string in the privacy amplification phase. For the scenario where Alice and Bob as well as Eve have access to the output of a binary symmetric source by means of (three) binary symmetric channels, there are several advantage distillation and information reconciliation protocols proposed.In this paper, we present a general protocol to implement both advantage distillation and information reconciliation. Simulation results are compared with known protocols. A connection between our protocol and the known protocols is given.     

Functional calculus under the Tadmor-Ritt condition, and free interpolation by polynomials of a given degree

For Banach space operators T satisfying the Tadmor-Ritt condition ||(zI−T)⁻¹||?C|z−1|⁻¹, |z|>1, we prove that the best-possible constant C_T(n) bounding the polynomial calculus for T, ||p(T)||?C_T(n)||p||_∞, deg(p)?n, behaves (in the worst case) as as n→∞. This result is based on a new free (Carleson type) interpolation theorem for polynomials of a given degree.     

对我国期货市场波动性的分阶段实证研究

波动性是经济和金融研究的热点问题。本文首先采用无条件波动度量方法对我国三大期货市场1997年—2004年的波动性进行了估计,发现第一阶段97年—02年期货价格总体呈下跌趋势,三大市场整体波动性不大,较高的波动性都出现在期货价格下跌时期,较低的波动性都出现在期货价格上涨时期;第二阶段03年—04年三大市场波动性显著提高,总体价格呈上升趋势,较高的波动性都出现在期货价格上涨时期,而较低的波动性都出现在期货价格下跌时期;本文进一步采用条件波动模型对我国三大期货市场两个阶段收益率与波动性的相关关系及波动性的杠杆效应进行了研究,结果表明铜期货收益率与波动性显著相关,大豆期货收益率与波动性不显著相关;我国三大期货市场均存在杠杆效应,并且两个阶段波动性的杠杆效应相反,其中铜期货市场的杠杆效应更显著。     

Local means,wavelet bases and wavelet isomorphisms in Besov‐Morrey and Triebel‐Lizorkin‐Morrey spaces

We consider local means with bounded smoothness for Besov‐Morrey and Triebel‐Lizorkin‐Morrey spaces. Based on those we derive characterizations of these spaces in terms of Daubechies, Meyer, Bernstein (spline) and more general r‐regular (father) wavelets, finally in terms of (biorthogonal) wavelets which can serve as molecules and local means, respectively. Hereby both, local means and wavelet decompositions satisfy natural conditions concerning smoothness and cancellation (moment conditions). Moreover, the given representations by wavelets are unique and yield isomorphisms between the considered function spaces and appropriate sequence spaces of wavelet coefficients. These wavelet representations lead to wavelet bases if, and only if, the function spaces coincide with certain classical Besov‐Triebel‐Lizorkin spaces.     

Minimal and maximal unconditional bases with respect to framings

This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if （xi, fi） is a framing of a Banach space X, and （eimin） and （eimax） are the minimal unconditional basis and the maximal unconditional basis with respect to （xi, fi）, respectively, then for any unconditional basis （ei） associated with （xi, fi）, there are A,B 〉 0 such that A｜｜i=1∑∞aieimin｜｜≤｜｜i=1∑∞aiei｜｜≤B｜｜i=1∑∞aieimax｜｜ for all （ai） ∈ c00.
It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds.     

基于条件贝塔信息对横截面收益的解释

以1995年6月-2005年12月期间在我国沪深A股市场上市的全部股票为样本,本文实证发现,FF三因子模型不能对横截面收益作出合理的解释。为了基于现代金融理论的基本观点对横截面收益现象作出更为合理的解释,本文利用贝塔条件变化信息对无条件的FF三因子模型进行改进,实证发现,改进后的条件定价模型对横截面收益的解释力提高了,并且该解释力在2006年1月-2008年5月、1995年6月-2008年5月期间均具有稳健性。由此得出结论认为,在解释横截面收益时,贝塔条件变化的条件定价模型是一个优于无条件FF三因子模型的模型。     

Weakly null sequences in

We construct a weakly null normalized sequence in so that for each , the Haar basis is -equivalent to a block basis of every subsequence of . In particular, the sequence has no unconditionally basic subsequence. This answers a question raised by Bernard Maurey and H. P. Rosenthal in 1977. A similar example is given in an appropriate class of rearrangement invariant function spaces.

     

整函数插值序列的稳定性

本文证明了指数π型整函数Bπ，p，1＜p＜∞中某些实插值序列的稳定性，从而证明了存在一个和p有关的正常数δp，使得当sup|uj－j＜δp，u0＝0时，｛Gj（x）｝j∈Z为Bπ，p，1＜p＜∞的一组无条基，其中并且我们还证得是Bπ，p，1＜p＜∞的一组稳定的无条件基．     

A nonuniform L2 formula of Caputo derivative and its application to a fractional Benjamin–Bona–Mahony-type equation with nonsmooth solutions

To recover the full accuracy of discretized fractional derivatives, nonuniform mesh technique is a natural and simple approach to efficiently resolve the initial singularities that always appear in the solutions of time-fractional linear and nonlinear differential equations. We first construct a nonuniform L2 approximation for the fractional Caputo's derivative of order 1 < α < 2 and present a global consistency analysis under some reasonable regularity assumptions. The temporal nonuniform L2 formula is then utilized to develop a linearized difference scheme for a time-fractional Benjamin–Bona–Mahony-type equation. The unconditional convergence of our scheme on both uniform and nonuniform (graded) time meshes are proven with respect to the discrete H¹-norm. Numerical examples are provided to justify the accuracy.     

立方Schr?dinger方程的半隐格式BDF2-FEM无条件最优误差估计

研究了立方Schrodinger方程的二阶向后差分有限元方法(BDF2-FEM)的无条件最优误差估计.首先,将误差分为时间误差和空间误差两部分.通过引入时间离散方程,得到时间离散方程解的一致有界性,并给出时间误差估计.从而得到该方程在半隐格式下BDF2-FEM无条件最优误差估计.最后,用数值算例验证了理论分析.