Approximately spectrum-preserving maps

Let X and Y be superreflexive complex Banach spaces and let B(X) and B(Y) be the Banach algebras of all bounded linear operators on X and Y, respectively. If a bijective linear map Φ:B(X)→B(Y) almost preserves the spectra, then it is almost multiplicative or anti-multiplicative. Furthermore, in the case where X=Y is a separable complex Hilbert space, such a map is a small perturbation of an automorphism or an anti-automorphism.     

Strong-stability-preserving 3-stage Hermite-Birkhoff time-discretization methods

Strong-stability-preserving (SSP) time-discretization methods have a nonlinear stability property that makes them particularly suitable for the integration of hyperbolic conservation laws. A collection of SSP explicit 3-stage Hermite-Birkhoff methods of orders 3 to 7 with nonnegative coefficients are constructed as k-step analogues of third-order Runge-Kutta methods, incorporating a function evaluation at two off-step points. Generally, these new methods have larger effective CFL coefficients than the hybrid methods of Huang with the same step number k. They have larger maximum scaled step sizes than hybrid methods on Burgers' equations.     

5G环境下移动用户位置隐私保护方法研究

为解决5G环境下高频次位置服务（location based service,LBS）带来的位置隐私暴露问题,分析了5G环境下移动用户位置隐私泄露风险,梳理了已有隐私保护技术,并对3类常见方法进行分析对比,针对5G环境下位置隐私保护面临的新挑战,提出了一种适合5G环境的隐私保护方法,即融合定位隐私保护方法.该方法通过降维初步处理、融合隐私算法及传输加密方法,在不提升复杂度的情况下,处理了从定位维度选择、定位中间过程乃至传输全链路的风险.仿真分析结果表明,该方法能在混合场景下实现高效的隐私保护,适用于5G超密集高频次位置服务.      

Meyer-KnigandZeller算子的保形问题

讨论了 Meyer-Knig and Zeller算子的保形逼近问题 ,我们用基于算子特殊结构的分析方法得到了该算子的保单调性 .保凸性以及保形逆定理等保形性质 .     

数字图书馆与隐私权保护

传统图书馆正在向数字化、网络化的发展,隐私权的保护问题日益突出。隐私权保护关系到 数字图书馆的长远发展。主要是加快立法工作,做好行业自律,加强网络监管。     

保单调的有理三次样条插值

构造了一种C^1连续的保单调的有理三次插值函数。由于函数表达式中含有调节参数，使得插值曲线更具灵活性。     

保参数方向的形状可调过渡曲线与曲面

针对保参数方向构造过渡曲线曲面方法的不足, 构造了任意参数曲线曲面间既保持参数方向又具有形状可调性的C¹与C²连续过渡曲线曲面。首先,基于2类带1个自由参数的调配函数,分别构造满足C¹与C²连续的过渡曲线,并讨论基于能量优化模型的最佳过渡曲线构造问题;然后,将所提出的方法推广到过渡曲面的构造。 实例结果表明,2被过渡曲线曲面为任意参数曲线曲面时,利用该方法构造的过渡曲线曲面不仅与2被过渡曲线曲面的参数方向保持一致,而且可利用所带的自由参数对其形状进行调整。通过能量优化模型确定自由参数的取值,可获得尽可能光顺的过渡曲线曲面。 所提方法弥补了保参数方向构造过渡曲线曲面方法的不足,是一种实用的过渡曲线曲面构造方法。     

Differentially Private Precision Matrix Estimation

In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample covariance matrix. Then we develop a differentially private graphical lasso estimator by using the alternating direction method of multipliers (ADMM) algorithm. Furthermore, we prove theoretical results showing that the differentially private ridge estimator for the precision matrix is consistent under fixed-dimension asymptotic, and establish a convergence rate of differentially private graphical lasso estimator in the Frobenius norm as both data dimension p and sample size n are allowed to grow. The empirical results that show the utility of the proposed methods are also provided.     

The extendible cell method for closest point problems

The extendible cell method is an application of order preserving extendible hashing to multidimensional point files. We derive some of its performance characteristics and show its expected case optimality for closest point problems.     

Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties

Let be a surjective mapping from a uniform algebra on a compact Hausdorff space onto a uniform algebra on a compact Hausdorff space . Suppose that holds for every . Then we have that is an almost isometric isomorphism, which is a generalization of results of Molnár (2002) and Rao and Roy (2005).