LF拓扑空间的商空间的同胚

利用满映射f:X→Y诱导的L值Zadeh型函数f:L^X→L^Y和LF拓扑空间（L^X,δ）构造商空间（L^Y,μ）；又由f建立X上等价关系－，得出自然投影P：X→X／－，再得用P诱导的L值Zadeh型函数P：L^X→L^X/-和（L^X,δ）构造商空间（L^X/-,μ^*），证明了两商空间同胚。     

On Optimality of Bayesian Wavelet Estimators

Abstract.  We investigate the asymptotic optimality of several Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of a mass function at zero and a Gaussian density. We show that in terms of the mean squared error, for the properly chosen hyperparameters of the prior, all the three resulting Bayesian wavelet estimators achieve optimal minimax rates within any prescribed Besov space     for p  ≥ 2. For 1 ≤  p  < 2, the Bayes Factor is still optimal for (2 s +2)/(2 s +1) ≤  p  < 2 and always outperforms the posterior mean and the posterior median that can achieve only the best possible rates for linear estimators in this case.     

Orlicz教授和他创造性的工作

本文介绍了著名数学家和教育家Orlicz教授和他创造性的工作,以及他对中国数学研究工作的重大影响     

关于参数化测度（Ⅱ）

引进一类拓扑向量空间，用以描述测度的偏导。使用的工具是所谓的参数化鞅。建立了若干参数化鞅的收敛定理。     

Multilevel maximum likelihood estimation with application to covariance matrices

The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of covariance models to the sample, which is important in data assimilation. The hierarchical maximum likelihood approach is applied to the spectral diagonal covariance model with different parameterizations of eigenvalue decay, and to the sparse inverse covariance model with specified parameter values on different sets of nonzero entries. It is shown computationally that using smaller sets of parameters can decrease the sampling noise in high dimension substantially.     

Asymptotic theory for maximum likelihood estimates in reduced-rank multivariate generalized linear models

Reduced-rank regression is a dimensionality reduction method with many applications. The asymptotic theory for reduced rank estimators of parameter matrices in multivariate linear models has been studied extensively. In contrast, few theoretical results are available for reduced-rank multivariate generalized linear models. We develop M-estimation theory for concave criterion functions that are maximized over parameter spaces that are neither convex nor closed. These results are used to derive the consistency and asymptotic distribution of maximum likelihood estimators in reduced-rank multivariate generalized linear models, when the response and predictor vectors have a joint distribution. We illustrate our results in a real data classification problem with binary covariates.     

Spaces of Muslim Identity in Inverness,Scotland

Each generation of immigrants has its own challenges; for example, how to maintain already constructed identities among first generation immigrants and how to construct identities of the second generation of immigrants. Numerous literature suggests that the previous studies on these topics have been conducted within larger cities such as London, Glasgow or Edinburgh. This article examines how Muslim immigrants in a small city maintain and modify some aspects of their religious and cultural identities. The data consist of 30 interviews conducted with first and second generation of Muslim immigrants in Scotland, analysis of which suggests the size of the city does not appear to affect daily Muslim practices nor their ability to maintain Muslim identity. Rather, access to shared spaces, such as Inverness Masjid and the local halal meat shop, become critical to how Muslim's maintain and modify their identity in a new place.     

“It’s like this Myth of the Supernegro”: resisting narratives of damage and struggle in the neoliberal educational policy context

As pathologizing, racialized, and patriarchal rhetoric undergirds neoliberal education reform, deficit narratives characterize the education of Black youth. Such narratives present deep challenges for educational policy and community-based educational spaces. This article explores the ways in which community-based educators resist narratives of damage and struggle in their own personal and professional narratives in order to prevent the cycle of deficit-oriented discourse that follow Black youth through myriad educational spaces. By situating the narratives of community-based educators within a broader policy context shaped by race, class, and gender, this article illustrates the challenges that arise for community-based educators that seek to frame Black youth beyond deficit narratives and who avoid framing themselves as heroes and saviors of Black youth.