Local principal differential analysis: Graphical methods for functional data with covariates

We focus on principal differential analysis (PDA) of functional data for obtaining a low-dimensional representation of a collection of curves. PDA assumes there exists a linear differential operator that results in the zero-function when it is applied to each of the data curves, or equivalently, that the curves belong to a low-dimensional subspace of a normed linear space. PDA sets out to estimate this linear differential operator from the data and proceeds from there. Our contribution is to explain how subject covariates can be incorporated into a PDA analysis for graphical exploration of patterns in the data.     

Revisiting the role of pedagogic contexts in social class analysis: a Bernsteinian approach

This paper revisits the development of Basil Bernstein’s theoretical armories and reinvigorates its relevance to social class analysis in education, while identifying some of the challenges and promises in doing so. The main arguments are grounded in an empirical analysis of the recent Liberal Studies reform in Hong Kong’s senior secondary education. An extended discussion of using a Bernsteinian approach to pedagogy-specific class explanations is developed: (a) transition of code modalities between stages of education; (b) differentiated pedagogic identities in the middle class; (c) pedagogic grammars of specialized habituses; and (d) possibilities for an interruption in the process of social reproduction. It is concluded that continuing to build on Bernstein’s legacy will allow us to achieve a more nuanced understanding of the ways that class works through different pedagogic contexts in order for the conception of an interruption of class reproduction to be useful in guiding transformative practices in it.     

乡村振兴背景下陕西产业扶贫的路径选择与模式分析

产业是乡村最为重要的经济基础,产业兴旺是乡村振兴的第一要务,通过产业兴旺实现扶贫开发,是精准扶贫的重要组成部分和实现路径。陕西在产业扶贫实践过程中,涌现出了省供销合作社主导的“政府（扶贫办）+供销社（供销企业集团）+农户（贫困户）+企业（合作社）+金融（保险）”模式、以商南、延长为代表的“先借后还”无本脱贫模式、以大荔、洛南为代表的扶贫资金量化折股模式、千阳县 “项目超市”菜单式扶贫模式、白水县的 “果园托管”模式、榆阳赵家峁村的“三变”等模式。本文通过对典型模式的分析,提出在推进产业精准扶贫过程中要尊重扶贫对象的主体地位,适度兼顾扶贫政策的公平性,充分发挥财政扶贫资金的引导作用,积极调动新型经营主体参与扶贫开发的积极性,并优化新型经营主体与贫困群众的利益联结机制,最大限度地发挥产业扶贫的辐射带动效应。     

关于一个线性算子群的问题

在一个线性算子群应用于二阶线性发展方程求解的思路基础上［１］，归纳其中的生成算子为ｎ阶矩阵形式，进一步提出了该生成算子的线性算子群，在巴拿赫空间中证明了这个线性算子群的基本特征，且是高阶线性发展方程求解理论的基础部分。当然，低阶线性发展方程的解为其特殊情况     

电信运营商业务投资的优化模型

提出了电信运营商业务投资的数学优化模型,再以X省运营商在业务投资方面的额度限制为例描述了四个约束条件,并给出求解方法。这种优化模型对电信运营商在实际投资中有较大的参考意义。     

Posterior convergence rates for Dirichlet mixtures of beta densities

We consider Bayesian density estimation for compactly supported densities using Bernstein mixtures of beta-densities equipped with a Dirichlet prior on the distribution function. We derive the rate of convergence for α$\alpha$-smooth densities for 0<α?2$0<\alpha ?2$ and show that a faster rate of convergence can be obtained by using fewer terms in the mixtures than proposed before. The Bayesian procedure adapts to the unknown value of α$\alpha$. The modified Bayesian procedure is rate-optimal if α$\alpha$ is at most one. This result can be extended to two dimensions.     

Projection de hájek et polynômes de bernstein

Under the hypothesis of white noise, the authors derive the explicit form of the asymptotic representation of linear rank statistics resulting from Hájek's (1968) celebrated projection lemma for linear rank statistics in the so‐called approximate score case. This representation based on Bernstein polynomials is better, in the quadratic mean sense, than the traditional one due to Hájek (1961, 1962). The polynomial representation allows for a new derivation of classical asymptotic results (asymptotic normality, Berry‐Essten bounds). Moreover, a simulation study shows that the quality of the polynomial approximation to the exact finite‐sample distributions of rank statistics is sizeably better than that resulting from the traditional approach.     

SU(2)和SU(1,1)在相空间中指数算符的正规乘积和反正规乘积的简单实现

通过指数算符的分解,给出了SU(2)和SU(1,1)在相空间中指数算符的正规和反正规乘积形式.     

关于减算子的正特征值问题

证明了在一定条件下,非线性算子方程 Ax=λx 有唯一确定的正解 x_λ,并且 x_λ关于λ是严格单减的、连续的,且当λ→ ∞时,‖x_λ‖→0;当λ→0~ 时,‖x_λ‖→ ∞。最后,利用该结论来研究一类非线性积分方程的正解。     

保反零积线性映射

给出了Ｂ（Ｘ）到Ｂ（Ｙ）上保反零积线性映射的具体形式