A robin-neumann problem in bounded domains with splitting boundary

We consider a mixed boundary-value problem for the homogeneous Laplace equation in a bounded domain which boundary splits up into two disjoint smooth components. On the one boundary component we pose a homogeneous Robin condition and an inhomogeneous Neumann condition on the other. We give a weak formulation, interpret this problem as a generalized spectral (eigenvalue) problem in the sense of F.Stummel (cf.[12]) and investigate existence, uniqueness and regularity of weak solutions. This problem is a cut-off version of a basic problem in water-wave theory (cf.Ramm [8], pp.394-395, Simon/Ursell [10] Stoker [11])     

“素养为本”的化学课堂教学设计研究的特征与启示*——基于CNKI 253篇文献的知识图谱研究

利用CiteSpace可视化文献计量分析软件,对2016年以来,我国化学教育教学领域最具影响力的3本学术期刊《化学教育》《化学教学》和《中学化学教学参考》中“素养为本”的化学课堂教学设计相关文献进行统计分析,探析其研究热点和发展趋势,以期为后续“素养为本”的化学课堂教学设计提供有益的参考。     

从知识考古学视角看课堂中的“化学平衡”

从知识考古学的视角,分析当前“课堂中的化学平衡”的历史根源。作为简化的学科知识,“教材中的化学平衡”不仅划定了知识的边界,而且内隐了知识的结构;作为演进的理解表现,“高考中的化学平衡”逐步形成了稳定的考查角度和方式。作为实然的教学内容,“课堂中的化学平衡”是多元主体社会协商形成的“共识”,具有区域性特征,包含特定的话语,是一种高度依赖于学校情境的工具化、条件化了的知识。     

基于学科理解的“醛的结构与性质探究”教学设计与实施

学科理解是教师教学的坚实基础,教学设计环节首先进行学科理解研究,通过阐释“如何基于极性多重键认识羰基化合物的结构与性质？”本原性问题,对主题学科大概念“有机物构性关系”进行本原性、结构化地理解。从教学目标、教学思路、教学实施过程阐述“醛的结构与性质探究”一课的教学。课后阶段进行学生访谈及分析、专家评价和教师反思总结。系统地呈现基于学科理解的素养为本的课堂教学研究。     

Paranormal and ( p, k )-quasihyponormal operators: Spectral continuity

Continuity of the set theoretic functions spectrum, Weyl spectrum, Browder spectrum and essential surjectivity spectrum on the classes consisting of (p, k)-quasihyponormal,M-hyponormal, totally *-paranormal and paranormal (Hilbert space) operators is proved.     

Generalized inverses in<Emphasis Type="Italic">C</Emphasis><Superscript>*</Superscript>-algebras, 2

Sea é un elemento di unaC ^*-algebra tale chepa=a per qualche proiezionep, alloraa é una unitá inversa generalizzata, chiamata inversa di Moore-Penrose, e si denotata cona ⁺. Per leC ^*-algebras, si ottiene altrest un risultato sulla minimizzazione di ∥axb−c∥.      

Polaroid operators,SVEP and perturbed Browder,Weyl theorems

A Banach space operatorT ɛB(X) is polaroid,T ɛP, if the isolated points of the spectrum ofT are poles of the resolvent ofT. LetPS denote the class of operators inP which have have SVEP, the single-valued extension property. It is proved that ifT is polynomiallyPS andA ɛB(X) is an algebraic operator which commutes withT, thenf(T+A) satisfies Weyl’s theorem andf(T ^*+A ^*) satisfiesa-Weyl’s theorem for everyf which is holomorphic on a neighbourhood of σ(T+A).     

Variable selection in model-based discriminant analysis

A general methodology for selecting predictors for Gaussian generative classification models is presented. The problem is regarded as a model selection problem. Three different roles for each possible predictor are considered: a variable can be a relevant classification predictor or not, and the irrelevant classification variables can be linearly dependent on a part of the relevant predictors or independent variables. This variable selection model was inspired by a previous work on variable selection in model-based clustering. A BIC-like model selection criterion is proposed. It is optimized through two embedded forward stepwise variable selection algorithms for classification and linear regression. The model identifiability and the consistency of the variable selection criterion are proved. Numerical experiments on simulated and real data sets illustrate the interest of this variable selection methodology. In particular, it is shown that this well ground variable selection model can be of great interest to improve the classification performance of the quadratic discriminant analysis in a high dimension context.     

On a model selection problem from high-dimensional sample covariance matrices

Modern random matrix theory indicates that when the population size p is not negligible with respect to the sample size n, the sample covariance matrices demonstrate significant deviations from the population covariance matrices. In order to recover the characteristics of the population covariance matrices from the observed sample covariance matrices, several recent solutions are proposed when the order of the underlying population spectral distribution is known. In this paper, we deal with the underlying order selection problem and propose a solution based on the cross-validation principle. We prove the consistency of the proposed procedure.     

On signature-based expressions of system reliability

The concept of signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. This concept proved to be useful in the analysis of theoretical behaviors of systems. In particular, it provides an interesting signature-based representation of the system reliability in terms of reliabilities of k-out-of-n systems. In the non-i.i.d. case, we show that, at any time, this representation still holds true for every coherent system if and only if the component states are exchangeable. We also discuss conditions for obtaining an alternative representation of the system reliability in which the signature is replaced by its non-i.i.d. extension. Finally, we discuss conditions for the system reliability to have both representations.