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Acta Mathematica Scientia 2006年第4期26卷 720-728页

作者：刘永平杨连红 School of Mathematical Sciences beijing normal university Beijing 100875China Department of Applied Mathematics Communication university of China Beijing 100024China

For two subsets W and V of a Banach space X, let Kn（W, V, X） denote the relative Kolmogorov n-width of W relative to V defined by Kn（W,V,X）：=inf sup inf/Ln f∈W g∈V∩Ln‖f-g‖x, where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2（△^τ） denote the class of 2π-periodic functions f with d-variables satisfying ∫[-π, π]^d｜△^τf（x）｜^2dx≤1, while △^τ is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2（△^τ） relative to W2（△^τ） in Lq（[-π, π]^d）（1≤ q ≤ ∞）, and obtain its weak asymptotic result.

关键词： Multivariate function classes width relative width

从生态扶贫生态脱贫走向生态振兴:历程、挑战与路径——基于山西省吕梁山片区生态建设实践的调研

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全球化 2024年第4期 22-29,133,134页

作者：北京师范大学课题组刘学敏李强不详北京师范大学地理科学学部

本文围绕山西省吕梁山片区脱贫攻坚期的“购买式造林”生态建设实践,总结了其发展历程、成效和创新性。认为“购买式造林”通过制度、组织形式、利益联结机制诸方面的创新,成功实现了在一个战场同时打赢脱贫攻坚和生态建设两场攻坚战的... 详细信息

本文围绕山西省吕梁山片区脱贫攻坚期的“购买式造林”生态建设实践,总结了其发展历程、成效和创新性。认为“购买式造林”通过制度、组织形式、利益联结机制诸方面的创新,成功实现了在一个战场同时打赢脱贫攻坚和生态建设两场攻坚战的目标,是我国在脱贫攻坚期生态扶贫生态脱贫的一项创举。进入巩固脱贫攻坚成果与乡村振兴有效衔接时期,在客观因素和主观因素都发生变化的新形势下,“购买式造林”生态建设面临诸多问题和挑战。为此,首先应当推进合作社转型发展和制度建设,完善农户持续增收机制,引导社会资本进入生态振兴领域,推动脱贫地区生态振兴;其次是探索生态资源资产化制度,促进脱贫地区生态产品价值实现;最后是大力发展生态产业,以生态与产业融合助力乡村振兴,要把生态建设与经济发展、农户增收融合在一起,实现生态建设产业化、产业发展生态化,大力发展生态产业,构建生态与产业融合发展的产业体系。

关键词：生态振兴生态脱贫生态扶贫生态建设实践

维普期刊数据库博看期刊

Functional central limit theorem for super α-stable processes

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Science China Mathematics 2004年第6期47卷 874-881页

作者： HONG WenmingDepartment of Mathematics, beijing normal university, beijing 100875, China Department of Mathematics Beijing Normal University Beijing China

A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.

关键词：超级稳定的过程职业时间中央限制定理进化方程

On asymptotics of t-type regression estimation in multiple linear model

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Science China Mathematics 2004年第4期47卷 628-639页

作者： GUI HengjianDepartment of Mathematics, beijing normal university, beijing 100875, China Department of Mathematics Beijing Normal University Beijing China

We consider a robust estimator (t-type regression estimator) of multiple linear regression model by maximizing marginal likelihood of a scaled t-type error *** marginal likelihood can also be applied to the de-correlated response when the withinsubject correlation can be consistently estimated from an initial estimate of the model based on the independent working assumption. This paper shows that such a t-type estimator is consistent.

关键词： t-type regression estimator, M-estimator, one-step estimate, consistency, asymptotic normality.

THE HAUSDORFF MEASURE FOR THE SAMPLE PATH OF THE WESTWATER PROCESS

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Chinese Annals of Mathematics,Series B 1996年第3期17卷 375-388页

作者： ZHOU XIANYIN(Depatment of Mathematics, beijing normal university beijing 100875, China) Department of Mathematics Beijing Normal University Beijing 100875 China

It is proved that φ(s) = s2 log |logs| is the correct function to give the Hausdorff measureof a sample path of the Westwater process.

关键词： HAUSDORFF测量 Wiener过程 Westwater过程逗留时间

Quasi-critical ring of a primitive ring with nonzero socle

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Chinese Science Bulletin 1997年第3期42卷 189-192页

作者： JIANG ZimeiDepartment of Mathematics, beijing normal university, beijing 100875, China Department of Mathematics Beijing Normal University Beijing China

IN ref. [1] Jacobson proved the structure theorem for primitive rings with nonzero socles that R is a primitive ring withsocle S≠{0} if and only if there is a pair of dual vector spaces (M,M’) over a division ring Δ such that S=F(M, M’)(?) R(?)(?)(M, M’), where (?)(M, M’)-{ω∈Ω|ωM’(?)M’, Ω is the complete ring of linear transformations of M over Δ}, F(M, M’) is the set of all linear transformations of (?)(M, M’) of finite rank. After that, some people reproved this theorem by using different methods such as those in refs. [2, 3]. In

关键词： primitive ring socle conjugate space total subspace of conjugate space.

SINGLE BIRTH PROCESSES

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Chinese Annals of Mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(Department of Mathematics,beijing normal university,beijing 100875,China) Department of Mathematics Beijing Normal University Beijing 100875 China

***,theQ-matrixofasinglebirthprocessisasfollows:Throughoutthenote,weconsideronlytotallystableandconservativeQ-matrix:forallDuetothefactthattheboundaryofsuchQ-matrixisatmostsingleexit,thesinglebirthp... 详细信息

关键词：马尔可夫链单纯生过程唯一准则时间离散

Reaction-diffusion processes

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Chinese Science Bulletin 1998年第17期43卷 1409-1420页

作者： CHEN Mufa beijing normal university beijing 100875, China beijing normal university Beijing China

The main progress made in the past dozen years or more in the study of reaction-diffusion (abbrev. RD) processes is surveyed. The processes are motivated from some typical models in the modern non-equilibrium statistical physics and consist of an important class of interacting particle systems which is currently an active research field in probability and mathematical physics. The models are concrete but as a part of the infinite-dimensional mathematics, the topic is quite hard. It is explained how new problems arise, and how some new ideas and new mathematical tools are introduced. Surprisingly, the mathematical tools produced from the study on the simple models then turn to have a lot of powerful applications not only in probability theory but also in other branches of mathematics. Nevertheless, the story is still far from finished, and some important open problems are proposed for further study.

关键词： Reaction-diffusion process ergodicity phase transitions coupling.

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Saturated models

Chinese Science Bulletin 1998年第7期43卷 562-564页

作者： CHEN Guolong Department of Mathematics, beijing normal university, beijing 100875, China Department of Mathematics Beijing Normal University Beijing China

An equivalent description of saturated models is given, and some properties of countable saturated models, almost saturated models and full models are discussed. New proofs of two important theorems of the related doc... 详细信息

关键词： almost saturated model full model power type.

Recovery of functions via their irregular sampling values

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Chinese Science Bulletin 1998年第4期43卷 268-271页

作者： FANG Gensun Department of Mathematics, beijing normal university, beijing 100875, China Department of Mathematics Lkijing Normal University Beijing China

It is proved that if a function can be completely reconstructed by tempered splines which satisfy the real Kiesz basis condition as the degree of spline goes to infinity, then the function is band limited.

关键词： band limited function cardinal splines irregular sampling.