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Existence of the solutions and the attractors for the large-scale atmospheric equations

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Science china Earth Sciences 2006年第6期49卷 650-660页

作者： HUANG Haiyang1 & GUO Boling2.1. Department of mathematics, beijing normal university, {2. 100875, china 2. Institute of Applied Physics and Computational mathematics, {2. 100080, china Department of mathematics Beijing Normal University Beijing China Institute of Applied Physics and Computational mathematics Beijing China

In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik’s definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations. The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.

关键词： atmosphere equations, weak solution, trajectory attractor, global attractor, equilibrium.

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, {2. 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 2. (0 2., the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2. and higher dimensions d 2., the limiting process is Brownian motion.

关键词： super α-stable processes occupation time central limit theorem evolution equation

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, {2. 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 {2. 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 measure Wiener process Westwater process Sojourn time

Study on Green Residential Space Design

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IJLAI Transactions on Science and Engineering

IJLAI Transactions on Science and Engineering 2024年第1期2卷 32-37页

作者： Yu Jiang Shenyang normal university No.2.3 Huanghe North Street Shenyang 110034China

With the ever-changing nature,green ecology has become an international trend of ***,the green ecological design of residential space has become the main melody of people’s *** always implement the concept of ecological and environmental protection in the design process,attach importance to the ecological effect of residential space,carry out reasonable budget and use of environmentally friendly decorative materials,reduce the waste of materials,save money and save resources at the same time,and protect the *** the same time,people began to put their hopes on the residential space design,which made the green residential space design began to *** the bold exploration and practice of designers,the design of green residential space will be endowed with more distinctive characteristics and unique *** from the concept of green design,this paper explores the method of green space design through typical analysis.

关键词： Green Residential space Haze

An equality on Hochschild homology groups

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Chinese Science Bulletin 1997年第8期42卷 624-627页

作者： ZHANG Pu and LIU Shaoxue1. Department of mathematics, university of Science and Technology of{2., Hefei 2.002.,{2. 2. Department of mathematics, beijing normal university, beijing 100875,{2. Department of mathematics University of Science and Technology of China Hefei China Department of mathematics Beijing Normal University Beijing China

LET A be finite-dimensional algebra over field k,and Ae the enveloping algebra of A,i.e.Ae=A kAop,where Aop is the opposite algebra of *** A-bimodule has a natural left Ae-module structure as follows:

关键词： finite-dimensional algebra Hochschild homology groups dimensions.

Boundedness of solutions and existence of invariant tori for generalized pendulum type equation

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Chinese Science Bulletin 1997年第20期42卷 1673-1675页

作者： HUANG Hai and YUAN Rong1. Institute of mathematics, Chinese Academy of Sciences, beijing 100080,{2. 2. Department of mathematics, beijing normal university, beijing 100875,{2. Institute of mathematics Chinese Academy of Sciences Beijing China Department of mathematics Beijing Normal University Beijing China

MOTIVATED by various significant applications to non-Newtonian fluid theory, diffusion offlows in porous media, nonlinear elasticity, and theory of capillary surfaces, several authors(see refs.[1,2. and references cited therein ) have recently studied the existence of periodicsolutions and other properties for the following differential equation:

关键词： boundeduess of solutions invariant tori quasiperlodic solutions Moser’s small twist theorem.

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 {2. university,beijing 100875,china) Department of mathematics Beijing Normal University Beijing 100875 China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2.(this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

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, {2. 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 ... 详细信息

IN ref. [1] Jacobson proved the structure theorem for primitive rings with nonzero socles that R is a primitive ring withsocle S≠2. 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.