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LARGE DEVIATIONS FOR STATIONARY Φ-MIXING SEQUENCES IN τ-TOPOLOGY

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Chinese Annals of mathematics,Series B 1996年第2期17卷 149-158页

作者： Hu YIJUN department of mathematics, Wuhan university, Wuhan 430072, china. department of mathematics Wuhan University Wuhan 430072 China

The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.

关键词： Large deviation Empirical measure Stationary sequence Φ-mixing τ-topology

SIMPLE OCKHAM ALGEBRAS

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Chinese Annals of mathematics,Series B 1996年第2期17卷 213-218页

作者： FANG JIE department of mathematics, Zhongshan university, Guangzhou 510271, china. ZHONGSHAN UNIV DEPT MATHGUANGZHOU 510271PEOPLES R CHINA

An algeber L is said to be simple, if its congruence lattice Con L reduces to the 2-elementchain {ω,v}. This paper describes the structure of finite simple Ockham algebras.

关键词： Ockham algebra Simple algebra Congruence lattic 2-element chain

ON THE APPROXIMATELY SIMILARITY OF OPERATORS

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Chinese Annals of mathematics,Series B 1998年第4期19卷 465-472页

作者： WEI GUOQIANG (department of mathematics, East china.Normal university, Shanghai 200062, china.) E china.Normal Univ Dept Math Shanghai 200062 Peoples R China

The author shows that a rank-preserving *-isorporphism between separable C*-algebras with unity is approximately equivalent to the identity representation. Some applications are made for approximately similarity of n-... 详细信息

关键词： C*-algebra Rank-preserving *-isomorphism Approximately equevalent,Approximately similar n-tuples of operators

An algebraic invariant for Jordan automorphisms on B(H):The set of idempotents

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Science china.mathematics 2005年第12期48卷 1585-1596页

作者： CUI Jianlian & HOU Jinchuan department of Mathematical Science, Tsinghua university, Beijing 100084, china.department of Applied mathematics, taiyuan university of Technology, taiyuan 030024, china.department of mathematics, Shanxi Teachers university, Linfen 041004, china department of Mathematical Science Tsinghua University Beijing 100084 China department of Applied mathematics Taiyuan University of Technology Taiyuan 030024 China department of mathematics Shanxi Teachers University Linfen 041004 China

Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempo-tents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ {-1,1,2,3,1/2,1/3} and A, B ∈ B(H), A - λB ∈ I(H) (?) Φ(A) - λΦ(B) ∈ I(H), then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT-1 for all A ∈ B(H), or Φ(A) = TA*T-1 for all A ∈ B(H); if, in addition, A-iB ∈ I(H) (?) Φ(A) -ιΦ(B) ∈ I(H), here ι is the imaginary unit, then Φ is either an automorphism or an anti-automorphism.

关键词： Hilbert space operators,Jordan automorphisms,idempotents.

THE STABILITY OF THE PERIODIC SOLUTIONS OF SECOND ORDER HAMILTONIAN SYSTEMS

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Chinese Annals of mathematics,Series B 2000年第2期21卷 225-232页

作者： LIU CHUNGEN(department of mathematics, Nankai university, Tianjin 300071, china.) department of mathematics Nankai University Tianjin 300071 China

This paper studies the stability of the periodic solutions of the second order Hamiltonian systems with even superquadratic or subquadratic potentials. The author proves that in the subquadratic case, there exist infinite geometrically distinct elliptic periodic solutions, and in the superquadratic case, there exist infinite geometrically distinct periodic solutions with at most one instability direction if they are half period non-degenerate, otherwise they are elliptic.

关键词： Krein type Stability Periodic elliptic solution Hamitonian systems

DIMENSIONS OF SELF-AFFINE SETS WITH OVERLAPS

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Chinese Annals of mathematics,Series B 2003年第3期24卷 275-284页

作者： HUA Su department of mathematics, Tsinghua university, Beijing 100084, china. Tsing Hua Univ Dept Math Beijing 100084 Peoples R China

The authora develop an algorithm to show that a class of self-affine sets with overlaps can be viewed as sofic affine-invariant sets without overlaps,thus by using the results of [11] and [10],the hausdorff and minkow... 详细信息

关键词： self-affine set overlap hausdorff dimension minkowski dimension

CLASSICAL SOLUTION OF QUASI-STATIONARY STEFAN PROBLEM

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Chinese Annals of mathematics,Series B 1996年第2期17卷 175-186页

作者： YI FAHUAI department of mathematics, Suzhou university, Suzhou 215006, china. SUZHOU UNIV DEPT MATHSUZHOU 215006PEOPLES R CHINA

This paper considers the quasi-stationary Stefan problem:△u(x,t)=0 in space-time domain,u=0 and Vv +(?)u/(?)u=0 on the free boundary.Under the natural conditions the existence of classical solution locally in time is proved bymaking use of the property of Frechet derivative operator and fixed point theorem. For thesake of simplicity only the one-phase problem is dealt with. In fact two-phase problem can bedealt with in a similar way with more complicated calculation.

关键词： Classical solution Quasi-stationary Stefan problem Frechet derivative

LIMIT CYCLES AND BIFURCATION CURVES FOR THE QUADRATIC DIFFERENTIAL SYSTEM (III)_(m=0) HAVING THREE ANTI-SADDLES (I)

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Chinese Annals of mathematics,Series B 1996年第2期17卷 167-174页

作者： YE YANQIAN department of mathematics, Nanjing university, Nanjing 210008, china. 南京大学数学系江苏南京

For the quadratic system: x=-y+δx + lx2 + ny2, y=x(1+ax-y) under conditions -10 the author draws in the (a, ()) parameter plane the global bifurcationdiagram of trajectories around O(0,0). Notice that when na2+l < 0 ... 详细信息

关键词： Quadrtic systen Anti-saddle Bifurcation curve Limit cycle

THE GOLDBACH-VINOGRDOV THEOREM WITH THREE PRIMES IN A THIN SUBSET

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Chinese Annals of mathematics,Series B 1998年第4期19卷 479-488页

作者： LIU JIANYA (department of mathematics, Shandong university, Jinan 250100, china.) 山东大学数学系山东济南

It is proved constructively that there exists a thin subset S of primes, satisfying for some absolute constant c＞0, such that every sufficiently large odd integer N can beLet r be prime, and hi positive integers with (bj, r) = 1,j = 1, 2, 3. It is also proved that, for almost all prime moduli r＜ log- N, every sufficiently large odd integer N = b1 + b2 +ba(modr) can be represented as where c ＞ 0 is an absolute constant.

关键词： Goldbach-Vinogradov theorem Exponential sum Primes Arithmetic progression Mean-value theorem