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Multi-parameter infinite-dimensional(r,δ)-OU process

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Chinese Science Bulletin 1999年第5期44卷 418-423页

作者： WANG ZikunInstitute of mathematics, Shantou university, Shantou 515063, China {2., beijing normal university, beijing 100875, China Institute of mathematics Shantou University Shantou China department of mathematics Beijing Normal University Beijing China

The definition of n-parameter infinite-dimensional (r, δ) -Ornstein-Uhlenbeck process {X_t (·)}((r,δ)-OUP_n~∞ for short) is given. The absolute continuity of distribution μ_t of X_t(·) and the limit of X_t(·) w... 详细信息

关键词： multi-parameter (r δ)-OUPn∞ absolute continuity in hierarchy.

Coupling, spectral gap and related topics (Ⅱ)

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Chinese Science Bulletin 1997年第18期42卷 1409-1416页

作者： CHEN Muf adepartment of mathematics, beijing normal university,{2., China department of mathematics Beijing Normal University Beijing China

THIS is the second one of a series of three reviews. The ideas introduced in the last review are used to study the estimate of spectral gap and four classes of typical eigenvalue problems on manifolds. The comparison ... 详细信息

关键词： diffusions manifold Markov chains spectral gap couplings.

AVERAGE σ-K WIDTH OF CLASS OF L_p(R^n) IN L_q (R^n)

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Chinese Annals of mathematics,Series B 1995年第3期16卷 351-360页

作者： LIU YONGPING(department of mathematics, beijing normal university, Beliing {2., China.) beijing normal UNIV DEPT MATHBEIJING 100875PEOPLES R CHINA

The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2.Rn... 详细信息

关键词： Average σ-K width Optimal subspace,Sobolev-Wiener class,Riesz potential.

Output-back fuzzy logic systems and equivalence with feedback neural networks

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Chinese Science Bulletin 2000年第7期45卷 592-596页

作者： LI Hongxingdepartment of mathematics, beijing normal university,{2., China department of mathematics Beijing Normal University Beijing China

A new idea, output-back fuzzy logic systems, is proposed. It is proved that output-back fuzzy logic systems must be equivalent to feedback neural networks. After the notion of generalized fuzzy logic systems is defined, which contains at least a typical fuzzy logic system and an output-back fuzzy logic system, one important conclusion is drawn that generalized fuzzy logic systems are almost equivalent to neural networks.

关键词： output-back fuzzy logic systems generalized fuzzy logic systems feedforward neural networks feedback neural networks.

Linear operators preserving the generalized decomposable numerical range

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Chinese Science Bulletin 1997年第1期42卷 22-26页

作者： LEI Tiangangdepartment of mathematics, beijing normal university,{2., China department of mathematics Beijing Normal University Beijing China

LET G be a subgroup of the symmetric group Sm. Denote by CG the set of all functions f: G→C. A function f∈CG is said to be positive semi-definite （p. s. d. ） if there exists c∈CG such that for all τ∈G. In particular, the irreducible complex characters of G are p. s. d. Let Cn×m denote the set of all n×m complex matrices. For f∈CG, the

关键词： decomposable numerical range linear operator positive semi-definite function generalized matrix function.

Fuzzy controllers based on some fuzzy implication operators and their response functions

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Progress in Natural Science:Materials International 2004年第1期14卷 16-21页

作者： LI Hongxing 1*, YOU Fei 1 and PENG Jiayin 2.1. department of mathematics, beijing normal university,{2., China 2. department of mathematics, Neijiang Teacher's College, Neijiang 641112. China) beijing normal Univ Dept Math Beijing 100875 Peoples R China

The fuzzy controllers constructed by 2. fuzzy implication operators based on CRI algorithm and their response functions are discussed. The conclusions show that the fuzzy controllers constructed by 9 fuzzy implication operators are universal approximators to continuous functions and can be used in practical fuzzy control systems. And these 9 fuzzy implication operators except for Einstein operator intersection are all the adjoint pairs of some fuzzy implication operators. Besides, there are 3 other fuzzy controllers formed by fuzzy implication operators being regarded approximately as fitted functions.

关键词： fuzzy implication operators CRI algorithm fuzzy controllers response functions universal approximators

Homology classes that can be represented by embedded spheres in rational surfaces

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Science China mathematics 2004年第3期47卷 431-439页

作者： GAO Hongzhu GUO Ren department of mathematics,beijing {2. university, beijing 100875,China department of mathematics Beijing Normal University Beijing China

The problem of embedding spheres in rational surfaces CP 2.n $\overline {CP} $ 2.is studied. For homology classes u = (b 1 + k, b 2....,b n) with positive self-intersection numbers, a necessary and sufficient conditio... 详细信息

关键词： four manifold embedded sphere self-intersection number

A Remark on Multilinear Oscillatory Singular Integrals

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Acta Mathematica Sinica,English Series 2000年第4期16卷 655-668页

作者： Shanzhen Lu Dunyan Yan department of mathematics, beijing normal university,{2.. P. R. China department of mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper we study multilinear oscillatory singular integrals with rough kernel and give a criterion of certain boundedness for this kind of operator

关键词： Multilinear oscillatory integrals Calderon-Zygmund kernel BLO space

ENERGY FLOWS IN COMPLEX ECOLOGICAL SYSTEMS:A REVIEW

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Journal of Systems Science & Complexity 2009年第3期22卷 345-359页

作者： Jiang ZHANG department of Systems Science,School of Management,beijing {2. university,beijing 100875,China. department of Systems Science School of Management Beijing Normal University Beijing China

Energy flow drives the complex systems to *** allometric scaling as the universalenergy flow pattern has been found in different scales of ecological *** reflects the generalpower law relationship between flow and *** underlying mechanisms of energy flow patterns areexplained as the branching transportation networks which can be regarded as the result of systematicoptimization of a biological target under *** flows in the ecological system may bemodelled by the food web model and population dynamics on the *** paper reviews thelatest progress on the energy flow patterns,explanatory models for the allometric scaling and modellingapproach of flow and network evolution dynamics in ***,the possibility of generalizingthese flow patterns,modelling approaches to other complex systems is discussed.

关键词： Allometric scaling energy flow flows in complex systems food web.