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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 100875, 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.

Boundedness for commutators of fractional Hardy operators on Herz spaces

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Progress in Natural Science:Materials International 2007年第1期17卷 20-25页

作者： FU Zunwei, LIU Zongguang and LU Shanzhen ( School of Mathematical Sciences, beijing normal university, beijing 100875, china department of Mathematics, Linyi normal university, Linyi 276005, china department of Mathematics, china university of Mining and Technology, beijing 100083, china) [a]School of Mathematical Sciences Beijing Normal University Beijing China [b]Departhent of Mathematics Linyi Normal University Linyi China [c]Departhent of Mathematics China University of Mining and Technology Beijing China

Some boundedness results are established for commutators generated by classical fractional Hardy operators and one-sided CMO functions on the homogeneous Herz spaces, which extends some known results.

关键词： fractional Hardy operator Hardy’s integral inequality commutator one-sided CMO function homogeneous Herz space.

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, beijing 100875, 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.

Lookback time as a test for f(R) gravity in the Palatini approach

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Research in astronomy and Astrophysics 2011年第11期11卷 1257-1265页

作者： Zhong-Xu Zhai and Wen-Biao Liu department of Physics, Institute of Theoretical Physics, beijing normal university, beijing 100875, china department of Physics Institute of Theoretical Physics Beijing Normal University Beijing 100875 China

We use the recently released data of lookback time (LT)-redshift relation, the cosmic microwave background shift parameter and the baryon acoustic oscillation measurements to constrain cosmological parameters of f (R) gravity in the Palatini formalism by considering the f (R) form of type (a) f (R) = R β/Rn and (b) f (R) = R + α ln R β. Under the assumption of a Friedmann-Robertson-Walker universe, we achieved the best fitting results of the free parameters (Ωm0, n) for (a) and (Ωm0, α) for (b). We find that current LT data can provide interesting and effective constraints on gravity models. Compared with other data, the LT constraints favor a smaller value of the non-relativistic matter energy density.

关键词： cosmology cosmic microwave background

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, beijing 100875, china department of Mathematics Beijing Normal University Beijing 100875 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.

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, beijing 100875, china 2. Institute of Applied Physics and Computational Mathematics, beijing 100080, china 1. department of Mathematics Beijing Normal University Beijing 100875 China 2. Institute of Applied Physics and Computational Mathematics Beijing 100080 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.

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 normal university, beijing 100875,china 1. department of Mathematics Beijing Normal University 100875 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

The toxicity of Cu^(2+) to Microcystis aeruginosa using dielectric spectroscopy

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Science china Chemistry 2010年第3期53卷 631-636页

作者： YU YanLi1,BAI Wei1,ZHAO KongShuang1& ZHOU YunLong2 1College of Chemistry,beijing normal university,beijing 100875,china 2College of Life Science,beijing normal university,beijing 100875,china 1. College of Chemistry Beijing Normal University Beijing 100875 China2. College of Life Science Beijing Normal University Beijing 100875 China

Dielectric spectroscopy(DS) was utilized to investigate the toxicity of the Cu2+ solution to Microcystis *** was found that 0.04 mM Cu2+ had no effect on dielectric increment,whereas the Cu2+ concentrations above 0.1 mM decreased the value of Δε/Δε *** toxic effect of Cu2+ on *** cells was time-dependent and *** was a threshold concentration between 0.04 mM and 0.1 mM,which affected the cell membrane,suggesting that Cu2+ at the concentrations higher than 0.1 mM caused serious plasmalemma damage to *** *** addition of 1 mM Ca2+ or Mg2+ did not protect *** cells from 1 mM Cu2+ *** study demonstrates that DS monitors cell biomass facilitating observation of the toxic effects of metal ions.

关键词： Microcystis aeruginosa dielectric spectroscopy dielectric increment cupric ion toxicity

Development and application of ergodicity model with FRCM and FLAR for hydrological process

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Science china(Technological Sciences) 2009年第2期52卷 379-386页

作者： WANG HongRui1, FENG QiLei2, LIN Xin3 & ZENG WenYi4 1 College of Water Science, Key Laboratory for Water and Sediment Sciences of the Ministry of Education, beijing normal university, beijing 100875, china 2 School of Science, beijing Institute of Education, beijing 100011, china 3 School of Mathematical Sciences, beijing normal university, beijing 100875, china 4 College of Information Science and Technology, beijing normal university, beijing 100875, china 1. College of Water Science Key Laboratory for Water and Sediment Sciences of the Ministry of Education Beijing Normal University Beijing 100875 China 2. School of Science Beijing Institute of Education Beijing 100011 China 3. School of Mathematical Sciences Beijing Normal University Beijing 100875 China 4. College of Information Science and Technology Beijing Normal University Beijing 100875 China

In this paper, a new ergodic property analysis model of hydrological process is proposed based on fuzzy-rough c-means clustering (FRCM), autocorrelogram, and fuzzy least absolute regression (FLAR). A precipitation time series (1951―2004) from Shanghai Hydrology Station is then analyzed with the model. The results show that the precipitation time series of April, May, June, and September has er-godic property. We conclude that in the long run, the precipitation of April, May, June, and September will not keep decreasing; it will converge to its mean value in some period.

关键词： hydrological process ergodic autocorrelogram fuzzy-rough c-means clustering fuzzy least absolute regression