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Theoretical studies on the mechanism of the thermal decarboxylation and decarbonylation of a number of α-keto-acids

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Chinese Journal of Chemistry 1995年第6期13卷 487-492页

作者： CHEN,Li-Tao CHEN,Guang-Ju FU,Xiao-YuanChemistry department,beijing normal university,beijing 100875.china Chemistry department Beijing Normal University Beijing 100875 China

Both processes of decarboxylation and decarbonylation of a number of acids including RCOCO2H,R=H,CH3,CH2F,CF3,CH=CH2,Ph,OH have been studied by semi-empirical MO theory AMI method to verify the reaction mechanism of each process and the effect of different substituents on *** calculated results are consistent with the experimental reports and can be summed up as follows:(1) The decarboxylation of these acids to form aldehydes and carbon dioxide is concerted and takes place through a 4.membered ring transition state in which a partial negative charge develops on the carbon of the α-carbonyl group,so that the inductive effect of some substituents is favourable for this process.(2) Their decarbonylation into carboxylic acids and carbon monoxide however is the attack of the OH on the carbon of the alkyl portion of the acid,forming a 3-membered ring transition state.(3) The activation energy of decarbonylation is lower than that of decarboxylation,since oxygen is more nucleophilic than hydrogen and also the strong OH bond need not to be broken.

关键词： Decarboxylation decarbonylation a-keto-acid

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 {4., Linyi 276005, china department of Mathematics, china {4. 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.

Optimal reactions for the synthesis of superheavy nucleus ^(270)Hs

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Science china(physics,Mechanics & Astronomy) 2006年第6期49卷 641-648页

作者： LIU Zuhua1,3 & BAO Jingdong1,2 1. Key Laboratory of Beam Technology and Material Modification of Ministry of Education, beijing normal university, beijing 100875. china 2. physics department, beijing normal university, beijing 100875. china 3. china Institute of Atomic Energy, beijing 1024.3, china Key Laboratory of Beam Technology Material Modification of Ministry of Education Beijing Normal University Beijing 100875 China physics department Beijing Normal University Beijing 100875 China china Institute of Atomic Energy Beijing 102413 China

The superheavy nucleus 270Hs is expected to be a “double-magic” deformed nucleus. We have calculated its cross sections of evaporation residue for the reactions 24.Cm(26Mg,4.)270Hs, 24.Pu(30Si,4.)270Hs, 238U(36S,4.)270Hs and 226Ra(4.Ca,4.)270Hs using a two-parameter Smoluchowski equation. It is found from our results that 226Ra(4.Ca,4.)270Hs and 238U(36S,4.)270Hs are two optimal reactions for the synthesis of the superheavy nucleus 270Hs due to their large negative Q-values.

关键词： diffused fusion barrier,Smoluchowski equation,superheavy nuclei.

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.

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

Information flow and controlling in regularization inversion of quantitative remote sensing

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Science china Earth Sciences 2005年第1期48卷 74-83页

作者： YANG Hua, XU Wangli, ZHAO Hongrui, CHEN Xue & WANG Jindi Research Center for Remote Sensing and GIS, School of Geography, beijing normal university, State Key Laboratory of Remote Sensing Science, beijing Key Laboratory for Remote Sensing of Environment and Digital Cities, beijing 100875. china department of Mathematics, beijing normal university, beijing 100875. china 1. Research Center for Remote Sensing and GIS School of Geography Beijing Normal University State Key Laboratory of Remote Sensing Science Beijing Key Laboratory for Remote Sensing of Environment and Digital Cities 100875 Beijing China 2. department of Mathematics Beijing Normal University 100875 Beijing China

In order to minimize uncertainty of the inversed parameters to the largest extent by making full use of the limited information in remote sensing data, it is necessary to understand what the information flow in quantitative remote sensing model inversion is, thus control the information flow. Aiming at this, the paper takes the linear kernel-driven model inversion as an example. At first, the information flow in different inversion methods is calculated and analyzed, then the effect of information flow controlled by multi-stage inversion strategy is studied, finally, an information matrix based on USM is defined to control information flow in inversion. It shows that using Shannon entropy decrease of the inversed parameters can express information flow more properly. Changing the weight of a priori knowledge in inversion or fixing parameters and partitioning datasets in multi-stage inversion strategy can control information flow. In regularization inversion of remote sensing, information matrix based on USM may be a better tool for quantitatively controlling information flow.

关键词： regularization inversion, information flow, Shannon entropy decrease, information matrix.

Conformational Analysis of γ-Butyrolactones by Nuclear Magnetic Resonance Spectroscopy

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Chinese Chemical Letters 1997年第10期8卷 885-888页

作者： Fu An KANG and Cheng Lie YIN (department of Chemistry beijing normal university , beijing 100875. beijing normal UNIV DEPT CHEMBEIJING 100875PEOPLES R CHINA

A series of trans-4. 5-disubstituted -γ-butyrolactones are found to assume two different envelope conformations by means of nuclear magnetic resonance spectroscopy.

关键词： Conformational Analysis of Butyrolactones by Nuclear Magnetic Resonance Spectroscopy