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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 china, Hefei 2.002., china 2. Department of Mathematics, Beijing normal university, Beijing 100875, china 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.

The normal numbers of the fuzzy systems and their classes

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Science china(Information Sciences) 2010年第11期53卷 2215-2229页

作者： LI HongXing1,3, YUAN XueHai1, WANG JiaYin2.& LI YuCheng3 1Faculty of Electronic Information and Electrical Engineering, dalian university of Technology, dalian 11602., china 2.4} of Mathematical Sciences, Beijing normal university, Beijing 100875, china 3Department of Automation, North china university of Technology, Beijing 100144, china Faculty of Electronic Information and Electrical Engineering Dalian University of Technology school of Mathematical Sciences Beijing Normal University

R-fuzzy set is defined in this paper, which is regarded as the generalization of the Zadeh fuzzy set. By means of CRI method, some fuzzy systems are constructed by suitably using several kinds of R-fuzzy sets as fuzzy inference antecedents, such as interpolation fuzzy system, Bernstein fuzzy system, Lagrange fuzzy system and Hermite fuzzy system. A notion of the normal number of the fuzzy system is defined here, we have shown that all fuzzy systems are able to be classified as three classes such as the normal fuzzy systems, the regular fuzzy systems and the singular fuzzy systems under the significance of the normal numbers of fuzzy systems. Finally, the generalized Bernstein polynomial is obtained by constructing Bernstein fuzzy system, it is proved that the generalized Bernstein polynomial is uniformly convergent in C[a,b] under a weaker condition, and it is pointed out that there exist generalized Bernstein polynomials to be not convergent in C[a,b] by use of constructing a counterexample.

关键词： R-fuzzy set fuzzy system the normal number of fuzzy system universal approximation property for fuzzy system

Scenario simulation and forecast of land use/cover in northern china

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Chinese Science Bulletin 2008年第9期53卷 1401-1412页

作者： LI YueChen 1,2.3 & HE ChunYang 3 1 College of Geographical Science, Chongqing normal university, Chongqing 400047,{2. 2.College of Resources and environmental Science, Chongqing university, Chongqing 400044,{2. 3 College of Resources Science & Technology, Beijing normal university, Beijing 100875,{2. College of Geographical Science Chongqing Normal University Chongqing 400047 China College of Resources and environmental Science Chongqing University Chongqing 400044 China College of Resources Science & Technology Beijing Normal University Beijing 100875 China

Modeling land use/cover scenario changes and its potential impacts on structure and functions of ecosystem in typical regions are helpful to understanding the interactive mechanism between land use/cover system and ecosystem. Based on the analysis of the existing land use/cover simulation and forecast models, a land use/cover scenario dynamics model by the integration of System Dynamics (SD) model, Back Propagation Neural Network (BPNN) and Cellular Automata (CA) model is developed with land use/cover scenario changes in northern china in the next 30 years and simulated in this paper. The model is to simulate the land use/cover scenario demands by using a SD model at first, and then allocating the land use scenario patterns at the local scale with the considerations of land use/cover suitability, inheritance ability and neighborhood effect by using BPNN-CA model to satisfy the balance between land use/cover scenario demands and supplies. It integrates the advantages of SD, BPNN and CA. Macro-driving factors and the micro-spatial pattern are also fully taken into account. The BPNN simplifies the identification of the factors’ weights used in CA model and improves the reliability of the simulation results. The simulation accuracy of the model developed in this paper was found to be about 74%. It suggests that the model has the ability to reflect the complexity of land use/cover system at different scales to some extent and it is a useful tool for assessing the potential impacts of land use system on ecosystem. The simulated results also indicate that the urban land, water area and forest will increase significantly, and farmland and unable land will decrease gradually. Obvious land use/cover changes will take place in the farming-pastoral zone and the southeast area of northern china.

关键词：土地利用中国北方细胞自动机系统动力学

Extension of isometries on the unit sphere of l^p (Γ) space

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Science china Mathematics 2010年第4期53卷 1085-1096页

作者： FANG XiNian 1,& WANG JianHua 2.1 school of Mathematics and Statistics,Nanjing Audit university,Nanjing 2.002.,{2. 2.Department of Mathematics,Anhui normal university,Wuhu 2.1000,{2. school of Mathematics and Statistics Nanjing Audit University Department of Mathematics Anhui Normal University

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 < p < ∞,p≠2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto ... 详细信息

In this paper,we obtain that every isometry from the unit sphere S(l p (Γ)) of l p (Γ) (1 2. onto the unit sphere S(E) of a Banach space E can be extended to be a (real) linear isometry of l p (Γ) onto E,so,we give an affirmative answer to the corresponding Tingley’s problem.

关键词： isometric extension l p (Γ) space isometry 1-Lipschitz mapping

Degradation of anthracene, pyrene and benzo[a]-anthracene in aqueous solution by chlorine dioxide

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Science china Chemistry 2006年第6期49卷 565-572页

作者： LIU Jinquan1, HUANG Junli1, SU Liqiang2. CAO Xiangyu1 & JI Ying1 1. school of Municipal and environmental Engineering, Harbin Institute of Technology, Harbin 150090,{2. 2. school of Chemistry and Chemical Engineering, Qiqihar university, Qiqihar 161006,{2. school of Municipal and environmental Engineering Harbin Institute of Technology Harbin China school of Chemistry and Chemical Engineering Qiqihar University Qiqihar China

Polycyclic aromatic hydrocarbons (PAHs) constitute an important group of micropollutants, which are known to be mutagenic, carcinogenic and/or co-carcinogenic and relatively persistent in the environment. The effects of chlorine dioxide (ClO2. on the degradation of anthracene (ANTH), pyrene (PYR) and benzo[a]anthracene (BaA) in aqueous solution were investigated using high performance liquid chromatography (HPLC). In preliminary experiments, it was observed that ClO2.could remove these three PAHs effectively within a short time. Several factors including reaction time, the concentration of ClO2.and pH of the reaction mixture influencing the degradation ratio of PAHs have been studied by batch experiments. The results showed that the degradation ratio of PAHs was affected by reaction time and the concentration of ClO2.instead of pH. The degradation ratio of ANTH, PYR and BaA could reach their maximum as approximately 99.0%, 67.5% and 89.5%, respectively, under the condition as follows: reaction time 30, 60 and 12. min, the concentration of ClO2.0.1, 0.4 and 0.5 mmol·L-1, and pH 7.2. ANTH was selected as the representative to study the reaction mechanism with ClO2. The oxidation products formed in the reaction of ANTH with ClO2.were tentatively identified by gas chromatography-mass spectrometry (GC-MS), and the results showed that the main product was 9, 10-anthraquinone, which could be biodegraded more easily and quickly than ANTH. Through analyzing the reaction properties of ANTH and ClO2. the possible pathway for the ANTH-ClO2.reaction was proposed based on the theory of single electron transfer (SET).

关键词： chlorine dioxide, anthracene, pyrene, benzo[a]anthracene, degradation, reaction mechanism.

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试析2.世纪40年代的新自由主义思潮

史学集刊 2010年第3期 63-69页

作者：林建华辽宁师范大学政治与行政学院辽宁大连116029

2.世纪40年代自由主义思潮的最大特点就是把自由主义思想的提倡与当时中国社会的迫切需求结合在一起:既要解决政治民主问题,又要实现经济平等的目标。这就需要最大限度地调和政治民主与经济平等之间的矛盾,建立一个政治民主与经济平等... 详细信息

2.世纪40年代自由主义思潮的最大特点就是把自由主义思想的提倡与当时中国社会的迫切需求结合在一起:既要解决政治民主问题,又要实现经济平等的目标。这就需要最大限度地调和政治民主与经济平等之间的矛盾,建立一个政治民主与经济平等齐头并进的社会。为了适应这种社会需要,自由主义在坚持原有的自由、民主、平等、法治等基本理念的基础上,吸收了许多社会主义的思想要素,用当时形象的话说就是"大家有饭吃,各人选路走"。这种调和自由主义和社会主义的思潮在中国社会引起了极大的反响和共鸣,形成了系统、完整的思想体系,一时间成为思想界关注的焦点,许多人将其称为"新自由主义"。

关键词：自由主义社会主义政治平等经济自由

Optimal reactions for the synthesis of superheavy nucleus ^(2.0)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,{2. 2. Physics Department, Beijing normal university, Beijing 100875,{2. 3.{2. Institute of Atomic Energy, Beijing 102.13,{2. Key Laboratory of Beam Technology and Material Modification of Ministry of Education Beijing Normal University Beijing China china Institute of Atomic Energy Beijing China Physics Department Beijing Normal University Beijing China

The superheavy nucleus 2.0Hs is expected to be a “double-magic” deformed nucleus. We have calculated its cross sections of evaporation residue for the reactions 2.8Cm(2.Mg,4n)2.0Hs, 2.4Pu(30Si,4n)2.0Hs, 2.8U(36S,4n)2.0Hs and 2.6Ra(48Ca,4n)2.0Hs using a two-parameter Smoluchowski equation. It is found from our results that 2.6Ra(48Ca,4n)2.0Hs and 2.8U(36S,4n)2.0Hs are two optimal reactions for the synthesis of the superheavy nucleus 2.0Hs due to their large negative Q-values.

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

Palaeorunoff estimations achieved from palaeoclimatic information for the southwest part of the North china Plain: an attempt to apply a climatological approach to palaeohydrology

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Journal of environmental Sciences 2000年第3期12卷 330-336页

作者： WANG Hong\|ya, XIE Qiang (Department of urban and environmental Sciences, Peking {2.,Beijing 100871, china) 北京大学北京 1 0 0 871

Palaeoclimatic scenario projecting annual temperature and annual precipitation is firstly formalized with data available and speculations for the southwest part of the North china Plain (35— 37°N, 115—119°E) during the last 2.000 years. Then, with three regression equations relating annual runoff to annual precipitation and derived with data of modern hydrological and meteorological records, values of annual runoff are calculated in terms of the corresponding values of annual precipitation from this palaeoclimatic scenario for this region during this temporal interval. These results indicate that runoff is the most during 8000—3000 a B.P. and the least during 2.000—12.00 a B.P.; runoff occurring during 12.00—8000 a B.P. and during 3000—0 a B.P. is less than the one occurring during 8000—3000 a B.P. and more than the one occurring during 2.000—12.00 a B.P.; and the runoff occurring during 2.000—12.00 a B.P., 12.00—8000 a B.P., and 3000—0 a B.P. is respectively 43, 46 and 66 percent of the one occurring during 8000—3000 a B.P. Values of bankfull discharge for palaeochannels of the Yellow River flowing in this region during the same interval are calculated from available estimates of slope of stream bed of these palaeochannels with a regression equation relating bankfull discharge to slope of stream bed and ratios of bankfull discharge are further calculated from these values for different groups of palaeochannel formed during different time spans embraced in this interval. To conduct a cross check, these values and ratios of bankfull discharge are compared to the corresponding values and ratios of runoff occurring during roughly the same time spans. The same direction and similar relative magnitude of changes of the surface water occurring in this region during the last 2.000 years are indicated by these comparisons.

关键词： palaeorunoff the southwest part of the North china Plain palaeoclimate

A note on the crossed product R(A, α) associated with PSL_2.R)

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Science china Mathematics 2008年第11期51卷 2081-2088页

作者： WU WenMing 1 school of Mathematical and Computer Science, Chongqing normal {2., Chongqing 400047, china 2.Department of Mathematical Science, Tsinghua {2., Beijing 100084, china school of Mathematical and Computer Science Chongqing Normal University Chongqing China Department of Mathematical Science Tsinghua University Beijing China

Given the hyperbolic measure dxdy/y2.on the upper half plane H, the rational actions of PSL2.R) on H induces a continuous unitary representation α of this group on the Hilbert space L2.H, dxdy/y2.. Supposing that A = {Mf : f ∈ L∞(H, dxdy/y2.}, we show that the crossed product R(A,α) is of type I. In fact, the crossed product R(A,α) is *-isomorphic to the von Neumann algebra B(L2.P,ν))■LK, where LK is the abelian group von Neumann algebra generated by the left regular representation of K.

关键词： crossed product rational actions PSL2.R) von Neumann algebras