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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 1.0875,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

A secure multi-party computation solution to intersection problems of sets and rectangles

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Progress in Natural Science:Materials International 2006年第5期16卷 538-545页

作者： LI Shundong, DAI Yiqi, WANG Daoshun and LUO Ping (department of Computer Science and Technology, beijing normal university, beijing 1.0875, china department of Computer Science and Technology, Tsinghua university, beijing 100084, china) [a]department of computer Science and Technology Beijing Normal University Beijing China [b]department of Computer Science and Technology Tsinghua University Beijing China

Secure multi-party computation (SMC) is a research focus in international cryptographic community. At present, there is no SMC solution to the intersection problem of sets. In this paper, we first propose a SMC solution to this problem. Applying Cantor encoding method to computational geometry problems, and based on the solution to set-intersection problem, we further propose solutions to points inclusion problem and intersection problem of rectangles and further prove their privacy-preserving property with widely accepted simulation paradigm. Compared with the known solutions, these new solutions are of less computational complexity and less communication complexity, and have obvious superiority in computational and communication complexity.

关键词： Cantor encoding secure multi-party computation set-intersection rectangle-intersection computational complexity.

Existence and Application of Optimal Markovian Coupling with Respect to Non-Negative Lower Semi-Continuous Functions

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Acta Mathematica Sinica,English Series 2000年第2期16卷 261-270页

作者： Shaoyi Zhangdepartment of Mathematics.beijing normal university,beijing 1.0875,P.R.china department of Mathematics,Hubei normal university,Huangshi 435002,P.R.china department of Mathematics Beijing Normal University Beijing 100875 P. R. China department of Mathematics Hubei Normal University Huangshi 435002 P. R. China

In this paper,for two given transition probabilities,the existence of the optimal Markovian coupling with respect to a non-negative lower semi-continuous function is *** an application of this result,the well-known Strassen’s theorem is ***,it is proved that the existence of an order-preserving Markovian coupling of two given jump processes is equivalent to their stochastical comparability.

关键词： Transition probability Markovian coupling Jump process

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 1.0875, china 2 School of Science, beijing Institute of Education, beijing 100011, china 3 School of Mathematical Sciences, beijing normal university, beijing 1.0875, china 4 College of Information Science and Technology, beijing normal university, beijing 1.0875, 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

A MESSAGE-DRIVING FORMALISM FOR MODELING AND SIMULATION OF MULTI-AGENT SUPPLY CHAIN SYSTEMS

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Journal of Systems Science and Systems Engineering 2011年第4期20卷 385-399页

作者： Wenzhe TAN1 Yueting CHAI2 Yi LIU3 1department of Automation, Tsinghua university, beijing, 100084, china 2department of Automation, Tsinghua university, beijing, 100084, china 3department of Automation, Tsinghua university, beijing, 100084, china department of Automation Tsinghua University Beijing China

To acquire a competitive advantage in the expanding market, manufacturing enterprises should be able to manage their supply chains as effectively as possible. It is now becoming popular to model supply chains as multi-agent systems and use discrete event simulation to learn more about their behaviors or investigate the implications of alternative configurations. In order to enhance the computational efficiency and keep the simulation credibility, this paper proposes a message-driving formalism for the simulation of multi-agent supply chain systems. Through the message-driving formalism, the problem of shared variables is addressed and the parallel operation of agents is implemented. Simulation experiments with a prototype implementation show that the message-driving formalism is able to provide credible results in significantly less simulation time.

关键词： Supply chain multi-agent system modeling and simulation parallel discrete event simulation message-driving formalism

Entropy number and non-linear approximations on multivariate Besov space by manifolds of finite pseudo-dimension

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Progress in Natural Science:Materials International 2006年第3期16卷 260-265页

作者： LONG Jingfan and FANG Gensun (School of Mathematical Sciences, beijing normal university, beijing 1.0875, china department of Computer Science, Information Technology Institute, beijing 100101, china) [a]School of Mathematical Sciences Beijing Normal University Beijing China [b]department of Computer Science Information Technology Institute Beijing China

We determine the asymptotic order of entropy number and optimal non -linear approximations of anisotropic periodic Besov class of Bpθr(Td') (1≤p≤∞,1≤0≤∞) by manifolds of finite pseudo-dimension in the metric Lq... 详细信息

关键词： Pseudo-dimension anisotropic Besov class of functions entropy number nonlinear width.

Moderate deviation for super-Brownian motion with immigration

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Science china Mathematics 2004年第3期47卷 440-452页

作者： ZHANG Mei department of Mathematics, beijing normal university, beijing 1.0875, china department of Mathematics, The Central university of Finance and Economics, beijing 100081, china 1. department of Mathematics Beijing Normal University 100875 Beijing China 2. department of Mathematics The Central University of Finance and Economics 100081 Beijing China

We prove a moderate deviation principle for a super-Brownian motion with immigration of all dimensions, and consequently fill the gap between the central limit theorem and large deviation principle.

关键词： moderate deviation principle super-Brownian motion with immigration large deviation principle evolution equation

Eigenvalues, inequalities and ergodic theory

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Chinese Science Bulletin 2000年第9期45卷 769-774页

作者： CHEN Mufadepartment of Mathematics, beijing normal university, beijing 1.0875, china department of Mathematics Beijing Normal University Beijing China

This paper surveys the main results obtained during the period 1992-1999 on three aspects mentioned in the title. The first result is a new and general variational formula for the lower bound of spectral gap (i.e. the first non-trivial eigenvalue) of elliptic operators in Euclidean space, Laplacian on Riemannian manifolds or Markov chains (?). Here, a probabilistic method -coupling method is adopted. The new formula is a dual of the classical variational formula. The last formula is actually equivalent to Poincare inequality. To which, there are closely related logarithmic Sobolev inequality, Nash inequality, Liggett inequality and so on. These inequalities are treated in a unified way by using Cheeger’s method which comes from Riemannian geometry. This consists of ?2. The results on these two aspects are mainly completed by the author joint with F. Y. Wang. Furthermore, a diagram of the inequalities and the traditional three types of ergodicity is presented (?3). The diagram extends the ergodic

关键词： eigenvalue inequality ergodic theory Markov process.

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 230026, china 2. department of Mathematics, beijing normal university, beijing 1.0875, 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.