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On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2 and YU Yuanhong 3.1. Department of Applied Mathematics, beijing institute of technology, beijing 100081, china 2. Department of Mathematics, Yunnan University, Kunming 650091, china 3. institute of Applied Mathematics, C Department of Applied Mathematics Beijing Institute of Technology Beijing China Department of Mathematics Yunnan University Kunming China institute of Applied Mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

The mathematical model of wetting angle of heterogeneous nucleation

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Science china(Technological Sciences) 2004年第4期47卷 391-397页

作者： HUANG Cheng1, SONG Bo1, MAO Jinghong2 & ZHAO Pei3.1. School of Metallurgical and Ecological Engineering, University of Science and technology beijing, beijing 100083.{3. 2. School of Material Science, University of Science and technology beijing, beijing 100083.{3. 3. Central Iron and Steel Research institute, beijing 100081,{3. 1. School of Metallurgical and Ecological Engineering University of Science and Technology Beijing 100083 Beijing China 2. School of Material Science University of Science and Technology Beijing 100083 Beijing China 3. Central Iron and Steel Research institute 100081 Beijing China

The heterogeneous nucleation has been analyzed in terms of the thermodynamic theory, and the mathematical model of wetting angle of heterogeneous nucleation has been developed based on the dynamic requirements of hetero- and homogeneous nucleation. With the wetting angel model, the wetting angles of different catalysts in liquid iron have been calculated. The result shows that the wetting angle of most catalysts is smaller than 40, and the value of f() is far less than 1. The wetting angles of TiN, TiC and RE2O3.are smaller, while the wetting angle of MnO is bigger among the ordinary nucleation catalysts. The wetting angles calculated by this model are in agreement with the results of other research work.

关键词： heterogeneous nucleation, mathematical model, wetting angle, undercooling.

Solving the input data in error correc-tion of optical fabrication by finite Fourier coefficient algorithm

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Science china(Technological Sciences) 2006年第1期49卷 50-60页

作者： CHENG Haobo1,2, SUN Guozheng3.& FENG Zhijing2 1. Department of Optical Engineering, beijing institute of technology, beijing 100081, china 2. Department of Precision Instruments and Mechanology, Tsinghua University, {3. 100084, china 3. china North Industries Group Corporation, {3. 100089, china 1. Department of Optical Engineering Beijing Institute of Technology Beijing 100081 China 2. Department of Precision Instruments and Mechanology Tsinghua University Beijing 100084 China 3. china North Industries Group Corporation Beijing 100089 China

A free-form lens (FFL) is a special surface that is difficult to be fabricated. FFL are usually fabricated by computer-controlled optical surfacing (CCOS) technique. During CCOS, the material removal amount is determined by the unit removal function (URF) convoluting with the input data――the dwell time. When the removal amount and the URF are known, how to solve the input data involves the special algorithm――deconvolution. Usually, the input data are solved by virtue of low pass filter or iterative methods. However, an approximation solution would destroy the machining stability nec-essary to perform precisely CCOS. In this paper, to solve the input data, a new method that is based on the finite Fourier coefficient is put forward. It can give a continuous and accurate solution for fabricating choice. Several parameters are simulated, which influ-ence the process of CCOS, and evaluating on the effect of the method is also carried out. Experimental results verify that this method is suitable for guiding the manufacturing of high precision FFL.

关键词： optical fabrication, computer controlled optical surfacing, free-form lens, finite Fourier coefficient, error correction.

A preliminary study on seismic design criteria of offshore platforms in Bohai Sea of china

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Earthquake Engineering and Engineering Vibration 2010年第2期9卷 223-231页

作者： Peng Yanju1,Lu Yuejun1,Yan Jiaquan2,Tang Rongyu1,Wang Junqin3.and Li Jiagang3.1. institute of Crustal Dynamics,china Earthquake Administration,beijing 100085,china 2. institute of Geophysics,china Earthquake Administration,beijing 100081,china 3. beijing Research Center of china National Offshore Oil Corp.,beijing 100027,china institute of Crustal Dynamics China Earthquake Administration Beijing 100085 China

This paper analyzes the seismicity in Bohai Sea,introducing a shape factor K to characterize the seismic risk distribution in sub-regions of the sea. Based on the seismic design ground motions for 46 platforms located in the Bohai Sea,a statistical analysis was performed for different peak ground acceleration (PGA) ratios at two different probability levels. In accordance with the two-stage design method,a scheme of two seismic design levels is proposed,and two seismic design objectives are established respectively for the strength level earthquake and the ductility level earthquake. By analogy with and comparison to the Chinese seismic design code for buildings,it is proposed that the probability level for the strength level earthquake and ductility level earthquake have a return period of 200 and 1000 - 2500 years,respectively. The validity of these proposed values is discussed. Finally,the PGAs corresponding to these two probability levels are calculated for different sub-regions of the Bohai Sea.

关键词： fixed offshore platform seismic design level seismic design objective return period Bohai Sea

Dynamic information theory and information description of dynamic systems

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Science china(Physics,Mechanics & Astronomy) 2010年第4期53卷 607-627页

作者： XING XiuSan Department of Physics, beijing institute of technology, beijing 100081, china 1. Department of Physics Beijing Institute of Technology Beijing 100081 China

In this paper, we develop dynamic statistical information theory established by the author. Starting from the ideas that the state variable evolution equations of stochastic dynamic systems, classical and quantum nonequilibrium statistical physical systems and special electromagnetic field systems can be regarded as their information symbol evolution equations and the definitions of dynamic information and dynamic entropy, we derive the evolution equations of dynamic information and dynamic entropy that describe the evolution laws of dynamic information. These four kinds of evolution equations are of the same mathematical type. They show in unison when information transmits in coordinate space outside the systems that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes, and that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes. When space noise can be neglected, an information wave will appear. If we only consider the information change inside the systems, dynamic information evolution equations reduce to information equations corresponding to the dynamic equations which describe evolution laws of the above dynamic systems. This reveals that the evolution laws of respective dynamic systems can be described by information equations in a unified fashion. Hence, the evolution processes of these dynamic systems can be abstracted as the evolution processes of information. Furthermore, we present the formulas for information flow, information dissipation rate, and entropy production rate. We prove that the information production probably emerges in a dynamic system with internal attractive interaction between the elements, and derive a formula for this information production

关键词： dynamic information evolution equation informationization of dynamic equation information wave information flow and force information dissipation and production degradation and evolution

A formal model of fair exchange protocols

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Science in china(Series F) 2005年第4期48卷 499-512页

作者： QING Sihan1,2,3.& LI Gaicheng1,2,3.1. Engineering Research Center for Information Security technology, institute of software, Chinese Aca- demy of Sciences, {3. 100080, china 2. {3. Zhongke Ansheng Corporation of Information technology, {3. 100080, china 3. Graduate School of the Chinese Academy of Sciences, {3. 10003., china 1. Engineering Research Center for Information Security technology Institute of Software Chinese Academy of Sciences 100080 Beijing China 2. beijing Zhongke Ansheng Corporation of Information technology 100080 Beijing China 3. Graduate School of the Chinese Academy of Sciences 100039 Beijing China

Based on the study of existing fair exchange protocols, this paper sets up an accurate formal model by stepwise refinement. In the process of refinement an unreliable channel is employed to simulate an attack behavior. The model provides a novel formal definition of exchanged items, and presents the formal goals for fairness, accountability, etc., reflecting the inherent requirements for fair exchange protocols across-the-board. In order to check, prove, and design fair exchange protocols effectively and efficiently, the model puts forward a novel property of abuse-freeness which applies to all fair exchange protocols, gives a formal definition for trust strand of the third party, and presents general criteria of designing a secure and effective fair exchange protocol. Taking a typical fair exchange protocol as an example, this paper presents the analysis steps of fair exchange protocols appealing to our model. An unknown attack is uncovered. The analysis reveals the process of a complete attack, discovering deeper reasons for causing an attack. Finally, we modify the flawed protocol and the revised protocol ensures the desirable properties.

关键词： events local causal relation local temporal relation global relation exchanged item security goals.

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,{3. 2. Physics Department, beijing Normal University, beijing 100875,{3. 3.{3. institute of Atomic Energy, beijing 102413.{3. 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 248Cm(26Mg,4n)270Hs, 244Pu(3.Si,4n)270Hs, 23.U(3.S,4n)270Hs and 226Ra(48Ca,4n)270Hs using a two-parameter Smoluchowski equation. It is found from our results that 226Ra(48Ca,4n)270Hs and 23.U(3.S,4n)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.

Formal analysis and design of multi-party fair exchange protocols

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Science in china(Series F) 2006年第2期49卷 155-174页

作者： QING Sihan1,2,3.& LI Gaicheng1,3.1. Engineering Research Center for Information Security technology, institute of software, Chinese Academy of Sciences, {3. 100080, china 2. {3. Zhongke Ansheng Corporation of Information technology, {3. 100080, china 3. Graduate School of the Chinese Academy of Sciences, {3. 10003., china 1. Engineering Research Center for Information Security technology Institute of Software Chinese Academy of Sciences Beijing 100080 China 2. beijing Zhongke Ansheng Corporation of Information technology Beijing 100080 China 3. Graduate School of the Chinese Academy of Sciences Beijing 100039 China

Based on the origin of message items and channel combination between transacting parties, and events and relations among events, this paper presents a concise, precise, and hierarchical model for general fair exchange protocols, formally specifies various security requirements which are able to reflect inherent requirements for fair exchange protocols more rigorously, and partition these security requirements with fine granularity. This work helps analyze, debug, and design multi-party fair exchange protocols more effectively and elaborately,

关键词： fair exchange logical protocol formal model security requirement.

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

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Science china(Physics,Mechanics & Astronomy) 2010年第12期53卷 2194-2215页

作者： XING XiuSan Department of Physics, beijing institute of technology, beijing 100081, china 1. Department of Physics Beijing Institute of Technology Beijing 100081 China

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3.dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or anothe

关键词： stochastic velocity type’s Langevin equation in 6N dimensional phase space drift-diffusion duality nonequilibrium entropy evolution equation entropy diffusion formula for entropy production rate entropy change from internal interaction a