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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,{3. 2. department of Mathematics, Yunnan University, Kunming 650091,{3. 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.

Dehydration melting of solid amphibolite at 2.0 GPa: Effects of time and temperature

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Science china Earth Sciences 2005年第8期48卷 1120-1133页

作者： ZHOU Wenge1, XIE Hongsen1, LIU Yonggang1, ZHENG Xiaogang1, ZHAO Zhidan2 & ZHOU Hui3.1. Laboratory of Material in the Earth’s Interior, Institute of Geochemistry, Chinese Academy of Sciences, Guiyang 550002, china 2. department of Geology, china University of Geosciences, {3. 100083. china 3. department of Geology, Peking University, {3. 100871, china 1. Laboratory of Material in the Earth’s Interior Institute of Geochemistry Chinese Academy of Sciences 550002 Guiyang China 2. department of Geology China University of Geosciences 100083 Beijing China 3. department of Geology Peking University 100871 Beijing China

Two sets of dehydration-melting with a natural solid amphibolite, collected from North Himalayan structure zone, Tibet, have been carried out in multi-anvil apparatus at 2.0 GPa and 800―1000℃, for 12―200 h. One is keeping the pressure at 2.0 GPa and the annealing time of 12 h, changing the temperature (800―1000℃). The other is keeping the pressure at 2.0 GPa and temperature at 850℃, varying the annealing time (12―200 h). The products are inspected with microscope and electron probe. The results indicate that at 2.0 GPa, annealing time of 12 h, garnets, melts and clinopyroxenes occur in amphibolite gradually with increasing temperature and the chemical compositions of melt vary from tonalite to granodiorite, and then to tonalite. However, at 2.0 GPa and 850℃, with the annealing time increasing, the garnets, melts and cli-nopyroxenes also occur in amphibolite gradually and the chemical compositions of melt vary from tonalite to granodiorite. In both cases, melts interconnect with each other when the contents of melt are over the 5 vol.%. the viscosities of the melt produced in amphibolite at temperature higher than 850℃ are on a level with 104 Pa·s. The interconnected melt with such a viscosity may segregate from the source rock and form the magma over reasonable geological time. Therefore, it is believed that at the lower part of the overthickened crust, the tonlitic and grano-dioritic magma may be generated through the dehydration melting of amphibolite.

关键词： solid amphibolite, high pressure, high temperature, time, partial melting.

A novel mullite anti-gyroid/SiC gyroid ceramic metastructure based on digital light processing 3. printing with enhanced electromagnetic wave absorption and mechanical properties

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Journal of Advanced Ceramics 2024年第8期13卷 1212-1222页

作者： chaoyang Wang Xiao Chen Zhicheng Wang Jjalin Bai Jie Tang Yulong She Zhengren Huang Yong Yang State Key Laboratory of High Performance Ceramics and Superfine Microstructures Shanghai Institute of CeramicsChinese Academy of SciencesShanghai 200050China College of Materials Science and Opto-Electronic Technology University of Chinese Academy of SciencesBeijing 100049China

Sic-based composites are widely used as electromagnetic wave absorbers due to their excellent dielectric ***,the constraints associated with structural design and the intricacies of the preparation process hinder their broader *** this study,novel mullite anti-gyroid/SiC gyroid metastructures are designed to integrate the mechanical and electromagnetic wave(EMW)absorption properties of composite *** anti-gyroid/SiC gyroid composites are fabricated utilizing a combination of digital light processing(DLP)three-dimensional(3.)printing and precursor infiltration and pyrolysis(PiP)*** the modulation of structural units,the electromagnetic parameters can be effectively regulated,thus improving the impedance matching characteristics of the *** structural composites show outstanding EMW absorption properties,with a minimum reflection loss of-54 dB at a thickness of 1.9 mm and an effective absorption bandwidth of 3.20 GHz at a thickness of 2.2 ***,the PIP process significantly enhances the mechanical properties of the composites;compared with those of the mullite/SiC ceramics,the flexural strength of the composites is improved by 3.69-5.85 times(13.28±1.15 MPa vs.(49.05±1.07)-(77.78±3.72)MPa),and the compressive strength is improved by 4.59-13.58 times(8.55±0.90 MPa vs.(3..02±1.63.-(116.13.2.58)MPa).This approach offers a novel and effective method for fabricating structural composites with an expanded range of higher electromagnetic wave absorption properties and improved mechanical properties.

关键词： mullite anti-gyroid/SiC gyroid metastructures digital light processing(DLP) precursor infiltration and pyrolysis(PIP) electromagnetic waveabsorption

The regular representation and regular covariant representation of crossed products of Woronowicz C^(*)-algebras

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Science china Mathematics 2005年第9期48卷 1245-1259页

作者： ZHANG Xiaoxia~(1,2) & GUO Maozheng~(1,3. 1. School of Mathematical Sciences,Peking University,beijing 100871,china 2. department of Mathematics,Yantai University,Yantai 264005,china 3. LMAM,Peking University,beijing 100871,china 1. School of Mathematical Sciences Peking University 100871 Beijing China 2. department of Mathematics Yantai University 264005 Yantai China 3. LMAM Peking University 100871 Beijing China

In this paper,it is shown that the regular representation and regular covariant representation of the crossed products A×α G correspond to the twisted multiplicative unitary operators,where A is a Woronowicz C~*-algebra acted upon by a discrete group ***,it is also shown that the regular covariant C~*-algebra is the Woronowicz C~*-algebra which corresponds to a multiplicative ***,an explicit description of the multiplicative unitary operator for C(SU_q(2) )×α (?) is given in terms of those of the Woronowicz C~*-algebra C(SU_q(2) ) and the discrete group G.

关键词： multiplicative unitary operator, Woronowicz C*-algebra, crossed product.

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,{3. 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

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,{3. 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

Reliability analysis of M/G/1 queues with general retrial times and server breakdowns

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Progress in Natural Science:Materials International 2006年第5期16卷 464-473页

作者： WANG Jinting (department of Mathematics, beijing Jiaotong University, beijing 100044,{3.) department of Mathematics Beijing Jiaotong University Beijing 100044 China

This paper concerns the reliability issues as well as queueing analysis of M/G/1 retrial queues with general retrial times and server subject to breakdowns and repairs. We assume that the server is unreliable and customers who find the server busy or down are queued in the retrial orbit in accordance with a first-come-first-served discipline. Only the customer at the head of the orbit queue is allowed for access to the server. The necessary and sufficient condition for the system to be stable is given. Using a supplementary variable method, we obtain the Laplace-Stieltjes transform of the reliability function of the server and a steady state solution for both queueing and reliability measures of interest. Some main reliability indexes, such as the availability, failure frequency, and the reliability function of the server, are obtained.

关键词： retrial queues general retrial times reliability server breakdowns and repairs.

SINGLE BIRTH PROCESSES

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Chinese Annals of Mathematics,Series B 1999年第1期20卷 77-82页

作者： CHEN MUFA(department of Mathematics,beijing Normal University,beijing 100875,{3.) beijing Normal Univ Dept Math Beijing 100875 Peoples R China

The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied

关键词： Markov chains Single birth process Uniqueness criterion

Some properties on multivariate filter banks with a matrix factorization

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Progress in Natural Science:Materials International 2005年第2期15卷 20-30页

作者： LIAN Qiaofang1, XIAO Hongying2* and CHEN Qiuhui3.1. department of Mathematics, beijing Jiaotong University, beijing 100044,{3. 2. Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, beijing 100080,{3. 3. department of Scientific Computing and Computer Applications, Zhongshan University, Guangzhou 510275,{3.) department of Mathematics Beijing Jiaotong University Beijing 100044 China. Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100080 China. department of Scientific Computing and Computer Applications Zhongshan University Guangzhou 510275 China

A class of multivariate filter banks with a matrix factorization has been developed by Chen et al. The main purpose of this paper is to discuss some further properties of this kind of filter bank, such as the completeness, accuracy of the corresponding scaling functions and the relationships with Daubechies' wavelets and the multi-wavelets provided by Chui and Lian. Moreover, some examples are given to show that this kind of filter bank has a higher accuracy for the scaling functions.

关键词： filter banks completeness accuracy matrix factorization