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On the stability of diffusion processes with state-dependent switching

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science china Mathematics 2006年第9期49卷 1258-1274页

作者： XI Fubao & ZHAO Liqin department of Mathematics, beijing institute of technology, beijing 100081, china school of Mathematical sciences, beijing Normal University, beijing 100875, china department of Mathematics Beijing Institute of Technology Beijing China school of Mathematical sciences Beijing Normal University Beijing China

In this paper we consider the stability for diffusion processes with state-dependent switching. We first prove their Feller continuity by the coupling methods. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions. Finally, we append a very brief discussion about the regularity of these processes.

关键词： Feller continuity, coupling, strong Feller continuity, exponential ergodicity,state-dependent switching.

Nontrivial homoclinic orbits for second-order singular and periodic Hamiltonian systems

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Chinese science Bulletin 1999年第2期44卷 123-129页

作者： LI Chengyue , FAN Tianyou TONG MingshengResearch Center of Materials science, beijing institute of technology, beijing 100081, china department of Mathematics, Central University for Nationalities, beijing 100081, china Computer Center, beijing institute of technology, beijing 100081, china Research Center of Materials science Beijing Institute of Technology Beijing China department of Mathematics Central University for Nationalities Beijing China Computer Center Beijing Institute of Technology Beijing China

The existence of nontrivial homoclinic orbits of periodic Hamiltonian systems: is proved, where q=（q1,q2,’',qn）, n>2; V（t, q）:R1×Rn\{e}→R1 is a potential With a singularity, i.e. -V（t, q）→+∞, as q→e. The m... 详细信息

关键词： Hamiltonian systems strong force condition homoclinic orbit.

Theoretical observation of hexaatomic molecules containing pentacoordinate planar carbon

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science china chemistry 2008年第11期51卷 1030-1035页

作者： LUO Qiong State Key Laboratory of Explosion science and technology, beijing institute of technology, beijing 100081, china State Key Laboratory of Explosion science and technology Beijing Institute of Technology Beijing China

The smallest molecules up to date containing a D5h pentacoordinate planar carbon (PPC) atom, CBe5 and CBe54-, are presented by means of ab initio calculations. To gain a better understanding about which electronic factors contribute to their stabilization, natural bond orbital (NBO) analysis and the nucleus independent chemical shifts (NICS) were calculated. The data reported here suggest that D5h CBe5 is σ aromaticity in nature, while in D5h CBe54- π aromaticity is dominating. The classical octet rule is well satisfied in both molecules, and is one of the fundamental reasons to understand the stability of the pentagon structures. The Be5 ring serves as σ donor in D5h CBe5, and π-acceptor in D5h CBe54-. The D5h CBe54- possessing 18 valence electrons with a closed-shell electron configuration is the most plau-sible candidate for experimental detection.

关键词： pentacoordinate planar carbon Be5 ring ab initio

Feller property and exponential ergodicity of diffusion processes with state-dependent switching

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science china Mathematics 2008年第3期51卷 329-342页

作者： XI FuBao department of Mathematics, beijing institute of technology, beijing 100081, china department of Mathematics Beijing Institute of Technology Beijing China

In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions.

关键词： Feller continuity Radon-Nikodym derivative strong Feller continuity exponential ergodicity state-dependent switching 60J60 34D25

Cleaning of Chromate Manufacture Process

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International Journal of Minerals,Metallurgy and Materials 2000年第2期14卷 132-134页

作者： Xing Zou Yi Zhang(Applied science school, University of science and technology beijing, beijing 100083, china)(institute of Engineering chemistry and Metallurgy, Chinese Academy of sciences, beijing 100080, china) Applied science school University of Science and Technology Beijing Beijing 100083 China institute of Engineering chemistry and Metallurgy Chinese Academy of Sciences Beijing 100080 China

Sodium chromate solubility is determined in the range of NaOH concentrations from 450 to 810 g/L andsolution temperatUres from 30 to 110℃. The optimized conditions to separate sodium chromate from NaOH inleached solution are resolved. It is first found the method to efficiently separate sbdium chromate from NaOH andsodium altuninate in crude sodium chromate. Bench-scale studies on the separating are performed. Finally, goodseparation results are achieved.

关键词： chromate separation clean process

Jet formation and penetration mechanism of W typed shaped charge

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Acta Mechanica Sinica 2009年第1期25卷 107-120页

作者： Cheng Wang Fenglei Huang Jianguo Ning State Key Laboratory of Explosion science and technology,beijing institute of technology, 100081 beijing, china State Key Laboratory of Explosion science and technology Beijing Institute of Technology Beijing China

Existing classical shaped charges are well known for their longer jets capable of achieving large hole depth to hole diameter ratios in metallic targets. However, in some situations, there arises demand to obtain 1：1 ratio for hole depth to hole diameter which is beyond normal shaped charges capability. A new variant of shape charge, named W typed shape charge （WSC）, is proposed in this paper, which can meet the demand of 1：1 ratio, and is based on the geometry that can produce annular jets upon proper initiation scheme. In this paper, we present formation and penetration results of WSC based on three different schemes. We also show that not all WSC designs can form annular jets, only annularly initiated WSC, which also fulfils the ＂Internal-External Liners Equal-Impulse＂ criterion, has the capability to form annular jet. The experimental and numerical results show that when the ratio between annular initiation ring diameter and the charge diameter is 0.75, an annular jet is formed, which was also supported by high speed photographs performed in vacuum. 2D numerical simulations are performed with indigenously developed simulation software, where Eulerian approach with multi-material interface tracking algorithm is utilized, to find various mechanisms involved during jet formation process. The calculation results are found in good agreement with the experimental results, indicating that the interface treatment algorithm proposed in this paper can not only deal with large deformation problem, but also depict clearly the variation of materials interface. It is especially suitable for simulation of the process from liner collapse to formation of shaped charge jet.

关键词： WSC Annular jet Interface tracking Numerical simulation

Highly sensitive response to dopamine at a modified electrode involving a composite film with Au nanoparticles dispersed in a fluorocarbon polymer

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science china chemistry 2010年第4期53卷 826-831页

作者： KONG LinLin, KAN MeiXiu, HAN DongMei, WANG Ting & ZHANG HuiMin school of science, beijing institute of technology, beijing 100081, china school of science Beijing Institute of Technology Beijing China

A new approach for the highly sensitive detection of dopamine by a novel composite film involving gold nanoparticles trapped in a negatively-charged fluorocarbon polymer (Nafion) on a glassy carbon (GC) electrode fabricated by a simple method is described. Gold nanoparticles with an average diameter of 2.3 nm ± 0.2 nm are dispersed throughout the whole Nafion film. The introduction of gold nanoparticles into the Nafion film not only gives a highly active electrode surface area but also increases the conductivity of the Nafion film and the resulting Au/Nafion/GC electrode combines the advantages of the properties of gold nanoparticles and the selective pre-concentration ability of Nafion. For positively charged dopamine, the results show a decrease in the redox peak separation and a high sensitivity. The oxidation peak current of dopamine was shown to vary linearly with dopamine concentration over a wide range from 0.4 to 50.0 μmol/L with a detection limit of 0.3 μmol/L. Negatively charged ascorbic acid shows no redox waves at concentrations up to 1.0 ×10-4 mol/L.

关键词： composite film gold nanoparticles Nafion dopamine ascorbic acid

Fiducial inference in the pivotal family of distributions

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science china Mathematics 2006年第3期49卷 410-432页

作者： XU Xingzhong & LI Guoying department of Mathematics, beijing institute of technology, beijing 100081, china Academy of Mathematics and Systems science, Chinese Academy of sciences, beijing 100080, china department of Mathematics Beijing Institute of Technology Beijing China Academy of Mathematics and Systems science Chinese Academy of Sciences Beijing China

In this paper a family, called the pivotal family, of distributions is considered.A pivotal family is determined by a generalized pivotal model. Analytical results show that a great many parametric families of distributions are pivotal. In a pivotal family of distributions a general method of deriving fiducial distributions of parameters is proposed. In the method a fiducial model plays an important role. A fiducial model is a function of a random variable with a known distribution, called the pivotal random element, when the observation of a statistic is *** method of this paper includes some other methods of deriving fiducial distributions. Specially the first fiducial distribution given by Fisher can be derived by the method. For the monotone likelihood ratio family of distributions, which is a pivotal family, the fiducial distributions have a frequentist property in the Neyman-Pearson view. Fiducial distributions of regular parametric functions also have the above frequentist property. Some advantages of the fiducial inference are exhibited in four applications of the fiducial distribution. Many examples are given, in which the fiducial distributions cannot be derived by the existing methods.

关键词： confidence bounds, fiducial distributions, fiducial model, frequentist prop-erty, generalized pivotal model, pivotal family of distributions, testing hypotheses.

A thermal-mechanical constitutive model for b-HMX single crystal and cohesive interface under dynamic high pressure loading

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science china(Physics,Mechanics & Astronomy) 2010年第2期53卷 218-226页

作者： WU YanQing & HUANG FengLei State Key Laboratory of Explosion science and technology,beijing institute of technology,beijing 100081,china State Key Laboratory of Explosion science and technology Beijing Institute of Technology Beijing China

Due to the significant thermal-mechanical effects during hot spot formation in PBX explosives,a thermodynamic constitutive model has been constructed for HMX anisotropic single crystal subjected to dynamic impact loading. The crystal plasticity model based on dislocation dynamics theory was employed to describe the anisotropic plastic behavior along the preferential slip systems. A modified equation of state (EOS) was introduced into the constitutive equations through the decomposing stress tensor and the nonlinear elasticity for materials was taken into account. The one-dimensional strain impact simulations for HMX single crystal and quasi-bicrystal were performed respectively,in which the cohesive elements were inserted over the interface areas for the latter. The predicted particle velocities for the single crystal sample agreed well with the experimental results in the literature. Furthermore,the effects of crystal orientations,interface,misorientations on localized strain,stress and temperature distributions were predicted and discussed.

关键词： energetic single crystal dynamic high pressure crystal plasticity thermodynamics interfacial model