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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 100081 China School of Mathematical Sciences Beijing Normal University Beijing 100875 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.

Small Random Perturbations of One-Dimensional Diffusion Processes

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Acta Mathematica Sinica,English Series 1998年第1期14卷 35-40页

作者： xi fubao department of Applied mathematics, beijing institute of technology, beijing 100081, china

In the present paper we consider the small random perturbations of one-dimensional diffosion processes. By virtue of stochastic analysis methods, we investigate the asymptotics of the mean exit times and probabilistic... 详细信息

关键词： Diffusion processes Small random perturbations Exit times

Invariant Measures for a Random Evolution Equation with Small Perturbations

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Acta Mathematica Sinica,English Series 2001年第4期17卷 631-642页

作者： Fu Bao xi department of Applied mathematics, beijing institute of technology, beijing 100081, P. R. china department of Applied mathematics Beijing Institute of Technology Beijing 100081 P. R. China

In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.

关键词： Invariant measures Large deviations Coupling Random evolution equation

STATIONARY SOLUTION FOR A STOCHASTIC LINARD EQUATION WITH MARKOVIAN SWITCHING

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Acta Mathematica Scientia 2005年第1期25卷 95-104页

作者：席福宝赵丽琴 department of mathematics beijing institute of technology Beijing 100081 China department of mathematics beijing Normal University Beijing 100875 China

This paper considers a stochastic Lienard equation with Markovian switching. The Feller continuity of its solution is proved by the coupling method and a truncation argument. The existence of a stationary solution for... 详细信息

关键词： Coupling truncation feller continuity stationary solution

In situ Simulation of Thermal Reality

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Research 2024年第2期2023卷 685-690页

作者： Peng Jin Jinrong Liu fubao Yang Fabio Marchesoni Jian-Hua Jiang Jiping Huang department of Physics State Key Laboratory of Surface Physicsand Key Laboratory of Micro and Nano Photonic Structures(MOE)Fudan UniversityShanghai 200438China Center for Phononics and Thermal Energy Science Shanghai Key Laboratory of Special Artificial Microstructure Materials and TechnologySchool of Physics Science and EngineeringTongji UniversityShanghai 200092China department of Physics University of CamerinoCamerino 62032Italy Suzhou institute for Advanced Research University of Science and Technology of ChinaSuzhou 215123China

Simulated reality encompasses virtual,augmented,and mixed realities梕ach characterized by different degrees of truthfulness in the visual perception:"all false","coexistence of true and false,"and"difficult distinction between true and false,"*** all these technologies,however,the temperature rendering of virtual objects is still an unsolved ***,the lack of thermal tactile functions substantially reduces the quality of the user's real-experience *** address this challenge,we propose theoretically and realize experimentally a technological platform for the in situ simulation of thermal *** this purpose,we design a thermal metadevice consisting of a reconfigurable array of radiating units,capable of generating the thermal image of any virtual object,and thus rendering it in situ together with its thermal *** is a substantial technological advance,which opens up new possibilities for simulated reality and its applications to human activities.

关键词： false rendering signature

The Hausdorff Dimension of Sections

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Chinese Annals of mathematics,Series B 2007年第2期28卷 187-194页

作者： Min NIU Lifeng xi department of mathematics and Mechanics Beijing University of Science and Technology Beijing 100083China institute of mathematics Zhejimag Wanli University Ningbo 315100 Zhejiang China

The notion of finite-type open set condition is defined to calculate the Hausdorff dimensions of the sections of some self-similar sets, such as the dimension of intersection of the Koch curve and the line x=α with ... 详细信息

关键词： Hausdorff dimension Self-similar set Section Open set condition

Ab initio theoretical studies on N_(28),B_4N_(24),B_(12)N_(16), and B_(16)N_(12) with T_d symmetry

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Chinese Journal of Chemistry 1996年第6期14卷 490-496页

作者： JIANG, xin-Tian HU, Xu-Guang LI, Qian-Shu department of Chemistry, Shaanxi Teachers University, xi’an, Shanxi 710062, china institute of Theoretical Chemistry, National Laboratory of Theoretical and Computational Chemistry, JilinUniversity, Changchun, Jilin 130023, chinaSchool of Chemical Engineering and Materials Science, beijing institute of technology, beijing 100081,china department of Chemistry Shaanxi Teachers University Xi'an Shanxi 710062 China institute of Theoretical Chemistry National Laboratory of Theoretical and Computational Chemistry Jilin University Changchun Jilin 130023 China School of Chemical Engineering and Materials Science Beijing Institute of Technology Beijing 100081 China

Structures, energies and vibrational frequencies have been calculated for hollow cage clusters N28, B4N24, B12N16, and B16N12 with Td symmetry using ab initio quantum mechanical methods at the RHF/3-21G level. Each species is predicted to be both chemically and kinetically stable. Skeletal polyhedrons of all considered boron nitride hollow cage clusters are constructed from 5- and 6-membered rings.

关键词： Nitrogen cluster boron nitride cluster ab initio molecular orbital theory fullerene

Multi-objective robust control based on fuzzy singularly perturbed models for hypersonic vehicles

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Science china(Information Sciences) 2011年第3期54卷 563-576页

作者： HU YeNan 1 , YUAN Yuan 2 , MIN HaiBo 2,3 & SUN FuChun 1 1 department of Computer Science and technology, Tsinghua University, beijing 100084, china 2 department of Automation, xi’an Research institute of High-Tech, xi’an, Shaanxi 710025, china 3 beijing institute of Astronautical System Engineering, beijing 100076, china 1. department of Computer Science and technology Tsinghua University Beijing 100084 China2. Department of Automation Xi’an Research Institute of High-Tech Xi’an Shaanxi 710025 China3. Beijing Institute of Astronautical System Engineering Beijing 100076 China

In this paper, we propose a multi-objective robust controller based on fuzzy singularly perturbed models (FSPM) for the longitudinal motion of an air-breathing hypersonic vehicle. The control objective is to provide velocity and altitude tracking in the presence of the uncertainties and unknown nonlinearities in the model caused by variations in flight conditions. By approximating the multi-time-scale model with FSPM, ill-posed matrix calculations are circumvented. Under this framework, a fuzzy multi-objective robust controller is developed, and the linear matrix inequalities (LMI) condition is derived. Numerical simulation using the longitudinal model of a hypersonic aircraft is provided to demonstrate the effectiveness of the proposed strategy.

关键词： FSPM multi-objective robust control intelligent control hypersonic vehicle

Pairwise entanglement and local polarization of Heisenberg model

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Science china(Physics,Mechanics & Astronomy) 2008年第10期51卷 1515-1522页

作者： xi xiaoQiang1,2, ZHANG Tao3, YUE RuiHong3,4 & LIU WuMing2 1 department of Applied mathematics and Physics, xi’an institute of Post and Telecommunications, xi’an 710061, china 2 beijing National Laboratory for Condensed Matter Physics, institute of Physics, Chinese Academy of Sciences, beijing 100080, china 3 institute of Modern Physics, Northwest University, xi’an 710069, china 4 department of Physics, Ningbo University, Ningbo 315211, china department of Applied mathematics and Physics Xi’an Institute of Post and Telecommunications Xi’an 710061 China beijing National Laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing 100080 China institute of Modern Physics Northwest University Xi’an 710069 China department of Physics Ningbo University Ningbo 315211 China

The characteristics of pairwise entanglement and local polarization (LP) are dis-cussed by studying the ground state (states) of the Heisenberg XX model. The re-sults show that: the ground state (states) is (are) composed of the micro states with the minimal polarization (0 for even qubit and 1/2 for odd qubit); LP and the prob-ability of the micro state have an intimate relation, i.e. the stronger the LP, the smaller the probability, and the same LP corresponds to the same probability; the pairwise entanglement of the ground state is the biggest in all eigenvectors. It is found that the pairwise entanglement is decreased by the state degeneracy and the system size. The concurrence approaches a fixed value of about 0.3412 (for odd-qubit chain) or 0.3491 (for even-qubit chain) if the qubit number is large enough.

关键词： Heisenberg XX model local polarization pairwise entanglement