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L^p SOLUTIONS TO BSDES WITH MONOTONIC AND UNIFORMLY CONTINUOUS GENERATORS

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Annals of Differential Equations 2015年第2期31卷 175-181页

作者： Zhi Li Liping Xu Jiaowan Luo School of Information and math. Yangtze University School of math. and Information Sciences Guangzhou University

In this paper, we deal with Lp(p > 1) solutions to one dimensional backward stochastic differential equations(BSDEs) with discontinuous(left or right continuous)generators. We obtain an existence theorem of Lpsolution... 详细信息

关键词： backward stochastic differential equation existence theorem Lpsolution uniformly continuous condition

DISSIPATIVITY BEHAVIOR OF IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS

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Annals of Differential Equations 2007年第4期23卷 558-563页

作者： Yang Zhichun Xu Daoyi Dept. of math. Chongqing Normal University Chongqing 400047 Institute of Systems Science Chinese Academy of Sciences Beijing 100080 yangtze center of math. Sichuan University Chengdu 610064

In this paper, we investigate the dissipativity behavior and give the range estimate for solutions of impulsive functional differential equations. Also, some criteria on asymptotical stability and exponential stabilit... 详细信息

关键词： asymptotic behavior dissipativity stability impulsive differential equations

COMPLEX ISOCHRONICITY OF A SIXTH DEGREE SYSTEM

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Annals of Differential Equations 2007年第3期23卷 352-357页

作者： Wang Qinlong Song Shugang Liu Yirong Dept. of Information and math. Yangtze University Jingzhou 434023 Hubei Dept. of math. Central South University Changsha 410083

In this paper, we discuss the complex isochronicity of a sixth degree polynomial system. We first adopt a new algorithm to find necessary conditions for complex isochronicity, then prove the sufficient conditions usin... 详细信息

关键词： complex isochronicity sixth degree system

EXISTENCE AND MOMENT ESTIMATES FOR SOLUTIONS TO NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

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Annals of Differential Equations 2014年第1期30卷 62-84页

作者： Daoyi Xu Bing Li Shujun Long Lingying Teng Weisong Zhou yangtze center of math. Sichuan University College of Science Chongqing Jiaotong University College of math.and Information Science Leshan Normal University College of Computer Science and Tech. Southwest University for Nationalities

In this paper, we show the existence and uniqueness of solutions to a large class of SFDEs with the generalized local Lipschitzian coefficients. Some moment estima- tes of the solutions are given by establishing new Ito operator inequalities based on the Razumikhin technique. These estimates improve, extend and unify some related results including exponential stability of Mao （1997） [20], decay stability of Wu et al. （2010,2011） [32,33], Pavlovic et al. （2012） [24], asymptotic behavior of Luo et al. （2011） [18] and Song et al. （2013） [26]. Moreover, stochastic version of Wintner theorem in continuous space is established by the comparison principle, which improve and extend the main results of Xu et al. （2008 [39], 2013 [36]）. When the methods presented are applied to the SFDEs with impulses and SFDEs in Hilbert spaces, we extend the related results of Govindana et al. （2013） [7], Liu et al. （2007） [15], Vinod- kumar （2010） [29] and Xu et al. （2012） [35]. Two examples are provided to illustrate the effectiveness of our results.

关键词： stochastic functional differential equations existence and uniqueness stochastic differential inequalities stability impulses equations in Hilbert spaces

LIMIT CYCLES BIFURCATED FROM THE ORIGIN AND EQUATOR FOR A CLASS OF FIFTH SYSTEM

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Annals of Differential Equations 2004年第1期20卷 92-98页

作者：王勤龙黄文韬 School of Information Tech. and math. Yangtze University Jinzhou 434020 The 7th Department of Guilin University of Electronic Technology Guilin 541004

For a class of real fifth system, the first 8 singular point quantities of the origin and the first 6 singular point quantities of the equator are obtained, and at the same time, the two highest-order cases are proved respectively. Moreover, the problems of stability and limit cycle bifurcated from the origin and the equator are studied comparatively, then some better results are obtained.

关键词： fifth system the equator limit cycle

Fault prediction of fighter based on nonparametric density estimation

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Journal of Systems Engineering and Electronics 2005年第4期16卷 831-836页

作者： Zhang Zhengdao Hu Shousong Coll. of Automation Engineering Nanjing Univ. of Aeronautics and Astronautics Nanjing 210016 P. R. China School of Communication & Control Engineering Southern Yangtze Univ. Wuxi'214036 P. R. China

Fighters and other complex engineering systems have many characteristics such as difficult modeling and testing, multiple working situations, and high cost. Aim at these points, a new kind of real-time fault predictor is designed based on an improved k-nearest neighbor method, which needs neither the math.model of system nc, the training data and prior knowledge. It can study and predict while system＇s running, so that it can overcome the difficulty of data acquirement. Besides, this predictor has a fast prediction speed, and the false alarm rate and missing alarm rate can be adjusted randomly. The method is simple and universalizable. The result of simulation on fighter F-16 proved the effidency.

关键词： fighter fault prediction k-nearest neighbor method.

Problems of air pollution prevention in key regions of China

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Science China(Life Sciences) 2014年第3期57卷 356-357页

作者： TAO XingJian Department of math.and Sciences Bard CollegeAnnandale-on-Hudson 12504New YorkUSA

According to the World Health Organization, around two million people die prematurely from the effects of polluted air every single year. Air pollution is a huge problem espe- cially for people living in ＂smog-choked＂ cities. In China, these polluted cities accumulate at Beijing-Tianjin-Hebei, yangtze River Delta, and Pearl River Delta regions, in- volving 19 provincial level jurisdictions and 117 cities. These places are called the key regions because of these three regions. These areas cover only 14% of the country＇s land area, but account for nearly half （48%） of the country＇s population, 71% of the nation＇s GDP, 52% of the country＇s coal consumption. More significantly, the air pollutant emission level is 2.9-3.6 times higher than the nation＇s av- erage. Therefore, a comprehensive plan of pollution control is desperately needed. Fortunately, on December 5, 2012, the Chinese government issued a comprehensive air pollu- tion prevention and control plan named ＂12th Five-Year Plan on Air Pollution Prevention and Control in Key Regions＂. The plan has a long list of specific projects that are estimated to require 55.6 billion USD （350 billion RMB） investment （http：//***/ogc/china/air%20pollution. pdf）. What is the goal of this plan？ Is there any problem？

关键词：空气污染防治中国政府珠江三角洲地区世界卫生组织国内生产总值大气污染防治长江三角洲空气污染物

Talagrand's T_2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations

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Chinese Annals of math.matics,Series B 2006年第3期27卷 243-262页

作者： Liming WU Zhengliang ZHANG Laboratoire de math.matiques Appliquées CNRS-UMR 6620 Université Blaise Pascal 63177 Aubière France School of math.matics and Statistics Wuhan University Wuhan 430072 China. School of math.matics and Statistics Wuhan University Wuhan 430072 China.

We establish Talagrand＇s T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type＇s approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to Reaction- Diffusion equations are provided.

关键词： Stochastic partial differential equations (SPDEs) Logarithmic Sobolev inequality Talagrand's transportation inequality Poincaré inequality

Fuzzy stochastic generalized reliability studies on embankment systems based on first-order approximation theorem

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Water Science and Engineering 2008年第4期1卷 36-46页

作者： Wang Yajun Zhang Wohua Jin Weiliang Wu Changyu Ren Dachun Key Laboratory of Soft Soils and Geoenvironmental Engineering Ministry of Education Zhejiang University Hangzhou 310027 P. R. China College of Civil Engineering and Architecture Zhejiang University Hangzhou 310027 P. R. China yangtze River Scientific Research Institute Wuhan 430010 P. R. China

In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy math.matical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic math.matical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.

关键词： first-order approximation stochastic finite element method fuzzy math.algorithm stability of embankment and foundation reliability