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Harnack Inequality and Applications for SDEs Driven by G-Brownian Motion

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Acta Mathematicae Applicatae Sinica 2020年第3期36卷 627-635页

作者： fen-fen yang Center for Applied Mathematics Tianjin UniversityTianjin 300072China

In this paper,Wang's Harnack and shift Harnack inequality for a class of stochastic differential equations driven by G-Brownian motion are *** results generalize the ones in the linear expectation ***,some application... 详细信息

关键词： Harnack inequality shift Harnack inequality stochastic differential equations G-Brownian motion G-expectation

Inequality Estimates of an Inhomogeneous Semilinear Biharmonic Equation in Entire Space

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Acta Mathematicae Applicatae Sinica 2019年第4期35卷 812-819页

作者： fen yang Department of Mathematics and Statistics Wuhan University of Science and Technology

In this paper,we consider the inequality estimates of the positive solutions for the inhomogeneous biharmonic equation■-△^2u+u^p+f(x)=0 in R^n where △^2 is the biharmonic operator,p>1,n≥5 and 0≡f∈C(R^n)is a given nonnegative *** obtain different inequality estimates of Eq.(*),with which the necessary conditions of existence on f and p are also established.

关键词： inhomogeneous biharmonic equation positive solution inequality estimates

Harnack Inequalities for G-SDEs with Multiplicative Noise

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Communications in Mathematics and Statistics 2024年第2期12卷 279-305页

作者： fen-fen yang Department of Mathematics Shanghai UniversityShanghai 200444People’s Republic of China

The Harnack inequality for stochastic differential equation driven by G-Brownian motion with multiplicative noise is derived by means of the coupling by change of measure,which extends the corresponding results derived in Wang(*** Related Fields 109:417–424)under the linear ***,we generalize the gradient estimate under nonlinear expectation appeared in Song(*** Math.64:1093–1108).

关键词： Harnack inequality Gradient estimate Multiplicative noise G-Brownian motion SDEs

Harnack inequality and gradient estimate for G-SDEs with degenerate noise

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Science China Mathematics 2022年第4期65卷 813-826页

作者： Xing Huang fen-fen yang Center for Applied Mathematics Tianjin UniversityTianjin300072China

In this paper,the Harnack inequality for G-SDEs with degenerate noise is derived by the method of coupling by change of the ***,for any bounded and continuous function f,the gradient estimate∣∇P_(t)f∣≤c(p,t)(Pt|f|p)^(1/p),p>1,t>0 is obtained for the associated nonlinear semigroup P¯*** an application of the Harnack inequality,we prove the existence of the weak solution to degenerate G-SDEs under some integrable ***,an example is *** of the above results extend the existing ones in the linear expectation setting.

关键词： Harnack inequality degenerate noise G-SDE gradient estimate weak solution invariant expectation

Path independence of additive functionals for stochastic differential equations under G-framework

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Frontiers of Mathematics in China 2019年第1期14卷 135-148页

作者： Panpan REN fen-fen yang Departmen t of Mat hematics Swansea University Swansea SAI 8EN UK Center for Applied Mathematics Tianjin University Tianjin 300072 China

The path independence of additive functionals for stochastic differential equations (SDEs) driven by the G-Brownian motion is characterized by the nonlinear partial differential equations. The main result generalizes ... 详细信息

关键词： Stochastic differential equation (SDE) partial differential equation (PDE) additive functional G-SDEs G-Brownian motion nonlinear PDE

Neural cell co-culture induced differentiation of bone marrow mesenchymal stem cells into neuronal-like cells

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Neural Regeneration Research 2008年第6期3卷 581-584页

作者： Nailong yang Lili Xu fen yang Department of VIP Healthcare the Affiliated Hospital of Medical College Qingdao University Qingdao 266003 Shandong Province China Department of Endocrinology the Affiliated Hospital of Medical College Qingdao University Qingdao 266003 Shandong Province China

BACKGROUND： It has been previously demonstrated that the neural cell microenvironment has the ability to induce differentiation of bone marrow mesenchymal stem cells （BMSCs） into the neural cells. OBJECTIVE： To establish a co-culture system of human BMSCs and neural cells, and to observe effects of this co-culture system on differentiation of human BMSCs into neural cells. DESIGN, TIME AND SETTING： A comparative observation experiment, performed at the Center Labora-tory of the Affiliated Hospital of Medical College Qingdao University from October 2006 to December 2007. MATERIALS： Neural cells were obtained from human fetal brain tissue. BMSCs were harvested from fe-male patients that underwent autonomous stem cell transplantation. METHODS： BMSCs in the co-culture group consisted of BMSCs and third passage neural cells. BMSCs in the control group were solely cultured in vitro. MAIN OUTCOME MEASURES： Morphological changes of BMSCs were observed, and expression of the neuronal specific marker, neuron-specific enolase （NSE）, was analyzed by immunofluorescence staining after 4-5-day co-culture. RESULTS： The number of neural cells in the co-culture group increased and the cells spread on the culture bottle surface. Radial dendrite formed and connected with each other. NSE-immunoreactive cells were also detected. The positive ratio of NSE-positive cells reached （32.7±11.5）%, with morphological characteristics similar to neuronal cells. Human BMSCs did not express NSE in the control group. CONCLUSION： The microenvironment provided by neurons induced differentiation of BMSCs into neu-ronal-like cells.

关键词： bone marrow mesenchymal stem cells stem cell transplantation cell differentiation neurons

Harnack inequality and gradient estimate for functional G-SDEs with degenerate noise

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Probability, Uncertainty and Quantitative Risk 2022年第2期7卷 119-132页

作者： fen-fen yang Department of Mathematics Shanghai UniversityShanghai 2004China

In this paper,the Harnack and shift Harnack inequalities for functional G-SDEs with degenerate noise are derived by the method of coupling by change of ***,the gradient estimate for the associated nonlinear semigroup ... 详细信息

关键词： Harnack inequality Gradient estimate Degenerate noise Functional G-SDEs

Elliptic systems involving multiple critical nonlinearities and symmetric multi-polar potentials

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Science China Mathematics 2014年第5期57卷 1011-1024页

作者： KANG DongSheng yang fen School of Mathematics and Statistics South-Central University For Nationalities

In this paper,a system of elliptic equations is investigated,which involves multiple critical Sobolev exponents and symmetric multi-polar *** variational methods and analytic techniques,the relevant best constants are... 详细信息

关键词： elliptic equation Hardy potential solution critical exponent variational method

Pade Expansion and Nucleon-Nucleon Scattering in Coupled Channels

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Communications in Theoretical Physics 2009年第7期52卷 115-118页

作者： LIU Dan yang Ji-fen Department of Physics East China Normal University Shanghai 200062 China

We extend our Pade-aided analysis of the nonperturbative renormalization of nucleon-nucleon scatteringto the case of coupled channels.

关键词： nucleon-nucleon scattering nonperturbative renormalization effective field theories