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CAVITY FORMATION AT THE center OF A SPHERE COMPOSED OF TWO COMPRESSIBLE HYPER-ELASTIC MATERIALS

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Applied mathematics and Mechanics(English Edition) 2003年第9期24卷 1009-1016页

作者：任九生程昌钧朱正佑 Shanghai Institute of Applied mathematics and Mechanics

The cavitated bifurcation problem in a solid sphere composed of two compressible hyper_elastic materials under a uniform boundary radial stretch was examined. The solutions, including the trivial solution and the cavitated solutions, were obtained. The bifurcation curves and the stress contributions subsequent to cavitation were discussed. The phenomena of the right and the left bifurcations as well as the catastrophe and concentration of stresses are observed. The stability of solutions is discussed through the energy comparison.

关键词： compressible hyper_elastic material cavitated bifurcation catastrophe and concentration of stress energy comparison

Explicit Representations for Local Lagrangian Numerical Differentiation

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Acta Mathematica Sinica,English Series 2007年第2期23卷 365-372页

作者： He Yu WANG Feng CUI Xing Hua WANG Computing center Zhejiang University Department of mathematics Hong Kong Baptist University Department of mathematics Zhejiang University

It is shown that in Lagrangian numerical differentiation formulas, the coefficients are explicitly expressed by means of cycle indicator polynomials of symmetric group. Moreover, asymptotic expansions of the remainders are also explicitly represented as a fixed number of interpolation nodes approaching infinitely to the point at which the derivative is evaluated. This implies that complete explicit formulas for local Lagrangian numerical differentiation can be obtained.

关键词： numerical differentiation explicit representation local estimate symmetric group cycle indicator

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation

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National Science Review 2024年第7期11卷 135-147页

作者： Yue Zhao Wei Zhang Tiejun Li center for Data Science Peking University Zuse Institute Berlin Department of mathematics and Computer Science Freie Universit?t Berlin Laboratory of mathematics and Applied mathematics(LMAM)and School of Mathematical Sciences Peking University center for Machine Learning Research Peking University

We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state ***-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product ***, our loss function has an intimate connection with the steady entropy production rate(EPR),enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional(8D)limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.

关键词： high-dimensional potential landscape non-equilibrium system entropy production rate dimensionality reduction deep learning

p-arrangeable Graphs are Folkman Linear

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Acta Mathematicae Applicatae Sinica 2021年第1期37卷 69-74页

作者： Xun CHEN Qi-zhong LIN center for Discrete mathematics Fuzhou UniversityFuzhou 350108 China

For graphs F and G,let F→(G,G)denote that any red/blue edge coloring of F contains a monochromatic *** Folkman number f(G;t)to be the smallest order of a graph F such that F→(G,G)andω(F)≤*** is shown that f(G;t)≤... 详细信息

关键词： Folkman number Folkman linear Multi-partite regularity lemma

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

Propagation of chaos and conditional McKean-Vlasov SDEs with regime-switching

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Frontiers of mathematics in China 2022年第4期17卷 731-746页

作者： Jinghai SHAO Dong WEI center for Applied mathematics Tianjin UniversityTianjin300072China

We investigate a particle system with mean field interaction living in a random environment characterized by a regime-switching *** switching process is allowed to be dependent on the particle *** well-posedness and various properties of the limit conditional McKean-Vlasov SDEs are studied,and the conditional propagation of chaos is established with explicit estimate of the convergence rate.

关键词： Regime-switching propagation of chaos Wasserstein distance conditional McKean-Vlasov SDEs rate of convergence

Boundary behavior of harmonic functions on metric measure spaces with non-negative Ricci curvature

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Frontiers of mathematics in China 2022年第3期17卷 455-471页

作者： Wanwan YANG Bo LI center for Applied mathematics Tianjin UniversityTianjin 300072China

Let(X,d,μ)be a metric measure space with non-negative Ricci *** paper is concerned with the boundary behavior of harmonic function on the(open)upper half-space X×R_(+).We derive that a function f of bounded mean oscillation(BMO)is the trace of harmonic function u(x,t)on X×R_(+),u(x,0)=f(x),whenever u satisfies the following Carleson measure condition supx_(B),r_(B) ∫_(0)^(r_(B) ) f_(B(x_(B),r_(B))) |t■u(x,t)|^(2)dμ(x)dt/t≤Ccentered at x_(B) with radius r_(B).Conversely,the above condition characterizes all the harmonic functions whose traces are in BMO space.

关键词： Harmonic function metric measure space BMO Carleson measure

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

Distribution dependent reflecting stochastic differential equations

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Science China mathematics 2023年第11期66卷 2411-2456页

作者： Feng-Yu Wang center for Applied mathematics Tianjin UniversityTianjin 300072China

To characterize the Neumann problem for nonlinear Fokker-Planck equations,we investigate distribution dependent reflecting stochastic differential equations(DDRSDEs)in a *** first prove the well-posedness and establish functional inequalities for reflecting stochastic differential equations with singular drifts,and then extend these results to DDRSDEs with singular or monotone coefficients,for which a general criterion deducing the well-posedness of DDRSDEs from that of reflecting stochastic differential equations is established.

关键词： distribution dependent reflecting stochastic differential equations well-posedness log-Harnack inequality