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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

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

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

Factorization of Generalized Theta Functions Revisited

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Algebra Colloquium 2017年第1期24卷 1-52页

作者： Xiaotao Sun center of applied mathematics Tianjin University Tianjin 300072 China

This survey is based on my lectures given in the last few years. As a reference, constructions of moduli spaces of parabolic sheaves and generalized parabolic sheaves are provided. By a refinement of the proof of vanishing theorems, we show, without using vanishing theorems, a new observation that dim H0（Uc, θuc） is independent of all of the choices for any smooth curves. The estimate of various codimensions and computation of canonical line bundle of moduli space of generalized parabolic sheaves on a reducible curve are provided in Section 6, which is completely new.

关键词： moduli spaces parabolic sheaves degeneration

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

Optimal Investment Problem for an Insurer and a Reinsurer

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Journal of Systems Science & Complexity 2015年第6期28卷 1326-1343页

作者： LI Danping RONG Ximin ZHAO Hui School of Science Tianjin University center for applied mathematics Tianjin Uni-versity

This paper studies the optimal investment problem for an insurer and a reinsurer. The basic claim process is assumed to follow a Brownian motion with drift and the insurer can purchase proportional reinsurance from the reinsurer. The insurer and the reinsurer are allowed to invest in a risk-free asset and a risky asset. Moreover, the authors consider the correlation between the claim process and the price process of the risky asset. The authors first study the optimization problem of maximizing the expected exponential utility of terminal wealth for the insurer. Then with the optimal reinsurance strategy chosen by the insurer, the authors consider two optimization problems for the reinsurer： The problem of maximizing the expected exponential utility of terminal wealth and the problem of minimizing the ruin probability. By solving the corresponding Hamilton-Jacobi-Bellman equations, the authors derive the optimal reinsurance and investment strategies, explicitly. Finally, the authors illustrate the equality of the reinsurer＇s optimal investment strategies under the two cases.

关键词： Hamilton-Jacobi-Bellman equation optimal reinsurance and investment strategies proportional reinsurance ruin probability utility maximization

Modification of Maxwell model for conductivity prediction of carbon nanotubes-filled polymer composites with tunneling effect

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applied mathematics and Mechanics(English Edition) 2025年第1期46卷 25-36页

作者： Jue ZHU Longyuan LI Ningtao ZHU Zhejiang Provincial Engineering Research center for the Safety of Pressure Vessel and Pipeline Key Laboratory of Impact and Safety Engineering (Ningbo University) Ministry of Education School of Engineering Computing and Mathematics University of Plymouth Xi'an Zhanshi Testing & Engineering Co.Ltd.

Carbon nanotubes(CNTs) have garnered great attention in recent years due to their outstanding electrical, thermal, and mechanical properties. The incorporation of small amounts of CNTs in polymers can substantially improve the sensitivity of the polymer's electrical conductivity. This paper presents a modified Maxwell model to evaluate the electrical conductivity of CNTs-filled polymer composites by introducing a transition zone to account for the tunneling effect. In this modified Maxwell model, the CNTs-filled polymer composite is modeled as a three-phase composite, consisting of a matrix(polymer), inclusions(CNTs), and a transition zone(tunneling zone). The effective electrical conductivity(EEC) of the composite is calculated based on the volume fractions and electrical conductivities of the matrix, inclusions, and transition zone. The model's validity is confirmed through the use of available test data, which demonstrates its capability to accurately capture the nonlinear conductivity behavior observed in CNTs-polymer composites. This study offers valuable insights into the design of high-performance conductive polymer nanocomposites, and enhances the understanding of electrical conduction mechanisms in CNT-dispersed polymer composites.

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GOMA:functional enrichment analysis tool based on GO modules

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Chinese Journal of Cancer 2013年第4期32卷 195-204页

作者： Qiang Huang Ling-Yun Wu Yong Wang Xiang-Sun Zhang National center for mathematics and Interdisciplinary Sciences Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences

Analyzing the function of gene sets is a critical step in interpreting the results of high-throughput experiments in systems biology. A variety of enrichment analysis tools have been developed in recent years, but most output a long list of significantly enriched terms that are often redundant, making it difficult to extract the most meaningful functions. In this paper, we present GOMA, a novel enrichment analysis method based on the new concept of enriched functional Gene Ontology (GO) modules. With this method, we systematically revealed functional GO modules, i.e., groups of functionally similar GO terms, via an optimization model and then ranked them by enrichment scores. Our new method simplifies enrichment analysis results by reducing redundancy, thereby preventing inconsistent enrichment results among functionally similar terms and providing more biologically meaningful results.

关键词： GO enrichment analysis, modules, functional redundancy, network, relationships

On the Constant Metric Dimension of Generalized Petersen Graphs P(n,4)

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Acta Mathematica Sinica,English Series 2014年第7期30卷 1145-1160页

作者： Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed Ahtsham-ul-Haq BOKHARY center for Advanced Studies in Pure and applied mathematics Bahauddin Zakariya University

In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） and n = 4k ＋ 3 （k is odd）, we prove that the metric dimension of P（n,4） is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P（n, 4） has constant metric dimension.

关键词： Metric dimension constant metric dimension generalized Petersen graphs