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| 1 | On the Uniqueness of Heat Flow of Harmonic Maps and Hydrodynamic Flow of Nematic Liquid Crystals显示文摘For any n-dimensional compact Riemannian manifold (M,g) without boundary and another compact Riemannian manifold (N,h), the authors establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0,T),W1,n). For the hydrodynamic flow (u,d) of nematic liquid crystals in dimensions n = 2 or 3, it is shown that the uniqueness holds for the class of weak solutions provided either (i) for n = 2, u ∈ Lt∞ L2x∩L2tHx1, ▽P∈ Lt4/3 Lx4/3 , and ▽d∈ L∞t Lx2∩Lt2Hx2; or (ii) for n = 3, u ∈ Lt∞ Lx2∩L2tHx1∩ C([0,T),Ln), P ∈ Ltn/2 Lxn/2 , and ▽d∈ L2tLx2 ∩ C([0,T),Ln). This answers affirmatively the uniqueness question posed by Lin-Lin-Wang. The proofs are very elementary. | Fanghua LIN Changyou WANG | 2010 | Chinese Annals of Mathematics,Series B2010，31，6： | 11 |
| 2 | The Faddeev knots as stable solitons: Existence theorems显示文摘The problem of existence of knot-like solitons as the energy-minimizing configurations in the Faddeev model, topologically characterized by an Hopf invariant, Q, is considered. It is proved that, in the full space situation, there exists an infinite set S of integers so that for any m ∈ S, the Faddeev energy, E, has a minimizer among the class Q = m; in the bounded domain situation, the same existence theorem holds when S is the set of all integers. One of the important technical results is that E and Q satisfy the sublinear inequality E ≤ C|Q|3/4, where C >0 is a universal constant, which explains why knotted (clustered soliton) configurations are preferred over widely separated unknotted (multisoliton) configurations when |Q| is sufficiently large. | LIN Fanghua & YANG YisongCourant Institute of Mathematical Sciences, New York University, New York, New York 10012, U. S. A.School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U. S. A. Department of Mathematics, Polytechnic University, Brooklyn, New York 11201, U. S. A. | 2004 | Science China Mathematics2004，47，2： | 10 |
| 3 | Real-time control for fuel-optimal Moon landing based on an interactive deep reinforcement learning algorithm显示文摘In this study,a real-time optimal control approach is proposed using an interactive deep reinforcement learning algorithm for the Moon fuel-optimal landing problem.Considering the remote communication restrictions and environmental uncertainties,advanced landing control techniques are demanded to meet the high requirements of real-time performance and autonomy in the Moon landing missions.Deep reinforcement learning(DRL)algorithms have been recently developed for real-time optimal control but suffer the obstacles of slow convergence and difficult reward function design.To address these problems,a DRL algorithm is developed using an actor-indirect method architecture to achieve the optimal control of the Moon landing mission.In this DRL algorithm,an indirect method is employed to generate the optimal control actions for the deep neural network(DNN)learning,while the trained DNNs provide good initial guesses for the indirect method to promote the efficiency of training data generation.Through sufficient learning of the state-action relationship,the trained DNNs can approximate the optimal actions and steer the spacecraft to the target in real time.Additionally,a nonlinear feedback controller is developed to improve the terminal landing accuracy.Numerical simulations are given to verify the effectiveness of the proposed DRL algorithm and demonstrate the performance of the developed optimal landing controller. | Lin Cheng Zhenbo Wang Fanghua Jiang | 2019 | Astrodynamics2019，3，4： | 8 |
| 4 | Simulation of CO_2 variations at Chinese background atmospheric monitoring stations between 2000 and 2009: Applying a CarbonTracker model显示文摘We carried out a downscaling treatment over China using the CarbonTracker numerical model,which was applied using double grid nesting technology(3°×2°over the whole globe,1°×1°over China),simulating and analyzing atmospheric CO2concentrations over 10 recent years(2000–2009).The simulation results agreed very well with observed data from four background atmospheric monitoring stations in China(The periods for which the simulation results and observed values be compared were January2000 to December 2009 for the WLG station and June 2006 to December 2009 for the SDZ,LFS,and LAN stations),giving correlation coefficients of>0.7.The high-resolution simulation data correlated slightly better than the low resolution simulation data with the observed data for three of the regions’atmospheric background stations.Further analysis of the annual,seasonal CO2concentration variations at the background stations showed that the CO2concentration increased each year over the study period,with an average annual increase of more than 5%,and annual increases of more than 7%at the Shangdianzi and Lin’an stations.Seasonal CO2variations were greater at the Longfengshan station than at the Shangdianzi or Lin’an stations.However,the CO2concentrations were higher at the Shangdianzi and Lin’an stations because they are greatly affected by human activities in the Jingjinji and Changjiang Delta economic zones.Spatial distribution in CO2concentrations and fluxes were higher in eastern than in western China. | CHENG YanLi AN XingQin YUN FangHua ZHOU LingXi LIU LiXin FANG ShuangXi XU Lin | 2013 | Chinese Science Bulletin2013，58，32： | 8 |
| 5 | Extremum Problems of Laplacian Eigenvalues and Generalized Polya Conjecture(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)显示文摘In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known conjecture due to Polya, its connections to Weyl's asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed. | Fanghua LIN | 2017 | Chinese Annals of Mathematics,Series B2017，38，2： | 5 |
| 6 | Growth factor regulatory system:a new system for not truly recognized organisms显示文摘Growth,development,aging,and disease occurrence in organisms,especially animals or Homo sapiens,are regulated by different regulatory systems in vivo.The nervous,endocrine,metabolic,and immune systems are the traditional biological systems essential for the growth,development,and metabolism of the body.These systems maintain a balance and precisely biologically regulate every aspect of life activities under normal circumstances.However,in abnormal situations,owing to endogenous or exogenous attack,these regulatory systems result in dysfunction,subsequently leading to illness or injury(Muggianu et al.,2018).In the classical neuroendocrine regulatory system,Cushing’s syndrome is defined as a series of abnormal clinical symptoms with chronic overproduction of glucocorticoids in the adrenal cortex.Its clinical manifestations are“moon face”and“buffalo hump,”involving blood circulation,bone metabolism,and gonadal function,among others.In addition,severe trauma or burn leads to an imbalanced immune regulatory system,resulting in excessive inflammatory reactions and sepsis.Thus,an independent or cooperative regulation of multiple regulatory systems is critical in maintaining the body’s homeostasis,healthy development,and growth. | Jian Xiao Zhuofeng Lin Hua Qin Zhilong Zheng Fanghua Gong Yanlong Liu Xiaokun Li Xiaobing Fu | 2020 | Science China(Life Sciences)2020，63，3： | 5 |
| 7 | Soil erosion assessment by RUSLE with improved P factor and its validation:Case study on mountainous and hilly areas of Hubei Province,China显示文摘The Revised Universal Soil Loss Equation(RUSLE)is widely used to estimate regional soil erosion.However,quantitative impacts of soil and water conservation(SWC)measures on conservation practice factor(P)of the RUSLE remain largely unclear,especially for the mountainous and hilly areas.In this study,we improved the RUSLE by considering quantitative impacts of different SWC measures on the P factor value.The improved RUSLE was validated against the long-term(2000-2015)soil erosion monitoring data obtained from 96 runoff plots(15—35°)in mountainous and hilly areas of Hubei Province,China;the result presented a high accuracy with the determination coefficient of 0.89.Based on the erosion monitoring data of 2018 and 2019,the Root Mean Square Error of the result by the improved RUSLE was 28.0%smaller than that by the original RUSLE with decrement of 19.6%—24.0%in the average P factor values,indicating that the soil erosion modelling accuracy was significantly enhanced by the improved RUSLE.Relatively low P factor values appeared for farmlands with tillage measures(P<0.53),grasslands with engineering measures(P<0.23),woodlands with biological measures(P<0.28),and other land use types with biological measures(P<0.51).The soil erosion modulus showed a downward trend with the corresponding values of 1681.21,1673.14,1594.70,1482.40 and 1437.50 t km^(-2)a-1 in 2000,2005,2010,2015 and 2019,respectively.The applicability of the improved RUSLE was verified by the measurements in typical mountainous and hilly areas of Hubei Province,China,and arrangements of SWC measures of this area were proposed. | Pei Tian Zhanliang Zhu Qimeng Yue Yi He Zhaoyi Zhang Fanghua Hao Wenzhao Guo Lin Chen Muxing Liu | 2021 | International Soil and Water Conservation Research2021，9，3： | 4 |
| 8 | China’s local governments are combating COVID-19 with unprecedented responses——from a Wenzhou governance perspective显示文摘The COVID-19 caused by a novel strain of coronavirus has been spreading rapidly since its occurrence in December 2019.It is highly communicable through human-to-human transmission.China has been making unprecedented efforts in treating the confirmed cases,identifying and isolating their close contacts and suspected cases to control the source of infection and cut the route of transmission.China’s devotion in handling this epidemic has effectively and efficiently curbed communication domestically and across the border.Representative measures adopted by Wenzhou,the worst hit city out of Hubei Province,are examined to elucidate those massive undertakings with the aim of enhancing international understanding and building global rapport in fighting this evolving epidemic situation. | Fanghua Gong Yong Xiong Jian Xiao Li Lin Xiaodong Liu Dezhong Wang Xiaokun Li | 2020 | Frontiers of Medicine2020，14，2： | 4 |
| 9 | A review of progress in coupled ocean-atmosphere model developments for ENSO studies in China显示文摘El Nino-Southern Oscillation(ENSO) is the strongest interannual signal that is producedby basinscale processes in the tropical Pacific,with significant effects on weather and climate worldwide.In the past,extensive and intensive international efforts have been devoted to coupled model developments for ENSO studies.A hierarchy of coupled ocean-atmo sphere models has been formulated;in terms of their complexity,they can be categorized into intermediate coupled models(ICMs),hybrid coupled models(HCMs),and fully coupled general circulation models(CGCMs).ENSO modeling has made significant progress over the past decades,reaching a stage where coupled models can now be used to successfully predict ENSO events 6 months to one year in advance.Meanwhile,ENSO exhibits great diversity and complexity as observed in nature,which still cannot be adequately captured by current state-of-the-art coupled models,presenting a challenge to ENSO modeling.We primarily reviewed the long-term efforts in ENSO modeling continually and steadily made at different institutions in China;some selected representative examples are presented here to review the current status of ENSO model developments and applications,which have been actively pursued with noticeable progress being made recently.As ENSO simulations are very sensitive to model formulations and process representations etc.,dedicated efforts have been devoted to ENSO model developments and improvements.Now,different ocean-atmosphere coupled models have been available in China,which exhibit good model performances and have already had a variety of applications to climate modeling,including the Coupled Model Intercomparison Project Phase 6(CMIP6).Nevertheless,large biases and uncertainties still exist in ENSO simulations and predictions,and there are clear rooms for their improvements,which are still an active area of researches and applications.Here,model performances of ENSO simulations are assessed in terms of advantages and disadvantages with these differently formulated coupled models,pinpointing to the areas where they need to be further improved for ENSO studies.These analyses provide valuable guidance for future improvements in ENSO simulations and predictions. | ZHANG Rong-Hua YU Yongqiang SONG Zhenya REN Hong-Li TANG Youmin QIAO Fangli WU Tongwen GAO Chuan HU Junya TIAN Feng ZHU Yuchao CHEN Lin LIU Hailong LIN Pengfei WU Fanghua WANG Lin | 2020 | Journal of Oceanology and Limnology2020，38，4： | 4 |
| 10 | SEMICLASSICAL STATES OF HAMILTONIAN SYSTEM OF SCHROEDINGER EQUATIONS WITH SUBCRITICAL AND CRITICAL NONLINEARITIES显示文摘 | Ding Yanheng Lin Fanghua | 2006 | Journal of Partial Differential Equations2006，19，3： | 3 |
| 11 | On Regularity and Singularity of Free Boundaries in Obstacle Problems显示文摘The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems.This approach is based on the monotonicity of several variational integrals,the Federer-Almgren dimension reduction and stratification theorems,and some simple PDE arguments. | Fanghua LIN | 2009 | Chinese Annals of Mathematics,Series B2009，30，5： | 2 |
| 12 | The advantages of using traditional Chinese medicine as an adjunctive therapy in the whole course of cancer treatment instead of only terminal stage of cancer显示文摘 | Fanghua Q Lin Z Aiyan Z | 2015 | Bio Science Trends2015，9，1： | 1 |
| 13 | Existence of Energy Minimizers as Stable Knotted Solitons in the Faddeev Model显示文摘 | Fanghua Lin Yisong Yang | 2004 | Communications in Mathematical Physics2004，，2： | 1 |
| 14 | Cinobufacini an aqueousextract from Bufo bufo gararizans Cantor,induces apotosis through amitochondria-mediated pathway in human hepatocellular carcinomacells 显示文摘 | Fanghua Qi Anyuan Li Lin Zhao | 2010 | Ethnopharmacol2010，128，3： | 1 |
| 15 | Nonlinear theory of defects in nematic liquid crystals; phase transition and flow phenomena 显示文摘 | Lin Fanghua | 1989 | Comm Pure Appl Math1989，42，78： | 1 |
| 16 | Nonparabolic dissipative systems modeling the flow of liquid crystals 显示文摘 | Lin Fanghua Liu Chun | 1995 | Comm Pure Appl Math1995，48，50： | 1 |
| 17 | Partial regularity of the dynamic system modeling the flow of liquid crystals 显示文摘 | Lin Fanghua Liu Chun | 1996 | Discrete Contin Dynam Systems1996，2，1： | 1 |
| 18 | Solutions of perturbed Schr0dinger equation with critical nonlinearity 显示文摘 | Ding Yanheng Lin Fanghua | 2007 | Calculus of Variations and Partial Differ- ential Equations2007，30，2： | 1 |
| 19 | On Current Developments in Partial Differential Equations显示文摘The first part of this article is an overview on some recent major developments in the field of analysis and partial different equations.It is a brief presentation given by the author at a round table discussion.The second part is a supplement of various details provided by several outstanding researchers on subjects. | Fanghua Lin | 2020 | Communications in Mathematical Research2020，36，1： | 1 |
| 20 | On the Global Existence of Smooth Solution to the 2-D FENE Dumbbell Model显示文摘 | Fanghua Lin Ping Zhang Zhifei Zhang | 2008 | Communications in Mathematical Physics2008，，2： | 1 |
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