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A GLOBAL EXISTENCE RESULT FOR KORTEWEG SYSTEM IN THE CRITICAL L^P FRAMEWORK

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Acta Mathematica Scientia 2019年第6期39卷 1639-1660页

作者： Zhensheng GAO Yan LIANG zhong tan School of Mathematical Sciences Huaqiao UniversityQuanzhou 362021China School of Mathematical Sciences Xiamen UniversityXiamen 361005China

The purpose of this work is to investigate the initial value problem for a general isothermal model of capillary fluids derived by Dunn and Serrin [12], which can be used as a phase transition model. Motivated by [9], we aim at extending the work by DanchinDesjardins [11] to a critical framework which is not related to the energy space. For small perturbations of a stable equilibrium state in the sense of suitable L^p-type Besov norms,we establish the global existence. As a consequence, like for incompressible flows, one may exhibit a class of large highly oscillating initial velocity fields for which global existence and uniqueness holds true.

关键词： Korteweg system global existence L^p-type Besov norms

ON THE HEAT FLOW OF EQUATION OF H-SURFACE

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Acta Mathematica Scientia 2019年第5期39卷 1397-1405页

作者： Guochun WU zhong tan Jiankai XU Fujian Province University Key Laboratory of Computational Science School of Mathematical Sciences Huaqiao University Quanzhou 362021 China School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and Scientific Computing Xiamen University Xiamen 361005 China College of Information Science and Technology Hunan Agriculture University Changsha 410128 China

We study the heat flow of equation of H-surface with non-zero Dirichlet boundary in the present article. Introducing the "stable set" M2 and "unstable set" M1, we show that there exists a unique global solution provided the initial data belong to M2 and the global solution converges to zero in H^1 exponentially as time goes to infinity. Moreover, we also prove that the local regular solution must blow up at finite time provided the initial data belong to M1.

关键词： H-surface non-zero Dirichlet boundary singularity global solutions

Recursion-transform approach to compute the resistance of a resistor network with an arbitrary boundary

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Chinese Physics B 2015年第2期24卷 94-100页

作者：谭志中 Department of Physics Nantong University

We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary,which has not been solved before because the Green＇s function technique and the Laplacian matrix approach are invalid in this *** for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite *** this paper,we give a general resistance formula that is composed of a single summation by using the recursion-transform ***,several interesting results are derived by the general ***,the current distribution is given explicitly as a byproduct of the method.

关键词： exact solution resistor network matrix equation recursion-transform boundary conditions

Intravitreal brimonidine inhibits formdeprivation myopia in guinea pigs

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Eye and Vision 2021年第5期8卷 263-275页

作者： Yifang Yang Junshu Wu Defu Wu Qi Wei tan zhong Jun Yang Xiaowei Yang Meizhen Zeng Xingwu zhong State Key Laboratory of Ophthalmology Zhongshan Ophthalmic CenterSun Yat-sen UniversityGuangzhou 510060China Hainan Eye Hospital and Key Laboratory of Ophthalmology Zhongshan Ophthalmic CenterSun Yat-sen UniversityHaikou 570311Hainan ProvinceChina

Background:The use of ocular hypotensive drugs has been reported to attenuate myopia *** study explores whether brimonidine can slow myopia progression in the guinea pig form-deprivation(FD)***:Three-week-old pigmented male guinea pigs(Cavia porcellus)underwent monocular FD and were treated with 3 different methods of brimonidine administration(eye drops,subconjunctival or intravitreal injections).Four different concentrations of brimonidine were tested for intravitreal injection(2μg/μL,4μg/μL,20μg/μL,40μg/μL).All treatments continued for a period of 21 ***,retinoscopy,and A-scan ultrasonography were used to monitor intraocular pressure(IOP),refractive error and axial length(AL),*** day 21,guinea pigs were sacrificed for RNA sequencing(RNA-seq)to screen for associated transcriptomic ***:The myopia model was successfully established in FD animals(control eye *** eye,respectively:refraction at day 20,0.97±0.18 D vs.−0.13±0.38 D,F=6.921,P=0.02;AL difference between day 0 and day 21,0.29±0.04mm vs.0.45±0.03 mm,F=11.655,P=0.004).Among the 3 different brimonidine administration methods,intravitreal injection was the most effective in slowing myopia progression,and 4μg/μL was the most effective among the four different concentrations of brimonidine intravitreal injection *** AL and the refraction of the brimonidine intravitreal injection group was significantly shorter or more hyperopic than those of other 2 ***μg/μL produced the smallest difference in AL and spherical equivalent difference *** treatment significantly increased the *** was significantly lower at 1 day after intravitreal injections which was the lowest in FD eye of intravitreal injection of *** day 21,gene expression analyses using RNA-seq showed upregulation of Col1a1 and Mmp2 expression levels by intravitreal ***:Among the 3 different administration methods,intravitreal injection of brimonid

关键词： Brimonidine Myopia Form deprivation Retina

Supporting structure failure caused by the squeezing tunnel creep and its reinforcement measure

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Journal of Mountain Science 2023年第6期20卷 1774-1789页

作者： ZHAO Jin-peng tan zhong-sheng LI Lei WANG Xiu-ying Key Laboratory of Urban Underground Engineering of Ministry of Education Beijing Jiaotong UniversityBeijing 100044China School of Civil Engineering Beijing Jiaotong UniversityBeijing 100044China

Tunnels deeply buried have high crustal stress and are prone to large deformation disasters when encountering soft *** large deformation phenomenon during the construction process of the Maoxian Tunnel on the Chengdu-Lanzhou Railway is particularly *** article focuses on the large deformation problem of the No.1 inclined shaft of the Maoxian Tunnel,and uses on-site monitoring methods to explore the reasons for tunnel structure failure,and analyzes the mechanical behavior of the tunnel *** using numerical simulation methods,the effectiveness of the second-layer support in resisting creep loads in tunnels was studied,and the influence of the construction time of the secondlayer support on the mechanical properties of the tunnel was *** results indicate that the first-layer support in the tunnel is a structural failure caused by asymmetric deformation caused by creep,while the second-layer support has a good effect on resisting creep *** research results can provide a technical reference for deformation control of squeezing tunnels.

关键词： Squeezing tunnel Mechanical responses Long-term creep Second-layer support On-site monitoring

Behavior and control of chlorine in dyestuff residue incineration

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Journal of Environmental Sciences 2006年第3期18卷 577-582页

作者： YAN Jian-hua tan zhong-xin JIANG Xue-guang CHI Yong CEN Ke-fa State key Laboratory of Clean Energy Institute for Thermal Power Engineering Zhejiang University Hangzhou 310027 China

Dyestuffresidue, a type of hazardous waste, is incinerated in the tubular furnace, and thermodynamic equilibrium model is used to calculate and analyze the chlorine behavior. The HCI emission and its effects on the behaviors of heavy metals are studied. Meanwhile, the effects of three dechlorine reagents are predicted at a high temperature. Results show that HCI emission is dependent on incineration temperature. The HCl evaporated mainly derives from the organic chlorine. Under the working condition of 500-- 900℃, the main products of rig, Pb, Cu, Ni, Zn, and Mn in reaction with HCl are HgCl2 （g）, PbCl4（g）, PbCI2 （g）, （CuCl）3 （g）, NiCl2 （s）, NiCl2 （g）, ZnCl2 （s）, ZnCl2 （g）, Zn （g）, MnCl2 （s）, and MnCl2 （g）, respectively. Among the three dechlorine reagents, CaCO3 is optimal to remove chlorine at high temperature, little of HCl is released below 800℃, whereas Fe3O4 is unstable at high temperature.

关键词： hazardous waste thermodynamic equilibrium model HCl heavy metals dechlorine reagents

A NECESSARY CONDITION FOR CERTAIN INTEGRAL EQUATIONS WITH NEGATIVE EXPONENTS

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Acta Mathematica Scientia 2019年第1期39卷 284-296页

作者： Jiankai XU zhong tan Weiwei WANG Zepeng XIONG College of Sciences College of Computer Science Hunan Agriculture University School of Mathematical Sciences Xiamen University College of Mathematics and Computer Science Fuzhou University The First Middle School of Longhui

This paper is devoted to studying the existence of positive solutions for the following integral system {u(x)=∫_(R^n)|x-y|~λv-~q(y)dy, ∫_(R^n)|x-y|~λv-~p(y)dy,p,q>0,λ∈(0,∞),n≥*** is shown that if(u,v) is a pair of positive Lebesgue measurable solutions of this integral system, then 1/(p-1)+1/(q-1)=λ/n, which is different from the well-known case of the Lane-Emden system and its natural extension, the Hardy-Littlewood-Sobolev type integral equations.

关键词： integral equations Lane-Emden system conformal invariance positive solutions existence

A Computer Software-Epitimulator~ for Simulating Temporal Dynamics of Plant Disease Epidemic Progress

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Agricultural Sciences in China 2010年第2期9卷 242-248页

作者： tan Wan-zhong LI Cheng-wen BI Chao-wei SUN Xian-chao Fungal Pathology Laboratory Southwest University Beibei 400716 P.R.China Agricultural Department of Wushan County Chongqing 404700 P.R.China

The objective of the present study was to develop a computer software for simulating the temporal development of plant disease epidemics using Richards, logistic, Gompertz, monomolecular, and exponential functions, respectively, and for predicting disease with a fitted model. The software was programmed using Visual Basic （VB6.0） and packaged with the Wise Installation System. The Fibonacci （＇0.618＇） section strategy was used to find out the most appropriate value for the shape parameter （m） in Richards function simulation through looping procedures. The software program was repeatedly tested, debugged and edited until it was run through favorably and produced ideal outputs. It was named Epitimulator based on the phrase ＇epidemic time simulator＇ and has been registered by the National Copyright Department of China （Reg. no. 2007SR18489）. It can be installed and run on personal computers with all versions of Windows operational systems. Data of disease index and survey time are keyed in or imported from Access files. The output of fitted models and related data of parameters can be pasted into Microsoft Excel worksheet or into Word document for editing as required and the simulated disease progress curves can be stored in separate graphic files. After being finally tested and completed, Epitimulator was applied to simulate the epidemic progress of corn northern leaf blight （Exserohilum turcicum） with recorded data from field surveys of corn crops and the fitted models were output. Comparison of the simulation results showed that the disease progress was always best described by Richards function, which resulted in the most accurate simulation model. Result also showed that forecast of northern leaf blight development was highly accurate by using the computed progress model from Richards function.

关键词： plant disease dynamics Richards function Epitimulator fitted model output epidemic forecast

THE GLOBAL SOLUTION AND BLOWUP OF A SPATIOTEMPORAL EIT PROBLEM WITH A DYNAMICAL BOUNDARY CONDITION

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Acta Mathematica Scientia 2023年第4期43卷 1881-1914页

作者：谢明洪谭忠 School of Mathematics and Statistics Central China Normal UniversityWuhan 430079China School of Mathematical Science Xiamen UniversityXiamen 361005China Shenzhen Research Institute of Xiamen University Shenzhen 518057China

We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical *** are three major ingredients in this *** first is the finite time blowup and the decay estimate of the global solution with a lower-energy initial *** second ingredient is the L^(q)(2 ≤q <∞) estimate of the global solution applying the Moser iteration,which allows us to show that any global solution is a classical *** third,which is the main ingredient of this paper,explores the long time asymptotic behavior of global solutions close to the stationary solution and the bubbling phenomenons by means of a concentration compactness principle.

关键词： spatiotemporal EIT problem fractional Dirichlet-to-Neumann operator critical exponent bubbling phenomena