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THE DISCUSSION ABOUT HORSESHOES AND FINITE SUBHARMONIC BIFURCATIONS

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Acta Mechanica Sinica 1986年第4期2卷 373-379页

作者： liu zhengrong Li Deming (Anhui University) Anhui University China

In this paper,finite subharmonic bifurcations have been discussed by means of *** is found that for centrally symmetric system,under small disturbance,if it has twoindependant sequences of subharmonic bifurcations,the system passes to chaos(horesesboe)through finite subharmonie bifurcations,and that for noncentrally symmetric system,the relationbetween subharmonic bifurcations and horseshoe is complicated.

关键词： Hamihonian system Melnikov’s method subharmonic bifurcation chaos(horseshoe)

Methods and Prospects of Road and Linear Structure Automatic Extraction from Remote Sensing Images

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Geo-Spatial Information Science 2003年第2期6卷 63-68页

作者： liu zhengrong liu zhengrong, Research Center of Spatial Information and Digital Engineering, Wuhan University, 129 Luoyu Road, Wuhan 430079, China. Research Center of Spatial Information and Digital Engineering Wuhan University Wuhan China

Automatic extraction of road and linear structure from remote sensing images is a very important problem. This paper analyses several existing methods of the automatic road and linear structure extraction by using some multi-spectral remote sensing images acquired from different spatial resolutions, districts and road characteristics. Their advantages and disadvantages have been generalized.

关键词： extraction linear structures remote sensing image photogrammetry

The Association between Vitamin D and Hashimoto Thyroiditis:An Upto-date Systematic Review and Meta-analysis

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Food Materials Research 2022年第1期2卷 82-91页

作者： zhengrong liu Linfei Feng Yanfang He Sijie Yuan Chao Xu The Out Patient Department Nanfang HospitalSouthern Medical UniversityGuangzhou 510515China Psychology Department Nanfang HospitalSouthern Medical UniversityGuangzhou 510515China The Department of General Practice Nanfang HospitalSouthern Medical UniversityGuangzhou 510515China Office of The Standardized Residents Training in Hospitals Graduate SchoolSouthern Medical UniversityGuangzhou 510515China

The objective of the surrent study was to summarize the up-to-date studies to investigate the relationship between vitamin D and Hashimoto thyroiditis(HT).An online search of English and Chinese databases was *** studies concerned the investigation of the relationship between vitamin D and HT including meta-analysis,meanwhile the heterogeneities were revealed by subgroup *** six elated studies containing 15,336 participants(HT:6,138 versus control:9,198)were *** patients had lower levels of 25(OH)D_(3)(standardised mean difference,−1.09;95%CI:[−1.42,−0.75];P<0.01),and were more likely to be deficient in 25(OH)D_(3)(OR,2.77;95%CI,[1.88,3.91];P<0.05).Obvious heterogeneities in the results of meta-analysis were down to the difference of detection methods and criteria of vitamin D insufficiency among *** D deficiency was colncluded to have a significant relation with HT.

关键词： 25(OH)D_(3) vitamin insufficiency

Tuning exsolution of nanoparticles in defect engineered layered perovskite oxides for efficient CO_(2) electrolysis

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Journal of Energy Chemistry 2023年第9期84卷 219-227页

作者： zhengrong liu Jun Zhou Yueyue Sun Xiangling Yue Jiaming Yang Lei Fu Qinyuan Deng Hongfei Zhao Chaofan Yin Kai Wu Center of Nanomaterials for Renewable Energy State Key Laboratory of Electrical Insulation and Power EquipmentXi’an Jiaotong UniversityXi’an 710049ShaanxiChina School of Chemistry University of St AndrewsSt AndrewsFife KY169STUK

Solid oxide electrolysis cell(SOEC) could be a potential technology to afford chemical storage of renewable electricity by converting water and carbon *** this work,we present the Ni-doped layered perovskite oxides,(La_(4)Sr_(n-4))_(0.9)Ti_(0.9n)Ni_(0.1n)O_(3n+2) with n=5,8,and 12(LSTNn) for application as catalysts of CO_(2) electrolysis with the exsolution of Ni nanoparticles through a simple in-situ growth *** is found that the density,size,and distribution of exsolved Ni nanoparticles are determined by the number of n in LSTNn due to the different stack structures of TiO_6 octahedra along the c *** Ni doping in LSTNn significantly improved the electrochemical activity by increasing oxygen vacancies,and the Ni metallic nanoparticles afford much more active *** results show that LSTNn cathodes can successfully be manipulated the activity by controlling both the n number and Ni *** these LSTNn(n=5,8,and 12),LSTN8 renders a higher activity for electrolysis of CO_(2) with a current density of 1.50A cm^(-2)@2.0 V at 800℃ It is clear from these results that the number of n in(La_(4)Sr_(n-4))_(0.9)Ti_(0.9n)Ni_(0.1n)O_(3n+2)with Ni-doping is a key factor in controlling the electrochemical performance and catalytic activity in SOEC.

关键词： Layered perovskite oxides In-situ growth SOEC Titanate

NON-UNIFORM DEPENDENCE ON INITIAL DATA FOR THE MODIFIED CAMASSA-HOLM EQUATION ON THE LINE

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Acta Mathematica Scientia 2014年第6期34卷 1781-1794页

作者：傅仰耿刘正荣唐昊 School of Mathematical Sciences Huaqiao University Department of Mathematics South China University of Technology

In this paper, we study the Cauchy problem for the modified Camassa-Holm equation mt ＋ umx ＋ 2ux m = 0, m =（1- δx^2）^2u,u（x, 0） = u0（x） ∈ H^s（R）, x ∈ R, t 〉 0,and show that the solution map is not uniformly continuous in Sobolev spaces H^s（R） for s 〉 7/2. Compared with the periodic problem, the non-periodic problem is more difficult,e.g., it depends on the conservation law. Our proof is based on the estimates for the actual solutions and the approximate solutions, which consist of a low frequency and a high frequency part.

关键词： modified Camassa-Holm equation Cauchy problem non-uniform continuity Sobolev spaces

NEW EXPRESSIONS OF PERIODIC WAVES AND A NOVEL PHENOMENON IN A COMPRESSIBLE HYPERELASTIC ROD

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Journal of Partial Differential Equations 2007年第1期20卷 80-96页

作者： liu zhengrong Zhang Bengong School of Mathematics Science Center for Nonlinear Science Studies South China University of Technology Guangzhou Guangdong 510640 China

A In this paper, we employ both bifurcation method of dynamical systems and numerical exploration of differential equations to investigate the periodic waves of a general compressible hyperelastic rod equation ut＋3uux-uxxt-γ（2uxuxx＋uuxxx）=0, with parameter γ 〈 0. New expressions including explicit expressions and implicit expressions are obtained. Some previous results are extended. Specially, a new phenomenon is found： when the initial value tends to a certain number, the periodic shock wave suddenly changes into a smooth periodic wave. In dynamical systems, this represents that one of orbits can pass through the singular line. The coherency of numerical simulation and theoretical derivation implies the correctness of our results.

关键词： Hyperelastic rod bifurcation method numerical exploration periodic waves.

Angular Distribution of Element Contents in Tree Rings and the Environmental Information

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Pedosphere 1999年第1期9卷 69-76页

作者： KE SHANZHE liu zhengrong QIAN JUNLONG CHEN RUSONGI and KE XIAOKANG (Physics Department, Nanjing University, Nanjing 210095,China)(Nanjing Institute of Geogmphy and Limnology, the Chinese Academy of Sciences, Nanjing 210008, China)(Garded and Greenbelt 南京大学物理系江苏南京 210093 南京大学物理系江苏南京中科院南京地理与湖泊所江苏南京 210008 南京大学化学系江苏南京 210009

Element contents of tree rings and soils near tree roots collected from Deodar cedar (Cedrus deodara (Roxb.) G. Don) and Masson pine (Picks massoniana lamb.) were determined to study the relationship between the angular distribution of element contents in tree rings and the environmental information. The chemical composition and properties of soils are very much complicated, which leads to the non-uniform distribution of the element contents in tree rings. The statistical multi-variable regression method was used to got the information of the tree-centered distribution of element contents in the environment (soil) (C’), C’(z, θj ), from the distribution of element contents in tree rings (C), C(Z, θi), which depends on the plane azimuth angle (θi), i. e., C=C(Z,θi), where Z is the atomic number of the element, with a satisfactory result,though this study is only a primary one.

关键词： angular distribution element contents environmental information tree rings

Periodic blow-up solutions and their limit forms for the generalized Camassa-Holm equation

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Progress in Natural Science:Materials International 2008年第3期18卷 259-266页

作者： zhengrong liu a, Boling Guob a School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China b Institute of Applied Physics and Computational Mathematics, Beijing 100088, China School of Mathematical Sciences South China University of Technology Guangzhou 510640 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

In this paper, we consider the generalized Camassa-Holm equation ut+2kux-uxxt+ au~2ux=2uxuxx+uuxxxUnder substitution ξ=x-ct, some new explicit periodic wave solutions and their limit forms are presented through some special phase orbits. These periodic wave solutions tend to infinity on ξ-u plane periodically. Thus we call them periodic blow-up solutions. To our knowledge, such periodic blow-up solutions have not been found in any other equations.

关键词： Generalized Camassa–Holm equation Explicit solutions Periodic blow-up

Two new types of bounded waves of CH-γ equation

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Science China Mathematics 2005年第12期48卷 1618-1630页

作者： GUO Boling & liu zhengrong Institute of Applied Physics and Computational Mathematics, Beijing 100088, China School of Mathematical Sciences and Center for Nonlinear Science Studies, South China University of Technology, Guangzhou 510640, China Institute of Applied Physics and Computational Mathematics Beijing China School of Mathematical Sciences and Center for Nonlinear Science Studies South China University of Technology Guangzhou China

In this paper, the bifurcation method of dynamical systems and numerical approach of differential equations are employed to study CH-γ equation. Two new types of bounded waves are found. One of them is called the compacton. The other is called the generalized kink wave. Their planar graphs are simulated and their implicit expressions are given. The identity of theoretical derivation and numerical simulation is displayed.

关键词： CH-γ equation,compactons,generalized kink waves.