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Comparison of continuous homogenous azeotropic and pressure-swing distillation for a minimum azeotropic system ethyl acetate/nhexane separation 被引量:6
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作者 Liping Lü Lin Zhu +2 位作者 Huimin Liu Hang Li Shirui Sun 《Chinese Journal of Chemical Engineering》 SCIE EI CAS CSCD 2018年第10期2023-2033,共11页
Continuous homogenous azeotropic distillation(CHAD) and pressure-swing distillation(PSD) are explored to separate a minimum-boiling azeotropic system of ethyl acetate and n-hexane. The CHAD process with acetone as the... Continuous homogenous azeotropic distillation(CHAD) and pressure-swing distillation(PSD) are explored to separate a minimum-boiling azeotropic system of ethyl acetate and n-hexane. The CHAD process with acetone as the entrainer and the PSD process with the pressures of 0.1 MPa and 0.6 MPa in two columns are designed and simulated by Aspen Plus. The operating conditions of the two processes are optimized via a sequential modular approach to obtain the minimum total annual cost(TAC). The computational results show that the partially heat integrated pressure-swing distillation(HIPSD) has reduced in the energy cost and TAC by 40.79% and 35.94%, respectively, than the conventional PSD, and has more greatly reduced the energy cost and TAC by 62.61% and 49.26% respectively compared with the CHAD process. The comparison of CHAD process and partially HIPSD process illustrates that the partially HIPSD has more advantages in averting the product pollution, energy saving, and economy. 展开更多
关键词 Continuous homogenous azeotropic distillation Pressure-swing distillation Ethyl acetate/n-hexane Azeotrope
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Catalytic effect in lithium metal batteries: From heterogeneous catalyst to homogenous catalyst 被引量:1
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作者 Haining Fan Xuan-Wen Gao +3 位作者 Hailong Xu Yichun Ding Shi-Xue Dou Wen-Bin Luo 《Journal of Energy Chemistry》 SCIE EI CAS CSCD 2024年第3期305-326,I0008,共23页
Lithium metal batteries are regarded as prominent contenders to address the pressing needs owing to the high theoretical capacity.Toward the broader implementation,the primary obstacle lies in the intricate multi-elec... Lithium metal batteries are regarded as prominent contenders to address the pressing needs owing to the high theoretical capacity.Toward the broader implementation,the primary obstacle lies in the intricate multi-electron,multi-step redox reaction associated with sluggish conversion kinetics,subsequently giving rise to a cascade of parasitic issues.In order to smooth reaction kinetics,catalysts are widely introduced to accelerate reaction rate via modulating the energy barrier.Over past decades,a large amount of research has been devoted to the catalyst design and catalytic mechanism exploration,and thus the great progress in electrochemical performance has been realized.Therefore,it is necessary to make a comprehensive review toward key progress in catalyst design and future development pathway.In this review,the basic mechanism of lithium metal batteries is provided along with corresponding advantages and existing challenges detailly described.The main catalysts employed to accelerate cathode reaction with emphasis on their catalytic mechanism are summarized as well.Finally,the rational design and innovative direction toward efficient catalysts are suggested for future application in metal-sulfur/gas battery and beyond.This review is expected to drive and benefit future research on rational catalyst design with multi-parameter synergistic impacts on the activity and stability of next-generation metal battery,thus opening new avenue for sustainable solution to climate change,energy and environmental issues,and the potential industrial economy. 展开更多
关键词 Energy storage and conversion Metal battery Sulfur battery Air battery Catalytic effect Heterogeneous catalyst Homogeneous catalyst
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Integrability of Hamiltonian Systems with Two Degrees of Freedom and Homogenous Potential of Degree Zero
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作者 Jaume Llibre Claudia Valls 《Journal of Applied Mathematics and Physics》 2018年第11期2192-2201,共10页
We provide necessary conditions in order that the Hamiltonian systems with Hamiltonian ,?and one of the following potentials ?are integrable in the Liouville sense.
关键词 Hamiltonian system LIOUVILLE INTEGRABILITY DARBOUX Points Homogeneous Potentials of DEGREE ZERO
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Reviewing Stability Criteria for Positive Homogeneous Systems and Adding One for Discrete-Time Cases with Degree Less Than One
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作者 Nguyen Quang Tuan 《Circuits and Systems》 2024年第1期1-11,共11页
The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global expo... The article synthesizes and presents the results regarding the stability of positive homogeneous systems that have been researched and published in recent years. Next, we provide a sufficient condition for global exponential stability in the case of discrete-time positive homogeneous systems with an order less than one with time-varying delays. 展开更多
关键词 Exponential Stability Homogeneous systems Positive systems Positive Homogeneous systems
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Research status and prospects of the fractal analysis of metal material surfaces and interfaces
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作者 Qinjin Dai Xuefeng Liu +2 位作者 Xin Ma Shaojie Tian Qinghe Cui 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS 2025年第1期20-38,共19页
As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal... As a mathematical analysis method,fractal analysis can be used to quantitatively describe irregular shapes with self-similar or self-affine properties.Fractal analysis has been used to characterize the shapes of metal materials at various scales and dimensions.Conventional methods make it difficult to quantitatively describe the relationship between the regular characteristics and properties of metal material surfaces and interfaces.However,fractal analysis can be used to quantitatively describe the shape characteristics of metal materials and to establish the quantitative relationships between the shape characteristics and various properties of metal materials.From the perspective of two-dimensional planes and three-dimensional curved surfaces,this paper reviews the current research status of the fractal analysis of metal precipitate interfaces,metal grain boundary interfaces,metal-deposited film surfaces,metal fracture surfaces,metal machined surfaces,and metal wear surfaces.The relationship between the fractal dimensions and properties of metal material surfaces and interfaces is summarized.Starting from three perspectives of fractal analysis,namely,research scope,image acquisition methods,and calculation methods,this paper identifies the direction of research on fractal analysis of metal material surfaces and interfaces that need to be developed.It is believed that revealing the deep influence mechanism between the fractal dimensions and properties of metal material surfaces and interfaces will be the key research direction of the fractal analysis of metal materials in the future. 展开更多
关键词 metal material surfaces and interfaces fractal analysis fractal dimension HOMOGENEITY
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Porous Organic Cage‑Based Quasi‑Solid‑State Electrolyte with Cavity‑Induced Anion‑Trapping Effect for Long‑Life Lithium Metal Batteries
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作者 Wei-Min Qin Zhongliang Li +7 位作者 Wen‑Xia Su Jia‑Min Hu Hanqin Zou Zhixuan Wu Zhiqin Ruan Yue‑Peng Cai Kang Li Qifeng Zheng 《Nano-Micro Letters》 SCIE EI CAS 2025年第2期376-386,共11页
Porous organic cages(POCs)with permanent porosity and excellent host–guest property hold great potentials in regulating ion transport behavior,yet their feasibility as solid-state electrolytes has never been testifie... Porous organic cages(POCs)with permanent porosity and excellent host–guest property hold great potentials in regulating ion transport behavior,yet their feasibility as solid-state electrolytes has never been testified in a practical battery.Herein,we design and fabricate a quasi-solid-state electrolyte(QSSE)based on a POC to enable the stable operation of Li-metal batteries(LMBs).Benefiting from the ordered channels and cavity-induced anion-trapping effect of POC,the resulting POC-based QSSE exhibits a high Li+transference number of 0.67 and a high ionic conductivity of 1.25×10^(−4) S cm^(−1) with a low activation energy of 0.17 eV.These allow for homogeneous Li deposition and highly reversible Li plating/stripping for over 2000 h.As a proof of concept,the LMB assembled with POC-based QSSE demonstrates extremely stable cycling performance with 85%capacity retention after 1000 cycles.Therefore,our work demonstrates the practical applicability of POC as SSEs for LMBs and could be extended to other energy-storage systems,such as Na and K batteries. 展开更多
关键词 Porous organic cage Cavity-induced anion-trapping Quasi-solid-state electrolyte Homogeneous Li+flux Lithium metal battery
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Zero Distribution of a Class of Real Polynomial Systems
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作者 高堂安 王则柯 《Chinese Quarterly Journal of Mathematics》 CSCD 1989年第2期79+76-78,共4页
设P:IR^(2n)→IR~?(2n)是(q_1,…,q_(2n))次实多项式映射,满足q_(2j-1)-q_(2j),j=1,2,…,n。本文讨论这类多项式映射的实零点分布,并给出计算一批实零点的方法。
关键词 satisfying 数学季刊 POLYNOMIAL TRIVIAL doubled DISTINGUISH uniquely finding homogenous NONNEGATIVE
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Microstructure evolution of 7050 aluminum forgings during surface cumulative plastic deformation
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作者 Jian-liang HU Ze-xiong ZHANG +3 位作者 Cheng XING Xiu-jiang WU Shi-quan HUANG Hong BO 《中国有色金属学报》 北大核心 2025年第1期45-59,共15页
To elucidate the mechanisms of regulating the microstructure uniformity in 7050 aluminum forgings through surface cumulative plastic deformation(SCPD),the microstructure under different solution treatments was investi... To elucidate the mechanisms of regulating the microstructure uniformity in 7050 aluminum forgings through surface cumulative plastic deformation(SCPD),the microstructure under different solution treatments was investigated using metallographic observation(OM),electron backscatter diffraction(EBSD),transmission electron microscopy(TEM),and X-ray diffraction(XRD).The findings demonstrate that the most uniform microstructure in the forgings is achieved with a solution treatment at 470℃for 30 min.The SCPD process generates a significant number of needle-shaped precipitates,resulting in a higher dislocation density and stored energy.Solution treatments alleviate the pinning effect of second-phase particles and facilitate static recrystallization(SRX)in forgings,leading to a reduction in grain size.Additionally,mechanical testing results demonstrate 7%−13%increase in tensile strength and more uniform elongation of the forgings in different directions. 展开更多
关键词 microstructure homogeneity surface cumulative plastic deformation(SCPD) static recrystallization(SRX) dislocation density
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An Overview of Finite/Fixed-Time Control and Its Application in Engineering Systems 被引量:17
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作者 Yang Liu Hongyi Li +2 位作者 Zongyu Zuo Xiaodi Li Renquan Lu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2022年第12期2106-2120,共15页
The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability,the finite-time stability poss... The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability,the finite-time stability possesses the better control performance and disturbance rejection property. Different from the finite-time stability, the fixed-time stability has a faster convergence speed and the upper bound of the settling time can be estimated. Moreover, the convergent time does not rely on the initial information.This work aims at presenting an overview of the finite/fixed-time stabilization and tracking control and its applications in engineering systems. Firstly, several fundamental definitions on the finite/fixed-time stability are recalled. Then, the research results on the finite/fixed-time stabilization and tracking control are reviewed in detail and categorized via diverse input signal structures and engineering applications. Finally, some challenging problems needed to be solved are presented. 展开更多
关键词 Adding a power integrator finite/fixed-time control and application homogeneous theory sliding mode control
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BIFURCATION ANALYSIS AND FEEDBACK CONTROL OF A 3D CHAOTIC SYSTEM 被引量:11
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作者 Zhen Wang 《Analysis in Theory and Applications》 2007年第4期343-353,共11页
In this paper, we analyze a three-dimensional differential system derived from the Chen system based on the first Lyapunov coefficient, and apply it to investigate the local bifurcation. And we present some insights o... In this paper, we analyze a three-dimensional differential system derived from the Chen system based on the first Lyapunov coefficient, and apply it to investigate the local bifurcation. And we present some insights on bifurcation and stability, also obtain some conditions for subcfitical and supercritical. Finally, we give some numerical simulation studies of system in order to verify analytic results. 展开更多
关键词 Hopf bifurcation Chaotic system Homogeneous polynomials
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Systematic review of mixing technology for recycling waste tailings as cemented paste backfill in mines in China 被引量:6
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作者 Liuhua Yang Jincang Li +4 位作者 Hongbin Liu Huazhe Jiao Shenghua Yin Xinming Chen Yang Yu 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 2023年第8期1430-1443,共14页
The development of industry is inseparable from the support of mining.However,mining processes consume a large amount of energy,and increased tailing emissions can have a significant impact on the environment.In the p... The development of industry is inseparable from the support of mining.However,mining processes consume a large amount of energy,and increased tailing emissions can have a significant impact on the environment.In the past few decades,the mining industry developed many technologies that are related to mineral energy management,of which cemented paste backfill(CPB)is one of the representative technologies.CPB has been successfully applied to mine ground control and tailings management.In CPB technology,the mixing process is the key to achieving materials with good final quality and controlled properties.However,in the preparation process,the mixed homogeneity of the CPB is difficult to achieve because of fine tailings,high solid volume fraction,and high viscosity.Most research focused on the effect of mixing ingredients on CPB properties rather than on the preparation process of the CPB.Therefore,improving the performance and reducing the production cost of CPB by optimizing the mixing process are important.This review summarizes the current studies on the mixing technology of CPB and its application status in China.Then,it compares the advantages and disadvantages of multiple mixing equipment and discusses the latest results and research hotspots in paste preparation.Finally,it concludes the challenges and development trends of mixing technology on the basis of the relevant application cases in China to promoting cement-based material mixing technology development. 展开更多
关键词 cemented paste backfill mixed homogeneity mixing technology cement-based material
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A systematic investigation of secondary phase dissolution in Mg-Sn alloys 被引量:7
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作者 Arushi Dev Niladri Naskar +2 位作者 Nishant Kumar Ashutosh Jena Manas Paliwal 《Journal of Magnesium and Alloys》 SCIE 2019年第4期725-737,共13页
As-cast Mg-Sn alloys(3,6,and 9 wt%Sn)were solution treated at 653,703 and 753 K(380,430 and 480℃)for 1,4,8,12 and 24 h to determine the variation of secondary phase with respect to Sn content,temperature and time.Mg-... As-cast Mg-Sn alloys(3,6,and 9 wt%Sn)were solution treated at 653,703 and 753 K(380,430 and 480℃)for 1,4,8,12 and 24 h to determine the variation of secondary phase with respect to Sn content,temperature and time.Mg-3 wt%Sn exhibits Mg2Sn dissolution at all solution treatment temperatures whereas Mg-6 and 9 wt%Sn alloy displays Mg2Sn reprecipitation and dissolution depending on the heat treatment temperature.In addition,a combined mathematical model that predicts the secondary phase dissolution and solute redistribution as a function of temperature and time is presented in this work.This model is a significant improvement compared to the previous studies where the dissolution and homogenization processes are considered independently.The effect of grain size and solute mobility upon the dissolution and homogenization kinetics is discussed as well. 展开更多
关键词 Solution treatment HOMOGENIZATION DISSOLUTION Mg-Sn alloys
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A new tumor-associated antigen prognostic scoring system for spontaneous ruptured hepatocellular carcinoma after partial hepatectomy 被引量:4
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作者 Jingjing Wu Peng Zhu +7 位作者 Zhanguo Zhang Bixiang Zhang Chang Shu Lin Chen Renjie Feng Abdoul aziz Mba'nbo koumpa Ganxun Li Qianyun Ge 《Cancer Biology & Medicine》 SCIE CAS CSCD 2018年第4期415-424,共10页
Objective:Spontaneous hepatocellular carcinoma(HCC)rupture can be fatal,and hepatic resection could achieve a favorable long-term survival among all strategies of tumor rupture.However,there is no available prognostic... Objective:Spontaneous hepatocellular carcinoma(HCC)rupture can be fatal,and hepatic resection could achieve a favorable long-term survival among all strategies of tumor rupture.However,there is no available prognostic scoring system for patients with ruptured HCC who underwent partial hepatectomy.Methods:From January 2005 to May 2015,129 patients with spontaneous HCC rupture underwent partial hepatectomy.Preoperative clinical data were collected and analyzed.Independent risk factors affecting overall survival(OS)were used to develop the new scoring system.Harrell’s C statistics,Akaike information criterion(AIC),the relative likelihood,and the log likelihood ratio were calculated to measure the homogeneity and discriminatory ability of a prognostic system.Results:In the multivariable Cox regression analysis,three factors,including tumor size,preoperativeα-fetoprotein level,and alkaline phosphatase level,were chosen for the new tumor-associated antigen(TAA)prognostic scoring system.The 1-year OS rates were 88.1%,43.2%,and 30.2%for TAA scores of 0–5 points(low-risk group),6–9 points(moderate-risk group),and 10–13points(high-risk group),respectively.The TAA scoring system had superior homogeneity and discriminatory ability(Harrell’s C statistics,0.693 vs.0.627 and 0.634;AIC,794.79 vs.817.23 and 820.16;relative likelihood,both<0.001;and log likelihood ratio,45.21 vs.22.77 and 21.84)than the Barcelona Clinic Liver Cancer staging system and the Cancer of the Liver Italian Program in predicting OS.Similar results were found while predicting disease-free survival(DFS).Conclusions:The new prognostic scoring system is simple and effective in predicting both OS and DFS of patients with spontaneous ruptured HCC. 展开更多
关键词 Spontaneous RUPTURE PROGNOSTIC SCORING system HOMOGENEITY discriminatory ability overall SURVIVAL disease-free SURVIVAL HEPATOCELLULAR carcinoma
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Multivariable temperature measurement and control system of large-scaled vertical quench furnace based on temperature field 被引量:7
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作者 XuanZHOU ShouyiYU +1 位作者 JiangYU LiequanLIANG 《控制理论与应用(英文版)》 EI 2004年第4期401-405,共5页
A temperature control system of 31m vertical forced air-circulation quench furnace is proposed, which is a kind of equipment critical for thermal treatment of aluminum alloy components that are widely used in aerospac... A temperature control system of 31m vertical forced air-circulation quench furnace is proposed, which is a kind of equipment critical for thermal treatment of aluminum alloy components that are widely used in aerospace industry. For the effective operation of the furnace, it is essential to analyze the radial temperature distribution of the furnace. A set of thermodynamic balance equations modeling is established firsdy. By utilizing the numerical analysis result to modify the temperature measurements, the control accuracy and precision of the temperature are truly guaranteed. Furthermore, the multivariable decoupling self-learning PID control algorithm based on the characteristics of strong coupling between the multi-zones in the large-scaled furnace is implemented to ensure the true homogeneity of the axial temperature distribution. Finally, the redundant structure composed of industrial control computers and touch panels leads to great improvement of system reliability. 展开更多
关键词 Axial temperature distribution homogeneity Radial temperature distribution Decoupling self-learning PID control Redundant structure
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DISTANCE MEASURING MODELING AND ERROR ANALYSIS OF DUALCCD VISION SYSTEM SIMULATING HUMAN EYES AND NECK 被引量:3
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作者 Wang XuanyinXiao BaopingPan FengState Key Laboratory of Fluid PowerTransmission and Control,Zhejiang University,Hangzhou 310027, China 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2003年第4期396-399,共4页
A dual-CCD simulating human eyes and neck (DSHEN) vision system is putforward. Its structure and principle are introduced. The DSREN vision system can perform somemovements simulating human eyes and neck by means of f... A dual-CCD simulating human eyes and neck (DSHEN) vision system is putforward. Its structure and principle are introduced. The DSREN vision system can perform somemovements simulating human eyes and neck by means of four rotating joints, and realize preciseobject recognizing and distance measuring in all orientations. The mathematic model of the DSHENvision system is built, and its movement equation is solved. The coordinate error and measureprecision affected by the movement parameters are analyzed by means of intersection measuringmethod. So a theoretic foundation for further research on automatic object recognizing and precisetarget tracking is provided. 展开更多
关键词 Dual-CCD Simulating human eyes and neck (DSHEN) Intersection measure ERRORANALYSIS Homogeneous coordinate transformation
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Natural Oscillations of Viscoelastic Lamellar Mechanical Systems with Point Communications 被引量:3
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作者 Safarov Ismail Ibrahimovich Teshaev Muhsin Hudoyberdievich Madjidov Maqsud 《Applied Mathematics》 2014年第19期3018-3025,共8页
We investigated the natural oscillations of dissipative inhomogeneous plate mechanical systems with point connections. Based on the principle of virtual displacements, we equate to zero the sum of all active work forc... We investigated the natural oscillations of dissipative inhomogeneous plate mechanical systems with point connections. Based on the principle of virtual displacements, we equate to zero the sum of all active work force, including the force of inertia which obtain equations vibrations of mechanical systems. Frequency equation is solved numerically by the method of Muller. According to the result of numerical analysis we established nonmonotonic dependence damping coefficients of the system parameters. 展开更多
关键词 Plate VISCOELASTIC Properties NATURAL Frequencies Damping Ratios Structurally HOMOGENEOUS and Structurally Heterogeneous
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Fast self-adapting high-order sliding mode control for a class of uncertain nonlinear systems 被引量:3
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作者 GUO Fuhui LU Pingli 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2021年第3期690-699,共10页
A fast self-adapting high-order sliding mode(FSHOSM)controller is designed for a class of nonlinear systems with unknown uncertainties.As for uncertainty-free nonlinear system,a new switching condition is introduced i... A fast self-adapting high-order sliding mode(FSHOSM)controller is designed for a class of nonlinear systems with unknown uncertainties.As for uncertainty-free nonlinear system,a new switching condition is introduced into the standard geometric homogeneity.Different from the existing geometric homogeneity method,both state variables and their derivatives are considered to bring a reasonable effective switching condition.As a result,a faster convergence rate of state variables is achieved.Furthermore,based on the integral sliding mode(ISM)and above geometric homogeneity,a self-adapting high-order sliding mode(HOSM)control law is proposed for a class of nonlinear systems with uncertainties.The resulting controller allows the closed-loop system to conduct with the expected properties of strong robustness and fast convergence.Stable analysis of the nonlinear system is also proved based on the Lyapunov approach.The effectiveness of the resulting controller is verified by several simulation results. 展开更多
关键词 adaptive control law geometric homogeneity high-order sliding mode(HOSM) integral sliding mode(ISM)
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New Explicit Solitary Wave Solutions and Periodic Wave Solutions for the Generalized Coupled Hirota-Satsuma KdV System 被引量:1
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作者 CHEN Yong YAN Zhen-Ya LI Biao ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第9期261-266,共6页
In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitar... In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained. 展开更多
关键词 COUPLED Hirota Satsuma KDV system KP equation homogeneous balance method Riccati equa-tion solitary WAVE solution periodic WAVE SOLUTION
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Homogenous Balance Method and Exact Analytical Solutions for Whitham-Broer-Kaup Equations in Shallow Water 被引量:1
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作者 XIAZhi 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第3期240-246,共7页
Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and... Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan's, Xie's and Yan's results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations. 展开更多
关键词 improved homogenous balance method Backlund transformation solitary wave solution multiple solution exact analytical solution rational solution
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Finite Indeterminacy of Homogenous Polynomial Germs under Some Subgroups R_(I_r) of R 被引量:1
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作者 LIU Heng-xing ZHANG Dun-mu 《Wuhan University Journal of Natural Sciences》 CAS 2005年第5期803-807,共5页
Using the finite determinacy relation with the regular sequence in the Ring Theory and the complete intersection in Analytic Geometry, the finite indeterminacy of homogeneous polynomial germs under some subgroups R1(... Using the finite determinacy relation with the regular sequence in the Ring Theory and the complete intersection in Analytic Geometry, the finite indeterminacy of homogeneous polynomial germs under some subgroups R1(r) of R in both real and complex case is proven by the homogeneity of the polynomial germs. It results in the finite determinacy of homogeneous polynomial germs needn't be discussed respectively. 展开更多
关键词 homogeneous polynomial finitely determined algebraic set regular sequence complete intersection
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