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COMPUTATIONALINTELLECTUAL ANALYTICAL THEORYOF COMPUTATIONAL ANALYTICAL APPROACH TOROTATING FLOW OF NON_NEWTONIAN FLUID 被引量:1
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作者 韩式方 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第11期1237-1250,共14页
A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model lends to a computational intellectual analytical approach developed by the author. There is a principal diffe... A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model lends to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer, also difference between the numerical and symbolic calculations. In this investigation the computational analytical approach is extended, and an unsteady flow of non-Newtonian fluid in the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3 rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the initial and boundary conditions is then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1 st, 2 nd and 3 rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non-Newtonian fluid flows. There is a possibility of that to solve the problems in mathematics and mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non-unique. 展开更多
关键词 time-dependent rotating flow non-Newtonian fluid Oldroyd fluid B computational symbolic manipulation computational analytical approach
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Analytical Approach to Clusters in near Critical CO2 被引量:1
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作者 Boris Sedunov Ilia Brondz 《International Journal of Analytical Mass Spectrometry and Chromatography》 2016年第3期39-50,共13页
Clusters greatly influence thermophysical properties of near critical gases. The cluster structures of supercritical fluids in general and Carbon Dioxide especially are important for the advanced supercritical fluid t... Clusters greatly influence thermophysical properties of near critical gases. The cluster structures of supercritical fluids in general and Carbon Dioxide especially are important for the advanced supercritical fluid technologies and analytics development. The paper extends to near critical densities the developed earlier methods to extract the clusters’ properties from Online Electronic Database of NIST on thermophysical properties of fluids. This Database contains a hidden knowledge of cluster fractions’ properties in real gases. The discovered earlier linear chain clusters dominate at intermediate densities. Their properties can be extrapolated to high density gases, thus opening the way to study large 3D clusters in near critical zone. The potential energy density of a gas, cleared from the chain clusters’ contribution, reflects only the 3D clusters’ characteristics. A series expansion of this value by the Monomer Fraction density discovers properties of n-particle 3D clusters. The paper demonstrates a discrete row of 3D clusters’ particle numbers and gives estimations for bond energies of these clusters. 展开更多
关键词 Real Gas Supercritical Fluid CLUSTER Bond Energy Equilibrium Constant Potential Energy Theoretical and analytical approach to Clusters Energetic of Clusters Clusters in Extraction Process Clusters in analytical Chemistry
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Chemical structures,analytical approaches and toxicological effects of oxidative derivatives of triglycerides as potential hazards in lipid thermal processing:A review
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作者 Miao Zhang Chenxu Wang +2 位作者 Zhuohong Xie Boyan Gao Liangli Yu 《Grain & Oil Science and Technology》 CAS 2024年第4期270-279,共10页
There is an increasing attention on oxidative derivatives of triglycerides,a group of potential thermal processing induced food toxicants,which are formed during the thermal processing of food lipids.This review aims ... There is an increasing attention on oxidative derivatives of triglycerides,a group of potential thermal processing induced food toxicants,which are formed during the thermal processing of food lipids.This review aims to summarize current knowledge about their formation mechanisms,detection approaches,and toxicology impacts.Oxidative derivatives of triglycerides are generated through the oxidation,cyclization,polymerization,and hydrolysis of triglycerides under high-temperature and abundant oxygen.The analytical techniques,including GC,HPSEC,MS,^(1)H-NMR were discussed in analyzing these components.In addition,their toxic effects on human health,including effects on the liver,intestines,cardiovascular system,immune system,and metabolism were elucidated.Information in this review could be used to improve the understanding of oxidative derivatives of triglycerides and ultimately improve academic and industrial strategies for eliminating these compounds in thermal processing food systems. 展开更多
关键词 Oxidative derivatives of triglycerides Food thermal processing Formation mechanism analytical approaches Toxicological effects
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Contemporary strategies and approaches for characterizing composition and enhancing biofilm penetration targeting bacterial extracellular polymeric substances
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作者 Lan Lu Yuting Zhao +4 位作者 Mingxing Li Xiaobo Wang Jie Zhu Li Liao Jingya Wang 《Journal of Pharmaceutical Analysis》 SCIE CAS CSCD 2024年第4期506-524,共19页
Extracellular polymeric substances(EPS)constitutes crucial elements within bacterial biofilms,facili-tating accelerated antimicrobial resistance and conferring defense against the host's immune cells.Developing pr... Extracellular polymeric substances(EPS)constitutes crucial elements within bacterial biofilms,facili-tating accelerated antimicrobial resistance and conferring defense against the host's immune cells.Developing precise and effective antibiofilm approaches and strategies,tailored to the specific charac-teristics of EPS composition,can offer valuable insights for the creation of novel antimicrobial drugs.This,in turn,holds the potential to mitigate the alarming issue of bacterial drug resistance.Current analysis of EPS compositions relies heavily on colorimetric approaches with a significant bias,which is likely due to the selection of a standard compound and the cross-interference of various EPS compounds.Considering the pivotal role of EPS in biofilm functionality,it is imperative for EPS research to delve deeper into the analysis of intricate compositions,moving beyond the current focus on polymeric materials.This ne-cessitates a shift from heavy reliance on colorimetric analytic methods to more comprehensive and nuanced analytical approaches.In this study,we have provided a comprehensive summary of existing analytical methods utilized in the characterization of EPS compositions.Additionally,novel strategies aimed at targeting EPS to enhance biofilm penetration were explored,with a specific focus on high-lighting the limitations associated with colorimetric methods.Furthermore,we have outlined the challenges faced in identifying additional components of EPS and propose a prospective research plan to address these challenges.This review has the potential to guide future researchers in the search for novel compounds capable of suppressing EPS,thereby inhibiting biofilm formation.This insight opens up a new avenue for exploration within this research domain. 展开更多
关键词 Analytic strategies and approaches Composition characterization Extracellular polymeric substances(EPS) Promoting biofilm penetration
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Nonlinear Study on the Mechanical Performance of Built-Up Cold-Formed Steel Concrete-Filled Columns under Compression
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作者 Oulfa Harrat Yazid Hadidane +4 位作者 S.M.Anas Nadhim Hamah Sor Ahmed Farouk Deifalla Paul O.Awoyera Nadia Gouider 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第6期3435-3465,共31页
Given their numerous functional and architectural benefits,such as improved bearing capacity and increased resistance to elastic instability modes,cold-formed steel(CFS)built-up sections have become increasingly devel... Given their numerous functional and architectural benefits,such as improved bearing capacity and increased resistance to elastic instability modes,cold-formed steel(CFS)built-up sections have become increasingly developed and used in recent years,particularly in the construction industry.This paper presents an analytical and numerical study of assembled CFS two single channel-shaped columns with different slenderness and configurations(backto-back,face-to-face,and box).These columns were joined by double-row rivets for the back-to-back and box configurations,whereas they were welded together for the face-to-face design.The built-up columns were filled with ordinary concrete of good strength.Finite element models were applied,using ABAQUS software,to assess mechanical performance and study the influence of assembly techniques on the behavior of cold-formed columns under axial compression.Analytical approaches based on Eurocode 3 and Eurocode 4 recommendations for un-filled and concrete-filled columns respectively were followed for the numerical analysis,and concrete confinement effects were also considered per American Concrete Institute(ACI)standards for face-to-face and box configurations.The obtained results indicated a good correlation between the numerical results and the proposed analytical methodology which did not exceed 8%.The failure modes showed that the columns failed due to instabilities such as local and global buckling. 展开更多
关键词 Cold-formed steel built-up sections SLENDERNESS rivets WELDED axial compression analytical approaches CONFINEMENT BUCKLING
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Analytical solution for slope instability assessment considering impact of confined aquifer 被引量:3
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作者 冉启华 钱群 +2 位作者 王光谦 傅旭东 苏丹阳 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第4期1502-1509,共8页
An analytical approach was presented for estimating the factor of safety(FS) for slope failure, with consideration of the impact of a confined aquifer. An upward-moving wetting front from the confined water was assume... An analytical approach was presented for estimating the factor of safety(FS) for slope failure, with consideration of the impact of a confined aquifer. An upward-moving wetting front from the confined water was assumed and the pore water pressure distribution was then estimated and used to obtain the analytical expression of FS. Then, the validation of the theoretical analysis was applied based on an actual case in Hong Kong. It is shown that the presence of a confined aquifer leads to a lower FS value, and the impact rate of hydrostatic pressure on FS increases as the confined water pressure increases, approaching to a maximum value determined by the ratio of water density to saturated soil density. It is also presented that the contribution of hydrostatic pressure and hydrodynamic pressure to the slope stability vary with the confined aquifer pressure. 展开更多
关键词 confined/artesian groundwater slope stability factor of safety analytical approach
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Modeling approaches to pressure balance dynamic system in shield tunneling 被引量:2
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作者 李守巨 于申 屈福政 《Journal of Central South University》 SCIE EI CAS 2014年第3期1206-1216,共11页
In order to deal with modeling problem of a pressure balance system with time-delay, nonlinear, time-varying and uncertain characteristics, an intelligent modeling procedure is proposed, which is based on artificial n... In order to deal with modeling problem of a pressure balance system with time-delay, nonlinear, time-varying and uncertain characteristics, an intelligent modeling procedure is proposed, which is based on artificial neural network(ANN) and input-output data of the system during shield tunneling and can overcome the precision problem in mechanistic modeling(MM) approach. The computational results show that the training algorithm with Gauss-Newton optimization has fast convergent speed. The experimental investigation indicates that, compared with mechanistic modeling approach, intelligent modeling procedure can obviously increase the precision in both soil pressure fitting and forecasting period. The effectiveness and accuracy of proposed intelligent modeling procedure are verified in laboratory tests. 展开更多
关键词 intelligent modeling neural network pressure balance system excavation chamber analytically modeling approach
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G-type dispersion equation under suppressed rigid boundary:analytic approach
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作者 S.K.VISHWAKARMA Runzhang XU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第4期501-512,共12页
This paper studies dispersion of a G-type earthquake wave under the influence of a suppressed rigid boundary. Inside the Earth, the density and rigidity of the crustal layer and the mantle of the Earth vary exponentia... This paper studies dispersion of a G-type earthquake wave under the influence of a suppressed rigid boundary. Inside the Earth, the density and rigidity of the crustal layer and the mantle of the Earth vary exponentially and periodically along the depth. The displacements of the wave are found in the individual medium followed by a dispersion equation using a suitable analytic approach and a boundary condition. The prominent effect of inhomogeneity contained in the media, the rigid boundary plane, and the initial stress on the phase and group velocities is shown graphically. 展开更多
关键词 G-type wave analytic approach dispersion equation group velocity rigid boundary
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Analytic equation of state for solids with multi-exponential potential based on analytic mean field potential approach and applied to the epsilon phase of solid oxygen
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作者 王立国 孙久勋 杨维 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第8期2867-2873,共7页
The thermodynamic properties of the ε phase of solid oxygen are studied by using the analytic mean field approach (AMFP). Analytic expressions for the Helmholtz free energy, internal energy and equation of state of... The thermodynamic properties of the ε phase of solid oxygen are studied by using the analytic mean field approach (AMFP). Analytic expressions for the Helmholtz free energy, internal energy and equation of state of solid oxygen have been derived based on the multi-exponential potential. The formulism for the case of double-exponential (DE) model is applied to the ε phase of solid oxygen. Its four potential parameters are determined through fitting the experimental compression data of the ε phase of solid oxygen. Numerical results of the pressure dependence of the volume calculated by using the AMFP are in good agreement with the original experimental data. This suggests that the AMFP is a useful approach to study the thermodynamic properties of the ε phase of solid oxygen. Furthermore, we predict the variation of the volume, lattice parameters and intermolecular distances with pressure, and some thermodynamic quantities versus volume, at several higher temperatures. 展开更多
关键词 analytic equation of state analytic mean field approach solid oxygen ε phase
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Nonlinear dynamics of two degree of freedom systems with linear and nonlinear stiffnesses 被引量:2
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作者 Bayat Mahmoud I.Pakar 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2013年第3期411-420,共10页
In this study, a new analytical approach is developed to analyze the free nonlinear vibration of conservative two-degree-of-freedom (TDOF) systems. The mathematical models of these systems are governed by second--or... In this study, a new analytical approach is developed to analyze the free nonlinear vibration of conservative two-degree-of-freedom (TDOF) systems. The mathematical models of these systems are governed by second--order nonlinear partial differential equations. Nonlinear differential equations were transferred into a single equation by using some intermediate variables. The single nonlinear differential equations are solved by using the first order of the Hamiltonian approach (HA). Different parameters, which have a significant impact on the response of the systems, are considered and discussed. Some comparisons are presented to verify the results between the Hamiltonian approach and the exact solution. The maximum relative error is less than 2.2124 % for large amplitudes of vibration. It has been established that the first iteration of the Hamiltonian approach achieves very accurate results, does not require any small perturbations, and can be used for a wide range of nonlinear problems. 展开更多
关键词 nonlinear vibration two-degree-of-freedom (TDOF) analytical approach Hamitonian approach (HA)
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Winding Inductance and Performance Prediction of a Switched Reluctance Motor with an Exterior-rotor Considering the Magnetic Saturation 被引量:3
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作者 Minjie Zhang Nasir Ali Qiang Gao 《CES Transactions on Electrical Machines and Systems》 CSCD 2021年第3期212-223,共12页
This paper deals with an analytical method to effectively calculate the inductance of an exterior-rotor switched reluctance motor(SRM),which evaluates the winding inductance of both the active section and the end sect... This paper deals with an analytical method to effectively calculate the inductance of an exterior-rotor switched reluctance motor(SRM),which evaluates the winding inductance of both the active section and the end section,accounting for the influence of core saturation.According to the inductance calculated by the analytical model,the flux linkage table and torque table can be established,and the steady state performance such as phase current,flux linkage,copper loss and core loss can be predicted.Effectiveness of this method is verified by the finite element method as well as by experimental results of a 12/8 SRM prototype. 展开更多
关键词 analytical approach Exterior-rotor switched reluctance motor Magnetic saturation INDUCTANCE
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Seismic earth pressures on flexible cantilever retaining walls with deformable inclusions 被引量:3
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作者 Ozgur L.Ertugrul Aurelian C.Trandafir 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2014年第5期417-427,共11页
In this study, the results of 1-g shaking table tests performed on small-scale flexible cantilever wallmodels retaining composite backfill made of a deformable geofoam inclusion and granular cohesionlessmaterial were ... In this study, the results of 1-g shaking table tests performed on small-scale flexible cantilever wallmodels retaining composite backfill made of a deformable geofoam inclusion and granular cohesionlessmaterial were presented. Two different polystyrene materials were utilized as deformable inclusions.Lateral dynamic earth pressures and wall displacements at different elevations of the retaining wallmodel were monitored during the tests. The earth pressures and displacements of the retaining wallswith deformable inclusions were compared with those of the models without geofoam inclusions.Comparisons indicated that geofoam panels of low stiffness installed against the retaining wall modelaffect displacement and dynamic lateral pressure profile along the wall height. Depending on the inclusioncharacteristics and the wall flexibility, up to 50% reduction in dynamic earth pressures wasobserved. The efficiency of load and displacement reduction decreased as the flexibility ratio of the wallmodel increased. On the other hand, dynamic load reduction efficiency of the deformable inclusionincreased as the amplitude and frequency ratio of the seismic excitation increased. Relative flexibility ofthe deformable layer (the thickness and the elastic stiffness of the polystyrene material) played animportant role in the amount of load reduction. Dynamic earth pressure coefficients were compared withthose calculated with an analytical approach. Pressure coefficients calculated with this method werefound to be in good agreement with the results of the tests performed on the wall model having lowflexibility ratio. It was observed that deformable inclusions reduce residual wall stresses observed at theend of seismic excitation thus contributing to the post-earthquake stability of the retaining wall. Thegraphs presented within this paper regarding the dynamic earth pressure coefficients versus the wallflexibility and inclusion characteristics may serve for the seismic design of full-scale retaining walls withdeformable polystyrene inclusions. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved. 展开更多
关键词 Cantilever retaining wall Deformable geofoam panel 1-g shaking table tests Dynamic earth pressure Polystyrene Flexibility ratio analytical approach
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Extension of analytical indicial aerodynamics to generic trapezoidal wings in subsonic flow 被引量:3
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作者 Andrea DA RONCH Antonino VENTURA +3 位作者 Marcello RIGHI Matteo FRANCIOLINI Marco BERCI Daniel KHARLAMOV 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2018年第4期617-631,共15页
Analytical indicial aerodynamic functions are calculated for several trapezoidal wings in subsonic flow, with a Mach number 0.3 Ma 0.7. The formulation herein proposed extends wellknown aerodynamic theories, which are... Analytical indicial aerodynamic functions are calculated for several trapezoidal wings in subsonic flow, with a Mach number 0.3 Ma 0.7. The formulation herein proposed extends wellknown aerodynamic theories, which are limited to thin aerofoils in incompressible flow, to generic trapezoidal wing planforms. Firstly, a thorough study is executed to assess the accuracy and limitation of analytical predictions, using unsteady results from two state-of-the-art computational fluid dynamics solvers as cross-validated benchmarks. Indicial functions are calculated for a step change in the angle of attack and for a sharp-edge gust, each for four wing configurations and three Mach numbers. Then, analytical and computational indicial responses are used to predict dynamic derivatives and the maximum lift coefficient following an encounter with a one-minus-cosine gust. It is found that the analytical results are in excellent agreement with the computational results for all test cases. In particular, the deviation of the analytical results from the computational results is within the scatter or uncertainty in the data arising from using two computational fluid dynamics solvers. This indicates the usefulness of the developed analytical theories. 展开更多
关键词 analytical approach CFD Compressible flow Gust response Indicial aerodynamics Trapezoidal wing
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Optimization of the mechanical performance and damage failure characteristics of laminated composites based on fiber orientation
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作者 Hussein DALFI Anwer AL-OBAIDI +2 位作者 Abdalameer TARIQ Hussein RAZZAQ Roham RAFIEE 《Frontiers of Structural and Civil Engineering》 SCIE EI CSCD 2023年第9期1357-1369,共13页
In this study,the effect of fiber angle on the tensile load-bearing performance and damage failure characteristics of glass composite laminates was investigated experimentally,analytically,and numerically.The glass fa... In this study,the effect of fiber angle on the tensile load-bearing performance and damage failure characteristics of glass composite laminates was investigated experimentally,analytically,and numerically.The glass fabric in the laminate was perfectly aligned along the load direction(i.e.,at 0°),offset at angles of 30°and 45°,or mixed in different directions(i.e.,0°/30°or 0°/45°).The composite laminates were fabricated using vacuum-assisted resin molding.The influence of fiber orientation angle on the mechanical properties and stiffness degradation of the laminates was studied via cyclic tensile strength tests.Furthermore,simulations have been conducted using finite element analysis and analytical approaches to evaluate the influence of fiber orientation on the mechanical performance of glass laminates.Experimental testing revealed that,although the composite laminates laid along the 0°direction exhibited the highest stiffness and strength,their structural performance deteriorated rapidly.We also determined that increasing the fiber offset angle(i.e.,30°)could optimize the mechanical properties and damage failure characteristics of glass laminates.The results of the numerical and analytical approaches demonstrated their ability to capture the mechanical behavior and damage failure modes of composite laminates with different fiber orientations,which may be used to prevent the catastrophic failures that occur in composite laminates. 展开更多
关键词 fiber orientation composite laminates stiffness degradation analytical approaches finite element analysis
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Quantitative analysis of CO_(2) embodiment in international trade:An overview of emerging literatures 被引量:5
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作者 Xianbing LIU Can WANG 《Frontiers of Environmental Science & Engineering》 SCIE EI CSCD 2009年第1期12-19,共8页
The increasing volume of CO_(2) embodiment in international trade adds a layer of complexity to environmental policies and has raised arguments on the traditional production based responsibility for CO_(2) emissions.I... The increasing volume of CO_(2) embodiment in international trade adds a layer of complexity to environmental policies and has raised arguments on the traditional production based responsibility for CO_(2) emissions.In order to help understand the quantity of CO_(2) embodiment in trade and its policy implications,this paper gives observations to recently emerging literatures that quantitatively discuss CO_(2) embodiment in trade.The analytical approaches share the principle of using input and output modeling but vary dramatically in study boundary and estimation accuracy.The calculations can be roughly categorized into three types:direct quantification of CO_(2) embodiments in multiregional trade,direct quantification of CO_(2) embodiment in bilateral trade,and indirect analysis by comparing the scenarios with or without trade.The practical estimations strongly rely on trade partner selection and data availability.An obvious imbalance of net CO_(2) embodiment in the commodity trade between major developed countries and developing economies as a whole was confirmed by these literatures.Carbon taxes and other possible limitations on CO_(2) emissions have been addressed.The consistency across the calculations could be enhanced by systematic analyses in more detail to convince the international community to take binding commitments for the reduction of global CO_(2) emissions. 展开更多
关键词 CO_(2)embodiment international trade quantitative estimation analytical approach
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SOCIAL MEDIA RESEARCH:A REVIEW 被引量:4
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作者 Junjie WU Haoyan SUN Yong TAN 《Journal of Systems Science and Systems Engineering》 SCIE EI CSCD 2013年第3期257-282,共26页
Social media is fundamentally changing the way people communicate, consume and collaborate. It provides companies a new platform to interact with their customers. In academia, there is a surge in research efforts on u... Social media is fundamentally changing the way people communicate, consume and collaborate. It provides companies a new platform to interact with their customers. In academia, there is a surge in research efforts on understanding its effects. This paper aims to provide a review of current status of social media research. We discuss the specific domains in which the impacts of social media have been examined. A brief review of applicable research methodologies and approaches is also provided. 展开更多
关键词 social media empirical models experimental methods analytical approaches predictive analytics
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SHM-based F-AHP bridge rating system with application to Tsing Ma Bridge 被引量:1
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作者 Qi LI You-lin XU +3 位作者 Yue ZHENG An-xin GUO Kai-yuen WONG Yong XIA 《Frontiers of Structural and Civil Engineering》 SCIE EI 2011年第4期465-478,共14页
This paper aims at developing a structural health monitoring(SHM)-based bridge rating method for bridge inspection of long-span cable-supported bridges.The fuzzy based analytic hierarchy approach is employed,and the h... This paper aims at developing a structural health monitoring(SHM)-based bridge rating method for bridge inspection of long-span cable-supported bridges.The fuzzy based analytic hierarchy approach is employed,and the hierarchical structure for synthetic rating of each structural component of the bridge is proposed.The criticality and vulnerability analyses are performed largely based on the field measurement data from the SHM system installed in the bridge to offer relatively accurate condition evaluation of the bridge and to reduce uncertainties involved in the existing rating method.The procedures for determining relative weighs and fuzzy synthetic ratings for both criticality and vulnerability are then suggested.The fuzzy synthetic decisions for inspection are made in consideration of the synthetic ratings of all structural components.The SHM-based bridge rating method is finally applied to the Tsing Ma suspension bridge in Hong Kong as a case study.The results show that the proposed method is feasible and it can be used in practice for longspan cable-supported bridges with SHM system. 展开更多
关键词 structural health monitoring(SHM) bridge rating method fuzzy based analytic hierarchy approach criticality and vulnerability rating Tsing Ma Bridge
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Exponential Convergence Rates of Markov Chains under a Weaken Minorization Condition
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作者 Shu Lan HU Xin Yu WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第12期1829-1836,共8页
In this paper, we obtain the quantitative bound of the exponential convergence rates of Markov chains under a weaken minorization condition, using the coupling method and the analytic approach. And also, we obtain the... In this paper, we obtain the quantitative bound of the exponential convergence rates of Markov chains under a weaken minorization condition, using the coupling method and the analytic approach. And also, we obtain the convergence rates for continuous time Markov processes. 展开更多
关键词 Convergence rates Markov chains coupling method analytic approach
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