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Critical Analysis of Increasingly Mathematical Economics in the Modern Society
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作者 YU Renze 《Management Studies》 2024年第4期248-251,共4页
This paper critically examines the escalating trend of mathematization in economics,highlighting its implications and controversies in contemporary economic research.While the application of sophisticated mathematical... This paper critically examines the escalating trend of mathematization in economics,highlighting its implications and controversies in contemporary economic research.While the application of sophisticated mathematical models and statistical techniques has enhanced the precision,rigor,and status of economics within academia and practical application,concerns arise regarding the potential oversimplification and detachment from real-world complexities.The adoption of mathematical tools has arguably led to a focus on theoretically tractable problems at the expense of those more relevant to practical economic and social issues.This paper explores both the benefits and limitations of this trend,discussing how the reliance on quantitative methods affects the innovation,comprehensibility,and application of economic theories.We argue for a balanced approach that fosters innovation by integrating qualitative insights and embracing interdisciplinary methods to ensure economics remains both rigorous and relevant to societal needs. 展开更多
关键词 mathematization of economics quantitative methods economic models interdisciplinary integration
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Dispersive propagation of optical solitions and solitary wave solutions of Kundu-Eckhaus dynamical equation via modified mathematical method
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作者 Aly R.Seadawy Mujahid Iqbal 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第1期16-26,共11页
In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,br... In this research work,we constructed the optical soliton solutions of nonlinear complex Kundu-Eckhaus(KE)equation with the help of modified mathematical method.We obtained the solutions in the form of dark solitons,bright solitons and combined dark-bright solitons,travelling wave and periodic wave solutions with general coefficients.In our knowledge earlier reported results of the KE equation with specific coefficients.These obtained solutions are more useful in the development of optical fibers,dynamics of solitons,dynamics of adiabatic parameters,dynamics of fluid,problems of biomedical,industrial phenomena and many other branches.All calculations show that this technique is more powerful,effective,straightforward,and fruitfulness to study analytically other higher-order nonlinear complex PDEs involves in mathematical physics,quantum physics,Geo physics,fluid mechanics,hydrodynamics,mathematical biology,field of engineering and many other physical sciences. 展开更多
关键词 Kundu-Eckhaus equation modified mathematical method solitons and solitary wave solutions
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Geological Environmental Adaptability of Qingdao Rural Urbanization Based on Fuzzy Mathematical Method 被引量:1
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作者 HOU Xin-wen YIN Zhi-xuan +4 位作者 ZHANG Jian-wei YUAN Xi-long YIN Ming-quan LI Qing-ping DONG Jie 《Asian Agricultural Research》 2010年第6期56-59,共4页
Fuzzy mathematics comprehensive evaluation method is used to evaluate the geological environment suitability of rural urbanization in Qingdao City,China.A total of 5 first-level evaluation factors are selected,includi... Fuzzy mathematics comprehensive evaluation method is used to evaluate the geological environment suitability of rural urbanization in Qingdao City,China.A total of 5 first-level evaluation factors are selected,including environmental geological condition,geological resources,engineering geological condition,geological disaster and environmental geological problem,and human engineering activity.And there are 27 second-level evaluation factors,such as topography,land type and vegetation,nature reserve,water source protection area,groundwater quality division,and major engineering project.Qingdao City is divided into four districts of suitable area,relatively suitable area,moderately suitable area and relatively unsuitable area of ecological environment.And their characteristics are introduced.Suggestions for the developing direction of urban construction are put forward.Region of Laoshan District lying to the west of the Shilaoren is suitable to set up high-rise building;west Hongshiya may establish a waste landfill site;Jiaozhou Bay,the downstream of Dagu River,and Jihongtan Reservoir should be built as the key geological environment protection area and water source protection area.And the north Hongdao should be strictly monitored in order to control the expansion of urban construction to Jihongtan Reservoir.Mocheng District and the area north of it,Jiaozhou District and the area east of it are the ideal urban construction development areas in Qingdao City in the future. 展开更多
关键词 Rural urbanization Qingdao Fuzzy mathematical method Geological environment ADAPTABILITY China
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Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua 被引量:1
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作者 Karan S. Surana Emilio N. Alverio 《Applied Mathematics》 2020年第7期546-578,共33页
Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous... Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (<i>I</i>) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (<em>δI</em>) set to zero is a necessary condition for an extremum of <i>I</i>. In this approach one could use <i>δI</i> = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from <i>δI</i> = 0, which is also satisfied by a solution obtained from <i>δI</i> = 0. The Euler’s equations obtained from <i>δI</i> = 0 indeed are the mathematical model associated with the energy functional <i>I</i>. In case of BVPs we follow the same approach except in this case, the energy functional <i>I</i> consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles <i>i.e.</i> conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper. 展开更多
关键词 Energy methods Principle of Virtual Work Calculus of Variations Euler’s Equation mathematical Model Classical and Non-Classical Continuum Mechanics
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Preliminary Research on the Mathematical Methods and Order of Problems in the“Fungcheng”Chapter of Yang Hui's Mathematical Methods(1261 CE) 被引量:1
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作者 Zhou Xiaohan 《Chinese Annals of History of Science and Technology》 2020年第1期1-62,共62页
Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earlie... Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earliest extant work attributed to Yang Hui.From the thirteenth to the fifteenth century,this work played a crucial role in the circulation and popularization of The Nine Chapters on Mathematical Procedures(Jiuzhang suanshu九章算术).However,the only surviving printed edition of Mathematical Methods is incomplete and contains many mistakes obstructing contemporary researchers'understanding of this work.The "Fangcheng" chapter of The Nine Chapters deals with problems related to solving what today are known as simultaneous sets of linear equations.However,interpreting the text in this chapter of Mathematical Methods and recovering the mathematical practices relating to fangcheng are difficult.Through detailed textual and mathematical analyses,the author of this paper explains Yang Hufs understanding and practice relating to〃the fangcheng method"and"the method of the positive and the negative".This paper includes an appendix that provides a detailed translation of the ambiguous text relating to"the method of the positive and the negative"and gives reasons supporting the interpretation provided here.Yang Hufs understanding of the concepts of"positive"and"negative"and his practice relating to these two concepts may easily be confused with their apparent counterparts in modem mathematics.Also,careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hufs Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters([Xiangjie jiuzhang suanfa zuanlei詳解九章算法纂類],namely,the last section of Mathematical Methods)were rearranged according to commentaries to specific methods that appear in Mathematical Methods.Some textual clues referring to the zzprevious question"(qianwen前問)in certain commentaries of Mathematical Methods indeed reflect the order of problems in Reclassifications.Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work,The Nine Chapters.All these discoveries reveal and serve to prove a close relationship between Yang Hufs Mathematical Methods and his Reclassifications. 展开更多
关键词 mathematical methods Explaining in Detail The Nine Chapters Reclassifications of mathematical methods Explaining in Detail The Nine Chapters The Nine Chapters Yang Hui the fangcheng method the method of the positive and the negative translations of ancient mathematical writing
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Dynamic Factor Method of Computing Dynamic Mathematical Model for System Simulation
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作者 老大中 吴娟 +1 位作者 杨策 蒋滋康 《Journal of Beijing Institute of Technology》 EI CAS 2003年第2期143-148,共6页
The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of t... The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor. 展开更多
关键词 system simulation dynamic mathematical model computational method dynamic factor ERROR
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A Numerical Method for Rigid-plastic FEM Analysis Basing on Mathematical Programming
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作者 Li Di Lin Zhongqin Chen Guanlong Zhang Weigang Li Shuhui 《上海交通大学学报》 EI CAS CSCD 北大核心 2004年第z2期32-37,共6页
The rigid-plastic analysis of mental forming simulation is formulated as a discrete nonlinear mathematical programming problem with equality and inequality constraints by means of the finite element technique. An iter... The rigid-plastic analysis of mental forming simulation is formulated as a discrete nonlinear mathematical programming problem with equality and inequality constraints by means of the finite element technique. An iteration algorithm is used to solve this formulation, which distinguishes the integration points of the rigid zones and the plastic zones and solves a series of the quadratic programming to overcome the difficulties caused by the nonsmoothness and the nonlinearity of the objective function. This method has been used to carry out the rigid-plastic FEM analysis. An example is given to demonstrate the effectiveness of this method. 展开更多
关键词 RIGID-PLASTIC mathematical PROGRAMMING FINITE ELEMENT method
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Mathematical modelling of a biofilm: The Adomian decomposition method
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作者 Subramanian Muthukaruppan Alagu Eswari Lakshmanan Rajendran 《Natural Science》 2013年第4期456-462,共7页
A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expre... A mathematical modelling by a biofilm under steady state conditions is discussed. The nonlinear differential Equations in biofilm reaction is solved using the Adomian decomposition method. Approximate analytical expressions for substrate concentration have been derived for all values of parameters δ and SL. These analytical results are compared with the available numerical results and are found to be in good agreement. 展开更多
关键词 mathematical Modeling Simulation Adomian DECOMPOSITION method INITIAL BOUNDARY VALUE Problems
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A two-parameter mathematical model for immobilizedenzymes and Homotopy analysis method
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作者 Rathinasamy Angel Joy Athimoolam Meena +1 位作者 Shunmugham Loghambal Lakshmanan Rajendran 《Natural Science》 2011年第7期556-565,共10页
A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten ki... A two parameter mathematical model was developed to find the concentration for immobilized enzyme systems in porous spherical particles. This model contains a non-linear term related to reversible Michaelies-Menten kinetics. Analytical expression pertaining to the substrate concentration was reported for all possible values of Thiele module φ and α . In this work, we report the theoretically evaluated steady-state effectiveness factor for immobilized enzyme systems in porous spherical particles. These analytical results were found to be in good agreement with numerical results. Moreover, herein we employ new “Homotopy analysis method” (HAM) to solve non-linear reaction/diffusion equation. 展开更多
关键词 mathematical Modeling MICHAELIS-MENTEN KINETICS HOMOTOPY Analysis method Reaction/Diffusion Equation EFFECTIVENESS factor
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An Effective Numerical Calculation Method for Multi-Time-Scale Mathematical Models in Systems Biology
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作者 Yohei Motomura Hiroyuki Hamada Masahiro Okamoto 《Applied Mathematics》 2016年第17期2241-2268,共28页
The improvements of high-throughput experimental devices such as microarray and mass spectrometry have allowed an effective acquisition of biological comprehensive data which include genome, transcriptome, proteome, a... The improvements of high-throughput experimental devices such as microarray and mass spectrometry have allowed an effective acquisition of biological comprehensive data which include genome, transcriptome, proteome, and metabolome (multi-layered omics data). In Systems Biology, we try to elucidate various dynamical characteristics of biological functions with applying the omics data to detailed mathematical model based on the central dogma. However, such mathematical models possess multi-time-scale properties which are often accompanied by time-scale differences seen among biological layers. The differences cause time stiff problem, and have a grave influence on numerical calculation stability. In the present conventional method, the time stiff problem remained because the calculation of all layers was implemented by adaptive time step sizes of the smallest time-scale layer to ensure stability and maintain calculation accuracy. In this paper, we designed and developed an effective numerical calculation method to improve the time stiff problem. This method consisted of ahead, backward, and cumulative algorithms. Both ahead and cumulative algorithms enhanced calculation efficiency of numerical calculations via adjustments of step sizes of each layer, and reduced the number of numerical calculations required for multi-time-scale models with the time stiff problem. Backward algorithm ensured calculation accuracy in the multi-time-scale models. In case studies which were focused on three layers system with 60 times difference in time-scale order in between layers, a proposed method had almost the same calculation accuracy compared with the conventional method in spite of a reduction of the total amount of the number of numerical calculations. Accordingly, the proposed method is useful in a numerical analysis of multi-time-scale models with time stiff problem. 展开更多
关键词 Finite Difference method Stiff Equation Multi-Time-Scale Systems Biology mathematical Analysis
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Levenberg-Marquardt Method for Mathematical Programs with Linearly Complementarity Constraints
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作者 Cong Zhang Limin Sun +1 位作者 Zhibin Zhu Minglei Fang 《American Journal of Computational Mathematics》 2015年第3期239-242,共4页
In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary ... In this paper, a new method for solving a mathematical programming problem with linearly complementarity constraints (MPLCC) is introduced, which applies the Levenberg-Marquardt (L-M) method to solve the B-stationary condition of original problem. Under the MPEC-LICQ, the proposed method is proved convergent to B-stationary point of MPLCC. 展开更多
关键词 mathematical PROGRAMS with Linear Complementarity CONSTRAINTS MPEC-LICQ B-Stationarity LEVENBERG-MARQUARDT method
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Mathematical Programming Method as a Means of Calibration of NIR Analyzers
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作者 Ilya Skutin Konstantin Zharinov Maria Sushkova 《Journal of Chemistry and Chemical Engineering》 2012年第8期692-697,共6页
In addition to the conventional methods of the calibration model construction, such as PCR (principal components regression) and PLS (partial least-squares), a MPM (mathematical programming method) is developed ... In addition to the conventional methods of the calibration model construction, such as PCR (principal components regression) and PLS (partial least-squares), a MPM (mathematical programming method) is developed and proposed for practical use in NIR analyses of agricultural and food products. The proposed method involves the mathematical programming techniques to seek the regression coefficients for the calibration model calculation. It is based on the optimization theory used for finding the extremum of the objective function in the given domain of a vector space and employs the method of the complementarity problems solving. The MPM algorithm is described in detail. The MPM was tested on an InfraLUM FT-10 NIR analyzer of Lumex company with samples of dry milk (for fat), corn (for protein) and rye flour (for moisture). The obtained results show that the MPM can be used for constructing multivariate calibrations with the qualitative characteristics superior over those of the classical PCR and PLS methods of analysis. 展开更多
关键词 CHEMOMETRICS multivariate calibration mathematical programming simplex table method.
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SIMULTANEOUS DETERMINATION OF MULTICOMPONENT IN MIXED ACIDS BY MATHEMATICAL METHOD
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作者 Yong Nian NI Department of Chemistry,Jiangxi University,Nanchang,330047 《Chinese Chemical Letters》 SCIE CAS CSCD 1990年第2期105-108,共4页
A new method for the determination of components in mixed acids has been developed.The mathematical model is obtained from samples of known composition and is then used to predict the concentrations of components in u... A new method for the determination of components in mixed acids has been developed.The mathematical model is obtained from samples of known composition and is then used to predict the concentrations of components in unknown sample.The practical utility of this method is demonstrated for simultaneous determination of two systems of ternary mixed acids and the results are satisfactory. 展开更多
关键词 ACID SIMULTANEOUS DETERMINATION OF MULTICOMPONENT IN MIXED ACIDS BY mathematical method
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Research on the Teaching Design of Advanced Mathematics Courses Based on Outcome-Based Education Concept
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作者 Xinyu Huang 《Journal of Contemporary Educational Research》 2024年第6期148-154,共7页
This paper first analyzes the characteristics and current situation of the Advanced Mathematics course;secondly,it proposes a teaching model that integrates the outcome-based education(OBE)philosophy and blended teach... This paper first analyzes the characteristics and current situation of the Advanced Mathematics course;secondly,it proposes a teaching model that integrates the outcome-based education(OBE)philosophy and blended teaching method,reorganizing the teaching objectives,teaching content,and assessment evaluation process of the Advanced Mathematics course;lastly,through practice,it is proved that this approach can effectively improve students’mastery of course content,enhance students’ability to apply mathematical knowledge,and strengthen teaching effectiveness. 展开更多
关键词 Advanced mathematics Outcome-based education concept Blended teaching method Online publication:July 3 2024
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STREAMLINE-BASED MATHEMATICAL MODEL FOR CO_2 MISCIBLE FLOODING 被引量:8
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作者 侯健 《应用数学和力学》 EI CSCD 北大核心 2004年第6期635-642,共8页
According to the research theory of improved black oil simulator, a practical mathematical model for CO2 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas... According to the research theory of improved black oil simulator, a practical mathematical model for CO2 miscible flooding was presented. In the model, the miscible process simulation was realized by adjusting oil/gas relative permeability and effective viscosity under the condition of miscible flow. In order to predict the production performance(fast,) streamline method is employed to solve this model as an alternative to traditional finite(difference) (methods.) Based on streamline distribution of steady-state flow through porous media with complex boundary confirmed with the boundary element method (BEM), an explicit total variation diminishing (TVD) method is used to solve the one-dimensional flow problem. At the same time, influences of development scheme, solvent slug size, and injection periods on CO2 drive recovery are discussed. The model has the advantages of less(information) need, fast calculation, and adaptation to calculate CO2 drive performance of all kinds of patterns in a random shaped porous media with assembly boundary. It can be an(effective) tool for early stage screening and reservoir dynamic management of the CO2(miscible) oil field. 展开更多
关键词 混相驱 流线 数学模型 边界元法 提高采收率
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On Application of Mathematic Idea and Method in English Grammar Teaching and Learning
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作者 李海 《海外英语》 2011年第1X期35-37,共3页
English grammar is at any time the important part of English learning,even if under the implementation of the New Course Standard.However,English grammar is considered to be difficult due to its complexity.My paper he... English grammar is at any time the important part of English learning,even if under the implementation of the New Course Standard.However,English grammar is considered to be difficult due to its complexity.My paper here is to explore and study the application of mathematic ideas and methods in English grammar teaching and learning,helping to facilitate the students to master the regularities,accuracy and systematization of English grammar,to improve learning efficiency,to enhance the learners' logic thinking,and at the same time,pointing out the specific strategies in practical use,which can be of great significance to the students' innovation and creativity and the students' development of the ability of cross-subject study advocated by both the Quality-Education and New Curriculum Standard. 展开更多
关键词 mathematic ideas and methods English GRAMMAR APPLICATION specific strategies FEASIBILITY and significance
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A methodology for laser tool setters calibration and its precise mathematical model
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作者 Tao FANG Zixi FANG +1 位作者 Ze Zhong CHEN Zhiyong CHANG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2024年第7期564-581,共18页
On-machine tool setting is a pivotal approach in achieving intelligent manufacturing,and laser tool setters have become a crucial component of smart machine tools.Laser tool setters play a crucial role in precisely me... On-machine tool setting is a pivotal approach in achieving intelligent manufacturing,and laser tool setters have become a crucial component of smart machine tools.Laser tool setters play a crucial role in precisely measuring the dimensions of cutting tools during the part machining process,focusing on tool length and diameter.As a measuring instrument,the positions of the laser axis of the laser tool setter need to be accurately calibrated before use.However,in actual calibration scenarios,traditional calibration methods face challenges due to installation errors in the tool setter and geometric errors in the measuring rod.To address this issue,this study proposes a novel calibration method.Initially,the calibration mechanism of the laser beam axis is established.Based on the accurate mathematical model of the laser beam and the measuring rod,and using the polygon clipping algorithm,the mathematical mechanism of the laser tool setter’s work is established.Then,a novel method is introduced to calculate the compensation distance between the laser beam reference point and the rod bottom center point at each moment during calibration.Furthermore,by utilizing the kinematic chain of the tool setter calibration system,a new calibration method is developed to accurately calibrate the position of the laser beam axis in the machine tool coordinate system.Finally,the accuracy of the calibration method is verified through simulation experiments and calibration tests.This method improves the calibration accuracy of the tool setter,and the mathematical model of the laser tool setter can be extended to the measurement of tools,thereby improving the precision of tool measurements.This research significantly improves the efficient production performance of smart machine tools. 展开更多
关键词 On-machine tool setting Smart machine tools mathematical model Calibration method Laser tool sette
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A Class of Smoothing-regularization Methods to Mathematical Programs with Vanishing Constraints
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作者 HU Qingjie MA Lili CHEN Yu 《数学进展》 CSCD 北大核心 2024年第5期953-973,共21页
this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.... this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods. 展开更多
关键词 mathematical programs with vanishing constraints smoothing-regularization method VC-MFCQ strong stationary point
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Improvements to the fuzzy mathematics comprehensive quantitative method for evaluating fault sealing 被引量:4
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作者 Da-Wei Dong Ji-Yan Li +2 位作者 Yong-Hong Yang Xiao-Lei Wang Jian Liu 《Petroleum Science》 SCIE CAS CSCD 2017年第2期276-285,共10页
Fuzzy mathematics is an important means to quantitatively evaluate the properties of fault sealing in petroleum reservoirs.To accurately study fault sealing,the comprehensive quantitative evaluation method of fuzzy ma... Fuzzy mathematics is an important means to quantitatively evaluate the properties of fault sealing in petroleum reservoirs.To accurately study fault sealing,the comprehensive quantitative evaluation method of fuzzy mathematics is improved based on a previous study.First,the single-factor membership degree is determined using the dynamic clustering method,then a single-factor evaluation matrix is constructed using a continuous grading function,and finally,the probability distribution of the evaluation grade in a fuzzy evaluation matrix is analyzed.In this study,taking the F1 fault located in the northeastern Chepaizi Bulge as an example,the sealing properties of faults in different strata are quantitatively evaluated using both an improved and an un-improved comprehensive fuzzy mathematics quantitative evaluation method.Based on current oil and gas distribution,it is found that our evaluation results before and after improvement are significantly different.For faults in"best"and"poorest"intervals,our evaluation results are consistent with oil and gas distribution.However,for the faults in"good"or"poor"intervals,our evaluation is not completelyconsistent with oil and gas distribution.The improved evaluation results reflect the overall and local sealing properties of target zones and embody the nonuniformity of fault sealing,indicating the improved method is more suitable for evaluating fault sealing under complicated conditions. 展开更多
关键词 Fault sealing property Fuzzy mathematics Dynamic clustering method Quantitative study
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Mathematical modeling of elastic inverted pendulum control system 被引量:3
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作者 ChaoXU XinYU 《控制理论与应用(英文版)》 EI 2004年第3期281-282,共2页
Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described... Inverted pendulums are important objects of theoretical investigation and experiment in the area of control theory and engineering. The researches concentrate on the rigid finite dimensional models which are described by ordinary differential equations (ODEs) .Complete rigidity is the approximation of practical models ; Elasticity should be introduced into mathematical models in the analysis of system dynamics and integration of highly precise controller. A new kind of inverted pendulum, elastic inverted pendulum was proposed, and elasticity was considered. Mathematical model was derived from Hamiltonian principle and variational methods, which were formulated by the coupling of partial differential equations (PDE) and ODE. Because of infinite dimensional, system analysis and control of elastic inverted pendulum is more sophisticated than the rigid one. 展开更多
关键词 Elastic inverted pendulum Hamiltonian principle Variational methods mathematical model Coupling equation array
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