The gravity-capillary water Waves in two-layer density-stratified fluid are investigated by using a singular perturbation method,and the third-order asymptotic solutions of the velocity potentials and the third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-ordei;nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depths of each layer,wave amplitude but also the surface tension.
{"title":"Second-order Stokes wave solutions for gravity capillary water waves in three-layer dendity-stratified fluid","authors":"Yan Zaizai, C. Wei, M. Ren","doi":"10.7498/APS.63.140301","DOIUrl":"https://doi.org/10.7498/APS.63.140301","url":null,"abstract":"The gravity-capillary water Waves in two-layer density-stratified fluid are investigated by using a singular perturbation method,and the third-order asymptotic solutions of the velocity potentials and the third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-ordei;nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depths of each layer,wave amplitude but also the surface tension.","PeriodicalId":18427,"journal":{"name":"Mathematics in Practice and Theory","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2011-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78576849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2010-01-01DOI: 10.1007/978-3-642-13938-3_38
L. Dang, Zhou Ling
{"title":"Integrated Method of Grey Multi-attribute Risk Group Decision-Making","authors":"L. Dang, Zhou Ling","doi":"10.1007/978-3-642-13938-3_38","DOIUrl":"https://doi.org/10.1007/978-3-642-13938-3_38","url":null,"abstract":"","PeriodicalId":18427,"journal":{"name":"Mathematics in Practice and Theory","volume":"82 1","pages":"437-448"},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89157799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper discusses the application types and characteristics and the restriction condition of the amount control optimization model of atmospheric pollutant in the environment management;put forward the models of the pollution reduction expenses minimum and the environment using of resources maximizes.Based on the economic development area of Datong, the paper develops the optimization model of amount control of atmospheric pollutant and the application in the environment evaluation.It provides the decision support for the environment management of the economic development area.
{"title":"Application of Optimization Method in Atmospheric Pollutant Amount Control","authors":"Zhang Zhi-yao","doi":"10.2495/meee20130291","DOIUrl":"https://doi.org/10.2495/meee20130291","url":null,"abstract":"This paper discusses the application types and characteristics and the restriction condition of the amount control optimization model of atmospheric pollutant in the environment management;put forward the models of the pollution reduction expenses minimum and the environment using of resources maximizes.Based on the economic development area of Datong, the paper develops the optimization model of amount control of atmospheric pollutant and the application in the environment evaluation.It provides the decision support for the environment management of the economic development area.","PeriodicalId":18427,"journal":{"name":"Mathematics in Practice and Theory","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82142341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-01-01DOI: 10.1142/9789814289313_0015
Liang Jian-hua
We propose a new GL method for solving the ordinary and the partial differential equation.These equations govern the electromagnetic field etc.macro and micro physical,chemical,financial problems in the sciences and engineering.The domain can be finite,infinite,or part of the infinite domain with a curve surface.The differential equation is held in an infinite domain which includes a finite inhomogeneous domain.The inhomogeneous domain is divided into finite sub domains.We present the solution of the differential equation as an explicit recursive sum of the integrals in the inhomogeneous sub domains.We discover the explicit relationship between forward modeling and inversion.The analytical solution of the equation in the infinite homogeneous domain is called as an initial global field.The global field is updated by local scattering field successively subdomain by subdomain.Once all subdomains are scattered and the finite updating process is finished in all the sub domains,the solution of the equation is obtained.We call our method as Global and Local field method,in short GL method.The GL method is totally different from Finite Element Method(FEM) method and Finite Difference Method(FD),the GL method directly assemble inverse matrix and get solution successively subdomain by subdomain.There is no big matrix equation needs to solve in the GL method which overcome FEM' and FD's difficult for solving big matrix equation.When the FEM and FD are used to solve the differential equation in the infinite domain,the artificial boundary and absorption boundary condition are necessary and difficult.The error reflections from the artificial absorption boundary condition downgrade the accuracy of the forward solution and damage the inversion resolution.The GL method resolves the artificial boundary difficulty in FEM and FD methods.There is no artificial boundary and no absorption boundary condition for infinite domain in the GL method.We proposed a triangle integral equation of the Green's functions and proved several theorems for the theoretical analysis of the GL method.The numerical discretization of the GL method is presented.We proved that the numerical solution of the GL method is convergent to the exact solution when the maximum diameter of the sub domain is going to zero.The error estimation of the GL method for solving the wave equation is presented.The simulations show that the GL method is accurate,fast,and stable for solving elliptic,parabolic,and hyperbolic equations.The GL method has wide applications in the 3D electromagnetic (EM) field,3D elastic and plastic etc seismic field,acoustic field,flow field,and quantum field.The GL method software for the above 3D EM etc field is developed by authors in GL Geophysical Laboratory.
提出了求解常微分方程和偏微分方程的一种新的GL方法。这些方程控制着电磁场等宏观和微观的物理、化学、科学和工程中的金融问题。定义域可以是有限的、无限的，也可以是具有曲面的无限定义域的一部分。微分方程在包含有限非齐次域的无限定义域内成立。将非齐次域划分为有限个子域。我们将微分方程的解表示为非齐次子域中积分的显式递推和。我们发现了正演模拟和反演之间的明确关系。方程在无限齐次域中的解析解称为初始全局场。全局场由局部散射场逐子域更新。当所有子域分散后，在所有子域上完成有限更新过程，得到方程的解。我们称我们的方法为Global and Local field method，简称GL method。GL法与有限元法(FEM)和有限差分法(FD)完全不同，GL法直接对逆矩阵进行组合，逐子域逐次求解。GL法不需要求解大矩阵方程，克服了有限元法和FD法求解大矩阵方程的困难。用有限元法和有限元法求解无限域中的微分方程时，人工边界和吸收边界条件是必要的，也是困难的。人工吸收边界条件产生的误差反射降低了正演解的精度，破坏了反演分辨率。GL方法解决了有限元法和FD法中存在的人工边界问题。该方法不存在人工边界，也不存在无限域的吸收边界条件。我们提出了格林函数的三角形积分方程，并证明了GL方法的理论分析的几个定理。给出了GL方法的数值离散化方法。证明了当子域的最大直径趋于0时，GL方法的数值解收敛于精确解。给出了求解波动方程的GL法的误差估计。仿真结果表明，该方法对于求解椭圆型、抛物线型和双曲型方程具有准确、快速和稳定的特点。GL方法在三维电磁场、三维弹塑性、地震场、声场、流场、量子场等领域有着广泛的应用。笔者在GL地球物理实验室开发了用于上述三维电磁等场的GL方法软件。
{"title":"A New GL Method for Mathematical and Physical Problem","authors":"Liang Jian-hua","doi":"10.1142/9789814289313_0015","DOIUrl":"https://doi.org/10.1142/9789814289313_0015","url":null,"abstract":"We propose a new GL method for solving the ordinary and the partial differential equation.These equations govern the electromagnetic field etc.macro and micro physical,chemical,financial problems in the sciences and engineering.The domain can be finite,infinite,or part of the infinite domain with a curve surface.The differential equation is held in an infinite domain which includes a finite inhomogeneous domain.The inhomogeneous domain is divided into finite sub domains.We present the solution of the differential equation as an explicit recursive sum of the integrals in the inhomogeneous sub domains.We discover the explicit relationship between forward modeling and inversion.The analytical solution of the equation in the infinite homogeneous domain is called as an initial global field.The global field is updated by local scattering field successively subdomain by subdomain.Once all subdomains are scattered and the finite updating process is finished in all the sub domains,the solution of the equation is obtained.We call our method as Global and Local field method,in short GL method.The GL method is totally different from Finite Element Method(FEM) method and Finite Difference Method(FD),the GL method directly assemble inverse matrix and get solution successively subdomain by subdomain.There is no big matrix equation needs to solve in the GL method which overcome FEM' and FD's difficult for solving big matrix equation.When the FEM and FD are used to solve the differential equation in the infinite domain,the artificial boundary and absorption boundary condition are necessary and difficult.The error reflections from the artificial absorption boundary condition downgrade the accuracy of the forward solution and damage the inversion resolution.The GL method resolves the artificial boundary difficulty in FEM and FD methods.There is no artificial boundary and no absorption boundary condition for infinite domain in the GL method.We proposed a triangle integral equation of the Green's functions and proved several theorems for the theoretical analysis of the GL method.The numerical discretization of the GL method is presented.We proved that the numerical solution of the GL method is convergent to the exact solution when the maximum diameter of the sub domain is going to zero.The error estimation of the GL method for solving the wave equation is presented.The simulations show that the GL method is accurate,fast,and stable for solving elliptic,parabolic,and hyperbolic equations.The GL method has wide applications in the 3D electromagnetic (EM) field,3D elastic and plastic etc seismic field,acoustic field,flow field,and quantum field.The GL method software for the above 3D EM etc field is developed by authors in GL Geophysical Laboratory.","PeriodicalId":18427,"journal":{"name":"Mathematics in Practice and Theory","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84275761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2004-01-01DOI: 10.3969/j.issn.1000-0984.2004.11.003
Wenbing Xu, Zhishan Guo
The passage points out the disadvantages of current systems for various football matches by analysis and comparing several main football match systems adopted in current football games and meanwhile, on the base of it, suggests a new system by the name of Three—failure Match (TFM). The knowledge of probability and emulating by computer are used to have a quantitative analysis and comparison for this new system and the current ones, and the result shows that TFM sums up the advantages of elimination and group round match and also avoids the disadvantages of them. Therefore, TFM is a rational football match system and it applies to all sorts of middle or short term football matches.
{"title":"Three-Failure Match","authors":"Wenbing Xu, Zhishan Guo","doi":"10.3969/j.issn.1000-0984.2004.11.003","DOIUrl":"https://doi.org/10.3969/j.issn.1000-0984.2004.11.003","url":null,"abstract":"The passage points out the disadvantages of current systems for various football matches by analysis and comparing several main football match systems adopted in current football games and meanwhile, on the base of it, suggests a new system by the name of Three—failure Match (TFM). The knowledge of probability and emulating by computer are used to have a quantitative analysis and comparison for this new system and the current ones, and the result shows that TFM sums up the advantages of elimination and group round match and also avoids the disadvantages of them. Therefore, TFM is a rational football match system and it applies to all sorts of middle or short term football matches.","PeriodicalId":18427,"journal":{"name":"Mathematics in Practice and Theory","volume":"2 1","pages":"14"},"PeriodicalIF":0.0,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90221049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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