In this paper I propose a method for founding solutions of Navier-Stokes equations. Purpose of the research is to solve equations giving form to relations between pressure, velocity and stream. Starting from the fact ...In this paper I propose a method for founding solutions of Navier-Stokes equations. Purpose of the research is to solve equations giving form to relations between pressure, velocity and stream. Starting from the fact we do not know the form of functions we give a general representation in Maclaurin Series and prove that with reasonable values of parameters, representation holds and therefore has meaning in continuum. Then we solve the system of equations with respect to the pressure and match equations relation between parameters: matches of equations are possible because of the physical dimensions of equations. Then values of Continuity Equation are verified. The result is a polynomial finite and that coincides with the function in continuum, or is anyway one of its representation. The result under hydrostatic condition returns Stevino formula.展开更多
In this paper, multidimensional weakly singular integrals are solved by using rectangular quadrature rules which base on quadrature rules of one dimensional weakly singular and multidimensional regular integrals with ...In this paper, multidimensional weakly singular integrals are solved by using rectangular quadrature rules which base on quadrature rules of one dimensional weakly singular and multidimensional regular integrals with their Euler-Maclaurin asymptotic expansions of the errors. The presented method is suit for solving multidimensional and singular integrals by comparing with Gauss quadrature rule. The error asymptotic expansions show that the convergence order of the initial quadrature rules is , where . The order of accuracy can reach to by using extrapolation and splitting extrapolation, where h0 is the maximum mesh width. Some numerical examples are constructed to show the efficiency of the method.展开更多
The Maclaurin symmetric mean(MSM)operator exhibits a desirable characteristic by effectively capturing the correlations among multiple input parameters,and it serves as an extension of certain existing aggregation ope...The Maclaurin symmetric mean(MSM)operator exhibits a desirable characteristic by effectively capturing the correlations among multiple input parameters,and it serves as an extension of certain existing aggregation operators through adjustments to the parameter k.The hesitant q-rung orthopair set(Hq-ROFSs)can serve as an extension of the existing orthopair fuzzy sets,which provides decision makers more freedom in describing their true opinions.The objective of this paper is to present an MSM operator to aggregate hesitant q-rung orthopair numbers and solve the multiple attribute decision making(MADM)problems in which the attribute values take the form of hesitant q-rung orthopair fuzzy sets(H-qROFSs).Firstly,the definition of H-qROFSs and some operational laws of H-qROFSs are proposed.Then we develop a family of hesitant q-rung orthopair fuzzy maclaurin symmetric mean aggregation operators,such as the hesitant q-rung orthopair fuzzy maclaurin symmetric mean(Hq-ROFMSM)operator,the hesitant q-rung orthopair fuzzy weighted maclaurin symmetric mean(Hq-ROFWMSM)operator,the hesitant q-rung orthopair fuzzy dual maclaurin symmetric mean(Hq-ROFDMSM)operator,the hesitant q-rung orthopair fuzzy weighted dual maclaurin symmetric mean(Hq-ROFWDMSM)operator.And the properties and special cases of these proposed operators are studied.Furthermore,an approach based on the Hq-ROFWMSM operator is proposed for multiple attribute decision making problems under hesitant q-rung orthopair fuzzy environment.Finally,a numerical example and comparative analysis is given to illustrate the application of the proposed approach.展开更多
文摘In this paper I propose a method for founding solutions of Navier-Stokes equations. Purpose of the research is to solve equations giving form to relations between pressure, velocity and stream. Starting from the fact we do not know the form of functions we give a general representation in Maclaurin Series and prove that with reasonable values of parameters, representation holds and therefore has meaning in continuum. Then we solve the system of equations with respect to the pressure and match equations relation between parameters: matches of equations are possible because of the physical dimensions of equations. Then values of Continuity Equation are verified. The result is a polynomial finite and that coincides with the function in continuum, or is anyway one of its representation. The result under hydrostatic condition returns Stevino formula.
文摘In this paper, multidimensional weakly singular integrals are solved by using rectangular quadrature rules which base on quadrature rules of one dimensional weakly singular and multidimensional regular integrals with their Euler-Maclaurin asymptotic expansions of the errors. The presented method is suit for solving multidimensional and singular integrals by comparing with Gauss quadrature rule. The error asymptotic expansions show that the convergence order of the initial quadrature rules is , where . The order of accuracy can reach to by using extrapolation and splitting extrapolation, where h0 is the maximum mesh width. Some numerical examples are constructed to show the efficiency of the method.
基金Supported by the Key Project of Humanities and Social Research Science Institute of Chongqing Municipal Education Commission(22SKGH432,22SKGH428)2023 Chongqing Education Commission Humanities and Social Sciences Research General Project(23SKGH353)Science and Technology Research Project of Chongqing Education Commission(KJQN202101524)。
文摘The Maclaurin symmetric mean(MSM)operator exhibits a desirable characteristic by effectively capturing the correlations among multiple input parameters,and it serves as an extension of certain existing aggregation operators through adjustments to the parameter k.The hesitant q-rung orthopair set(Hq-ROFSs)can serve as an extension of the existing orthopair fuzzy sets,which provides decision makers more freedom in describing their true opinions.The objective of this paper is to present an MSM operator to aggregate hesitant q-rung orthopair numbers and solve the multiple attribute decision making(MADM)problems in which the attribute values take the form of hesitant q-rung orthopair fuzzy sets(H-qROFSs).Firstly,the definition of H-qROFSs and some operational laws of H-qROFSs are proposed.Then we develop a family of hesitant q-rung orthopair fuzzy maclaurin symmetric mean aggregation operators,such as the hesitant q-rung orthopair fuzzy maclaurin symmetric mean(Hq-ROFMSM)operator,the hesitant q-rung orthopair fuzzy weighted maclaurin symmetric mean(Hq-ROFWMSM)operator,the hesitant q-rung orthopair fuzzy dual maclaurin symmetric mean(Hq-ROFDMSM)operator,the hesitant q-rung orthopair fuzzy weighted dual maclaurin symmetric mean(Hq-ROFWDMSM)operator.And the properties and special cases of these proposed operators are studied.Furthermore,an approach based on the Hq-ROFWMSM operator is proposed for multiple attribute decision making problems under hesitant q-rung orthopair fuzzy environment.Finally,a numerical example and comparative analysis is given to illustrate the application of the proposed approach.
