In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two...In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(2<sup>1/2</sup>) and a sharp error estimate is given about the iterative sequence.展开更多
In order to reduce both the weight of vehicles and the damage of occupants in a crash event simultaneously, it is necessary to perform a multi-objective optimal design of the automotive energy absorbing components. Mo...In order to reduce both the weight of vehicles and the damage of occupants in a crash event simultaneously, it is necessary to perform a multi-objective optimal design of the automotive energy absorbing components. Modified non-dominated sorting genetic algorithm II(NSGA II) was used for multi-objective optimization of automotive S-rail considering absorbed energy(E), peak crushing force(Fmax) and mass of the structure(W) as three conflicting objective functions. In the multi-objective optimization problem(MOP), E and Fmax are defined by polynomial models extracted using the software GEvo M based on train and test data obtained from numerical simulation of quasi-static crushing of the S-rail using ABAQUS. Finally, the nearest to ideal point(NIP)method and technique for ordering preferences by similarity to ideal solution(TOPSIS) method are used to find the some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. Results represent that the optimum design point obtained from TOPSIS method exhibits better trade-off in comparison with that of optimum design point obtained from NIP method.展开更多
This paper proposes the use of the flexible tolerance method(FTM) modified with scaling of variables and hybridized with different unconstrained optimization methods to solve real constrained optimization problems.The...This paper proposes the use of the flexible tolerance method(FTM) modified with scaling of variables and hybridized with different unconstrained optimization methods to solve real constrained optimization problems.The benchmark problems used to analyze the performance of the methods were taken from G-Suite functions.The original method(FTM) and other four proposed methods:(i) FTM with scaling of variables(FTMS),(ii) FTMS hybridized with BFGS(FTMS-BFGS),(iii) FTMS hybridized with modified Powell's method(FTMS-Powell)and(iv) FTMS hybridized with PSO(FTMS-PSO), were implemented. The success rates of the methods were 80%,100%, 75%, 95% and 85%, for FTM, FTMS, FTMS-BFGS, FTMS-Powell and FTMS-PSO, respectively. Numerical experiments including real constrained problems indicated that FTMS gave the best performance, followed by FTMSPowell and FTMS-PSO. Despite the inferior performance compared to FTMS and FTMS-Powell, the FTMS-PSO method presented some advantages since good different initial points could be obtained, which allow exploring different routes through the solution space and to escape from local optima. The proposed methods proved to be an effective way of improving the performance of the original FTM.展开更多
Our purpose of this paper is to apply the improved Kudryashov method for solving various types of nonlinear fractional partial differential equations. As an application, the time-space fractional Korteweg-de Vries-Bur...Our purpose of this paper is to apply the improved Kudryashov method for solving various types of nonlinear fractional partial differential equations. As an application, the time-space fractional Korteweg-de Vries-Burger (KdV-Burger) equation is solved using this method and we get some new travelling wave solutions. To acquire our purpose a complex transformation has been also used to reduce nonlinear fractional partial differential equations to nonlinear ordinary differential equations of integer order, in the sense of the Jumarie’s modified Riemann-Liouville derivative. Afterwards, the improved Kudryashov method is implemented and we get our required reliable solutions where the results are justified by mathematical software Maple-13.展开更多
In this study, the multistep method is applied to the STF system. This method has been tested on the STF system, which is a three-dimensional system of ODE with quadratic nonlinearities. A computer based Matlab progra...In this study, the multistep method is applied to the STF system. This method has been tested on the STF system, which is a three-dimensional system of ODE with quadratic nonlinearities. A computer based Matlab program has been developed in order to solve the STF system. Stable and unstable position of the system has been analyzed graphically and finally a comparison as well as accuracy between two-step sizes with detail. Newton’s method has been applied to show the best convergence of this system.展开更多
From the 1-BuOH-soluble fraction of a MeOH extract of the leaves of Symplocos cochinchinensis var. philippinensis, 12 compounds were isolated. Spectroscopic analyses of compounds 1 - 3 established their structures to ...From the 1-BuOH-soluble fraction of a MeOH extract of the leaves of Symplocos cochinchinensis var. philippinensis, 12 compounds were isolated. Spectroscopic analyses of compounds 1 - 3 established their structures to be megastig-mane glycosides, named symplocosionosides A-C. The absolute structure of 1 was determined by the modified Mosher’s method. Compound 4 was found to be a neolignan glucoside and named symplocosneolignan. The structures of com-pounds 5 and 6, named symplocosins A and B, were elucidated to be the saponins of hederagenin sugar esters. The structures of the remaining known compounds (7 - 12) were identified by comparison of spectroscopic data with those reported in the literature.展开更多
In this paper, Bayesian computational method is used to estimate inverse Rayleigh Scale parameter with fuzzy data. Based on imprecision data, the Bayes estimates cannot be obtained in explicit form. Therefore, we prov...In this paper, Bayesian computational method is used to estimate inverse Rayleigh Scale parameter with fuzzy data. Based on imprecision data, the Bayes estimates cannot be obtained in explicit form. Therefore, we provide Tierney and Kadane’s approximation to compute the Bayes estimates of the scale parameter under Square error and Precautionary loss function using Non-informative Jefferys Prior. Also, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the scale parameter in terms of mean squared error values.展开更多
Polyhydroxy enyne compound （＋）-（1＇S, 2R, 3S, 5S, 6S）-5,6-dimethoxy-5, 6-dimethyl- 2-（1＇-hydroxylpropyl-2-ne）-3-vinyl-l,4-dioxane has been synthesized from D-（-）-tartaric acid. A new chiral center was establ...Polyhydroxy enyne compound （＋）-（1＇S, 2R, 3S, 5S, 6S）-5,6-dimethoxy-5, 6-dimethyl- 2-（1＇-hydroxylpropyl-2-ne）-3-vinyl-l,4-dioxane has been synthesized from D-（-）-tartaric acid. A new chiral center was established by nucleophilic addition with 87% de. The modified Mosher＇s method was employed to confirm the absolute configuration of 17, which assigned the S-configuration at the new chiral center.展开更多
基金Jointly supported by China Major Key Project for Basic Researcher and Provincial Natrural Science Foundation.
文摘In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(2<sup>1/2</sup>) and a sharp error estimate is given about the iterative sequence.
文摘In order to reduce both the weight of vehicles and the damage of occupants in a crash event simultaneously, it is necessary to perform a multi-objective optimal design of the automotive energy absorbing components. Modified non-dominated sorting genetic algorithm II(NSGA II) was used for multi-objective optimization of automotive S-rail considering absorbed energy(E), peak crushing force(Fmax) and mass of the structure(W) as three conflicting objective functions. In the multi-objective optimization problem(MOP), E and Fmax are defined by polynomial models extracted using the software GEvo M based on train and test data obtained from numerical simulation of quasi-static crushing of the S-rail using ABAQUS. Finally, the nearest to ideal point(NIP)method and technique for ordering preferences by similarity to ideal solution(TOPSIS) method are used to find the some trade-off optimum design points from all non-dominated optimum design points represented by the Pareto fronts. Results represent that the optimum design point obtained from TOPSIS method exhibits better trade-off in comparison with that of optimum design point obtained from NIP method.
基金CAPES(Coordenacao de Aperfeicoamento de Pessoal de Nível Superior)CNPq(Conselho Nacional de Desenvolvimento Científicoe Tecnológico,grant number 161464/2013-0)for the financial support
文摘This paper proposes the use of the flexible tolerance method(FTM) modified with scaling of variables and hybridized with different unconstrained optimization methods to solve real constrained optimization problems.The benchmark problems used to analyze the performance of the methods were taken from G-Suite functions.The original method(FTM) and other four proposed methods:(i) FTM with scaling of variables(FTMS),(ii) FTMS hybridized with BFGS(FTMS-BFGS),(iii) FTMS hybridized with modified Powell's method(FTMS-Powell)and(iv) FTMS hybridized with PSO(FTMS-PSO), were implemented. The success rates of the methods were 80%,100%, 75%, 95% and 85%, for FTM, FTMS, FTMS-BFGS, FTMS-Powell and FTMS-PSO, respectively. Numerical experiments including real constrained problems indicated that FTMS gave the best performance, followed by FTMSPowell and FTMS-PSO. Despite the inferior performance compared to FTMS and FTMS-Powell, the FTMS-PSO method presented some advantages since good different initial points could be obtained, which allow exploring different routes through the solution space and to escape from local optima. The proposed methods proved to be an effective way of improving the performance of the original FTM.
文摘Our purpose of this paper is to apply the improved Kudryashov method for solving various types of nonlinear fractional partial differential equations. As an application, the time-space fractional Korteweg-de Vries-Burger (KdV-Burger) equation is solved using this method and we get some new travelling wave solutions. To acquire our purpose a complex transformation has been also used to reduce nonlinear fractional partial differential equations to nonlinear ordinary differential equations of integer order, in the sense of the Jumarie’s modified Riemann-Liouville derivative. Afterwards, the improved Kudryashov method is implemented and we get our required reliable solutions where the results are justified by mathematical software Maple-13.
文摘In this study, the multistep method is applied to the STF system. This method has been tested on the STF system, which is a three-dimensional system of ODE with quadratic nonlinearities. A computer based Matlab program has been developed in order to solve the STF system. Stable and unstable position of the system has been analyzed graphically and finally a comparison as well as accuracy between two-step sizes with detail. Newton’s method has been applied to show the best convergence of this system.
文摘From the 1-BuOH-soluble fraction of a MeOH extract of the leaves of Symplocos cochinchinensis var. philippinensis, 12 compounds were isolated. Spectroscopic analyses of compounds 1 - 3 established their structures to be megastig-mane glycosides, named symplocosionosides A-C. The absolute structure of 1 was determined by the modified Mosher’s method. Compound 4 was found to be a neolignan glucoside and named symplocosneolignan. The structures of com-pounds 5 and 6, named symplocosins A and B, were elucidated to be the saponins of hederagenin sugar esters. The structures of the remaining known compounds (7 - 12) were identified by comparison of spectroscopic data with those reported in the literature.
文摘In this paper, Bayesian computational method is used to estimate inverse Rayleigh Scale parameter with fuzzy data. Based on imprecision data, the Bayes estimates cannot be obtained in explicit form. Therefore, we provide Tierney and Kadane’s approximation to compute the Bayes estimates of the scale parameter under Square error and Precautionary loss function using Non-informative Jefferys Prior. Also, we provide compared numerically through Monte-Carlo simulation study to obtained estimates of the scale parameter in terms of mean squared error values.
文摘Polyhydroxy enyne compound （＋）-（1＇S, 2R, 3S, 5S, 6S）-5,6-dimethoxy-5, 6-dimethyl- 2-（1＇-hydroxylpropyl-2-ne）-3-vinyl-l,4-dioxane has been synthesized from D-（-）-tartaric acid. A new chiral center was established by nucleophilic addition with 87% de. The modified Mosher＇s method was employed to confirm the absolute configuration of 17, which assigned the S-configuration at the new chiral center.
