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 this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmeth...In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.展开更多
A modified Kadomtsev-Petviashvili （mKP） equation in （3＋1） dimensions is presented. We reveal multiple front-waves solutions for this higher-dimensional developed equation, and multiple singular front-wave solutio...A modified Kadomtsev-Petviashvili （mKP） equation in （3＋1） dimensions is presented. We reveal multiple front-waves solutions for this higher-dimensional developed equation, and multiple singular front-wave solutions as well. The constraints on the coefficients of the spatial variables, that assure the existence of these multiple front-wave solutions are investigated. We also show that this equation falls the Painleve test, and we conclude that it is not integrable in the sense of possessing the Painleve property, although it gives multiple front-wave solutions.展开更多
This paper establishes the phase space in the light of spacial series data , discusses the fractal structure of geological data in terms of correlated functions and studies the chaos of these data . In addition , it i...This paper establishes the phase space in the light of spacial series data , discusses the fractal structure of geological data in terms of correlated functions and studies the chaos of these data . In addition , it introduces the R/S analysis for time series analysis into spacial series to calculate the structural fractal dimensions of ranges and standard deviation for spacial series data -and to establish the fractal dimension matrix and the procedures in plotting the fractal dimension anomaly diagram with vector distances of fractal dimension . At last , it has examples of its application .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
The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three differen...The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three different computing methods： the same starting point method, the striding averaging method, and the stagger phase averaging method. All of them can be used to calculate the Hurst index, which quantifies fluctuation and randomness. This study used real water quality data from Shazhu monitoring station on Taihu Lake in Wuxi, Jiangsu Province. The results show that, of the three methods, the stagger phase averaging method is best for calculating the Hurst index of a pollutant time series from the perspective of statistical regularity.展开更多
This paper mainly talks about a popular approach of volatility of a GARCH-type model in R, while the disturbances are independent and have identical Student-t distribution. It uses the Metropolis-Hastings method to pe...This paper mainly talks about a popular approach of volatility of a GARCH-type model in R, while the disturbances are independent and have identical Student-t distribution. It uses the Metropolis-Hastings method to perform the computations and gives the programs in details in R.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
The study of imine-bridged organics has been the hot spot synthesis of second order nonlinear optical (SONLO) and photo-responsive materials in recent years. Herein we present a study of synthesis, growth, and charact...The study of imine-bridged organics has been the hot spot synthesis of second order nonlinear optical (SONLO) and photo-responsive materials in recent years. Herein we present a study of synthesis, growth, and characterization of ([paranitrophenyl]imino)benzene (PNPIB) NLO single crystal. The title compound was synthesized in one step by Schiff base formation. PNPIB single crystal of diameter of 40 mmand length 50 mmwas successfully grown by SR method using a seed as the nucleus. The growth rate formula is derived for the SR method. PNPIB single crystals of 10 mmdiameter and 60 mmheight have been grown at an average growth rate of 3 mmper day from the point seed in a glass crystallizer. Almost 100% stable crystal conversion efficiency was achieved. The as grown PNPIB crystals were characterized using single crystal X-ray diffraction (XRD), X-ray powder diffraction (XRPD), Fourier Transform Infrared (FTIR), Ultraviolet-Visible-Near Infrared (UV-Vis-NIR), 1H & 13C NMR spectral studies, dielectric measurement and NLO studies. Single crystal XRD analysis confirms that the grown ingot belongs to the space group of P2 of monoclinic system thus exhibiting noncentrosymmetric structure. The crystalline perfection was assessed by XRPD. The powder diffraction pattern of the grown crystal has been indexed. The presence of C=N bond with intramolecular hydrogen bonding and the protonation of ions were confirmed by FTIR analysis. The UV-Vis-NIR spectrum of the crystal shows that the crystal has a cut-off at 298 nm. The 1H & 13C NMR spectra confirm the molecular structure. The dielectric behaviour was measured in the frequency range 1 KHz - 10 KHz for the temperature range from 30℃ to 170℃. The slight decrease in dielectric constant has been observed as the frequency is increased and the dielectric loss is very low for the entire frequency range. The second harmonic generation (SHG) in the crystal was observed by Kurtz powder technique.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.
基金Supported by the National Natural Science Foundation of China under Grant No. 10735030Shanghai Leading Academic Discipline Project under Grant No. B412+2 种基金National Natural Science Foundation of China under Grant No. 90718041Program for Changjiang Scholars and Innovative Research Team in University under Grant No. IRT0734K.C. Wong Magna Fund in Ningbo University
文摘In this paper, first, we employ classic Lie symmetry groups approach to obtain the Lie symmetry groupsof the well-known (2+1)-dimensional Generalized Sasa-Satsuma (GSS) equation. Second, based on a modified directmethod proposed by Lou [J. Phys. A: Math. Gen. 38 (2005) L129], more general symmetry groups are obtained andthe relationship between the new solution and known solution is set up. At the same time, the Lie symmetry groupsobtained are only special cases of the more general symmetry groups. At last, some exact solutions of GSS equationsare constructed by the relationship obtained in the paper between the new solution and known solution.
文摘A modified Kadomtsev-Petviashvili （mKP） equation in （3＋1） dimensions is presented. We reveal multiple front-waves solutions for this higher-dimensional developed equation, and multiple singular front-wave solutions as well. The constraints on the coefficients of the spatial variables, that assure the existence of these multiple front-wave solutions are investigated. We also show that this equation falls the Painleve test, and we conclude that it is not integrable in the sense of possessing the Painleve property, although it gives multiple front-wave solutions.
文摘This paper establishes the phase space in the light of spacial series data , discusses the fractal structure of geological data in terms of correlated functions and studies the chaos of these data . In addition , it introduces the R/S analysis for time series analysis into spacial series to calculate the structural fractal dimensions of ranges and standard deviation for spacial series data -and to establish the fractal dimension matrix and the procedures in plotting the fractal dimension anomaly diagram with vector distances of fractal dimension . At last , it has examples of its application .
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.
基金supported by the Eleventh Five-Year Key Technology R and D Program,China(Grant No.2006BAC02A15)the Colleges and Universities in Jiangsu Province Natural Science-Based Research Projects(Grant No.2006BAC02A15)+1 种基金the Jiangsu Province Post-Doctoral Fund Projects(Grant No.0801006C)the China Post-Doctoral Science Foundation(Grant No.20080441032)
文摘The significance of the fluctuation and randomness of the time series of each pollutant in environmental quality assessment is described for the first time in this paper. A comparative study was made of three different computing methods： the same starting point method, the striding averaging method, and the stagger phase averaging method. All of them can be used to calculate the Hurst index, which quantifies fluctuation and randomness. This study used real water quality data from Shazhu monitoring station on Taihu Lake in Wuxi, Jiangsu Province. The results show that, of the three methods, the stagger phase averaging method is best for calculating the Hurst index of a pollutant time series from the perspective of statistical regularity.
文摘This paper mainly talks about a popular approach of volatility of a GARCH-type model in R, while the disturbances are independent and have identical Student-t distribution. It uses the Metropolis-Hastings method to perform the computations and gives the programs in details in R.
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The study of imine-bridged organics has been the hot spot synthesis of second order nonlinear optical (SONLO) and photo-responsive materials in recent years. Herein we present a study of synthesis, growth, and characterization of ([paranitrophenyl]imino)benzene (PNPIB) NLO single crystal. The title compound was synthesized in one step by Schiff base formation. PNPIB single crystal of diameter of 40 mmand length 50 mmwas successfully grown by SR method using a seed as the nucleus. The growth rate formula is derived for the SR method. PNPIB single crystals of 10 mmdiameter and 60 mmheight have been grown at an average growth rate of 3 mmper day from the point seed in a glass crystallizer. Almost 100% stable crystal conversion efficiency was achieved. The as grown PNPIB crystals were characterized using single crystal X-ray diffraction (XRD), X-ray powder diffraction (XRPD), Fourier Transform Infrared (FTIR), Ultraviolet-Visible-Near Infrared (UV-Vis-NIR), 1H & 13C NMR spectral studies, dielectric measurement and NLO studies. Single crystal XRD analysis confirms that the grown ingot belongs to the space group of P2 of monoclinic system thus exhibiting noncentrosymmetric structure. The crystalline perfection was assessed by XRPD. The powder diffraction pattern of the grown crystal has been indexed. The presence of C=N bond with intramolecular hydrogen bonding and the protonation of ions were confirmed by FTIR analysis. The UV-Vis-NIR spectrum of the crystal shows that the crystal has a cut-off at 298 nm. The 1H & 13C NMR spectra confirm the molecular structure. The dielectric behaviour was measured in the frequency range 1 KHz - 10 KHz for the temperature range from 30℃ to 170℃. The slight decrease in dielectric constant has been observed as the frequency is increased and the dielectric loss is very low for the entire frequency range. The second harmonic generation (SHG) in the crystal was observed by Kurtz powder technique.
