ON AMODIFIED NEWTON'S METHOD AND CONVERGENCE

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(21/2) and a sharp error estimate is given about the iterative sequence.

Symmetry and Exact Solutions of (2+1)-Dimensional Generalized Sasa-Satsuma Equation via a Modified Direct Method

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.

The higher-order modified Korteweg-de Vries equation:Its soliton,breather and approximate solutions

In this study,the fifth-order modified Korteweg-de Vries(F-MKdV)equation is first addressed using Hi-rota’s bilinear method.Thereafter,the exact and approximative solutions of the generalized form of the F-MKdV equation are investigated using the modified Kudryashov method,the Riccati equation and its Backlund transformation method,the solitary wave ansatz method,and the homotopy perturbation trans-form method(HPTM).As a result,solitons,breather,and solitary wave solutions are derived from these methods.In particular,we obtain some new solutions such as the dark soliton,bright soliton,singular soliton,periodic trigonometric,exponential,hyperbolic,and rational solutions.The constraint conditions associated with the resulting solutions are also discussed in detail.The HPTM is employed to construct approximate solutions to the aforementioned generalized model due to its strong nonlinear terms and only a few terms are required to obtain accurate solutions.These findings may help to understand com-plex nonlinear phenomena.

Nonlinear constrained optimization using the flexible tolerance method hybridized with different unconstrained methods

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.

Application of the Improved Kudryashov Method to Solve the Fractional Nonlinear Partial Differential Equations

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.

Stability Control of Stretch-Twist-Fold Flow by Using Numerical Methods

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.

基于改进的D-S证据理论在设备故障诊断中的应用

多传感器、多手段检测的信息融合技术在设备检测中的应用日益广泛,而常用的基于D-S证据理论的融合技术除了没有给出可信度的分配方法外,融合结果上还有很多不足之处。探讨了可信度的分配问题,提出了几种改进的融合方法,较好地解决了证据冲突时的否定性、积化性和敏感性问题。

国际汇率分形特征的实证研究:修正的R/S分析

首先对修正的R/S方法进行了介绍;然后通过实证研究指出国际汇率变化不服从正态分布并且汇率波动的相关性不显著;最后运用修正的R/S方法实证研究了国际汇率波动的分形特征,与使用传统R/S方法所得结论不同,通过实证说明外汇波动并不存在明显的长程相关性。

耦合Burgers方程的对称群和新精确解

利用推广的CK直接方法,求出了耦合Burgers方程的一般对称群,建立了方程新旧解之间的关系,进一步利用对称求得了耦合Burgers方程的不变量和若干约化,通过约化方程求得耦合Burgers方程大量新的精确解,包括有理函数解、三角函数解和双曲函数解.

Adomian分解法在完全非线性S-G方程中的运用

为分析具有高非线性强度下的偏微分方程的初值问题,简化变量分离等方法带来的繁杂计算,研究了一类完全非线性Sine-Gordon方程以及它的近似方程(在|up|很小的情况下),经过适当的函数变换,运用改进的Ado-mian分解法解决了一些特殊情况下它们的初值问题,结合Talyor级数展开式,得到了一些精确解:扭结解(kink)、紧孤子解(compacton)、多重紧孤子解、compacton-kink解。另外运用线性化的方法结合不同形式的解得到它们一些更加丰富的新形式的精确解。

Symmetry Groups and New Exact Solutions to （2＋1）-Dimensional Variable Coefficient Canonical Generalized KP Equation

In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.

Symplocosionosides A-C, Three Megastigmane Glycosides, a Neolignan Glucoside, and Symplocosins A and B, Two Triterpene Glycosyl Esters from the Leaves of <i>Symplocos cochinchinensis</i>var. <i>Philippinensis</i>

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.

Synthesis and Determination of Absolute Configuration of a Divergent Polyhydroxy Enyne Compound

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.

Symmetry Groups and New Exact Solutions of(2+1)-Dimensional Dispersive Long-Wave Equations

Using the modified CK＇s direct method, we derive a symmetry group theorem of （2＋1）-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of （2＋1）- dimensional dispersive long-wave equations are obtained.

Bayesian Estimations with Fuzzy Data to Estimation Inverse Rayleigh Scale Parameter

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.

Modified Kadomtsev-Petviashvili Equation in (3+1) Dimensions:Multiple Front-Wave Solutions

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.

重力场匹配导航的重力图生成技术

通过对当前用于海洋重力场格网插值的四种常用算法(距离倒数加权法、Kriging法、径向基函数法和改进的二次曲面Shepard方法)进行分析,以相对规则、不同密度的两组数据作为基准数据进行了插值比较。实验结果表明,基于改进的Shepard插值算法相对于其它三种算法具有速度快、精度高的优点,比较符合当前海洋重力数据获取的现状,是进行高精度重力图生成的有效方法。

基于数据融合的DEM插值与可视化

针对某航海训练仿真系统对三维地形实时性及逼真性的需要,提出了对DEM数据进行插值以提高数据的精度。在概略介绍空间插值原理及分类的基础上,分别着重介绍了克里金插值算法及改进谢别德插值算法的原理和特点。为了兼顾这两种插值算法的优点,克服单一插值方法的不足,提出了基于数据融合的插值方法。详细阐述了DEM插值的过程,并结合实例,利用SRTM3数据进行了测试,实现了DEM的可视化。仿真结果表明,与单独采用两种插值算法相比,基于数据融合所得数据插值效果较好,插值精度得到了明显的提升。

基于支持向量机的散乱数据拟合

文章提出了一种有效的大规模散乱点拟合方法,它是采用最小均方支持向量机局部拟合对Shepard插值方法进行改进。支持向量机基于结构风险最小化准则,在数据拟合方面具有较好的泛化能力,而改进的Shepard法能有效拟合大规模样本点。实验结果表明该算法对大规模散乱数据点具有较好的拟合性能。

改进的人工鱼群算法和Powell法结合的医学图像配准

针对目前基于互信息图像配准的局部极值问题,提出了一种改进的人工鱼群算法和Powell算法结合的多分辨率医学图像配准算法.该算法采用新的相似性测度方法即归一化模糊加权互信息和归一化局部能量加权匹配度,利用多分辨率策略采用HPV插值,并采用改进的人工鱼群算法结合Powell算法完成医学图像的配准.采用改进的人工鱼群算法在图像的最低分辨率上进行全局优化,以全局最优值为初始值,结合Powell算法完成图像配准.这不仅基本解决了互信息函数和Powell算法的局部极值问题,还减少了数据的处理量,加快了配准速度.实验结果表明,文中算法与其他经典的配准算法相比,提高了配准的精确度和性能.