VECTORIAL EKELAND'S VARIATIONAL PRINCIPLE WITH A W-DISTANCE AND ITS EQUIVALENT THEOREMS

By using the properties of w-distances and Gerstewitz＇s functions, we first give a vectorial Takahashi＇s nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland＇s variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland＇s variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346（2008）, 9-16] are weakened or even completely relieved.

STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES

In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems.

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

Research on the discrete variational method for a Birkhoffian system

In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.

A Comparative Study of Variational Iteration Method and He-Laplace Method

In this paper, variational iteration method and He-Laplace method are used to solve the nonlinear ordinary and partial differential equations. Laplace transformation with the homotopy perturbation method is called He-Laplace method. A comparison is made among variational iteration method and He-Laplace. It is shown that, in He-Laplace method, the nonlinear terms of differential equation can be easily handled by the use of He’s polynomials and provides better results.

Application of He’s Variational Iteration Method for the Analytical Solution of Space Fractional Diffusion Equation

Spatially fractional order diffusion equations are generalizations of classical diffusion equations which are increasingly used in modeling practical super diffusive problems in fluid flow, finance and others areas of application. This paper presents the analytical solutions of the space fractional diffusion equations by variational iteration method (VIM). By using initial conditions, the explicit solutions of the equations have been presented in the closed form. Two examples, the first one is one-dimensional and the second one is two-dimensional fractional diffusion equation, are presented to show the application of the present techniques. The present method performs extremely well in terms of efficiency and simplicity.

Numerical Solution of Generalized Abel’s Integral Equation by Variational Iteration Method

In this paper, a user friendly algorithm based on the variational iteration method (VIM) is proposed to solve singular integral equations with generalized Abel’s kernel. It is observed that an approximate solutions yn(x) converges to the exact solution irrespective of the initial choice y0 (x). Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the method in solving these types of singular integral equations.

Analytical Solution of Two Extended Model Equations for Shallow Water Waves by He’s Variational Iteration Method

In this paper, we consider two extended model equations for shallow water waves. We use He’s variational iteration method (VIM) to solve them. It is proved that this method is a very good tool for shallow water wave equations and the obtained solutions are shown graphically.

Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic Solid Continua

Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary condition for an extremum of I. In this approach one could use δI = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from δI = 0, which is also satisfied by a solution obtained from δI = 0. The Euler’s equations obtained from δI = 0 indeed are the mathematical model associated with the energy functional I. In case of BVPs we follow the same approach except in this case, the energy functional I consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. Similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs designed using energy functional and principle of virtual work, their consistency and validity are also investigated. Classical continuum mechanics (CCM) principles i.e. conservation and balance laws of CCM with consistent constitutive theories and the elements of calculus of variations are employed in the investigations presented in this paper.

一类具有扰动非线性项和奇异项的Schrödinger-Poisson系统的多重正解

本文考虑一类具有扰动非线性项和奇异项的Schrödinger-Poisson系统的多重正解的存在性.通过扰动方法解决奇异项在零点不可微的问题,利用Ekeland变分原理和山路引理,得到两个正解的存在性.

Variational principles for two kinds of extended Korteweg-de Vries equations

Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg-de Vries （KdV） equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct.

Neumann＇s method for boundary problems of thin elastic shells

The possibility of using Neumann＇s method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann＇s method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann＇s method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.

Parametric Iteration Method for Solving Linear Optimal Control Problems

This article presents the Parametric Iteration Method (PIM) for finding optimal control and its corresponding trajectory of linear systems. Without any discretization or transformation, PIM provides a sequence of functions which converges to the exact solution of problem. Our emphasis will be on an auxiliary parameter which directly affects on the rate of convergence. Comparison of PIM and the Variational Iteration Method (VIM) is given to show the preference of PIM over VIM. Numerical results are given for several test examples to demonstrate the applicability and efficiency of the method.

成组法疲劳试件个数选取方法研究

目的 在成组法疲劳试验过程中,确定最少疲劳试件个数判据,获取有效可靠的疲劳试验结果。方法基于疲劳可靠性的基本原理,在疲劳寿命对数正态分布的假设下,根据t分布理论,结合船舶及海洋工程一般构件具有95%置信度和可靠度p=97.72%下的P-S-N曲线的基本要求,推算出相应置信度和可靠度下5%误差限度内的疲劳试件个数与允许的最大变异系数数值的对应关系,以此作为成组法疲劳试验最少试件个数的判据,开展典型节点的疲劳试验。结果 得到了具有95%置信度的百位估计值Np,并通过线性相关系数r,判断对数疲劳应力Y=lg S与X=lg Np之间线性相关的程度,采用最小二乘法对对数疲劳寿命lg Np和对数疲劳应力lg S进行线性拟合,得到了具有95%置信度的P-S-N曲线,与IIW规范中相应的曲线一致。结论 文中给出的成组法疲劳试验个数确定方法是合理、可靠的,为船舶与海洋工程结构物典型焊接接头成组法疲劳试验个数的确定提供了依据。

基于Kendall与R/S法的年最大洪峰流量变化特性分析

应用线性回归法、Kendall秩次相关检验法等方法分析年最大洪峰流量序列总体变化趋势,根据重标极差R/S法求出年最大洪峰流量序列的变异点并划分序列,采用Kendall秩次相关检验法或线性回归法分析每段序列变化趋势,并根据R/S法分析每段序列的持续性特征,以两者的结果综合分析序列未来的变化特性。以闽江十里庵站年最大洪峰流量序列为例进行的分析表明,Kendall与R/S法应用于年最大洪峰流量变化特性分析可行,可以为流域汛前防汛备汛工作提供参考。

S-M(M=Al,Co)复合掺杂LiMn_2O_4的结构稳定性

应用量子化学电荷自洽离散变分Xα(SCC-DV-Xα)方法,研究了S-Al、S-Co复合掺杂增强尖晶石结构锂锰氧化物稳定性的作用机制.计算结果表明,S-Al复合掺杂锂锰尖晶石和S-Co复合掺杂锂锰尖晶石中的共价键强度均比未掺杂尖晶石LiMn2O4中的强,且与MnO2中的共价键强度相近;S-Al,S-Co复合掺杂尖晶石中Mn的电荷也与MnO2模型Mn6O2628-中十分接近.Mn原子的电荷密度次序是MnO2≈掺硫铝后锰锂尖晶石≈掺硫钴后的锂锰尖晶石<锰锂尖晶石.即LixMn3Co3O20S6n-和LixMn3Al3O20S6n-中Mn的状态与MnO2中的Mn相似.上述结果揭示了S和非Jahn-Teller效应阳离子(Al3+,Co3+)复合掺杂尖晶石结构锂锰氧化物在电化学过程中不会发生Jahn-Teller畸变的内在原因.

2008年汶川M_(S)8.0地震前后地电阻率时空变化

采用归一化速率变化方法对2008年汶川M_(S)8.0地震震中周边19个定点台站观测到的地电阻率的时空变化过程进行了计算分析。时序分析结果显示:在汶川地震前,震中周边多个地电阻率台站准同步地出现了中短期前兆异常;空间分布过程显示,地震孕震过程中地电阻率在震中区域有负异常丛集和由远及近的迁移现象,负异常丛集呈象限分布,长轴方向与震源机制解主压力方向基本吻合,且受孕震断裂、台站位置、观测装置布设方向等的影响。

Kendall与R/S分析法在降雨特性分析中的应用

应用Kendall秩次相关检验法、重标极差R/S分析法以及两者相结合的分析方法对南平市年平均降雨量变化特性进行研究。结果表明,南平市近50年来年降雨量总体上在均值附近摆动、呈微弱减少趋势,但趋势不明显,相对来说随机性明显,20世纪90年代以后降水的年际波动大,今后几年年降雨量序列存在增加趋势。

连杆用20CrMnTi钢根据疲劳S-N曲线进行安全性设计的探讨

在某早期疲劳断裂失效的20CrMnTi钢连杆上取样,采用升降法和成组法对其进行旋转弯曲疲劳试验,获取0.1%失效概率、95%置信度下的S-N曲线,据此合理地设计其安全服役应力。结果表明:根据在0.1%失效概率、95%置信度下的S-N曲线函数可以获得该连杆在疲劳寿命达到2×106循环周次设计要求下的最大交变载荷应控制在229 MPa以下,以确保连杆在使用寿命内不发生疲劳失效。

基于线性回归与重标极差R/S法的年平均流量变化趋势分析

采用重标极差R/S法寻找年平均流量序列的变异点,对序列进行分割,然后运用线性回归法分析年平均流量分割样本序列变化趋势,利用R/S法求出分形Hurst指数并分析序列的持久性或反持久性特征,最后综合两者的结果分析序列未来的变化趋势特征。并以某站年平均流量序列为例进行分析,结果表明:基于线性回归与重标极差R/S法的年平均流量变化趋势分析方法可行。