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1.
Mohammed Harunor Rashid 《计算数学(英文版)》2022,40(1):44-69
In the present paper,we study the restricted inexact Newton-type method for solving the generalized equation 0∈f(x)+F(x),where X and Y are Banach spaces,f:X→Y is a Frechet differentiable function and F:X■Y is a set-valued mapping with closed graph.We establish the convergence criteria of the restricted inexact Newton-type method,which guarantees the existence of any sequence generated by this method and show this generated sequence is convergent linearly and quadratically according to the particular assumptions on the Frechet derivative of f.Indeed,we obtain semilocal and local convergence results of restricted inexact Newton-type method for solving the above generalized equation when the Frechet derivative of f is continuous and Lipschitz continuous as well as f+F is metrically regular.An application of this method to variational inequality is given.In addition,a numerical experiment is given which illustrates the theoretical result. 相似文献
2.
The observation and study of nonlinear dynamical systems has been gaining popularity over years in different fields. The intrinsic complexity of their dynamics defies many existing tools based on individual orbits, while the Koopman operator governs evolution of functions defined in phase space and is thus focused on ensembles of orbits, which provides an alternative approach to investigate global features of system dynamics prescribed by spectral properties of the operator. However, it is difficult to identify and represent the most relevant eigenfunctions in practice. Here, combined with the Koopman analysis, a neural network is designed to achieve the reconstruction and evolution of complex dynamical systems. By invoking the error minimization, a fundamental set of Koopman eigenfunctions are derived, which may reproduce the input dynamics through a nonlinear transformation provided by the neural network. The corresponding eigenvalues are also directly extracted by the specific evolutionary structure built in. 相似文献
3.
Triple Positive Solutions of Boundary Value Problems for High-order Fractional Differential Equation at Resonance with Singularities 下载免费PDF全文
In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity. 相似文献
4.
5.
暴露于硫酸盐环境中的混凝土输水管易遭受硫酸盐化学侵蚀,导致其耐久性退化、提前失效;而环境中硫酸根离子传输进入混凝土是其化学侵蚀的前提.为获得混凝土内硫酸根离子的扩散进程,首先基于Fick定律及质量守恒定律,建立饱和混凝土管内硫酸根离子的扩散-反应模型.其次,将扩散-反应模型的边界条件齐次化,建立其有限元控制方程.然后,开展硫酸钠溶液中水泥砂浆圆柱试件的腐蚀试验,测定试件不同深度处的硫酸根离子浓度,与模型计算结果对比,以验证模型.最后,开展数值模拟研究,分析混凝土输水管外表面、内外表面暴露于浓度恒定或振荡的硫酸盐溶液情况下管内硫酸根离子浓度的时空分布. 相似文献
6.
矩阵平方根在数学的许多应用中起着重要的作用.本文研究M-矩阵平方根的计算问题,提出一种计算正则M-矩阵平方根的迭代方法.首先将这个问题转化为M-矩阵代数Riccati方程,进而提出一种有效的方法来求解这个特殊的MARE.理论分析表明,该方法在一定条件下是收敛的.数值实验表明该方法是可行的,且优于二项式迭代法. 相似文献
7.
In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases. Based on the linearizing operator and adjoint linearizing operator for the two real systems, adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair (SA) method. Relationships between the nonlinear self-adjointness method and the SA method are investigated. 相似文献
8.
盛晓伟 《原子与分子物理学报》2022,39(3):031002-21
理论上对分子间色散相互作用能的精确计算一直是个难点问题.密度矩阵泛函基于非定域量一阶密度矩阵为基本变量,它与色散相互作用起源于电子间的非定域关联特性相吻合.论文以最简单的氢分子为研究对象,通过分析两相互平行的氢分子间色散相互作用能,构造出了该体系中色散相互作用能的自然轨道泛函.结果表明:描述该体系中色散相互作用能的自然轨道泛函形式为包含有4个轨道的非交换和库伦积分.该结果对发展色散相互作用能的密度矩阵泛函理论具有重要的参考价值. 相似文献
9.
氧化石墨烯(GO)片的基面和边缘上存在大量的含氧官能团,能很好地分散在水中,因而具有很好的加工性和广阔的应用前景。在较高浓度范围下,GO水分散液中存在着强烈的竞争性相互作用,从而对流变行为产生较大影响。在本文中,通过稳态、动态等流变实验以及理论分析,研究了pH值、温度和不同的有机溶剂对GO分散液流变行为的影响。结果表明,降低pH值、适当增加温度以及加入吡啶均可促进GO水分散液从粘弹性液体到凝胶态的转变。利用DLVO (Deryagin-Landau-Verwey-Overbeek)理论,探讨了GO片之间的范德华作用力以及双电层排斥作用的相互关系,及其对流变性能的影响。通过群体平衡模型(PBE)分析了GO分散液的屈服应力与体积分数的正相关关系。同时,通过蠕变和松弛实验发现,高浓度的GO分散液中结构变化及流变行为在很多方面与高聚物相似,利用Poyting-Thomson模型能较好地拟合其粘弹性行为。上述研究结果为深入研究复杂的GO分散体系提供理论支撑和实验依据。 相似文献
10.
Aimed at the internal short circuit problem due to large deformation of the prismatic lithium-ion battery cell under impact loadings, a simplified battery model was first established. Then the motion equations of velocity and displacement based on the membrane factor method were proposed. With the effects of the face-sheet thickness and the densification region on the normalized final deflection, impact response characteristics of prismatic battery cells were investigated in detail. The results show that, the improved motion equations involving the membrane factor can reflect the dynamic response mechanisms of the prismatic battery cell under impact loadings, and the large deflection under high-speed impact can be predicted. With the increase of the face-sheet thickness, the deflection of the battery cell’s lower part decreases obviously. However, the densification region expands with the face-sheet thickness. The deflection and the densification region of the cell’s lower part both increase with the inner core density of the battery. This proposed impact model provides a theoretical guidance for the multi-functional integrated dynamic design of prismatic battery cells. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved. 相似文献