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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.
采用固相反应法合成了一种Zr Cu Si As型准二维层状锰基化合物Th Mn Sb N.基于X射线粉末衍射的结构精修显示,该化合物属于P4/nmm空间群.其晶胞参数为a=4.1731?, c=9.5160?.电输运测量显示,该化合物电阻率随温度下降缓慢上升,且在16 K附近出现电阻率异常.与此同时,该材料的磁化率在同一温度附近出现异常,显示出类似磁性相变的行为.进一步的比热测量中没有观察到磁相变导致的比热异常.另外,低温下的比热分析显示,该材料的电子比热系数为γ=19.7 m J·mol–1·K–2,远高于其他同类锰基化合物.该结果与电输运测量中观察到的低电阻率行为相符,暗示Th Mn Sb N中费米面附近存在可观的电子态密度.基于对一系列Zr Cu Si As型化合物晶体结构细节的比较,分析了含有萤石型Th2N2层的系列化合物中导电层所受化学压力的不同作用形式. 相似文献
9.
课程体系是人才培养的载体。为了更好地培养拔尖创新人才,南京大学化学国家级实验教学示范中心依据化学学科的特点和发展趋势,以科学内容的内在联系和研究规律为主线构建了“化学实验基础?化学合成与表征+化学原理与测量?化学功能分子实验+化学生物学综合实验+基于项目的研究实验”实验课程新体系,按照一流课程建设要求(高阶性、创新性和挑战度)对实验教学内容进行了优化,并建立起与之相适应的实验教学平台。新课程体系综合考虑了化学一级学科的整体性和关联学科的交叉性,在南京大学化学化工学院“拔尖计划”和“强基计划”学生中实施,教学效果显著。 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