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1.
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.
3.
本文研究了数值求解非自治随机微分方程的正则Euler-Maruyama分裂(CEMS)方法,该方程的漂移项系数带有刚性且允许超线性增长,扩散项系数满足全局Lipschitz条件.首先,证明了CEMS方法的强收敛性及收敛速度.其次,证明了在适当条件下CEMS方法是均方稳定的.进一步,利用离散半鞅收敛定理,研究了CEMS方法的几乎必然指数稳定性.结果表明,CEMS方法在漂移系数的刚性部分满足单边Lipschitz条件下可保持几乎必然指数稳定性.最后通过数值实验,检验了CEMS方法的有效性并证实了我们的理论结果.  相似文献   
4.
A reasonable prediction of photofission observables plays a paramount role in understanding the photofission process and guiding various photofission-induced applications, such as short-lived isotope production, nuclear waste disposal, and nuclear safeguards. However, the available experimental data for photofission observables are limited, and the existing models and programs have mainly been developed for neutron-induced fission processes. In this study, a general framework is proposed for characterizing the photofission observables of actinides, including the mass yield distributions (MYD) and isobaric charge distributions (ICD) of fission fragments and the multiplicity and energy distributions of prompt neutrons (np) and prompt γ rays (γp). The framework encompasses various systematic neutron models and empirical models considering the Bohr hypothesis and does not rely on the experimental data as input. These models are then validated individually against experimental data at an average excitation energy below 30 MeV, which shows the reliability and robustness of the general framework. Finally, we employ this framework to predict the characteristics of photofission fragments and the emissions of prompt particles for typical actinides including 232Th, 235, 238U and 240Pu. It is found that the 238U(γ, f) reaction is more suitable for producing neutron-rich nuclei compared to the 232Th(γ, f) reaction. In addition, the average multiplicity number of both np and γp increases with the average excitation energy.  相似文献   
5.
Based on the primal mixed variational formulation, a stabilized nonconforming mixed finite element method is proposed for the linear elasticity on rectangular and cubic meshes. Two kinds of penalty terms are introduced in the stabilized mixed formulation, which are the jump penalty term for the displacement and the divergence penalty term for the stress. We use the classical nonconforming rectangular and cubic elements for the displacement and the discontinuous piecewise polynomial space for the stress, where the discrete space for stress are carefully chosen to guarantee the well-posedness of discrete formulation. The stabilized mixed method is locking-free. The optimal convergence order is derived in the $L^2$-norm for stress and in the broken $H^1$-norm and $L^2$-norm for displacement. A numerical test is carried out to verify the optimal convergence of the stabilized method.  相似文献   
6.
This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.  相似文献   
7.
This paper concerns about the regularity conditions of weak solutions to the magnetic Bénard fluid system in $\mathbb{R}^3$. We show that a weak solution $(u,b,θ)(·,t)$ of the 3D magnetic Bénard fluid system defined in $[0,T),$ which satisfies some regularity requirement as $(u,b,θ),$ is regular in $\mathbb{R}^3×(0,T)$ and can be extended as a $C^∞$ solution beyond $T$.  相似文献   
8.
A new fast algorithm based on the augmented immersed interface method and a fast Poisson solver is proposed to solve three dimensional elliptic interface problems with a piecewise constant but discontinuous coefficient. In the new approach, an augmented variable along the interface, often the jump in the normal derivative along the interface is introduced so that a fast Poisson solver can be utilized. Thus, the solution of the Poisson equation depends on the augmented variable which should be chosen such that the original flux jump condition is satisfied. The discretization of the flux jump condition is done by a weighted least squares interpolation using the solution at the grid points, the jump conditions, and the governing PDEs in a neighborhood of control points on the interface. The interpolation scheme is the key to the success of the augmented IIM particularly. In this paper, the key new idea is to select interpolation points along the normal direction in line with the flux jump condition. Numerical experiments show that the method maintains second order accuracy of the solution and can reduce the CPU time by 20-50%. The number of the GMRES iterations is independent of the mesh size.  相似文献   
9.
本文基于房价长期趋势和短期波动层面,基于HP滤波法分离北京、上海、广州和深圳四大一线城市的房价,采用有向无环图和信息溢出指数方法剖析了核心城市房价之间的同期联动效应和信息溢出效应,并结合滚动窗口估计法分析了信息溢出对外部信息和调控政策的反应程度。结果显示:一线城市房价之间有紧密的联系程度和较高的信息溢出规模。在同期联动效应上,深圳房价趋势的对外联动效应最明显,北京房价趋势在同期最易受其它城市影响;上海房价波动存在较强的对外联动效应,深圳房价波动受其它一线城市的波动冲击较迅速。在信息溢出效应上,深圳房价趋势有引领作用,对外溢出效应最强;上海房价波动处于引导地位,中长期对其它市场影响最大。核心城市房价趋势之间的溢出指数随着利好政策信息的出现而上升,随着限制政策等不利信息的出现而下降。核心城市房价波动之间的溢出效应对于外部信息反应更为灵敏,国家对房地产市场的调控政策增大核心城市房价波动的信息溢出规模。  相似文献   
10.
Let $G$ be a stratified Lie group and let $\{X_1, \cdots, X_{n_1}\}$ be a basis of the first layer of the Lie algebra of $G$. The sub-Laplacian $\Delta_G$ is defined by $$\Delta_G= -\sum^{n_1}_{j=1} X^2_j. $$ The operator defined by $$\Delta_G-\sum^{n_1}_{j=1}\frac{X_jp}{p}X_j$$ is called the Ornstein-Uhlenbeck operator on $G$, where $p$ is a heat kernel at time 1 on $G$. In this paper, we investigate Gaussian BV functions and Gaussian BV capacities associated with the Ornstein-Uhlenbeck operator on the stratified Lie group.  相似文献   
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