检索结果-南通市图书馆

Normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for the SDE

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Science China mathematics 2024年第8期67卷 1865-1880页

作者： Xiequan Fan Haijuan Hu Lihu Xu Center for Applied mathematics Tianjin University School of mathematics and Statistics Northeastern University at Qinhuangdao department of mathematics Faculty of Science and TechnologyUniversity of Macau

In this paper, we establish normalized and self-normalized Cramér-type moderate deviations for the Euler-Maruyama scheme for SDE. Due to our results, Berry-Esseen's bounds and moderate deviation principles are also o... 详细信息

关键词： Euler-Maruyama scheme Cramér-type moderate deviations self-normalized sequences Berry-Esseen's bounds

IMAGE SUPER-RESOLUTION RECONSTRUCTION BY HUBER REGULARIZATION AND TAILORED FINITE POINT METHOD

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Journal of Computational mathematics 2024年第2期42卷 313-336页

作者： Wenli Yang Zhongyi Huang Wei Zhu School of mathematics China University of Mining and TechnologyXuzhou 221116China department of mathematics Tsinghua UniversityBeijing 100084China department of mathematics University of AlabamaTuscaloosaAL 35487USA

In this paper,we propose using the tailored finite point method(TFPM)to solve the resulting parabolic or elliptic equations when minimizing the Huber regularization based image super-resolution model using the augmented Lagrangian method(ALM).The Hu-ber regularization based image super-resolution model can ameliorate the staircase for restored images.TFPM employs the method of weighted residuals with collocation tech-nique,which helps get more accurate approximate solutions to the equations and reserve more details in restored images.We compare the new schemes with the Marquina-Osher model,the image super-resolution convolutional neural network(SRCNN)and the classical interpolation methods:bilinear interpolation,nearest-neighbor interpolation and bicubic interpolation.Numerical experiments are presented to demonstrate that with the new schemes the quality of the super-resolution images has been improved.Besides these,the existence of the minimizer of the Huber regularization based image super-resolution model and the convergence of the proposed algorithm are also established in this paper.

关键词： Image super-resolution Variational model Augmented Lagrangian methods Tailored finite point method

Stability and Time-Step Constraints of Implicit-Explicit Runge-Kutta Methods for the Linearized Korteweg-de Vries Equation

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications on Applied mathematics and Computation 2024年第1期6卷 658-687页

作者： Joseph Hunter Zheng Sun Yulong Xing department of mathematics The Ohio State UniversityColumbusOH43210USA department of mathematics The University of AlabamaTuscaloosaAL35487USA

This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.

关键词： Linearized Korteweg-de Vries(KdV)equation Implicit-explicit(IMEX)Runge-Kutta(RK)method Stability Courant-Friedrichs-Lewy(CFL)condition Finite difference(FD)method Local discontinuous Galerkin(DG)method

Integrability and solutions of a nonsymmetric discrete Korteweg-de Vries equation

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2024年第2期76卷 45-50页

作者： Maebel Mesfun Da-jun Zhang Song-lin Zhao department of mathematics Shanghai UniversityShanghai 200444China Newtouch Center for mathematics of Shanghai University Shanghai 200444China department of Applied mathematics Zhejiang University of TechnologyHangzhou 310023China

In this paper,we present Lax pairs and solutions for a nonsymmetric lattice equation,which is a torqued version of the lattice potential Korteweg-de Vries equation.This nonsymmetric equation is special in the sense that it contains only one spacing parameter but consists of two consistent cubes with other integrable lattice equations.Using such a multidimensionally consistent property we are able to derive its two Lax pairs and also construct solutions using B?cklund transformations.

关键词： discrete Korteweg-de Vries equation nonsymmetric multi-dimensional consistency Backlund transformation solution

Numerical Treatments for Crossover Cancer Model of Hybrid Variable-Order Fractional Derivatives

在线全文

学校读者我要写书评

暂无评论

Computer Modeling in Engineering & Sciences 2024年第8期140卷 1619-1645页

作者： Nasser Sweilam Seham Al-Mekhlafi Aya Ahmed Ahoud Alsheri Emad Abo-Eldahab mathematics department Faculty of ScienceCairo UniversityGiza12613Egypt mathematics department Faculty of EducationSana’a UniversitySana’a1247Yemen mathematics department Faculty of ScienceHelwan UniversityCairo11795Egypt department of mathematics College of ScienceUniversity of BishaAl Namas67398-5644Saudi Arabia

In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.

关键词： Cancer diseases hybrid variable-order fractional derivatives adams bashfourth fifth step generalized fifth order Runge-Kutta method

Deep bed filtration model for cake filtration and erosion

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Applied mathematics and Mechanics(English Edition) 2024年第2期45卷 355-372页

作者： L.I.KUZMINA Y.V.OSIPOV A.R.PESTEREV department of Applied mathematics HSE UniversityMoscow 101000Russia department of Computer Science and Applied mathematics Moscow State University of Civil EngineeringMoscow 129337Russia

Many phenomena in nature and technology are associated with the filtration of suspensions and colloids in porous media. Two main types of particle deposition,namely, cake filtration at the inlet and deep bed filtration throughout the entire porous medium, are studied by different models. A unified approach for the transport and deposition of particles based on the deep bed filtration model is proposed. A variable suspension flow rate, proportional to the number of free pores at the inlet of the porous medium, is considered. To model cake filtration, this flow rate is introduced into the mass balance equation of deep bed filtration. For the cake filtration without deposit erosion,the suspension flow rate decreases to zero, and the suspension does not penetrate deep into the porous medium. In the case of the cake filtration with erosion, the suspension flow rate is nonzero, and the deposit is distributed throughout the entire porous medium. An exact solution is obtained for a constant filtration function. The method of characteristics is used to construct the asymptotics of the concentration front of suspended and retained particles for a filtration function in a general form. Explicit formulae are obtained for a linear filtration function. The properties of these solutions are studied in detail.

关键词： deep bed filtration cake filtration porous medium particle deposition and erosion analytical solution concentration front

PC synchronization of a class of chaotic systems via event-triggered control

在线全文

学校读者我要写书评

暂无评论

Chinese Physics B 2014年第7期23卷 323-330页

作者：罗润梓何龙敏 department of mathematics Nanchang University department of mathematics Shanghai University

The PC synchronization of a class of chaotic systems is investigated in this paper. The drive system is assumed to have only one state variable available. By constructing proper observers, some novel criteria for PC synchronization are proposed via event-triggered control scheme. The Lii system and Chen system are taken as examples to demonstrate the efficiency of the proposed approach.

关键词： chaotic system state observer event-triggered control

∞-Tilting Subcategories in Extriangulated Categories

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of mathematics,Series B 2024年第1期45卷 151-160页

作者： Zhen ZHANG Jiaqun WEI Shance WANG department of mathematics Qilu Normal UniversityJinan 250200China Institution of mathematics School of Mathematics ScienceNanjing Normal UniversityNanjing 210023China

In this paper, the authors introduce a new definition of ∞-tilting(resp. cotilting) subcategories with infinite projective dimensions(resp. injective dimensions) in an extriangulated category. They give a Bazzoni characterization of ∞-tilting(resp. cotilting)subcategories. Also, they obtain a partial Auslander-Reiten correspondence between ∞-tilting(resp. cotilting) subcategories and coresolving(resp. resolving) subcategories with an E-projective generator(resp. E-injective cogenerator) in an extriangulated category.

关键词： Extriangulated category ∞-Tilting subcategory Auslander-Reiten correspondence Bazzoni characterization

Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System

在线全文

学校读者我要写书评

暂无评论

Acta Mathematicae Applicatae Sinica 2024年第1期40卷 45-74页

作者： Ya-zhou Chen Hakho Hong Xiao-ding Shi department of mathematics College of Mathematics and PhysicsBeijing University of Chemical TechnologyBeijing100029China Institute of mathematics State Academy of SciencesPyongyangKorea

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.

关键词： Navier-Stokes/Allen-Cahn system existence uniqueness large time behavior decay rate