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High-order finite volume methods for solving compressible multicomponent flows

Science China Mathematics 2025年第3期68卷 729-760页

作者： Feng Zheng Jianxian Qiu School of Mathematics and Statistics Fujian Key Laboratory of Mathematical Analysis and ApplicationFujian Normal UniversityFuzhou 350117China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling&High-Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, we propose a high-order finite volume method for solving multicomponent fluid problems. Our method couples the quasi-conservative form with the reconstruction of conservative variables in a characteristic manner. The source term and numerical fluxes are carefully designed to maintain the pressure and velocity equilibrium for the interface-only problem and preserve the equilibrium of physical parameters in a single-component fluid. These ingredients enable our scheme to achieve both high-order accuracy in the smooth region and the high resolution in the discontinuity region of the solution. Extensive numerical tests are performed to verify the high resolution and accuracy of the scheme.

关键词： finite volume high-order multicomponent flows

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CENTRAL LIMIT THEOREM FOR TEMPORAL AVERAGE OF BACKWARD EULER-MARUYAMA METHOD

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Journal of Computational Mathematics 2025年第3期43卷 588-614页

作者： Diancong Jin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific ComputingHuazhong University of Science and TechnologyWuhan 430074China

This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in *** the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM *** the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original *** experiments are performed to illustrate the theoretical *** main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.

关键词： Central limit theorem Temporal average Ergodicity Backward Euler-Maruyama method

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Adaptive cyclic gradient methods with interpolation

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Computational Optimization and Applications 2025年 1-25页

作者： Xie, Yixin Sun, Cong Yuan, Ya-Xiang Beijing100876 China Ministry of Education Beijing100876 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

Gradient method is an important method for solving large scale problems. In this paper, a new gradient method framework for unconstrained optimization problem is proposed, where the stepsize is updated in a cyclic way. The Cauchy step is approximated by the quadratic interpolation. And the cycle for stepsize update is adjusted adaptively. Combining with the adaptive nonmonotone line search technique, we prove the global convergence of the proposed method. Furthermore, its sublinear convergence rate for convex problems and R-linear convergence rate for problems with quadratic functional growth property are analyzed. Numerical results show that our proposed algorithm enjoys good performances in terms of both computational cost and obtained function values. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Interpolation

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A HIGH ORDER SCHEME FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO-HADAMARD DERIVATIVE

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Journal of Computational Mathematics 2025年第3期43卷 615-640页

作者： Xingyang Ye Junying Cao Chuanju Xu School of Science Jimei UniversityXiamen 361021China School of Data Science and Information Engineering Guizhou Minzu UniversityGuiyang 550025China School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper,we consider numerical solutions of the fractional diffusion equation with theαorder time fractional derivative defined in the Caputo-Hadamard sense.A high order time-stepping scheme is constructed,analyzed,and numerically *** contribution of the paper is twofold:1)regularity of the solution to the underlying equation is investigated,2)a rigorous stability and convergence analysis for the proposed scheme is performed,which shows that the proposed scheme is 3+αorder *** numerical examples are provided to verify the theoretical statement.

关键词： Caputo-Hadamard derivative Fractional differential equations High order scheme Stability and convergence analysis

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Adapted Runge-Kutta Methods for Nonlinear First-Order Delay BVPs with Time-variable Delay

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Acta Mathematicae Applicatae Sinica 2025年第2期41卷 400-413页

作者： Cheng-jian ZHANG Yang WANG Hao HAN School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta(ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν +1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.

关键词： delay boundary value problems adapted Runge-Kutta method Lagrange interpolation error analysis global stability

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MSMAE-Net: multi-semantic and multi-attention enhanced network for image forgery localization

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Signal, Image and Video Processing 2025年第7期19卷 1-11页

作者： Liao, Jianjun Su, Lichao Lu, Menghan Engineering Research Center of Big Data Intelligence Ministry of Education Fuzhou China Fujian Key Laboratory of Network Computing and Intelligent Information Processing Fuzhou University Fuzhou China

The popularization of modern digital image technology has brought convenience to us, but it also poses many risks. The advancement of image editing software allows anyone to modify image content effortlessly. If these modified images are abused, they can severely impact societal safety and stability. To address these risks, we propose an end-to-end multi-scale collaborative enhancement image forgery localization network, termed MSMAE-Net. The method first employs a multi-branch feature extractor to initially capture both global and local information, with each branch optimized for different contextual information and features of the image. Next, to enhance the model’s ability to capture forged traces at various levels while maintaining the correlation between different spatial hierarchies, a boundary information aggregation module is designed. By constructing multiple branches with different receptive fields and collaborative learning with each other, a nested collaborative enhancement branch is designed to make the backbone network pay more attention to key features, so as to obtain better feature representation capability. Furthermore, to further fuse different semantic information, a novel strongly compatible semantic attention fusion module is proposed in this paper. Finally, an attention enhancement module is introduced in the localization of forgery regions to adaptively concentrate on key forged areas in the image and effectively capture the relationships between different pixels. In the experiments, we demonstrate that MSMAE-Net exhibits significant advantages in both localization accuracy and robustness in complex forgery scenarios when compared to other SOTA image forgery detection methods. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2025.

关键词： Photointerpretation

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A numerical magnitude aware multi-channel hierarchical encoding network for math word problem solving

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Neural computing and Applications 2025年第3期37卷 1651-1672页

作者： Xu, Junjie Chen, Yuzhong Xiao, Lingsheng Liao, Hongmiao Zhong, Jiayuan Dong, Chen College of Computer and Data Science Fuzhou University Fujian Province Fuzhou350108 China Engineering Research Center of Big Data Intelligence Ministry of Education Fuzhou China Fujian Provincial Key Laboratory of Network Computing and Intelligent Information Processing Fujian Province Fuzhou350108 China

Math word problem (MWP) represents a critical research area within reading comprehension, where accurate comprehension of math problem text is crucial for generating math expressions. However, current approaches still grapple with unresolved challenges in grasping the sensitivity of math problem text and delineating distinct roles across various clause types, and enhancing numerical representation. To address these challenges, this paper proposes a Numerical Magnitude Aware Multi-Channel Hierarchical Encoding Network (NMA-MHEA) for math expression generation. Firstly, NMA-MHEA implements a multi-channel hierarchical context encoding module to learn context representations at three different channels: intra-clause channel, inter-clause channel, and context-question interaction channel. NMA-MHEA constructs hierarchical constituent-dependency graphs for different levels of sentences and employs a Hierarchical Graph Attention Neural Network (HGAT) to learn syntactic and semantic information within these graphs at the intra-clause and inter-clause channels. NMA-MHEA then refines context clauses using question information at the context-question interaction channel. Secondly, NMA-MHEA designs a number encoding module to enhance the relative magnitude information among numerical values and type information of numerical values. Experimental results on two public benchmark datasets demonstrate that NMA-MHEA outperforms other state-of-the-art models. © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024.

关键词： Semantics

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On greedy randomized coordinate updating iteration methods for solving symmetric eigenvalue problems

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Applied Numerical Mathematics 2025年 216卷 76-97页

作者： Bai, Zhong-Zhi State Key Laboratory of Mathematical Sciences Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences P.O. Box 2719 Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In order to compute the smallest eigenvalue and its corresponding eigenvector of a large-scale, real, and symmetric matrix, we propose a class of greedy randomized coordinate updating iteration methods based on the principle that the indices of larger entries in absolute value of the current residual are selected with a higher probability and, with respect to this index set, the next iterate is updated from the current iterate along with the selected coordinate such that the corresponding entry of the residual is annihilated, resulting in fast convergence rates of the proposed iteration methods. Under appropriate conditions, we prove the convergence of both sequences of the Rayleigh-quotients and the acute angles between the iterates and the eigenvector in terms of the expectation. By numerical experiments, we show that this class of greedy randomized coordinate updating iteration methods are advantageous over the parameterized power method and the coordinate descent method in both iteration counts and computing times. Moreover, with theoretical analysis and computational performance, we confirm that the convergence property of this class of iteration methods can be improved significantly by suitably choosing the arbitrary nonnegative parameter involved in the greedy probability criterion. © 2025 IMACS

关键词： Eigenvalues and eigenfunctions

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A DECOUPLED,LINEARLY IMPLICIT AND UNCONDITIONALLY ENERGY STABLE SCHEME FOR THE COUPLED CAHN-HILLIARD SYSTEMS

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Journal of Computational Mathematics 2025年第3期43卷 708-730页

作者： Dan Zhao Dongfang Li Yanbin Tang Jinming Wen School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China College of Information Science and Technology Jinan UniversityGuangzhou 510632China

We present a decoupled,linearly implicit numerical scheme with energy stability and mass conservation for solving the coupled Cahn-Hilliard *** time-discretization is done by leap-frog method with the scalar auxiliary variable(SAV)*** only needs to solve three linear equations at each time step,where each unknown variable can be solved *** is shown that the semi-discrete scheme has second-order accuracy in the temporal *** convergence results are proved by a rigorous analysis of the boundedness of the numerical solution and the error estimates at different *** examples are presented to further confirm the validity of the methods.

关键词： Coupled Cahn-Hilliard system Leap-frog method Scalar auxiliary variable Error estimate

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Progressive Semantic-Visual Alignment and Refinement for Vision-Language Tracking

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IEEE Transactions on Circuits and Systems for Video Technology 2025年第5期35卷 4271-4286页

作者： Liang, Yanjie Wu, Qiangqiang Cheng, Lin Xia, Changqun Li, Jia Peng Cheng Laboratory Shenzhen518000 China City University of Hong Kong Department of Computer Science Hong Kong Xiamen University Fujian Key Laboratory of Sensing and Computing for Smart City School of Informatics Xiamen361005 China Beihang University State Key Laboratory of Virtual Reality Technology and Systems School of Computer Science and Engineering Beijing100191 China

In recent years, vision-language tracking has drawn emerging attention in the tracking field. The critical challenge for the task is to fuse semantic representations of language information and visual representations of vision information. For this purpose, several vision-language tracking methods perform early or late fusion to fuse visual and semantic features. However, these methods cannot take full advantage of the transformer architecture to excavate useful cross-modal context at various levels. To this end, we propose a new progressive joint vision-language transformer (PJVLT) to progressively align and refine visual embedding with semantic embedding for vision-language tracking. Specifically, to align visual signals with semantic signals, we propose to insert a semantic-aware instance encoder layer (SAIEL) into each intermediate layer of transformer encoder to perform progressive alignment of visual and semantic features. Furthermore, to highlight the multi-modal feature channels and patches corresponding to target objects, we propose a unified channel communication patch interaction layer (CCPIL), which is plugged into each intermediate layer of transformer encoder to progressively activate target-aware channels and patches of aligned multi-modal features for fine-grained tracking. In general, by progressively aligning and refining visual features with semantic features in the transformer encoder, our PJVLT can adaptively excavate well-aligned vision-language context at coarse-to-fine levels, therefore highlighting target objects at various levels for more discriminative tracking. Experiments on several tracking datasets show that the proposed PJVLT can achieve favorable performance in comparison with both conventional trackers and other vision-language trackers. © 1991-2012 IEEE.

关键词： Semantics

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